What would be used for “coordinates” on a large asteroid?











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Assuming we had a non-spherical asteroid that doesn't have a magnetic "north", how would the inhabitants define areas on the asteroid? How would they explain to a visitor to go to a very specific spot to retrieve or leave something besides "head over the hill sunward for 50 km"










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The current answers do not contain enough detail.


The bounty is for an answer that uses orienteering trigonometry to determine the location of an individual on an asteroid which has visible landmarks which are of known distance from each other and a coordinate grid. Compasses do not work but one may take sightings on distant landmarks and determine the angle of a second landmark from the first. You cannot determine the distance between yourself and a distant landmark, only the angles of lines of sight. The answer will have examples and pictures and lay out the math at a high school level. Calculate your location on the grid by looking at the landmarks. If more than one answer has good math then one with an example using 3 dimensions (elevation) will get the bounty.












  • 4




    Welcome to Worldbuilding! Great first question!
    – kingledion
    Nov 30 at 0:57






  • 4




    FYI, the largest asteroid in the solar system is Ceres, 578 km by 458 km. using the larger dimension, this gives a circumference of 1815 km, and a surface area of 262 388 km^2, which is bigger than the UK. So navigation actually becomes a significant problem.
    – Chris Cudmore
    Nov 30 at 17:16










  • There is a convention for defining the poles of celestial bodies (en.wikipedia.org/wiki/Poles_of_astronomical_bodies), and you could define an arbitrary convention for defining their prime meridians, for example "the point nearest the parent body at its closest approach after 1 Jan 1970". That way, two independent sets of explorers from Earth wouldn't end up using different coordinate systems. But that is a separate question to what indigenous inhabitants might come up with, or what is the most useful system.
    – bobtato
    yesterday










  • could you be more precise about what you are asking? For instance, to meet my friend at the cinema, i usually say : 'meet me at the cinema'. I either use my knowledge of where it is, or google maps to find it. If i use google maps, i just follow the instructions ('left, right'). This would not change on an asteroid. Or is your question about what kind of map could represent a non-spherical object? (Then i'd recommend looking at maps of mountains) Or is your question about how to map said object? (Again, look at how mountains are mapped)
    – bukwyrm
    5 hours ago












  • Possibly related naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/…
    – Mołot
    2 hours ago















up vote
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Assuming we had a non-spherical asteroid that doesn't have a magnetic "north", how would the inhabitants define areas on the asteroid? How would they explain to a visitor to go to a very specific spot to retrieve or leave something besides "head over the hill sunward for 50 km"










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TChris Gardner is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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This question has an open bounty worth +500
reputation from Willk ending in 6 days.


The current answers do not contain enough detail.


The bounty is for an answer that uses orienteering trigonometry to determine the location of an individual on an asteroid which has visible landmarks which are of known distance from each other and a coordinate grid. Compasses do not work but one may take sightings on distant landmarks and determine the angle of a second landmark from the first. You cannot determine the distance between yourself and a distant landmark, only the angles of lines of sight. The answer will have examples and pictures and lay out the math at a high school level. Calculate your location on the grid by looking at the landmarks. If more than one answer has good math then one with an example using 3 dimensions (elevation) will get the bounty.












  • 4




    Welcome to Worldbuilding! Great first question!
    – kingledion
    Nov 30 at 0:57






  • 4




    FYI, the largest asteroid in the solar system is Ceres, 578 km by 458 km. using the larger dimension, this gives a circumference of 1815 km, and a surface area of 262 388 km^2, which is bigger than the UK. So navigation actually becomes a significant problem.
    – Chris Cudmore
    Nov 30 at 17:16










  • There is a convention for defining the poles of celestial bodies (en.wikipedia.org/wiki/Poles_of_astronomical_bodies), and you could define an arbitrary convention for defining their prime meridians, for example "the point nearest the parent body at its closest approach after 1 Jan 1970". That way, two independent sets of explorers from Earth wouldn't end up using different coordinate systems. But that is a separate question to what indigenous inhabitants might come up with, or what is the most useful system.
    – bobtato
    yesterday










  • could you be more precise about what you are asking? For instance, to meet my friend at the cinema, i usually say : 'meet me at the cinema'. I either use my knowledge of where it is, or google maps to find it. If i use google maps, i just follow the instructions ('left, right'). This would not change on an asteroid. Or is your question about what kind of map could represent a non-spherical object? (Then i'd recommend looking at maps of mountains) Or is your question about how to map said object? (Again, look at how mountains are mapped)
    – bukwyrm
    5 hours ago












  • Possibly related naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/…
    – Mołot
    2 hours ago













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Assuming we had a non-spherical asteroid that doesn't have a magnetic "north", how would the inhabitants define areas on the asteroid? How would they explain to a visitor to go to a very specific spot to retrieve or leave something besides "head over the hill sunward for 50 km"










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Assuming we had a non-spherical asteroid that doesn't have a magnetic "north", how would the inhabitants define areas on the asteroid? How would they explain to a visitor to go to a very specific spot to retrieve or leave something besides "head over the hill sunward for 50 km"







map-making asteroids






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edited Nov 30 at 0:57









kingledion

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asked Nov 30 at 0:33









TChris Gardner

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This question has an open bounty worth +500
reputation from Willk ending in 6 days.


The current answers do not contain enough detail.


The bounty is for an answer that uses orienteering trigonometry to determine the location of an individual on an asteroid which has visible landmarks which are of known distance from each other and a coordinate grid. Compasses do not work but one may take sightings on distant landmarks and determine the angle of a second landmark from the first. You cannot determine the distance between yourself and a distant landmark, only the angles of lines of sight. The answer will have examples and pictures and lay out the math at a high school level. Calculate your location on the grid by looking at the landmarks. If more than one answer has good math then one with an example using 3 dimensions (elevation) will get the bounty.








This question has an open bounty worth +500
reputation from Willk ending in 6 days.


The current answers do not contain enough detail.


The bounty is for an answer that uses orienteering trigonometry to determine the location of an individual on an asteroid which has visible landmarks which are of known distance from each other and a coordinate grid. Compasses do not work but one may take sightings on distant landmarks and determine the angle of a second landmark from the first. You cannot determine the distance between yourself and a distant landmark, only the angles of lines of sight. The answer will have examples and pictures and lay out the math at a high school level. Calculate your location on the grid by looking at the landmarks. If more than one answer has good math then one with an example using 3 dimensions (elevation) will get the bounty.










  • 4




    Welcome to Worldbuilding! Great first question!
    – kingledion
    Nov 30 at 0:57






  • 4




    FYI, the largest asteroid in the solar system is Ceres, 578 km by 458 km. using the larger dimension, this gives a circumference of 1815 km, and a surface area of 262 388 km^2, which is bigger than the UK. So navigation actually becomes a significant problem.
    – Chris Cudmore
    Nov 30 at 17:16










  • There is a convention for defining the poles of celestial bodies (en.wikipedia.org/wiki/Poles_of_astronomical_bodies), and you could define an arbitrary convention for defining their prime meridians, for example "the point nearest the parent body at its closest approach after 1 Jan 1970". That way, two independent sets of explorers from Earth wouldn't end up using different coordinate systems. But that is a separate question to what indigenous inhabitants might come up with, or what is the most useful system.
    – bobtato
    yesterday










  • could you be more precise about what you are asking? For instance, to meet my friend at the cinema, i usually say : 'meet me at the cinema'. I either use my knowledge of where it is, or google maps to find it. If i use google maps, i just follow the instructions ('left, right'). This would not change on an asteroid. Or is your question about what kind of map could represent a non-spherical object? (Then i'd recommend looking at maps of mountains) Or is your question about how to map said object? (Again, look at how mountains are mapped)
    – bukwyrm
    5 hours ago












  • Possibly related naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/…
    – Mołot
    2 hours ago














  • 4




    Welcome to Worldbuilding! Great first question!
    – kingledion
    Nov 30 at 0:57






  • 4




    FYI, the largest asteroid in the solar system is Ceres, 578 km by 458 km. using the larger dimension, this gives a circumference of 1815 km, and a surface area of 262 388 km^2, which is bigger than the UK. So navigation actually becomes a significant problem.
    – Chris Cudmore
    Nov 30 at 17:16










  • There is a convention for defining the poles of celestial bodies (en.wikipedia.org/wiki/Poles_of_astronomical_bodies), and you could define an arbitrary convention for defining their prime meridians, for example "the point nearest the parent body at its closest approach after 1 Jan 1970". That way, two independent sets of explorers from Earth wouldn't end up using different coordinate systems. But that is a separate question to what indigenous inhabitants might come up with, or what is the most useful system.
    – bobtato
    yesterday










  • could you be more precise about what you are asking? For instance, to meet my friend at the cinema, i usually say : 'meet me at the cinema'. I either use my knowledge of where it is, or google maps to find it. If i use google maps, i just follow the instructions ('left, right'). This would not change on an asteroid. Or is your question about what kind of map could represent a non-spherical object? (Then i'd recommend looking at maps of mountains) Or is your question about how to map said object? (Again, look at how mountains are mapped)
    – bukwyrm
    5 hours ago












  • Possibly related naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/…
    – Mołot
    2 hours ago








4




4




Welcome to Worldbuilding! Great first question!
– kingledion
Nov 30 at 0:57




Welcome to Worldbuilding! Great first question!
– kingledion
Nov 30 at 0:57




4




4




FYI, the largest asteroid in the solar system is Ceres, 578 km by 458 km. using the larger dimension, this gives a circumference of 1815 km, and a surface area of 262 388 km^2, which is bigger than the UK. So navigation actually becomes a significant problem.
– Chris Cudmore
Nov 30 at 17:16




FYI, the largest asteroid in the solar system is Ceres, 578 km by 458 km. using the larger dimension, this gives a circumference of 1815 km, and a surface area of 262 388 km^2, which is bigger than the UK. So navigation actually becomes a significant problem.
– Chris Cudmore
Nov 30 at 17:16












There is a convention for defining the poles of celestial bodies (en.wikipedia.org/wiki/Poles_of_astronomical_bodies), and you could define an arbitrary convention for defining their prime meridians, for example "the point nearest the parent body at its closest approach after 1 Jan 1970". That way, two independent sets of explorers from Earth wouldn't end up using different coordinate systems. But that is a separate question to what indigenous inhabitants might come up with, or what is the most useful system.
– bobtato
yesterday




There is a convention for defining the poles of celestial bodies (en.wikipedia.org/wiki/Poles_of_astronomical_bodies), and you could define an arbitrary convention for defining their prime meridians, for example "the point nearest the parent body at its closest approach after 1 Jan 1970". That way, two independent sets of explorers from Earth wouldn't end up using different coordinate systems. But that is a separate question to what indigenous inhabitants might come up with, or what is the most useful system.
– bobtato
yesterday












could you be more precise about what you are asking? For instance, to meet my friend at the cinema, i usually say : 'meet me at the cinema'. I either use my knowledge of where it is, or google maps to find it. If i use google maps, i just follow the instructions ('left, right'). This would not change on an asteroid. Or is your question about what kind of map could represent a non-spherical object? (Then i'd recommend looking at maps of mountains) Or is your question about how to map said object? (Again, look at how mountains are mapped)
– bukwyrm
5 hours ago






could you be more precise about what you are asking? For instance, to meet my friend at the cinema, i usually say : 'meet me at the cinema'. I either use my knowledge of where it is, or google maps to find it. If i use google maps, i just follow the instructions ('left, right'). This would not change on an asteroid. Or is your question about what kind of map could represent a non-spherical object? (Then i'd recommend looking at maps of mountains) Or is your question about how to map said object? (Again, look at how mountains are mapped)
– bukwyrm
5 hours ago














Possibly related naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/…
– Mołot
2 hours ago




Possibly related naif.jpl.nasa.gov/pub/naif/toolkit_docs/Tutorials/pdf/…
– Mołot
2 hours ago










17 Answers
17






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up vote
33
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My suggestion would be that you select a point on the asteroid to act as a pole. Perhaps the point of first landing? Then, using that point and asteroid's centre of gravity as references, you can map spherical coordinates.






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  • 2




    This is the only option. The details may vary: such as using geostationary satelites, but because astroids don't have poles and their arbitrary rotation makes external (independent of the asteroid) references almost meaningless, picking a point and pounding in the proverbial survey stake is all you can do to guarantee a predictable solution. Consider the Paris Meridian.
    – JBH
    Nov 30 at 0:40








  • 4




    How well do spherical coordinates map to an asteroid that isn't necessarily spherical? Many of them are pretty substantially "squished" in one direction or another.
    – Cadence
    Nov 30 at 2:26






  • 4




    Who says asteroids don't have poles? Most do, especially the larger ones. There are only a few which tumble: sciencedirect.com/science/article/abs/pii/S0019103504002568 (Though if you want to be pedantic, the Earth does a bit, too, with a precession that takes about 26K years.) So you just pick a spot to define your prime meridian, and you're set. Here's Ceres, for an example: planetary.org/multimedia/space-images/small-bodies/…
    – jamesqf
    Nov 30 at 6:56






  • 1




    It would probably be best for the initial landing point to be on the "equator" instead. If it was chosen as a pole,every direction would be worth from there
    – BillThePlatypus
    Nov 30 at 14:28






  • 2




    @BillThePlatypus perhaps "pole" isn't the best term; it might be better to refer to it as an "origin", in the graph sense. So, your "northern hemisphere" would be +y, "southern hemisphere" would be -y, west would be +x, and east would be -x.
    – anaximander
    Nov 30 at 15:12


















up vote
24
down vote













Whoever is going to be on that asteroid will necessarily used radio communication to keep in contact with the rest of the crew.



To ensure communication a network of antennas has to be established, since a single antenna could at best serve half of the asteroid.



Each position can then be simply referred to the distance from the (closest) antennas.






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  • 2




    Triangulation off know antennae makes perfect sense. If you’re occupying for long enough it would even make sense to set up a local gps network (yes, I know the acronym doesn’t make sense, but you get the drift).
    – Joe Bloggs
    Nov 30 at 16:08












  • True enough you could simply do that and make a network of what would be NDB's (Non Directional Beacons). That said perhaps better would be to pulse this as a second rotating directional signal passes through the 0 degree bearing from the transmitter, that is to say in other words upgrade your NDB's to VOR's that allow receivers to calculate their relative bearing to the transmitter easily with no moving parts like a directional receiver antenna (A fixed base station on the ground can accommodate a directional transmitter and machinery to move it more easily than a portable device).
    – MttJocy
    Nov 30 at 16:32










  • But then if you want to compute distances or optimal path between two points, you still need to know the position of their nearby antennas in some reference coordinate system applicable to the entire asteroid.
    – Alexis
    8 hours ago


















up vote
20
down vote













I would suggest that they use a GeoHash which subdivides the asteroid into a hierarchical grid that can be navigated based on any desired granularity



https://en.wikipedia.org/wiki/Geohash



The origin point of the geohash should be the starting outpost location and this would provide a mostly sequential means of describing location where "most" objects that are physically close to each other, share similar geohash values.



NOTE: there are some minor cases where the hash of nearby locations will not be similar, but for most things it should be good enough.



Also NOTE: Geohash is a competing system of location to What3Words which is used here in Ireland and which produces non-sequential descriptors for location. This makes it impossible to know if two locations are close to each other just based on their 3 words which is why I would recommend using Geohash instead.






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  • I'd say this is the answer. Use a series of GPS beacons around the asteroid for navigation and geo-hash specific locations. Good answer.
    – Ruadhan
    Nov 30 at 12:02






  • 3




    With a computer program that someone wrote to map asteroids... go figure. People who don't like that idea are probably the same people against using MechJeb in KSP.
    – Mazura
    2 days ago


















up vote
19
down vote













I'd maybe consider using the axis of rotation - it would be a very rare asteroid that isn't rotating somehow. Imagine sticking a skewer through the asteroid along the axis. That would give you a top and bottom, and then you can use spinwise and counter-spinwise (or something similar).



Obviously only works if you have an asteroid that is rotating nicely, something that is rotating a bit more chaotically might be more of an issue. If it's not rotating at all, or is spinning chaotically then Arkenstein XII's answer is definitely the way to go.






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  • 2




    That works great for most asteroids, as they would rotate around a principal axis.
    – M. Stern
    Nov 30 at 6:47






  • 2




    @M.Stern Probably for the largest ones like Ceres and such at least the smaller objects tend to tumble more than rotate in an orderly fashion and are of course heavily perturbed by gravitational interactions or even radiation pressure from the Sun over time especially given the highly non uniform distribution of mass and surface area common on the smaller objects. Course that said the smaller ones kinda have less need of a co-ordinate system as they have surface areas more like a large retail store than anything you need a map to navigate usefully.
    – MttJocy
    Nov 30 at 15:48








  • 2




    I think preservation of angular momentum is going to guarantee that there will always be a well defined axis of rotation.
    – kasperd
    2 days ago






  • 3




    @kasperd The relationship between angular momentum and rotation gets a lot wonkier when you introduce 3D objects that don't have symmetry about an axis. Most importantly, angular momentum does not have to lie on the same axis that the object rotates about. So while angular momentum is always constant, the axis of rotation will wobble around and precess for lumpy objects like asteroids.
    – el duderino
    2 days ago






  • 1




    Only rotation around a principal axis is stable. An unstable rotation leads to deformations of the body, such that rotational energy is converted to heat. Thus any rotation will decay to a rotation around a principal axis. I would add to this nice answer that even if the rotation is not stable yet, you could use the principal axes as a reference.
    – M. Stern
    yesterday


















up vote
6
down vote













Depending on the length of your characters' stay on the asteroid (is it a mining operation, or are we setting up a habitat?), I'd say just establish a series of beacons that your personal navigation system can triangulate with. If it's longer-term, you have to set up magnetic shielding against the worst bits of solar rays anyway, so you might as well use that system and have a magnetic north as your standard.



An alternative to either of those would be to use the rotation of the asteroid as your north/south, and set up from there. If it's not spinning, this obviously wouldn't work, but it's worth bearing in mind. There are lots of ways to do it, but if this is a corporate thing, then they'd be likely to do whatever is easiest. That would be the triangulation beacon system, which they'd need for comms on a large, dense body anyway, and it would work regardless of why the asteroid is being navigated. It could be standard procedure.






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  • 1




    The rotation also works less well when the object rotates on more than one axis (Common on minor bodies like asteroids due to their low mass and non uniform shapes making them very sensitive to gravitational or even solar radiation perturbing their orbits and rotations). For short stays using the principal axis of rotation might work not so much on longer time scales as this tends to change over time for the reasons stated above.
    – MttJocy
    Nov 30 at 15:51




















up vote
3
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You have to remember that even on Earth, apart from the poles and equator, the coordinate system is arbitrary. Greenwich isn't even a particularly important location in the grand scheme of things, apart from hosting the Royal Observatory that's used to define the 0 meridian.



The problem is the minimum number of points you need to define a coordinate system relative to a body. On a cube we conventionally select a vertex at one corner and three dimensions from that point. On a planet you take the axis of rotation to define the equator, and an arbitrary point on the surface to define a 0 meridian, everything is then defined relative to the equator, the 0 meridian, and the direction of rotation.



Asteroids are irregular. If it's tumbling then you could take the longest axis instead of the axis of rotation and the point of landing as 0 meridian, it could then be modelled as rotating around that axis, even if the axis itself is not stable. If it's spinning then you have poles and the landing point can be the 0 meridian. If you haven't landed on it yet then any arbitrary distinctive point can act as 0 meridian.






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  • I believe the meridian is / was based on the Royal Observatory, which is on the hill above the Naval College (though it's also more or less due North of it so it doesn't make much difference)...
    – bobtato
    yesterday










  • @bobtato, the two aren't strictly independent, the Observatory came under the Admiralty as its funding was tied to work on navigation.
    – Separatrix
    11 hours ago


















up vote
2
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You can use the same coordinate system for celestial navigation (latitude and longitude) used by Terran mariners. What you need is : an almanac, a watch, a device for measuring the angle of the stars relative to some average horizon, and a map.



Almanac



The basic concept of celestial navigation is this : imagine several easily-recognizable stars. Next, imagine that you could draw a line from each of these stars that would pass through the center of whatever you are standing on. This line will touch the ground at one (only one) location. An almanac records these stars and the location (in latitude and longitude) of the point on the surface where the imaginary line from the star touches the ground.



Watch and Calendar



And, this spot will move as the object rotates around it's own axis (days); but will only move a little with the seasons.



Measurement Device (Sextant)



When you are standing on the spot where this imaginary line from your easily-recognizable star intersects the ground, that star will be directly overhead.



Map



Likely, you are not standing on one of these spots at any particular time. The angular measurement times the average radius of the asteroid provides you with the approximate circular (radial) distance between that point and where you are. Measure multiple stars to determine where these circles overlap on a map. That is your (approximate) location






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  • 1




    I suspect for regular navigation over the surface of a large asteroid that celestial navigation isn't going to be effective. Either the asteroid is spinning too fast to get decent measurements, or the granularity of the result isn't accurate enough for more than the most basic navigation.
    – Ruadhan
    Nov 30 at 12:00


















up vote
1
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Maybe the easiest way would be to add a number of beacons and then just run bearings off, or between, them.



Possibly designate one, or a few, as Prime(s), analogous to magnetic poles, and relate the bearings of the others to them.



There are a number of navigation systems that use, or have used, fixed beacons to determine locations with varying degrees of accuracy depending on range from the beacons.






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    up vote
    1
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    The center of mass would be the origin, all other coordinates (x, y, and z ~ latitude, longitude, elevation) would be pulled off that. You would orient and find the location of the CoM by triangulation of the stars as it rotates, with repeated measurements over time and in different places on the surface of the rock.






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    • CoM would be your first reference point, but what would you use for a second reference point?
      – Michael
      Nov 30 at 20:04










    • Literally every other point you define is the second point. The coordinates of that point would be with respect to the origin, i.e. the CoM.
      – kaas347
      yesterday






    • 1




      I'm saying one point isn't sufficient. If you use x,y,z then you need another point to define one of your axes; if you use lat/lon you need to define where your origin is on the surface.
      – Michael
      yesterday










    • There actually exist nonconvex asteroids. For such CoM might be easily located in outer space :)
      – მამუკა ჯიბლაძე
      yesterday










    • Three dimensions requires three points to define a unique coordinate basis. This won't work without a means of defining, absolutely or arbitrarily, two more points.
      – Nij
      9 hours ago


















    up vote
    1
    down vote













    TL;DR: Two spikes, a ruler and a protractor



    There is no perfect solution, just as there is no perfect solution for Earth. Witness differing data (as plural of datum, in which a datum is the basis of a specific system of reference). Here is a document describing conversion between two equally acceptable systems of datum: https://www.ngs.noaa.gov/CORS/Articles/WGS84NAD83.pdf



    Here's a short snippet from that paper which goes to the heart of this difference:




    First of all, one should understand that the 3-D Cartesian frames to
    which the coordinates of the NAD83 and WGS84 refer are not identical.
    Their origin, axes orientation in space, and the unit of scale
    differ. Why? Simply, because the definitions of these two frames are
    based on different sets of observations, processing algorithms, and
    perhaps, geodetic assumptions.




    So there is no one right answer for difficult surfaces -- we can't even get it settled rigorously for our relatively simple surface here on Earth. We simply agree which set of imperfections to try to work around. YET there must still be many more wrong answers than right answers.



    Here's my proposed less-wrong answer, which is similar to many answers provided here, but perhaps more complete:



    Select a north pole and drive a real or imaginary spike into it. Select an arbitrary prime meridien and drive another spike in where that intersects your chosen equator. We are unlikely to have a handy set of facts to support definitions like "equidistant at all longitude", so a naturally defined equator may not be available. Likewise, if the thing does not rotate appreciably, or if that rotation is perturbed or wholly inconsistent with an intuitional model of where poles and an equator "should" be, we can still get by with nothing more than our two chosen points -- a north pole, and a 0-0 point (corresponding to 0-0 in the Gulf of Guinea, check it out). With these two points we can always measure two facts:




    • angle of rotation about the north pole from the prime meridien

    • distance from the north pole as the space crow flies


    These are not perfect, but can be agreed upon and figured by independent observers. Any radio distancing scheme could also be based upon these two points to yield the same two facts about position. This would also support map projection such as we are familiar with, including all of the existing shortcomings.






    share|improve this answer




























      up vote
      1
      down vote













      Let me start by clearing one thing - poles are not defined by magnetic field. Poles are defined by axis of rotation. Magnetic poles are somewhat independent from geographic poles and are only used as handy approximation, especially when you can't get a hold of more accurate measurement e.g of sun and stars, when the sky is clouded.
      https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies



      As for your actual question - it depends on what you mean by large asteroid. Really big ones (bigger than 400km diameter) end up being nearly spherical due to their own gravity, we recently decided to call them dwarf planets. All dwarf planets rotate mostly regularly so you don't need to invent any new system, just choose a prime meridian, maybe a place of first landing, or the highest mountain, and you're good.
      https://en.wikipedia.org/wiki/Dwarf_planet



      Smaller, irregular asteroids, may not map nicely, especially if their rotation is very irregular, but you can still define the main axis by calculating mass distribution, choose the axis that gives maximum moment of intertia, which for regular bodies overlaps with axis of rotation, choose prime meridian (same as above), and you're good.
      https://en.wikipedia.org/wiki/Moment_of_inertia



      For very small asteroids, don't bother with Earth-like coordinates. If your total area is comparable with big cities like London, Moscow or Paris, do something similar. Define "districts" and "neighbourhoods" with memorable names. Place couple of beacons and plaques to make it clear which is where. Everybody will learn them after living there for couple of weeks.



      In conclusion.



      For any reasonably spherelike object you can define a
      North Pole, where the major axis crosses the surface, choose an arbitrary Prime Meridian and plot an Earth-like grid of coordinates by simply projecting an imagined sphere on the actual surface. The asteroid doesn't even have to be very regular. These basic rules will work for all kind of potato shapes, as long as it has mostly positive surface curvature, which will always be the case except for very small asteroids. For those, you don't need a grid because the very small area and irregularity allows you to name all sectors unambiguously and just use those names.






      share|improve this answer



















      • 1




        I'd probably go so far as to say that a spherical "globe" map of an asteroid is still both possible and possibly the best solution. You would still use longditude and lattitude to define position, even with irregular bodies - it's a measure of the direction from the centre of mass after all. A 2D map would end up a little distorted though, but I don't know how any projection could prevent that.
        – Baldrickk
        5 hours ago












      • @Baldrickk I agree, I added a conclusion that hopefully makes this clearer
        – Milo Bem
        3 hours ago


















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      The asteroid would be mapped before anybody ever landed on it, rotation, procession etc would not, I think, be used due to the relative impact on these things from habitation and industry.



      https://dawn.jpl.nasa.gov/multimedia/images/image-detail.html?id=PIA17480



      It doesn't seem logical either to adopt magnetic polar attributes, as these are un-managed variables.



      As with L Dutch & G.B. Robinson's answers, triangulation to communication antenna and 'relative stationary' satellites would be most useful, reliable & probably become ubiquitous. It's not like asteroid dwellers would be without electronic devices at any time, as their lives would depend on them. 3d mapping is not really any more complex, tho we would probably expect long term residents to develop abbreviations and colloquial terms as references






      share|improve this answer

















      • 1




        The last part is a good point most people rarely describe things by co-ordinates especially in settled areas where there are landmarks or pieces of infrastructure to use as reference points instead. This of course makes sense when you consider that our primate brains evolved to navigate the world using our eyes and things that we can physically see within the world and orient around rather than numbers assigned to virtual lines that exist only on paper.
        – MttJocy
        Nov 30 at 16:01










      • True, but we have plenty of examples of people adapting to organised cartographical/reference systems, travelling to major cities across the world that have different fundamental concepts for their mass transit systems or no city block systems can make for a headache to those used to a different system. Most of them take a great deal of getting used to, but they are fundamentally arbitrary but organised systems...and then you have London =)
        – Giu Piete
        2 days ago




















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      Expanding a bit on LDutch's answer and MttJocy's comment on it. Take a page from pre-GPS aerial and nautical navigation systems.



      Aviation commonly uses (fading as GPS is taking over, but still present) the VOR system and ADFs to figure positions and navigate. Essentially the various beacons all broadcast at a different frequency, with a directional pulse that varies in phase with the base signal. By calculating the phase difference between the primary and secondary phases your ADF provides your bearing from the station. Getting a bearing from two different stations gives you a very precise location. There are also some things that can be done in terms of phasing and signal strength to give an approximate distance from a single station, allowing for a rough position fix off of a single signal, but I am not aware of it being done in practice as the two bearing option is much more reliable. The major drawback for this system as currently implemented, and your intended use is that it is line of site and relatively short range (~200 miles). If you are too far from a station, or a pesky mountain (or the horizon of your asteroid) happens to be between you and it, you are not going to be able to pick up the signals. Meaning this system is not commonly used for surface travel.



      The LORAN system was developed in WW2 and used until fairly recently for nautical navigation. It again works by using a series of fixed position transmitters, but in this case they come in paired units. Each member of the pairing is separated by a known distance, and they pulse out synchronized signals. The receiver compares the time difference in receiving the two pulses and from that difference you can plot a line of your relative distance from the two. Grab readings from an alternate pair to plot your location. The major advantage this system has over the other is range (~1500 miles) and being much less sensitive to LoS issues, though it is also somewhat less accurate. With the sensitivity and precision of modern electronics, it is conceivable that someone could build a 3+ point LORAN system and pinpoint their location pretty accurately off of one reading, the challenge being keeping the signals synchronized across the additional broadcast stations.



      Now the range and LOS issues are primarily a function of the frequencies that are used in broadcasting the signals. So you could theoretically implement a VOR system in the frequency bands used by LORAN and have better performance in that respect, but it will also change the timing and phase calculations for determining direction. These would be engineering problems and may impact how quickly and reliably you could find you position. (Way too long since I studies this stuff to remember that level of detail)



      Once the beacon network is established your coordinates become a range and bearing to a convenient beacon. "10 klicks from beacon XYZ bearing 175".



      Note, I would advise against trying to establish a GPS network around an asteroid. That system is dependent on known orbits & timing for the satellites, and I suspect it would be very difficult to maintain such with the irregular shape and weak gravity of an asteroid.






      share|improve this answer





















      • Distance measurement using a single station these days is generally done using DME instead which basically works like secondary radar but with the roles reversed as the interrogator is on the aircraft and the transponder is on the ground. Those are more often found co-located with VOR/NDB/LNAV stations used in non precision approach procedures at airports though but there is no real reason why you couldn't have this on all your beacons on the asteroid if you wanted it. Could be useful especially if the asteroid is a very irregular shape where LoS to two or more stations might be an issue.
        – MttJocy
        2 days ago


















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      Assuming a sufficiently advanced society, what about artificial poles, magnetic or otherwise?






      share|improve this answer








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        A map with landmarks



        The asteroid would be mapped out and photographed to generate a 3d model with landmarks



        Like a pirate's map, directions would be given from the nearest landmark.






        share|improve this answer




























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          Use Peaks and Valleys, and polar coordinates



          In the old days, prior to GPS, cartography and mapping were major and necessary fields of study. Obviously without a magnetic pole you would be unable to create universal direction, but you could still create a 'map' by using surveying techniques found mainly in triangulation of mountain peaks.



          Basically, you identify the highest point in a field of view, triangulate this with others to determine its distance and height, allowing you to build up an accurate map of peaks.



          As it is an asteroid, it has a centre of mass, and should be relatively easy to determine which peak is the highest - this would be your reference point. The second tallest peak would be your reference base line, from which you could measure polar coordinates in a consistent anticlockwise direction from centre of gravity (z-axis) for all peaks thereon.



          Often, when exploring Australia, Charles Sturt would have to 'artificially' create mini-piles of rocks to serve as references to determine coordinates. If your asteroid is flat, this could be used to create artificial reference points too.






          share|improve this answer




























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            0
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            1. enter image description here


            You can apply a graph to your asteroid and find the distances of each point. From one another with this equation.



            AB^2=(Bx-Ax)^2+(By-Ay)^2…………………^2=squared



            If you make the same graph on four sided sections of asteroid you will have a rough grid.
            Next




            1. enter image description here


            This is a better way to make a three dimensional coordinate site system labeling each point from the center as a distance with the equation:



            The root of [(x2-x1)+(y2-y1)+(z2-z1)] where each point is a labeled coordinate at the surface of the asteroid.
            Next




            1. enter image description here


            Use a circle grid to plot points from center with meters or kilometers or centimeters.



            enter image description here



            Then you find the angle degree of the point with this type of equation. Remember your circle grid always has a 90 degree angle already.



            enter image description here



            One can also find angle this way



            enter image description here



            Now apply the equation.
            X^2 + y^2=(r cos @)^2. + (r sin @)^2 Where @ is a Greek representational letter for degrees or radians.



            And this gives a unique coordinate for any point and it’s distamce from center of asteroid. You can put a stake or pin at any point and create a grid by stretching a bright colored string from one to the other. And use these shapes to find area.
            Next




            1. Another way is calculus if the asteroid is spinning you can find sections of surface area as zones of the asteroid.


            enter image description here



            And use integration.



            enter image description here



            For this you need the radius or diameter at each given integrated section. It if one can imagine a large amount of sections and each having a sub measure of length sections to each sliced section it also makes a grid.



            There are few more possibilities and I will add if asked.



            This is a rough idea and I am a little rusty and just woke up. Will edit later. I had a better presentation but the pictures would not copy here.






            share|improve this answer






















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              17 Answers
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              up vote
              33
              down vote













              My suggestion would be that you select a point on the asteroid to act as a pole. Perhaps the point of first landing? Then, using that point and asteroid's centre of gravity as references, you can map spherical coordinates.






              share|improve this answer



















              • 2




                This is the only option. The details may vary: such as using geostationary satelites, but because astroids don't have poles and their arbitrary rotation makes external (independent of the asteroid) references almost meaningless, picking a point and pounding in the proverbial survey stake is all you can do to guarantee a predictable solution. Consider the Paris Meridian.
                – JBH
                Nov 30 at 0:40








              • 4




                How well do spherical coordinates map to an asteroid that isn't necessarily spherical? Many of them are pretty substantially "squished" in one direction or another.
                – Cadence
                Nov 30 at 2:26






              • 4




                Who says asteroids don't have poles? Most do, especially the larger ones. There are only a few which tumble: sciencedirect.com/science/article/abs/pii/S0019103504002568 (Though if you want to be pedantic, the Earth does a bit, too, with a precession that takes about 26K years.) So you just pick a spot to define your prime meridian, and you're set. Here's Ceres, for an example: planetary.org/multimedia/space-images/small-bodies/…
                – jamesqf
                Nov 30 at 6:56






              • 1




                It would probably be best for the initial landing point to be on the "equator" instead. If it was chosen as a pole,every direction would be worth from there
                – BillThePlatypus
                Nov 30 at 14:28






              • 2




                @BillThePlatypus perhaps "pole" isn't the best term; it might be better to refer to it as an "origin", in the graph sense. So, your "northern hemisphere" would be +y, "southern hemisphere" would be -y, west would be +x, and east would be -x.
                – anaximander
                Nov 30 at 15:12















              up vote
              33
              down vote













              My suggestion would be that you select a point on the asteroid to act as a pole. Perhaps the point of first landing? Then, using that point and asteroid's centre of gravity as references, you can map spherical coordinates.






              share|improve this answer



















              • 2




                This is the only option. The details may vary: such as using geostationary satelites, but because astroids don't have poles and their arbitrary rotation makes external (independent of the asteroid) references almost meaningless, picking a point and pounding in the proverbial survey stake is all you can do to guarantee a predictable solution. Consider the Paris Meridian.
                – JBH
                Nov 30 at 0:40








              • 4




                How well do spherical coordinates map to an asteroid that isn't necessarily spherical? Many of them are pretty substantially "squished" in one direction or another.
                – Cadence
                Nov 30 at 2:26






              • 4




                Who says asteroids don't have poles? Most do, especially the larger ones. There are only a few which tumble: sciencedirect.com/science/article/abs/pii/S0019103504002568 (Though if you want to be pedantic, the Earth does a bit, too, with a precession that takes about 26K years.) So you just pick a spot to define your prime meridian, and you're set. Here's Ceres, for an example: planetary.org/multimedia/space-images/small-bodies/…
                – jamesqf
                Nov 30 at 6:56






              • 1




                It would probably be best for the initial landing point to be on the "equator" instead. If it was chosen as a pole,every direction would be worth from there
                – BillThePlatypus
                Nov 30 at 14:28






              • 2




                @BillThePlatypus perhaps "pole" isn't the best term; it might be better to refer to it as an "origin", in the graph sense. So, your "northern hemisphere" would be +y, "southern hemisphere" would be -y, west would be +x, and east would be -x.
                – anaximander
                Nov 30 at 15:12













              up vote
              33
              down vote










              up vote
              33
              down vote









              My suggestion would be that you select a point on the asteroid to act as a pole. Perhaps the point of first landing? Then, using that point and asteroid's centre of gravity as references, you can map spherical coordinates.






              share|improve this answer














              My suggestion would be that you select a point on the asteroid to act as a pole. Perhaps the point of first landing? Then, using that point and asteroid's centre of gravity as references, you can map spherical coordinates.







              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited Nov 30 at 0:47

























              answered Nov 30 at 0:37









              Arkenstein XII

              2,004320




              2,004320








              • 2




                This is the only option. The details may vary: such as using geostationary satelites, but because astroids don't have poles and their arbitrary rotation makes external (independent of the asteroid) references almost meaningless, picking a point and pounding in the proverbial survey stake is all you can do to guarantee a predictable solution. Consider the Paris Meridian.
                – JBH
                Nov 30 at 0:40








              • 4




                How well do spherical coordinates map to an asteroid that isn't necessarily spherical? Many of them are pretty substantially "squished" in one direction or another.
                – Cadence
                Nov 30 at 2:26






              • 4




                Who says asteroids don't have poles? Most do, especially the larger ones. There are only a few which tumble: sciencedirect.com/science/article/abs/pii/S0019103504002568 (Though if you want to be pedantic, the Earth does a bit, too, with a precession that takes about 26K years.) So you just pick a spot to define your prime meridian, and you're set. Here's Ceres, for an example: planetary.org/multimedia/space-images/small-bodies/…
                – jamesqf
                Nov 30 at 6:56






              • 1




                It would probably be best for the initial landing point to be on the "equator" instead. If it was chosen as a pole,every direction would be worth from there
                – BillThePlatypus
                Nov 30 at 14:28






              • 2




                @BillThePlatypus perhaps "pole" isn't the best term; it might be better to refer to it as an "origin", in the graph sense. So, your "northern hemisphere" would be +y, "southern hemisphere" would be -y, west would be +x, and east would be -x.
                – anaximander
                Nov 30 at 15:12














              • 2




                This is the only option. The details may vary: such as using geostationary satelites, but because astroids don't have poles and their arbitrary rotation makes external (independent of the asteroid) references almost meaningless, picking a point and pounding in the proverbial survey stake is all you can do to guarantee a predictable solution. Consider the Paris Meridian.
                – JBH
                Nov 30 at 0:40








              • 4




                How well do spherical coordinates map to an asteroid that isn't necessarily spherical? Many of them are pretty substantially "squished" in one direction or another.
                – Cadence
                Nov 30 at 2:26






              • 4




                Who says asteroids don't have poles? Most do, especially the larger ones. There are only a few which tumble: sciencedirect.com/science/article/abs/pii/S0019103504002568 (Though if you want to be pedantic, the Earth does a bit, too, with a precession that takes about 26K years.) So you just pick a spot to define your prime meridian, and you're set. Here's Ceres, for an example: planetary.org/multimedia/space-images/small-bodies/…
                – jamesqf
                Nov 30 at 6:56






              • 1




                It would probably be best for the initial landing point to be on the "equator" instead. If it was chosen as a pole,every direction would be worth from there
                – BillThePlatypus
                Nov 30 at 14:28






              • 2




                @BillThePlatypus perhaps "pole" isn't the best term; it might be better to refer to it as an "origin", in the graph sense. So, your "northern hemisphere" would be +y, "southern hemisphere" would be -y, west would be +x, and east would be -x.
                – anaximander
                Nov 30 at 15:12








              2




              2




              This is the only option. The details may vary: such as using geostationary satelites, but because astroids don't have poles and their arbitrary rotation makes external (independent of the asteroid) references almost meaningless, picking a point and pounding in the proverbial survey stake is all you can do to guarantee a predictable solution. Consider the Paris Meridian.
              – JBH
              Nov 30 at 0:40






              This is the only option. The details may vary: such as using geostationary satelites, but because astroids don't have poles and their arbitrary rotation makes external (independent of the asteroid) references almost meaningless, picking a point and pounding in the proverbial survey stake is all you can do to guarantee a predictable solution. Consider the Paris Meridian.
              – JBH
              Nov 30 at 0:40






              4




              4




              How well do spherical coordinates map to an asteroid that isn't necessarily spherical? Many of them are pretty substantially "squished" in one direction or another.
              – Cadence
              Nov 30 at 2:26




              How well do spherical coordinates map to an asteroid that isn't necessarily spherical? Many of them are pretty substantially "squished" in one direction or another.
              – Cadence
              Nov 30 at 2:26




              4




              4




              Who says asteroids don't have poles? Most do, especially the larger ones. There are only a few which tumble: sciencedirect.com/science/article/abs/pii/S0019103504002568 (Though if you want to be pedantic, the Earth does a bit, too, with a precession that takes about 26K years.) So you just pick a spot to define your prime meridian, and you're set. Here's Ceres, for an example: planetary.org/multimedia/space-images/small-bodies/…
              – jamesqf
              Nov 30 at 6:56




              Who says asteroids don't have poles? Most do, especially the larger ones. There are only a few which tumble: sciencedirect.com/science/article/abs/pii/S0019103504002568 (Though if you want to be pedantic, the Earth does a bit, too, with a precession that takes about 26K years.) So you just pick a spot to define your prime meridian, and you're set. Here's Ceres, for an example: planetary.org/multimedia/space-images/small-bodies/…
              – jamesqf
              Nov 30 at 6:56




              1




              1




              It would probably be best for the initial landing point to be on the "equator" instead. If it was chosen as a pole,every direction would be worth from there
              – BillThePlatypus
              Nov 30 at 14:28




              It would probably be best for the initial landing point to be on the "equator" instead. If it was chosen as a pole,every direction would be worth from there
              – BillThePlatypus
              Nov 30 at 14:28




              2




              2




              @BillThePlatypus perhaps "pole" isn't the best term; it might be better to refer to it as an "origin", in the graph sense. So, your "northern hemisphere" would be +y, "southern hemisphere" would be -y, west would be +x, and east would be -x.
              – anaximander
              Nov 30 at 15:12




              @BillThePlatypus perhaps "pole" isn't the best term; it might be better to refer to it as an "origin", in the graph sense. So, your "northern hemisphere" would be +y, "southern hemisphere" would be -y, west would be +x, and east would be -x.
              – anaximander
              Nov 30 at 15:12










              up vote
              24
              down vote













              Whoever is going to be on that asteroid will necessarily used radio communication to keep in contact with the rest of the crew.



              To ensure communication a network of antennas has to be established, since a single antenna could at best serve half of the asteroid.



              Each position can then be simply referred to the distance from the (closest) antennas.






              share|improve this answer

















              • 2




                Triangulation off know antennae makes perfect sense. If you’re occupying for long enough it would even make sense to set up a local gps network (yes, I know the acronym doesn’t make sense, but you get the drift).
                – Joe Bloggs
                Nov 30 at 16:08












              • True enough you could simply do that and make a network of what would be NDB's (Non Directional Beacons). That said perhaps better would be to pulse this as a second rotating directional signal passes through the 0 degree bearing from the transmitter, that is to say in other words upgrade your NDB's to VOR's that allow receivers to calculate their relative bearing to the transmitter easily with no moving parts like a directional receiver antenna (A fixed base station on the ground can accommodate a directional transmitter and machinery to move it more easily than a portable device).
                – MttJocy
                Nov 30 at 16:32










              • But then if you want to compute distances or optimal path between two points, you still need to know the position of their nearby antennas in some reference coordinate system applicable to the entire asteroid.
                – Alexis
                8 hours ago















              up vote
              24
              down vote













              Whoever is going to be on that asteroid will necessarily used radio communication to keep in contact with the rest of the crew.



              To ensure communication a network of antennas has to be established, since a single antenna could at best serve half of the asteroid.



              Each position can then be simply referred to the distance from the (closest) antennas.






              share|improve this answer

















              • 2




                Triangulation off know antennae makes perfect sense. If you’re occupying for long enough it would even make sense to set up a local gps network (yes, I know the acronym doesn’t make sense, but you get the drift).
                – Joe Bloggs
                Nov 30 at 16:08












              • True enough you could simply do that and make a network of what would be NDB's (Non Directional Beacons). That said perhaps better would be to pulse this as a second rotating directional signal passes through the 0 degree bearing from the transmitter, that is to say in other words upgrade your NDB's to VOR's that allow receivers to calculate their relative bearing to the transmitter easily with no moving parts like a directional receiver antenna (A fixed base station on the ground can accommodate a directional transmitter and machinery to move it more easily than a portable device).
                – MttJocy
                Nov 30 at 16:32










              • But then if you want to compute distances or optimal path between two points, you still need to know the position of their nearby antennas in some reference coordinate system applicable to the entire asteroid.
                – Alexis
                8 hours ago













              up vote
              24
              down vote










              up vote
              24
              down vote









              Whoever is going to be on that asteroid will necessarily used radio communication to keep in contact with the rest of the crew.



              To ensure communication a network of antennas has to be established, since a single antenna could at best serve half of the asteroid.



              Each position can then be simply referred to the distance from the (closest) antennas.






              share|improve this answer












              Whoever is going to be on that asteroid will necessarily used radio communication to keep in contact with the rest of the crew.



              To ensure communication a network of antennas has to be established, since a single antenna could at best serve half of the asteroid.



              Each position can then be simply referred to the distance from the (closest) antennas.







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered Nov 30 at 0:51









              L.Dutch

              72k22173346




              72k22173346








              • 2




                Triangulation off know antennae makes perfect sense. If you’re occupying for long enough it would even make sense to set up a local gps network (yes, I know the acronym doesn’t make sense, but you get the drift).
                – Joe Bloggs
                Nov 30 at 16:08












              • True enough you could simply do that and make a network of what would be NDB's (Non Directional Beacons). That said perhaps better would be to pulse this as a second rotating directional signal passes through the 0 degree bearing from the transmitter, that is to say in other words upgrade your NDB's to VOR's that allow receivers to calculate their relative bearing to the transmitter easily with no moving parts like a directional receiver antenna (A fixed base station on the ground can accommodate a directional transmitter and machinery to move it more easily than a portable device).
                – MttJocy
                Nov 30 at 16:32










              • But then if you want to compute distances or optimal path between two points, you still need to know the position of their nearby antennas in some reference coordinate system applicable to the entire asteroid.
                – Alexis
                8 hours ago














              • 2




                Triangulation off know antennae makes perfect sense. If you’re occupying for long enough it would even make sense to set up a local gps network (yes, I know the acronym doesn’t make sense, but you get the drift).
                – Joe Bloggs
                Nov 30 at 16:08












              • True enough you could simply do that and make a network of what would be NDB's (Non Directional Beacons). That said perhaps better would be to pulse this as a second rotating directional signal passes through the 0 degree bearing from the transmitter, that is to say in other words upgrade your NDB's to VOR's that allow receivers to calculate their relative bearing to the transmitter easily with no moving parts like a directional receiver antenna (A fixed base station on the ground can accommodate a directional transmitter and machinery to move it more easily than a portable device).
                – MttJocy
                Nov 30 at 16:32










              • But then if you want to compute distances or optimal path between two points, you still need to know the position of their nearby antennas in some reference coordinate system applicable to the entire asteroid.
                – Alexis
                8 hours ago








              2




              2




              Triangulation off know antennae makes perfect sense. If you’re occupying for long enough it would even make sense to set up a local gps network (yes, I know the acronym doesn’t make sense, but you get the drift).
              – Joe Bloggs
              Nov 30 at 16:08






              Triangulation off know antennae makes perfect sense. If you’re occupying for long enough it would even make sense to set up a local gps network (yes, I know the acronym doesn’t make sense, but you get the drift).
              – Joe Bloggs
              Nov 30 at 16:08














              True enough you could simply do that and make a network of what would be NDB's (Non Directional Beacons). That said perhaps better would be to pulse this as a second rotating directional signal passes through the 0 degree bearing from the transmitter, that is to say in other words upgrade your NDB's to VOR's that allow receivers to calculate their relative bearing to the transmitter easily with no moving parts like a directional receiver antenna (A fixed base station on the ground can accommodate a directional transmitter and machinery to move it more easily than a portable device).
              – MttJocy
              Nov 30 at 16:32




              True enough you could simply do that and make a network of what would be NDB's (Non Directional Beacons). That said perhaps better would be to pulse this as a second rotating directional signal passes through the 0 degree bearing from the transmitter, that is to say in other words upgrade your NDB's to VOR's that allow receivers to calculate their relative bearing to the transmitter easily with no moving parts like a directional receiver antenna (A fixed base station on the ground can accommodate a directional transmitter and machinery to move it more easily than a portable device).
              – MttJocy
              Nov 30 at 16:32












              But then if you want to compute distances or optimal path between two points, you still need to know the position of their nearby antennas in some reference coordinate system applicable to the entire asteroid.
              – Alexis
              8 hours ago




              But then if you want to compute distances or optimal path between two points, you still need to know the position of their nearby antennas in some reference coordinate system applicable to the entire asteroid.
              – Alexis
              8 hours ago










              up vote
              20
              down vote













              I would suggest that they use a GeoHash which subdivides the asteroid into a hierarchical grid that can be navigated based on any desired granularity



              https://en.wikipedia.org/wiki/Geohash



              The origin point of the geohash should be the starting outpost location and this would provide a mostly sequential means of describing location where "most" objects that are physically close to each other, share similar geohash values.



              NOTE: there are some minor cases where the hash of nearby locations will not be similar, but for most things it should be good enough.



              Also NOTE: Geohash is a competing system of location to What3Words which is used here in Ireland and which produces non-sequential descriptors for location. This makes it impossible to know if two locations are close to each other just based on their 3 words which is why I would recommend using Geohash instead.






              share|improve this answer








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              bicarbon8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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              • I'd say this is the answer. Use a series of GPS beacons around the asteroid for navigation and geo-hash specific locations. Good answer.
                – Ruadhan
                Nov 30 at 12:02






              • 3




                With a computer program that someone wrote to map asteroids... go figure. People who don't like that idea are probably the same people against using MechJeb in KSP.
                – Mazura
                2 days ago















              up vote
              20
              down vote













              I would suggest that they use a GeoHash which subdivides the asteroid into a hierarchical grid that can be navigated based on any desired granularity



              https://en.wikipedia.org/wiki/Geohash



              The origin point of the geohash should be the starting outpost location and this would provide a mostly sequential means of describing location where "most" objects that are physically close to each other, share similar geohash values.



              NOTE: there are some minor cases where the hash of nearby locations will not be similar, but for most things it should be good enough.



              Also NOTE: Geohash is a competing system of location to What3Words which is used here in Ireland and which produces non-sequential descriptors for location. This makes it impossible to know if two locations are close to each other just based on their 3 words which is why I would recommend using Geohash instead.






              share|improve this answer








              New contributor




              bicarbon8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.


















              • I'd say this is the answer. Use a series of GPS beacons around the asteroid for navigation and geo-hash specific locations. Good answer.
                – Ruadhan
                Nov 30 at 12:02






              • 3




                With a computer program that someone wrote to map asteroids... go figure. People who don't like that idea are probably the same people against using MechJeb in KSP.
                – Mazura
                2 days ago













              up vote
              20
              down vote










              up vote
              20
              down vote









              I would suggest that they use a GeoHash which subdivides the asteroid into a hierarchical grid that can be navigated based on any desired granularity



              https://en.wikipedia.org/wiki/Geohash



              The origin point of the geohash should be the starting outpost location and this would provide a mostly sequential means of describing location where "most" objects that are physically close to each other, share similar geohash values.



              NOTE: there are some minor cases where the hash of nearby locations will not be similar, but for most things it should be good enough.



              Also NOTE: Geohash is a competing system of location to What3Words which is used here in Ireland and which produces non-sequential descriptors for location. This makes it impossible to know if two locations are close to each other just based on their 3 words which is why I would recommend using Geohash instead.






              share|improve this answer








              New contributor




              bicarbon8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.









              I would suggest that they use a GeoHash which subdivides the asteroid into a hierarchical grid that can be navigated based on any desired granularity



              https://en.wikipedia.org/wiki/Geohash



              The origin point of the geohash should be the starting outpost location and this would provide a mostly sequential means of describing location where "most" objects that are physically close to each other, share similar geohash values.



              NOTE: there are some minor cases where the hash of nearby locations will not be similar, but for most things it should be good enough.



              Also NOTE: Geohash is a competing system of location to What3Words which is used here in Ireland and which produces non-sequential descriptors for location. This makes it impossible to know if two locations are close to each other just based on their 3 words which is why I would recommend using Geohash instead.







              share|improve this answer








              New contributor




              bicarbon8 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.









              share|improve this answer



              share|improve this answer






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              answered Nov 30 at 11:07









              bicarbon8

              3013




              3013




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              New contributor





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              • I'd say this is the answer. Use a series of GPS beacons around the asteroid for navigation and geo-hash specific locations. Good answer.
                – Ruadhan
                Nov 30 at 12:02






              • 3




                With a computer program that someone wrote to map asteroids... go figure. People who don't like that idea are probably the same people against using MechJeb in KSP.
                – Mazura
                2 days ago


















              • I'd say this is the answer. Use a series of GPS beacons around the asteroid for navigation and geo-hash specific locations. Good answer.
                – Ruadhan
                Nov 30 at 12:02






              • 3




                With a computer program that someone wrote to map asteroids... go figure. People who don't like that idea are probably the same people against using MechJeb in KSP.
                – Mazura
                2 days ago
















              I'd say this is the answer. Use a series of GPS beacons around the asteroid for navigation and geo-hash specific locations. Good answer.
              – Ruadhan
              Nov 30 at 12:02




              I'd say this is the answer. Use a series of GPS beacons around the asteroid for navigation and geo-hash specific locations. Good answer.
              – Ruadhan
              Nov 30 at 12:02




              3




              3




              With a computer program that someone wrote to map asteroids... go figure. People who don't like that idea are probably the same people against using MechJeb in KSP.
              – Mazura
              2 days ago




              With a computer program that someone wrote to map asteroids... go figure. People who don't like that idea are probably the same people against using MechJeb in KSP.
              – Mazura
              2 days ago










              up vote
              19
              down vote













              I'd maybe consider using the axis of rotation - it would be a very rare asteroid that isn't rotating somehow. Imagine sticking a skewer through the asteroid along the axis. That would give you a top and bottom, and then you can use spinwise and counter-spinwise (or something similar).



              Obviously only works if you have an asteroid that is rotating nicely, something that is rotating a bit more chaotically might be more of an issue. If it's not rotating at all, or is spinning chaotically then Arkenstein XII's answer is definitely the way to go.






              share|improve this answer

















              • 2




                That works great for most asteroids, as they would rotate around a principal axis.
                – M. Stern
                Nov 30 at 6:47






              • 2




                @M.Stern Probably for the largest ones like Ceres and such at least the smaller objects tend to tumble more than rotate in an orderly fashion and are of course heavily perturbed by gravitational interactions or even radiation pressure from the Sun over time especially given the highly non uniform distribution of mass and surface area common on the smaller objects. Course that said the smaller ones kinda have less need of a co-ordinate system as they have surface areas more like a large retail store than anything you need a map to navigate usefully.
                – MttJocy
                Nov 30 at 15:48








              • 2




                I think preservation of angular momentum is going to guarantee that there will always be a well defined axis of rotation.
                – kasperd
                2 days ago






              • 3




                @kasperd The relationship between angular momentum and rotation gets a lot wonkier when you introduce 3D objects that don't have symmetry about an axis. Most importantly, angular momentum does not have to lie on the same axis that the object rotates about. So while angular momentum is always constant, the axis of rotation will wobble around and precess for lumpy objects like asteroids.
                – el duderino
                2 days ago






              • 1




                Only rotation around a principal axis is stable. An unstable rotation leads to deformations of the body, such that rotational energy is converted to heat. Thus any rotation will decay to a rotation around a principal axis. I would add to this nice answer that even if the rotation is not stable yet, you could use the principal axes as a reference.
                – M. Stern
                yesterday















              up vote
              19
              down vote













              I'd maybe consider using the axis of rotation - it would be a very rare asteroid that isn't rotating somehow. Imagine sticking a skewer through the asteroid along the axis. That would give you a top and bottom, and then you can use spinwise and counter-spinwise (or something similar).



              Obviously only works if you have an asteroid that is rotating nicely, something that is rotating a bit more chaotically might be more of an issue. If it's not rotating at all, or is spinning chaotically then Arkenstein XII's answer is definitely the way to go.






              share|improve this answer

















              • 2




                That works great for most asteroids, as they would rotate around a principal axis.
                – M. Stern
                Nov 30 at 6:47






              • 2




                @M.Stern Probably for the largest ones like Ceres and such at least the smaller objects tend to tumble more than rotate in an orderly fashion and are of course heavily perturbed by gravitational interactions or even radiation pressure from the Sun over time especially given the highly non uniform distribution of mass and surface area common on the smaller objects. Course that said the smaller ones kinda have less need of a co-ordinate system as they have surface areas more like a large retail store than anything you need a map to navigate usefully.
                – MttJocy
                Nov 30 at 15:48








              • 2




                I think preservation of angular momentum is going to guarantee that there will always be a well defined axis of rotation.
                – kasperd
                2 days ago






              • 3




                @kasperd The relationship between angular momentum and rotation gets a lot wonkier when you introduce 3D objects that don't have symmetry about an axis. Most importantly, angular momentum does not have to lie on the same axis that the object rotates about. So while angular momentum is always constant, the axis of rotation will wobble around and precess for lumpy objects like asteroids.
                – el duderino
                2 days ago






              • 1




                Only rotation around a principal axis is stable. An unstable rotation leads to deformations of the body, such that rotational energy is converted to heat. Thus any rotation will decay to a rotation around a principal axis. I would add to this nice answer that even if the rotation is not stable yet, you could use the principal axes as a reference.
                – M. Stern
                yesterday













              up vote
              19
              down vote










              up vote
              19
              down vote









              I'd maybe consider using the axis of rotation - it would be a very rare asteroid that isn't rotating somehow. Imagine sticking a skewer through the asteroid along the axis. That would give you a top and bottom, and then you can use spinwise and counter-spinwise (or something similar).



              Obviously only works if you have an asteroid that is rotating nicely, something that is rotating a bit more chaotically might be more of an issue. If it's not rotating at all, or is spinning chaotically then Arkenstein XII's answer is definitely the way to go.






              share|improve this answer












              I'd maybe consider using the axis of rotation - it would be a very rare asteroid that isn't rotating somehow. Imagine sticking a skewer through the asteroid along the axis. That would give you a top and bottom, and then you can use spinwise and counter-spinwise (or something similar).



              Obviously only works if you have an asteroid that is rotating nicely, something that is rotating a bit more chaotically might be more of an issue. If it's not rotating at all, or is spinning chaotically then Arkenstein XII's answer is definitely the way to go.







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered Nov 30 at 2:50









              PainlessDocJ

              3413




              3413








              • 2




                That works great for most asteroids, as they would rotate around a principal axis.
                – M. Stern
                Nov 30 at 6:47






              • 2




                @M.Stern Probably for the largest ones like Ceres and such at least the smaller objects tend to tumble more than rotate in an orderly fashion and are of course heavily perturbed by gravitational interactions or even radiation pressure from the Sun over time especially given the highly non uniform distribution of mass and surface area common on the smaller objects. Course that said the smaller ones kinda have less need of a co-ordinate system as they have surface areas more like a large retail store than anything you need a map to navigate usefully.
                – MttJocy
                Nov 30 at 15:48








              • 2




                I think preservation of angular momentum is going to guarantee that there will always be a well defined axis of rotation.
                – kasperd
                2 days ago






              • 3




                @kasperd The relationship between angular momentum and rotation gets a lot wonkier when you introduce 3D objects that don't have symmetry about an axis. Most importantly, angular momentum does not have to lie on the same axis that the object rotates about. So while angular momentum is always constant, the axis of rotation will wobble around and precess for lumpy objects like asteroids.
                – el duderino
                2 days ago






              • 1




                Only rotation around a principal axis is stable. An unstable rotation leads to deformations of the body, such that rotational energy is converted to heat. Thus any rotation will decay to a rotation around a principal axis. I would add to this nice answer that even if the rotation is not stable yet, you could use the principal axes as a reference.
                – M. Stern
                yesterday














              • 2




                That works great for most asteroids, as they would rotate around a principal axis.
                – M. Stern
                Nov 30 at 6:47






              • 2




                @M.Stern Probably for the largest ones like Ceres and such at least the smaller objects tend to tumble more than rotate in an orderly fashion and are of course heavily perturbed by gravitational interactions or even radiation pressure from the Sun over time especially given the highly non uniform distribution of mass and surface area common on the smaller objects. Course that said the smaller ones kinda have less need of a co-ordinate system as they have surface areas more like a large retail store than anything you need a map to navigate usefully.
                – MttJocy
                Nov 30 at 15:48








              • 2




                I think preservation of angular momentum is going to guarantee that there will always be a well defined axis of rotation.
                – kasperd
                2 days ago






              • 3




                @kasperd The relationship between angular momentum and rotation gets a lot wonkier when you introduce 3D objects that don't have symmetry about an axis. Most importantly, angular momentum does not have to lie on the same axis that the object rotates about. So while angular momentum is always constant, the axis of rotation will wobble around and precess for lumpy objects like asteroids.
                – el duderino
                2 days ago






              • 1




                Only rotation around a principal axis is stable. An unstable rotation leads to deformations of the body, such that rotational energy is converted to heat. Thus any rotation will decay to a rotation around a principal axis. I would add to this nice answer that even if the rotation is not stable yet, you could use the principal axes as a reference.
                – M. Stern
                yesterday








              2




              2




              That works great for most asteroids, as they would rotate around a principal axis.
              – M. Stern
              Nov 30 at 6:47




              That works great for most asteroids, as they would rotate around a principal axis.
              – M. Stern
              Nov 30 at 6:47




              2




              2




              @M.Stern Probably for the largest ones like Ceres and such at least the smaller objects tend to tumble more than rotate in an orderly fashion and are of course heavily perturbed by gravitational interactions or even radiation pressure from the Sun over time especially given the highly non uniform distribution of mass and surface area common on the smaller objects. Course that said the smaller ones kinda have less need of a co-ordinate system as they have surface areas more like a large retail store than anything you need a map to navigate usefully.
              – MttJocy
              Nov 30 at 15:48






              @M.Stern Probably for the largest ones like Ceres and such at least the smaller objects tend to tumble more than rotate in an orderly fashion and are of course heavily perturbed by gravitational interactions or even radiation pressure from the Sun over time especially given the highly non uniform distribution of mass and surface area common on the smaller objects. Course that said the smaller ones kinda have less need of a co-ordinate system as they have surface areas more like a large retail store than anything you need a map to navigate usefully.
              – MttJocy
              Nov 30 at 15:48






              2




              2




              I think preservation of angular momentum is going to guarantee that there will always be a well defined axis of rotation.
              – kasperd
              2 days ago




              I think preservation of angular momentum is going to guarantee that there will always be a well defined axis of rotation.
              – kasperd
              2 days ago




              3




              3




              @kasperd The relationship between angular momentum and rotation gets a lot wonkier when you introduce 3D objects that don't have symmetry about an axis. Most importantly, angular momentum does not have to lie on the same axis that the object rotates about. So while angular momentum is always constant, the axis of rotation will wobble around and precess for lumpy objects like asteroids.
              – el duderino
              2 days ago




              @kasperd The relationship between angular momentum and rotation gets a lot wonkier when you introduce 3D objects that don't have symmetry about an axis. Most importantly, angular momentum does not have to lie on the same axis that the object rotates about. So while angular momentum is always constant, the axis of rotation will wobble around and precess for lumpy objects like asteroids.
              – el duderino
              2 days ago




              1




              1




              Only rotation around a principal axis is stable. An unstable rotation leads to deformations of the body, such that rotational energy is converted to heat. Thus any rotation will decay to a rotation around a principal axis. I would add to this nice answer that even if the rotation is not stable yet, you could use the principal axes as a reference.
              – M. Stern
              yesterday




              Only rotation around a principal axis is stable. An unstable rotation leads to deformations of the body, such that rotational energy is converted to heat. Thus any rotation will decay to a rotation around a principal axis. I would add to this nice answer that even if the rotation is not stable yet, you could use the principal axes as a reference.
              – M. Stern
              yesterday










              up vote
              6
              down vote













              Depending on the length of your characters' stay on the asteroid (is it a mining operation, or are we setting up a habitat?), I'd say just establish a series of beacons that your personal navigation system can triangulate with. If it's longer-term, you have to set up magnetic shielding against the worst bits of solar rays anyway, so you might as well use that system and have a magnetic north as your standard.



              An alternative to either of those would be to use the rotation of the asteroid as your north/south, and set up from there. If it's not spinning, this obviously wouldn't work, but it's worth bearing in mind. There are lots of ways to do it, but if this is a corporate thing, then they'd be likely to do whatever is easiest. That would be the triangulation beacon system, which they'd need for comms on a large, dense body anyway, and it would work regardless of why the asteroid is being navigated. It could be standard procedure.






              share|improve this answer








              New contributor




              G. B. Robinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.














              • 1




                The rotation also works less well when the object rotates on more than one axis (Common on minor bodies like asteroids due to their low mass and non uniform shapes making them very sensitive to gravitational or even solar radiation perturbing their orbits and rotations). For short stays using the principal axis of rotation might work not so much on longer time scales as this tends to change over time for the reasons stated above.
                – MttJocy
                Nov 30 at 15:51

















              up vote
              6
              down vote













              Depending on the length of your characters' stay on the asteroid (is it a mining operation, or are we setting up a habitat?), I'd say just establish a series of beacons that your personal navigation system can triangulate with. If it's longer-term, you have to set up magnetic shielding against the worst bits of solar rays anyway, so you might as well use that system and have a magnetic north as your standard.



              An alternative to either of those would be to use the rotation of the asteroid as your north/south, and set up from there. If it's not spinning, this obviously wouldn't work, but it's worth bearing in mind. There are lots of ways to do it, but if this is a corporate thing, then they'd be likely to do whatever is easiest. That would be the triangulation beacon system, which they'd need for comms on a large, dense body anyway, and it would work regardless of why the asteroid is being navigated. It could be standard procedure.






              share|improve this answer








              New contributor




              G. B. Robinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.














              • 1




                The rotation also works less well when the object rotates on more than one axis (Common on minor bodies like asteroids due to their low mass and non uniform shapes making them very sensitive to gravitational or even solar radiation perturbing their orbits and rotations). For short stays using the principal axis of rotation might work not so much on longer time scales as this tends to change over time for the reasons stated above.
                – MttJocy
                Nov 30 at 15:51















              up vote
              6
              down vote










              up vote
              6
              down vote









              Depending on the length of your characters' stay on the asteroid (is it a mining operation, or are we setting up a habitat?), I'd say just establish a series of beacons that your personal navigation system can triangulate with. If it's longer-term, you have to set up magnetic shielding against the worst bits of solar rays anyway, so you might as well use that system and have a magnetic north as your standard.



              An alternative to either of those would be to use the rotation of the asteroid as your north/south, and set up from there. If it's not spinning, this obviously wouldn't work, but it's worth bearing in mind. There are lots of ways to do it, but if this is a corporate thing, then they'd be likely to do whatever is easiest. That would be the triangulation beacon system, which they'd need for comms on a large, dense body anyway, and it would work regardless of why the asteroid is being navigated. It could be standard procedure.






              share|improve this answer








              New contributor




              G. B. Robinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.









              Depending on the length of your characters' stay on the asteroid (is it a mining operation, or are we setting up a habitat?), I'd say just establish a series of beacons that your personal navigation system can triangulate with. If it's longer-term, you have to set up magnetic shielding against the worst bits of solar rays anyway, so you might as well use that system and have a magnetic north as your standard.



              An alternative to either of those would be to use the rotation of the asteroid as your north/south, and set up from there. If it's not spinning, this obviously wouldn't work, but it's worth bearing in mind. There are lots of ways to do it, but if this is a corporate thing, then they'd be likely to do whatever is easiest. That would be the triangulation beacon system, which they'd need for comms on a large, dense body anyway, and it would work regardless of why the asteroid is being navigated. It could be standard procedure.







              share|improve this answer








              New contributor




              G. B. Robinson is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.









              share|improve this answer



              share|improve this answer






              New contributor




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              answered Nov 30 at 5:53









              G. B. Robinson

              1137




              1137




              New contributor




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              New contributor





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              • 1




                The rotation also works less well when the object rotates on more than one axis (Common on minor bodies like asteroids due to their low mass and non uniform shapes making them very sensitive to gravitational or even solar radiation perturbing their orbits and rotations). For short stays using the principal axis of rotation might work not so much on longer time scales as this tends to change over time for the reasons stated above.
                – MttJocy
                Nov 30 at 15:51
















              • 1




                The rotation also works less well when the object rotates on more than one axis (Common on minor bodies like asteroids due to their low mass and non uniform shapes making them very sensitive to gravitational or even solar radiation perturbing their orbits and rotations). For short stays using the principal axis of rotation might work not so much on longer time scales as this tends to change over time for the reasons stated above.
                – MttJocy
                Nov 30 at 15:51










              1




              1




              The rotation also works less well when the object rotates on more than one axis (Common on minor bodies like asteroids due to their low mass and non uniform shapes making them very sensitive to gravitational or even solar radiation perturbing their orbits and rotations). For short stays using the principal axis of rotation might work not so much on longer time scales as this tends to change over time for the reasons stated above.
              – MttJocy
              Nov 30 at 15:51






              The rotation also works less well when the object rotates on more than one axis (Common on minor bodies like asteroids due to their low mass and non uniform shapes making them very sensitive to gravitational or even solar radiation perturbing their orbits and rotations). For short stays using the principal axis of rotation might work not so much on longer time scales as this tends to change over time for the reasons stated above.
              – MttJocy
              Nov 30 at 15:51












              up vote
              3
              down vote













              You have to remember that even on Earth, apart from the poles and equator, the coordinate system is arbitrary. Greenwich isn't even a particularly important location in the grand scheme of things, apart from hosting the Royal Observatory that's used to define the 0 meridian.



              The problem is the minimum number of points you need to define a coordinate system relative to a body. On a cube we conventionally select a vertex at one corner and three dimensions from that point. On a planet you take the axis of rotation to define the equator, and an arbitrary point on the surface to define a 0 meridian, everything is then defined relative to the equator, the 0 meridian, and the direction of rotation.



              Asteroids are irregular. If it's tumbling then you could take the longest axis instead of the axis of rotation and the point of landing as 0 meridian, it could then be modelled as rotating around that axis, even if the axis itself is not stable. If it's spinning then you have poles and the landing point can be the 0 meridian. If you haven't landed on it yet then any arbitrary distinctive point can act as 0 meridian.






              share|improve this answer























              • I believe the meridian is / was based on the Royal Observatory, which is on the hill above the Naval College (though it's also more or less due North of it so it doesn't make much difference)...
                – bobtato
                yesterday










              • @bobtato, the two aren't strictly independent, the Observatory came under the Admiralty as its funding was tied to work on navigation.
                – Separatrix
                11 hours ago















              up vote
              3
              down vote













              You have to remember that even on Earth, apart from the poles and equator, the coordinate system is arbitrary. Greenwich isn't even a particularly important location in the grand scheme of things, apart from hosting the Royal Observatory that's used to define the 0 meridian.



              The problem is the minimum number of points you need to define a coordinate system relative to a body. On a cube we conventionally select a vertex at one corner and three dimensions from that point. On a planet you take the axis of rotation to define the equator, and an arbitrary point on the surface to define a 0 meridian, everything is then defined relative to the equator, the 0 meridian, and the direction of rotation.



              Asteroids are irregular. If it's tumbling then you could take the longest axis instead of the axis of rotation and the point of landing as 0 meridian, it could then be modelled as rotating around that axis, even if the axis itself is not stable. If it's spinning then you have poles and the landing point can be the 0 meridian. If you haven't landed on it yet then any arbitrary distinctive point can act as 0 meridian.






              share|improve this answer























              • I believe the meridian is / was based on the Royal Observatory, which is on the hill above the Naval College (though it's also more or less due North of it so it doesn't make much difference)...
                – bobtato
                yesterday










              • @bobtato, the two aren't strictly independent, the Observatory came under the Admiralty as its funding was tied to work on navigation.
                – Separatrix
                11 hours ago













              up vote
              3
              down vote










              up vote
              3
              down vote









              You have to remember that even on Earth, apart from the poles and equator, the coordinate system is arbitrary. Greenwich isn't even a particularly important location in the grand scheme of things, apart from hosting the Royal Observatory that's used to define the 0 meridian.



              The problem is the minimum number of points you need to define a coordinate system relative to a body. On a cube we conventionally select a vertex at one corner and three dimensions from that point. On a planet you take the axis of rotation to define the equator, and an arbitrary point on the surface to define a 0 meridian, everything is then defined relative to the equator, the 0 meridian, and the direction of rotation.



              Asteroids are irregular. If it's tumbling then you could take the longest axis instead of the axis of rotation and the point of landing as 0 meridian, it could then be modelled as rotating around that axis, even if the axis itself is not stable. If it's spinning then you have poles and the landing point can be the 0 meridian. If you haven't landed on it yet then any arbitrary distinctive point can act as 0 meridian.






              share|improve this answer














              You have to remember that even on Earth, apart from the poles and equator, the coordinate system is arbitrary. Greenwich isn't even a particularly important location in the grand scheme of things, apart from hosting the Royal Observatory that's used to define the 0 meridian.



              The problem is the minimum number of points you need to define a coordinate system relative to a body. On a cube we conventionally select a vertex at one corner and three dimensions from that point. On a planet you take the axis of rotation to define the equator, and an arbitrary point on the surface to define a 0 meridian, everything is then defined relative to the equator, the 0 meridian, and the direction of rotation.



              Asteroids are irregular. If it's tumbling then you could take the longest axis instead of the axis of rotation and the point of landing as 0 meridian, it could then be modelled as rotating around that axis, even if the axis itself is not stable. If it's spinning then you have poles and the landing point can be the 0 meridian. If you haven't landed on it yet then any arbitrary distinctive point can act as 0 meridian.







              share|improve this answer














              share|improve this answer



              share|improve this answer








              edited 8 hours ago

























              answered Nov 30 at 16:16









              Separatrix

              73.9k30172292




              73.9k30172292












              • I believe the meridian is / was based on the Royal Observatory, which is on the hill above the Naval College (though it's also more or less due North of it so it doesn't make much difference)...
                – bobtato
                yesterday










              • @bobtato, the two aren't strictly independent, the Observatory came under the Admiralty as its funding was tied to work on navigation.
                – Separatrix
                11 hours ago


















              • I believe the meridian is / was based on the Royal Observatory, which is on the hill above the Naval College (though it's also more or less due North of it so it doesn't make much difference)...
                – bobtato
                yesterday










              • @bobtato, the two aren't strictly independent, the Observatory came under the Admiralty as its funding was tied to work on navigation.
                – Separatrix
                11 hours ago
















              I believe the meridian is / was based on the Royal Observatory, which is on the hill above the Naval College (though it's also more or less due North of it so it doesn't make much difference)...
              – bobtato
              yesterday




              I believe the meridian is / was based on the Royal Observatory, which is on the hill above the Naval College (though it's also more or less due North of it so it doesn't make much difference)...
              – bobtato
              yesterday












              @bobtato, the two aren't strictly independent, the Observatory came under the Admiralty as its funding was tied to work on navigation.
              – Separatrix
              11 hours ago




              @bobtato, the two aren't strictly independent, the Observatory came under the Admiralty as its funding was tied to work on navigation.
              – Separatrix
              11 hours ago










              up vote
              2
              down vote













              You can use the same coordinate system for celestial navigation (latitude and longitude) used by Terran mariners. What you need is : an almanac, a watch, a device for measuring the angle of the stars relative to some average horizon, and a map.



              Almanac



              The basic concept of celestial navigation is this : imagine several easily-recognizable stars. Next, imagine that you could draw a line from each of these stars that would pass through the center of whatever you are standing on. This line will touch the ground at one (only one) location. An almanac records these stars and the location (in latitude and longitude) of the point on the surface where the imaginary line from the star touches the ground.



              Watch and Calendar



              And, this spot will move as the object rotates around it's own axis (days); but will only move a little with the seasons.



              Measurement Device (Sextant)



              When you are standing on the spot where this imaginary line from your easily-recognizable star intersects the ground, that star will be directly overhead.



              Map



              Likely, you are not standing on one of these spots at any particular time. The angular measurement times the average radius of the asteroid provides you with the approximate circular (radial) distance between that point and where you are. Measure multiple stars to determine where these circles overlap on a map. That is your (approximate) location






              share|improve this answer

















              • 1




                I suspect for regular navigation over the surface of a large asteroid that celestial navigation isn't going to be effective. Either the asteroid is spinning too fast to get decent measurements, or the granularity of the result isn't accurate enough for more than the most basic navigation.
                – Ruadhan
                Nov 30 at 12:00















              up vote
              2
              down vote













              You can use the same coordinate system for celestial navigation (latitude and longitude) used by Terran mariners. What you need is : an almanac, a watch, a device for measuring the angle of the stars relative to some average horizon, and a map.



              Almanac



              The basic concept of celestial navigation is this : imagine several easily-recognizable stars. Next, imagine that you could draw a line from each of these stars that would pass through the center of whatever you are standing on. This line will touch the ground at one (only one) location. An almanac records these stars and the location (in latitude and longitude) of the point on the surface where the imaginary line from the star touches the ground.



              Watch and Calendar



              And, this spot will move as the object rotates around it's own axis (days); but will only move a little with the seasons.



              Measurement Device (Sextant)



              When you are standing on the spot where this imaginary line from your easily-recognizable star intersects the ground, that star will be directly overhead.



              Map



              Likely, you are not standing on one of these spots at any particular time. The angular measurement times the average radius of the asteroid provides you with the approximate circular (radial) distance between that point and where you are. Measure multiple stars to determine where these circles overlap on a map. That is your (approximate) location






              share|improve this answer

















              • 1




                I suspect for regular navigation over the surface of a large asteroid that celestial navigation isn't going to be effective. Either the asteroid is spinning too fast to get decent measurements, or the granularity of the result isn't accurate enough for more than the most basic navigation.
                – Ruadhan
                Nov 30 at 12:00













              up vote
              2
              down vote










              up vote
              2
              down vote









              You can use the same coordinate system for celestial navigation (latitude and longitude) used by Terran mariners. What you need is : an almanac, a watch, a device for measuring the angle of the stars relative to some average horizon, and a map.



              Almanac



              The basic concept of celestial navigation is this : imagine several easily-recognizable stars. Next, imagine that you could draw a line from each of these stars that would pass through the center of whatever you are standing on. This line will touch the ground at one (only one) location. An almanac records these stars and the location (in latitude and longitude) of the point on the surface where the imaginary line from the star touches the ground.



              Watch and Calendar



              And, this spot will move as the object rotates around it's own axis (days); but will only move a little with the seasons.



              Measurement Device (Sextant)



              When you are standing on the spot where this imaginary line from your easily-recognizable star intersects the ground, that star will be directly overhead.



              Map



              Likely, you are not standing on one of these spots at any particular time. The angular measurement times the average radius of the asteroid provides you with the approximate circular (radial) distance between that point and where you are. Measure multiple stars to determine where these circles overlap on a map. That is your (approximate) location






              share|improve this answer












              You can use the same coordinate system for celestial navigation (latitude and longitude) used by Terran mariners. What you need is : an almanac, a watch, a device for measuring the angle of the stars relative to some average horizon, and a map.



              Almanac



              The basic concept of celestial navigation is this : imagine several easily-recognizable stars. Next, imagine that you could draw a line from each of these stars that would pass through the center of whatever you are standing on. This line will touch the ground at one (only one) location. An almanac records these stars and the location (in latitude and longitude) of the point on the surface where the imaginary line from the star touches the ground.



              Watch and Calendar



              And, this spot will move as the object rotates around it's own axis (days); but will only move a little with the seasons.



              Measurement Device (Sextant)



              When you are standing on the spot where this imaginary line from your easily-recognizable star intersects the ground, that star will be directly overhead.



              Map



              Likely, you are not standing on one of these spots at any particular time. The angular measurement times the average radius of the asteroid provides you with the approximate circular (radial) distance between that point and where you are. Measure multiple stars to determine where these circles overlap on a map. That is your (approximate) location







              share|improve this answer












              share|improve this answer



              share|improve this answer










              answered Nov 30 at 3:11









              James McLellan

              5,6361632




              5,6361632








              • 1




                I suspect for regular navigation over the surface of a large asteroid that celestial navigation isn't going to be effective. Either the asteroid is spinning too fast to get decent measurements, or the granularity of the result isn't accurate enough for more than the most basic navigation.
                – Ruadhan
                Nov 30 at 12:00














              • 1




                I suspect for regular navigation over the surface of a large asteroid that celestial navigation isn't going to be effective. Either the asteroid is spinning too fast to get decent measurements, or the granularity of the result isn't accurate enough for more than the most basic navigation.
                – Ruadhan
                Nov 30 at 12:00








              1




              1




              I suspect for regular navigation over the surface of a large asteroid that celestial navigation isn't going to be effective. Either the asteroid is spinning too fast to get decent measurements, or the granularity of the result isn't accurate enough for more than the most basic navigation.
              – Ruadhan
              Nov 30 at 12:00




              I suspect for regular navigation over the surface of a large asteroid that celestial navigation isn't going to be effective. Either the asteroid is spinning too fast to get decent measurements, or the granularity of the result isn't accurate enough for more than the most basic navigation.
              – Ruadhan
              Nov 30 at 12:00










              up vote
              1
              down vote













              Maybe the easiest way would be to add a number of beacons and then just run bearings off, or between, them.



              Possibly designate one, or a few, as Prime(s), analogous to magnetic poles, and relate the bearings of the others to them.



              There are a number of navigation systems that use, or have used, fixed beacons to determine locations with varying degrees of accuracy depending on range from the beacons.






              share|improve this answer








              New contributor




              GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
              Check out our Code of Conduct.






















                up vote
                1
                down vote













                Maybe the easiest way would be to add a number of beacons and then just run bearings off, or between, them.



                Possibly designate one, or a few, as Prime(s), analogous to magnetic poles, and relate the bearings of the others to them.



                There are a number of navigation systems that use, or have used, fixed beacons to determine locations with varying degrees of accuracy depending on range from the beacons.






                share|improve this answer








                New contributor




                GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                Check out our Code of Conduct.




















                  up vote
                  1
                  down vote










                  up vote
                  1
                  down vote









                  Maybe the easiest way would be to add a number of beacons and then just run bearings off, or between, them.



                  Possibly designate one, or a few, as Prime(s), analogous to magnetic poles, and relate the bearings of the others to them.



                  There are a number of navigation systems that use, or have used, fixed beacons to determine locations with varying degrees of accuracy depending on range from the beacons.






                  share|improve this answer








                  New contributor




                  GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  Maybe the easiest way would be to add a number of beacons and then just run bearings off, or between, them.



                  Possibly designate one, or a few, as Prime(s), analogous to magnetic poles, and relate the bearings of the others to them.



                  There are a number of navigation systems that use, or have used, fixed beacons to determine locations with varying degrees of accuracy depending on range from the beacons.







                  share|improve this answer








                  New contributor




                  GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  share|improve this answer



                  share|improve this answer






                  New contributor




                  GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.









                  answered Nov 30 at 15:33









                  GeeTee

                  111




                  111




                  New contributor




                  GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.





                  New contributor





                  GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                  GeeTee is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






















                      up vote
                      1
                      down vote













                      The center of mass would be the origin, all other coordinates (x, y, and z ~ latitude, longitude, elevation) would be pulled off that. You would orient and find the location of the CoM by triangulation of the stars as it rotates, with repeated measurements over time and in different places on the surface of the rock.






                      share|improve this answer








                      New contributor




                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.


















                      • CoM would be your first reference point, but what would you use for a second reference point?
                        – Michael
                        Nov 30 at 20:04










                      • Literally every other point you define is the second point. The coordinates of that point would be with respect to the origin, i.e. the CoM.
                        – kaas347
                        yesterday






                      • 1




                        I'm saying one point isn't sufficient. If you use x,y,z then you need another point to define one of your axes; if you use lat/lon you need to define where your origin is on the surface.
                        – Michael
                        yesterday










                      • There actually exist nonconvex asteroids. For such CoM might be easily located in outer space :)
                        – მამუკა ჯიბლაძე
                        yesterday










                      • Three dimensions requires three points to define a unique coordinate basis. This won't work without a means of defining, absolutely or arbitrarily, two more points.
                        – Nij
                        9 hours ago















                      up vote
                      1
                      down vote













                      The center of mass would be the origin, all other coordinates (x, y, and z ~ latitude, longitude, elevation) would be pulled off that. You would orient and find the location of the CoM by triangulation of the stars as it rotates, with repeated measurements over time and in different places on the surface of the rock.






                      share|improve this answer








                      New contributor




                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.


















                      • CoM would be your first reference point, but what would you use for a second reference point?
                        – Michael
                        Nov 30 at 20:04










                      • Literally every other point you define is the second point. The coordinates of that point would be with respect to the origin, i.e. the CoM.
                        – kaas347
                        yesterday






                      • 1




                        I'm saying one point isn't sufficient. If you use x,y,z then you need another point to define one of your axes; if you use lat/lon you need to define where your origin is on the surface.
                        – Michael
                        yesterday










                      • There actually exist nonconvex asteroids. For such CoM might be easily located in outer space :)
                        – მამუკა ჯიბლაძე
                        yesterday










                      • Three dimensions requires three points to define a unique coordinate basis. This won't work without a means of defining, absolutely or arbitrarily, two more points.
                        – Nij
                        9 hours ago













                      up vote
                      1
                      down vote










                      up vote
                      1
                      down vote









                      The center of mass would be the origin, all other coordinates (x, y, and z ~ latitude, longitude, elevation) would be pulled off that. You would orient and find the location of the CoM by triangulation of the stars as it rotates, with repeated measurements over time and in different places on the surface of the rock.






                      share|improve this answer








                      New contributor




                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.









                      The center of mass would be the origin, all other coordinates (x, y, and z ~ latitude, longitude, elevation) would be pulled off that. You would orient and find the location of the CoM by triangulation of the stars as it rotates, with repeated measurements over time and in different places on the surface of the rock.







                      share|improve this answer








                      New contributor




                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.









                      share|improve this answer



                      share|improve this answer






                      New contributor




                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.









                      answered Nov 30 at 19:48









                      kaas347

                      111




                      111




                      New contributor




                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.





                      New contributor





                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.






                      kaas347 is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.












                      • CoM would be your first reference point, but what would you use for a second reference point?
                        – Michael
                        Nov 30 at 20:04










                      • Literally every other point you define is the second point. The coordinates of that point would be with respect to the origin, i.e. the CoM.
                        – kaas347
                        yesterday






                      • 1




                        I'm saying one point isn't sufficient. If you use x,y,z then you need another point to define one of your axes; if you use lat/lon you need to define where your origin is on the surface.
                        – Michael
                        yesterday










                      • There actually exist nonconvex asteroids. For such CoM might be easily located in outer space :)
                        – მამუკა ჯიბლაძე
                        yesterday










                      • Three dimensions requires three points to define a unique coordinate basis. This won't work without a means of defining, absolutely or arbitrarily, two more points.
                        – Nij
                        9 hours ago


















                      • CoM would be your first reference point, but what would you use for a second reference point?
                        – Michael
                        Nov 30 at 20:04










                      • Literally every other point you define is the second point. The coordinates of that point would be with respect to the origin, i.e. the CoM.
                        – kaas347
                        yesterday






                      • 1




                        I'm saying one point isn't sufficient. If you use x,y,z then you need another point to define one of your axes; if you use lat/lon you need to define where your origin is on the surface.
                        – Michael
                        yesterday










                      • There actually exist nonconvex asteroids. For such CoM might be easily located in outer space :)
                        – მამუკა ჯიბლაძე
                        yesterday










                      • Three dimensions requires three points to define a unique coordinate basis. This won't work without a means of defining, absolutely or arbitrarily, two more points.
                        – Nij
                        9 hours ago
















                      CoM would be your first reference point, but what would you use for a second reference point?
                      – Michael
                      Nov 30 at 20:04




                      CoM would be your first reference point, but what would you use for a second reference point?
                      – Michael
                      Nov 30 at 20:04












                      Literally every other point you define is the second point. The coordinates of that point would be with respect to the origin, i.e. the CoM.
                      – kaas347
                      yesterday




                      Literally every other point you define is the second point. The coordinates of that point would be with respect to the origin, i.e. the CoM.
                      – kaas347
                      yesterday




                      1




                      1




                      I'm saying one point isn't sufficient. If you use x,y,z then you need another point to define one of your axes; if you use lat/lon you need to define where your origin is on the surface.
                      – Michael
                      yesterday




                      I'm saying one point isn't sufficient. If you use x,y,z then you need another point to define one of your axes; if you use lat/lon you need to define where your origin is on the surface.
                      – Michael
                      yesterday












                      There actually exist nonconvex asteroids. For such CoM might be easily located in outer space :)
                      – მამუკა ჯიბლაძე
                      yesterday




                      There actually exist nonconvex asteroids. For such CoM might be easily located in outer space :)
                      – მამუკა ჯიბლაძე
                      yesterday












                      Three dimensions requires three points to define a unique coordinate basis. This won't work without a means of defining, absolutely or arbitrarily, two more points.
                      – Nij
                      9 hours ago




                      Three dimensions requires three points to define a unique coordinate basis. This won't work without a means of defining, absolutely or arbitrarily, two more points.
                      – Nij
                      9 hours ago










                      up vote
                      1
                      down vote













                      TL;DR: Two spikes, a ruler and a protractor



                      There is no perfect solution, just as there is no perfect solution for Earth. Witness differing data (as plural of datum, in which a datum is the basis of a specific system of reference). Here is a document describing conversion between two equally acceptable systems of datum: https://www.ngs.noaa.gov/CORS/Articles/WGS84NAD83.pdf



                      Here's a short snippet from that paper which goes to the heart of this difference:




                      First of all, one should understand that the 3-D Cartesian frames to
                      which the coordinates of the NAD83 and WGS84 refer are not identical.
                      Their origin, axes orientation in space, and the unit of scale
                      differ. Why? Simply, because the definitions of these two frames are
                      based on different sets of observations, processing algorithms, and
                      perhaps, geodetic assumptions.




                      So there is no one right answer for difficult surfaces -- we can't even get it settled rigorously for our relatively simple surface here on Earth. We simply agree which set of imperfections to try to work around. YET there must still be many more wrong answers than right answers.



                      Here's my proposed less-wrong answer, which is similar to many answers provided here, but perhaps more complete:



                      Select a north pole and drive a real or imaginary spike into it. Select an arbitrary prime meridien and drive another spike in where that intersects your chosen equator. We are unlikely to have a handy set of facts to support definitions like "equidistant at all longitude", so a naturally defined equator may not be available. Likewise, if the thing does not rotate appreciably, or if that rotation is perturbed or wholly inconsistent with an intuitional model of where poles and an equator "should" be, we can still get by with nothing more than our two chosen points -- a north pole, and a 0-0 point (corresponding to 0-0 in the Gulf of Guinea, check it out). With these two points we can always measure two facts:




                      • angle of rotation about the north pole from the prime meridien

                      • distance from the north pole as the space crow flies


                      These are not perfect, but can be agreed upon and figured by independent observers. Any radio distancing scheme could also be based upon these two points to yield the same two facts about position. This would also support map projection such as we are familiar with, including all of the existing shortcomings.






                      share|improve this answer

























                        up vote
                        1
                        down vote













                        TL;DR: Two spikes, a ruler and a protractor



                        There is no perfect solution, just as there is no perfect solution for Earth. Witness differing data (as plural of datum, in which a datum is the basis of a specific system of reference). Here is a document describing conversion between two equally acceptable systems of datum: https://www.ngs.noaa.gov/CORS/Articles/WGS84NAD83.pdf



                        Here's a short snippet from that paper which goes to the heart of this difference:




                        First of all, one should understand that the 3-D Cartesian frames to
                        which the coordinates of the NAD83 and WGS84 refer are not identical.
                        Their origin, axes orientation in space, and the unit of scale
                        differ. Why? Simply, because the definitions of these two frames are
                        based on different sets of observations, processing algorithms, and
                        perhaps, geodetic assumptions.




                        So there is no one right answer for difficult surfaces -- we can't even get it settled rigorously for our relatively simple surface here on Earth. We simply agree which set of imperfections to try to work around. YET there must still be many more wrong answers than right answers.



                        Here's my proposed less-wrong answer, which is similar to many answers provided here, but perhaps more complete:



                        Select a north pole and drive a real or imaginary spike into it. Select an arbitrary prime meridien and drive another spike in where that intersects your chosen equator. We are unlikely to have a handy set of facts to support definitions like "equidistant at all longitude", so a naturally defined equator may not be available. Likewise, if the thing does not rotate appreciably, or if that rotation is perturbed or wholly inconsistent with an intuitional model of where poles and an equator "should" be, we can still get by with nothing more than our two chosen points -- a north pole, and a 0-0 point (corresponding to 0-0 in the Gulf of Guinea, check it out). With these two points we can always measure two facts:




                        • angle of rotation about the north pole from the prime meridien

                        • distance from the north pole as the space crow flies


                        These are not perfect, but can be agreed upon and figured by independent observers. Any radio distancing scheme could also be based upon these two points to yield the same two facts about position. This would also support map projection such as we are familiar with, including all of the existing shortcomings.






                        share|improve this answer























                          up vote
                          1
                          down vote










                          up vote
                          1
                          down vote









                          TL;DR: Two spikes, a ruler and a protractor



                          There is no perfect solution, just as there is no perfect solution for Earth. Witness differing data (as plural of datum, in which a datum is the basis of a specific system of reference). Here is a document describing conversion between two equally acceptable systems of datum: https://www.ngs.noaa.gov/CORS/Articles/WGS84NAD83.pdf



                          Here's a short snippet from that paper which goes to the heart of this difference:




                          First of all, one should understand that the 3-D Cartesian frames to
                          which the coordinates of the NAD83 and WGS84 refer are not identical.
                          Their origin, axes orientation in space, and the unit of scale
                          differ. Why? Simply, because the definitions of these two frames are
                          based on different sets of observations, processing algorithms, and
                          perhaps, geodetic assumptions.




                          So there is no one right answer for difficult surfaces -- we can't even get it settled rigorously for our relatively simple surface here on Earth. We simply agree which set of imperfections to try to work around. YET there must still be many more wrong answers than right answers.



                          Here's my proposed less-wrong answer, which is similar to many answers provided here, but perhaps more complete:



                          Select a north pole and drive a real or imaginary spike into it. Select an arbitrary prime meridien and drive another spike in where that intersects your chosen equator. We are unlikely to have a handy set of facts to support definitions like "equidistant at all longitude", so a naturally defined equator may not be available. Likewise, if the thing does not rotate appreciably, or if that rotation is perturbed or wholly inconsistent with an intuitional model of where poles and an equator "should" be, we can still get by with nothing more than our two chosen points -- a north pole, and a 0-0 point (corresponding to 0-0 in the Gulf of Guinea, check it out). With these two points we can always measure two facts:




                          • angle of rotation about the north pole from the prime meridien

                          • distance from the north pole as the space crow flies


                          These are not perfect, but can be agreed upon and figured by independent observers. Any radio distancing scheme could also be based upon these two points to yield the same two facts about position. This would also support map projection such as we are familiar with, including all of the existing shortcomings.






                          share|improve this answer












                          TL;DR: Two spikes, a ruler and a protractor



                          There is no perfect solution, just as there is no perfect solution for Earth. Witness differing data (as plural of datum, in which a datum is the basis of a specific system of reference). Here is a document describing conversion between two equally acceptable systems of datum: https://www.ngs.noaa.gov/CORS/Articles/WGS84NAD83.pdf



                          Here's a short snippet from that paper which goes to the heart of this difference:




                          First of all, one should understand that the 3-D Cartesian frames to
                          which the coordinates of the NAD83 and WGS84 refer are not identical.
                          Their origin, axes orientation in space, and the unit of scale
                          differ. Why? Simply, because the definitions of these two frames are
                          based on different sets of observations, processing algorithms, and
                          perhaps, geodetic assumptions.




                          So there is no one right answer for difficult surfaces -- we can't even get it settled rigorously for our relatively simple surface here on Earth. We simply agree which set of imperfections to try to work around. YET there must still be many more wrong answers than right answers.



                          Here's my proposed less-wrong answer, which is similar to many answers provided here, but perhaps more complete:



                          Select a north pole and drive a real or imaginary spike into it. Select an arbitrary prime meridien and drive another spike in where that intersects your chosen equator. We are unlikely to have a handy set of facts to support definitions like "equidistant at all longitude", so a naturally defined equator may not be available. Likewise, if the thing does not rotate appreciably, or if that rotation is perturbed or wholly inconsistent with an intuitional model of where poles and an equator "should" be, we can still get by with nothing more than our two chosen points -- a north pole, and a 0-0 point (corresponding to 0-0 in the Gulf of Guinea, check it out). With these two points we can always measure two facts:




                          • angle of rotation about the north pole from the prime meridien

                          • distance from the north pole as the space crow flies


                          These are not perfect, but can be agreed upon and figured by independent observers. Any radio distancing scheme could also be based upon these two points to yield the same two facts about position. This would also support map projection such as we are familiar with, including all of the existing shortcomings.







                          share|improve this answer












                          share|improve this answer



                          share|improve this answer










                          answered 2 days ago









                          Haakon Dahl

                          1195




                          1195






















                              up vote
                              1
                              down vote













                              Let me start by clearing one thing - poles are not defined by magnetic field. Poles are defined by axis of rotation. Magnetic poles are somewhat independent from geographic poles and are only used as handy approximation, especially when you can't get a hold of more accurate measurement e.g of sun and stars, when the sky is clouded.
                              https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies



                              As for your actual question - it depends on what you mean by large asteroid. Really big ones (bigger than 400km diameter) end up being nearly spherical due to their own gravity, we recently decided to call them dwarf planets. All dwarf planets rotate mostly regularly so you don't need to invent any new system, just choose a prime meridian, maybe a place of first landing, or the highest mountain, and you're good.
                              https://en.wikipedia.org/wiki/Dwarf_planet



                              Smaller, irregular asteroids, may not map nicely, especially if their rotation is very irregular, but you can still define the main axis by calculating mass distribution, choose the axis that gives maximum moment of intertia, which for regular bodies overlaps with axis of rotation, choose prime meridian (same as above), and you're good.
                              https://en.wikipedia.org/wiki/Moment_of_inertia



                              For very small asteroids, don't bother with Earth-like coordinates. If your total area is comparable with big cities like London, Moscow or Paris, do something similar. Define "districts" and "neighbourhoods" with memorable names. Place couple of beacons and plaques to make it clear which is where. Everybody will learn them after living there for couple of weeks.



                              In conclusion.



                              For any reasonably spherelike object you can define a
                              North Pole, where the major axis crosses the surface, choose an arbitrary Prime Meridian and plot an Earth-like grid of coordinates by simply projecting an imagined sphere on the actual surface. The asteroid doesn't even have to be very regular. These basic rules will work for all kind of potato shapes, as long as it has mostly positive surface curvature, which will always be the case except for very small asteroids. For those, you don't need a grid because the very small area and irregularity allows you to name all sectors unambiguously and just use those names.






                              share|improve this answer



















                              • 1




                                I'd probably go so far as to say that a spherical "globe" map of an asteroid is still both possible and possibly the best solution. You would still use longditude and lattitude to define position, even with irregular bodies - it's a measure of the direction from the centre of mass after all. A 2D map would end up a little distorted though, but I don't know how any projection could prevent that.
                                – Baldrickk
                                5 hours ago












                              • @Baldrickk I agree, I added a conclusion that hopefully makes this clearer
                                – Milo Bem
                                3 hours ago















                              up vote
                              1
                              down vote













                              Let me start by clearing one thing - poles are not defined by magnetic field. Poles are defined by axis of rotation. Magnetic poles are somewhat independent from geographic poles and are only used as handy approximation, especially when you can't get a hold of more accurate measurement e.g of sun and stars, when the sky is clouded.
                              https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies



                              As for your actual question - it depends on what you mean by large asteroid. Really big ones (bigger than 400km diameter) end up being nearly spherical due to their own gravity, we recently decided to call them dwarf planets. All dwarf planets rotate mostly regularly so you don't need to invent any new system, just choose a prime meridian, maybe a place of first landing, or the highest mountain, and you're good.
                              https://en.wikipedia.org/wiki/Dwarf_planet



                              Smaller, irregular asteroids, may not map nicely, especially if their rotation is very irregular, but you can still define the main axis by calculating mass distribution, choose the axis that gives maximum moment of intertia, which for regular bodies overlaps with axis of rotation, choose prime meridian (same as above), and you're good.
                              https://en.wikipedia.org/wiki/Moment_of_inertia



                              For very small asteroids, don't bother with Earth-like coordinates. If your total area is comparable with big cities like London, Moscow or Paris, do something similar. Define "districts" and "neighbourhoods" with memorable names. Place couple of beacons and plaques to make it clear which is where. Everybody will learn them after living there for couple of weeks.



                              In conclusion.



                              For any reasonably spherelike object you can define a
                              North Pole, where the major axis crosses the surface, choose an arbitrary Prime Meridian and plot an Earth-like grid of coordinates by simply projecting an imagined sphere on the actual surface. The asteroid doesn't even have to be very regular. These basic rules will work for all kind of potato shapes, as long as it has mostly positive surface curvature, which will always be the case except for very small asteroids. For those, you don't need a grid because the very small area and irregularity allows you to name all sectors unambiguously and just use those names.






                              share|improve this answer



















                              • 1




                                I'd probably go so far as to say that a spherical "globe" map of an asteroid is still both possible and possibly the best solution. You would still use longditude and lattitude to define position, even with irregular bodies - it's a measure of the direction from the centre of mass after all. A 2D map would end up a little distorted though, but I don't know how any projection could prevent that.
                                – Baldrickk
                                5 hours ago












                              • @Baldrickk I agree, I added a conclusion that hopefully makes this clearer
                                – Milo Bem
                                3 hours ago













                              up vote
                              1
                              down vote










                              up vote
                              1
                              down vote









                              Let me start by clearing one thing - poles are not defined by magnetic field. Poles are defined by axis of rotation. Magnetic poles are somewhat independent from geographic poles and are only used as handy approximation, especially when you can't get a hold of more accurate measurement e.g of sun and stars, when the sky is clouded.
                              https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies



                              As for your actual question - it depends on what you mean by large asteroid. Really big ones (bigger than 400km diameter) end up being nearly spherical due to their own gravity, we recently decided to call them dwarf planets. All dwarf planets rotate mostly regularly so you don't need to invent any new system, just choose a prime meridian, maybe a place of first landing, or the highest mountain, and you're good.
                              https://en.wikipedia.org/wiki/Dwarf_planet



                              Smaller, irregular asteroids, may not map nicely, especially if their rotation is very irregular, but you can still define the main axis by calculating mass distribution, choose the axis that gives maximum moment of intertia, which for regular bodies overlaps with axis of rotation, choose prime meridian (same as above), and you're good.
                              https://en.wikipedia.org/wiki/Moment_of_inertia



                              For very small asteroids, don't bother with Earth-like coordinates. If your total area is comparable with big cities like London, Moscow or Paris, do something similar. Define "districts" and "neighbourhoods" with memorable names. Place couple of beacons and plaques to make it clear which is where. Everybody will learn them after living there for couple of weeks.



                              In conclusion.



                              For any reasonably spherelike object you can define a
                              North Pole, where the major axis crosses the surface, choose an arbitrary Prime Meridian and plot an Earth-like grid of coordinates by simply projecting an imagined sphere on the actual surface. The asteroid doesn't even have to be very regular. These basic rules will work for all kind of potato shapes, as long as it has mostly positive surface curvature, which will always be the case except for very small asteroids. For those, you don't need a grid because the very small area and irregularity allows you to name all sectors unambiguously and just use those names.






                              share|improve this answer














                              Let me start by clearing one thing - poles are not defined by magnetic field. Poles are defined by axis of rotation. Magnetic poles are somewhat independent from geographic poles and are only used as handy approximation, especially when you can't get a hold of more accurate measurement e.g of sun and stars, when the sky is clouded.
                              https://en.wikipedia.org/wiki/Poles_of_astronomical_bodies



                              As for your actual question - it depends on what you mean by large asteroid. Really big ones (bigger than 400km diameter) end up being nearly spherical due to their own gravity, we recently decided to call them dwarf planets. All dwarf planets rotate mostly regularly so you don't need to invent any new system, just choose a prime meridian, maybe a place of first landing, or the highest mountain, and you're good.
                              https://en.wikipedia.org/wiki/Dwarf_planet



                              Smaller, irregular asteroids, may not map nicely, especially if their rotation is very irregular, but you can still define the main axis by calculating mass distribution, choose the axis that gives maximum moment of intertia, which for regular bodies overlaps with axis of rotation, choose prime meridian (same as above), and you're good.
                              https://en.wikipedia.org/wiki/Moment_of_inertia



                              For very small asteroids, don't bother with Earth-like coordinates. If your total area is comparable with big cities like London, Moscow or Paris, do something similar. Define "districts" and "neighbourhoods" with memorable names. Place couple of beacons and plaques to make it clear which is where. Everybody will learn them after living there for couple of weeks.



                              In conclusion.



                              For any reasonably spherelike object you can define a
                              North Pole, where the major axis crosses the surface, choose an arbitrary Prime Meridian and plot an Earth-like grid of coordinates by simply projecting an imagined sphere on the actual surface. The asteroid doesn't even have to be very regular. These basic rules will work for all kind of potato shapes, as long as it has mostly positive surface curvature, which will always be the case except for very small asteroids. For those, you don't need a grid because the very small area and irregularity allows you to name all sectors unambiguously and just use those names.







                              share|improve this answer














                              share|improve this answer



                              share|improve this answer








                              edited 3 hours ago

























                              answered 5 hours ago









                              Milo Bem

                              991110




                              991110








                              • 1




                                I'd probably go so far as to say that a spherical "globe" map of an asteroid is still both possible and possibly the best solution. You would still use longditude and lattitude to define position, even with irregular bodies - it's a measure of the direction from the centre of mass after all. A 2D map would end up a little distorted though, but I don't know how any projection could prevent that.
                                – Baldrickk
                                5 hours ago












                              • @Baldrickk I agree, I added a conclusion that hopefully makes this clearer
                                – Milo Bem
                                3 hours ago














                              • 1




                                I'd probably go so far as to say that a spherical "globe" map of an asteroid is still both possible and possibly the best solution. You would still use longditude and lattitude to define position, even with irregular bodies - it's a measure of the direction from the centre of mass after all. A 2D map would end up a little distorted though, but I don't know how any projection could prevent that.
                                – Baldrickk
                                5 hours ago












                              • @Baldrickk I agree, I added a conclusion that hopefully makes this clearer
                                – Milo Bem
                                3 hours ago








                              1




                              1




                              I'd probably go so far as to say that a spherical "globe" map of an asteroid is still both possible and possibly the best solution. You would still use longditude and lattitude to define position, even with irregular bodies - it's a measure of the direction from the centre of mass after all. A 2D map would end up a little distorted though, but I don't know how any projection could prevent that.
                              – Baldrickk
                              5 hours ago






                              I'd probably go so far as to say that a spherical "globe" map of an asteroid is still both possible and possibly the best solution. You would still use longditude and lattitude to define position, even with irregular bodies - it's a measure of the direction from the centre of mass after all. A 2D map would end up a little distorted though, but I don't know how any projection could prevent that.
                              – Baldrickk
                              5 hours ago














                              @Baldrickk I agree, I added a conclusion that hopefully makes this clearer
                              – Milo Bem
                              3 hours ago




                              @Baldrickk I agree, I added a conclusion that hopefully makes this clearer
                              – Milo Bem
                              3 hours ago










                              up vote
                              0
                              down vote













                              The asteroid would be mapped before anybody ever landed on it, rotation, procession etc would not, I think, be used due to the relative impact on these things from habitation and industry.



                              https://dawn.jpl.nasa.gov/multimedia/images/image-detail.html?id=PIA17480



                              It doesn't seem logical either to adopt magnetic polar attributes, as these are un-managed variables.



                              As with L Dutch & G.B. Robinson's answers, triangulation to communication antenna and 'relative stationary' satellites would be most useful, reliable & probably become ubiquitous. It's not like asteroid dwellers would be without electronic devices at any time, as their lives would depend on them. 3d mapping is not really any more complex, tho we would probably expect long term residents to develop abbreviations and colloquial terms as references






                              share|improve this answer

















                              • 1




                                The last part is a good point most people rarely describe things by co-ordinates especially in settled areas where there are landmarks or pieces of infrastructure to use as reference points instead. This of course makes sense when you consider that our primate brains evolved to navigate the world using our eyes and things that we can physically see within the world and orient around rather than numbers assigned to virtual lines that exist only on paper.
                                – MttJocy
                                Nov 30 at 16:01










                              • True, but we have plenty of examples of people adapting to organised cartographical/reference systems, travelling to major cities across the world that have different fundamental concepts for their mass transit systems or no city block systems can make for a headache to those used to a different system. Most of them take a great deal of getting used to, but they are fundamentally arbitrary but organised systems...and then you have London =)
                                – Giu Piete
                                2 days ago

















                              up vote
                              0
                              down vote













                              The asteroid would be mapped before anybody ever landed on it, rotation, procession etc would not, I think, be used due to the relative impact on these things from habitation and industry.



                              https://dawn.jpl.nasa.gov/multimedia/images/image-detail.html?id=PIA17480



                              It doesn't seem logical either to adopt magnetic polar attributes, as these are un-managed variables.



                              As with L Dutch & G.B. Robinson's answers, triangulation to communication antenna and 'relative stationary' satellites would be most useful, reliable & probably become ubiquitous. It's not like asteroid dwellers would be without electronic devices at any time, as their lives would depend on them. 3d mapping is not really any more complex, tho we would probably expect long term residents to develop abbreviations and colloquial terms as references






                              share|improve this answer

















                              • 1




                                The last part is a good point most people rarely describe things by co-ordinates especially in settled areas where there are landmarks or pieces of infrastructure to use as reference points instead. This of course makes sense when you consider that our primate brains evolved to navigate the world using our eyes and things that we can physically see within the world and orient around rather than numbers assigned to virtual lines that exist only on paper.
                                – MttJocy
                                Nov 30 at 16:01










                              • True, but we have plenty of examples of people adapting to organised cartographical/reference systems, travelling to major cities across the world that have different fundamental concepts for their mass transit systems or no city block systems can make for a headache to those used to a different system. Most of them take a great deal of getting used to, but they are fundamentally arbitrary but organised systems...and then you have London =)
                                – Giu Piete
                                2 days ago















                              up vote
                              0
                              down vote










                              up vote
                              0
                              down vote









                              The asteroid would be mapped before anybody ever landed on it, rotation, procession etc would not, I think, be used due to the relative impact on these things from habitation and industry.



                              https://dawn.jpl.nasa.gov/multimedia/images/image-detail.html?id=PIA17480



                              It doesn't seem logical either to adopt magnetic polar attributes, as these are un-managed variables.



                              As with L Dutch & G.B. Robinson's answers, triangulation to communication antenna and 'relative stationary' satellites would be most useful, reliable & probably become ubiquitous. It's not like asteroid dwellers would be without electronic devices at any time, as their lives would depend on them. 3d mapping is not really any more complex, tho we would probably expect long term residents to develop abbreviations and colloquial terms as references






                              share|improve this answer












                              The asteroid would be mapped before anybody ever landed on it, rotation, procession etc would not, I think, be used due to the relative impact on these things from habitation and industry.



                              https://dawn.jpl.nasa.gov/multimedia/images/image-detail.html?id=PIA17480



                              It doesn't seem logical either to adopt magnetic polar attributes, as these are un-managed variables.



                              As with L Dutch & G.B. Robinson's answers, triangulation to communication antenna and 'relative stationary' satellites would be most useful, reliable & probably become ubiquitous. It's not like asteroid dwellers would be without electronic devices at any time, as their lives would depend on them. 3d mapping is not really any more complex, tho we would probably expect long term residents to develop abbreviations and colloquial terms as references







                              share|improve this answer












                              share|improve this answer



                              share|improve this answer










                              answered Nov 30 at 11:23









                              Giu Piete

                              894




                              894








                              • 1




                                The last part is a good point most people rarely describe things by co-ordinates especially in settled areas where there are landmarks or pieces of infrastructure to use as reference points instead. This of course makes sense when you consider that our primate brains evolved to navigate the world using our eyes and things that we can physically see within the world and orient around rather than numbers assigned to virtual lines that exist only on paper.
                                – MttJocy
                                Nov 30 at 16:01










                              • True, but we have plenty of examples of people adapting to organised cartographical/reference systems, travelling to major cities across the world that have different fundamental concepts for their mass transit systems or no city block systems can make for a headache to those used to a different system. Most of them take a great deal of getting used to, but they are fundamentally arbitrary but organised systems...and then you have London =)
                                – Giu Piete
                                2 days ago
















                              • 1




                                The last part is a good point most people rarely describe things by co-ordinates especially in settled areas where there are landmarks or pieces of infrastructure to use as reference points instead. This of course makes sense when you consider that our primate brains evolved to navigate the world using our eyes and things that we can physically see within the world and orient around rather than numbers assigned to virtual lines that exist only on paper.
                                – MttJocy
                                Nov 30 at 16:01










                              • True, but we have plenty of examples of people adapting to organised cartographical/reference systems, travelling to major cities across the world that have different fundamental concepts for their mass transit systems or no city block systems can make for a headache to those used to a different system. Most of them take a great deal of getting used to, but they are fundamentally arbitrary but organised systems...and then you have London =)
                                – Giu Piete
                                2 days ago










                              1




                              1




                              The last part is a good point most people rarely describe things by co-ordinates especially in settled areas where there are landmarks or pieces of infrastructure to use as reference points instead. This of course makes sense when you consider that our primate brains evolved to navigate the world using our eyes and things that we can physically see within the world and orient around rather than numbers assigned to virtual lines that exist only on paper.
                              – MttJocy
                              Nov 30 at 16:01




                              The last part is a good point most people rarely describe things by co-ordinates especially in settled areas where there are landmarks or pieces of infrastructure to use as reference points instead. This of course makes sense when you consider that our primate brains evolved to navigate the world using our eyes and things that we can physically see within the world and orient around rather than numbers assigned to virtual lines that exist only on paper.
                              – MttJocy
                              Nov 30 at 16:01












                              True, but we have plenty of examples of people adapting to organised cartographical/reference systems, travelling to major cities across the world that have different fundamental concepts for their mass transit systems or no city block systems can make for a headache to those used to a different system. Most of them take a great deal of getting used to, but they are fundamentally arbitrary but organised systems...and then you have London =)
                              – Giu Piete
                              2 days ago






                              True, but we have plenty of examples of people adapting to organised cartographical/reference systems, travelling to major cities across the world that have different fundamental concepts for their mass transit systems or no city block systems can make for a headache to those used to a different system. Most of them take a great deal of getting used to, but they are fundamentally arbitrary but organised systems...and then you have London =)
                              – Giu Piete
                              2 days ago












                              up vote
                              0
                              down vote













                              Expanding a bit on LDutch's answer and MttJocy's comment on it. Take a page from pre-GPS aerial and nautical navigation systems.



                              Aviation commonly uses (fading as GPS is taking over, but still present) the VOR system and ADFs to figure positions and navigate. Essentially the various beacons all broadcast at a different frequency, with a directional pulse that varies in phase with the base signal. By calculating the phase difference between the primary and secondary phases your ADF provides your bearing from the station. Getting a bearing from two different stations gives you a very precise location. There are also some things that can be done in terms of phasing and signal strength to give an approximate distance from a single station, allowing for a rough position fix off of a single signal, but I am not aware of it being done in practice as the two bearing option is much more reliable. The major drawback for this system as currently implemented, and your intended use is that it is line of site and relatively short range (~200 miles). If you are too far from a station, or a pesky mountain (or the horizon of your asteroid) happens to be between you and it, you are not going to be able to pick up the signals. Meaning this system is not commonly used for surface travel.



                              The LORAN system was developed in WW2 and used until fairly recently for nautical navigation. It again works by using a series of fixed position transmitters, but in this case they come in paired units. Each member of the pairing is separated by a known distance, and they pulse out synchronized signals. The receiver compares the time difference in receiving the two pulses and from that difference you can plot a line of your relative distance from the two. Grab readings from an alternate pair to plot your location. The major advantage this system has over the other is range (~1500 miles) and being much less sensitive to LoS issues, though it is also somewhat less accurate. With the sensitivity and precision of modern electronics, it is conceivable that someone could build a 3+ point LORAN system and pinpoint their location pretty accurately off of one reading, the challenge being keeping the signals synchronized across the additional broadcast stations.



                              Now the range and LOS issues are primarily a function of the frequencies that are used in broadcasting the signals. So you could theoretically implement a VOR system in the frequency bands used by LORAN and have better performance in that respect, but it will also change the timing and phase calculations for determining direction. These would be engineering problems and may impact how quickly and reliably you could find you position. (Way too long since I studies this stuff to remember that level of detail)



                              Once the beacon network is established your coordinates become a range and bearing to a convenient beacon. "10 klicks from beacon XYZ bearing 175".



                              Note, I would advise against trying to establish a GPS network around an asteroid. That system is dependent on known orbits & timing for the satellites, and I suspect it would be very difficult to maintain such with the irregular shape and weak gravity of an asteroid.






                              share|improve this answer





















                              • Distance measurement using a single station these days is generally done using DME instead which basically works like secondary radar but with the roles reversed as the interrogator is on the aircraft and the transponder is on the ground. Those are more often found co-located with VOR/NDB/LNAV stations used in non precision approach procedures at airports though but there is no real reason why you couldn't have this on all your beacons on the asteroid if you wanted it. Could be useful especially if the asteroid is a very irregular shape where LoS to two or more stations might be an issue.
                                – MttJocy
                                2 days ago















                              up vote
                              0
                              down vote













                              Expanding a bit on LDutch's answer and MttJocy's comment on it. Take a page from pre-GPS aerial and nautical navigation systems.



                              Aviation commonly uses (fading as GPS is taking over, but still present) the VOR system and ADFs to figure positions and navigate. Essentially the various beacons all broadcast at a different frequency, with a directional pulse that varies in phase with the base signal. By calculating the phase difference between the primary and secondary phases your ADF provides your bearing from the station. Getting a bearing from two different stations gives you a very precise location. There are also some things that can be done in terms of phasing and signal strength to give an approximate distance from a single station, allowing for a rough position fix off of a single signal, but I am not aware of it being done in practice as the two bearing option is much more reliable. The major drawback for this system as currently implemented, and your intended use is that it is line of site and relatively short range (~200 miles). If you are too far from a station, or a pesky mountain (or the horizon of your asteroid) happens to be between you and it, you are not going to be able to pick up the signals. Meaning this system is not commonly used for surface travel.



                              The LORAN system was developed in WW2 and used until fairly recently for nautical navigation. It again works by using a series of fixed position transmitters, but in this case they come in paired units. Each member of the pairing is separated by a known distance, and they pulse out synchronized signals. The receiver compares the time difference in receiving the two pulses and from that difference you can plot a line of your relative distance from the two. Grab readings from an alternate pair to plot your location. The major advantage this system has over the other is range (~1500 miles) and being much less sensitive to LoS issues, though it is also somewhat less accurate. With the sensitivity and precision of modern electronics, it is conceivable that someone could build a 3+ point LORAN system and pinpoint their location pretty accurately off of one reading, the challenge being keeping the signals synchronized across the additional broadcast stations.



                              Now the range and LOS issues are primarily a function of the frequencies that are used in broadcasting the signals. So you could theoretically implement a VOR system in the frequency bands used by LORAN and have better performance in that respect, but it will also change the timing and phase calculations for determining direction. These would be engineering problems and may impact how quickly and reliably you could find you position. (Way too long since I studies this stuff to remember that level of detail)



                              Once the beacon network is established your coordinates become a range and bearing to a convenient beacon. "10 klicks from beacon XYZ bearing 175".



                              Note, I would advise against trying to establish a GPS network around an asteroid. That system is dependent on known orbits & timing for the satellites, and I suspect it would be very difficult to maintain such with the irregular shape and weak gravity of an asteroid.






                              share|improve this answer





















                              • Distance measurement using a single station these days is generally done using DME instead which basically works like secondary radar but with the roles reversed as the interrogator is on the aircraft and the transponder is on the ground. Those are more often found co-located with VOR/NDB/LNAV stations used in non precision approach procedures at airports though but there is no real reason why you couldn't have this on all your beacons on the asteroid if you wanted it. Could be useful especially if the asteroid is a very irregular shape where LoS to two or more stations might be an issue.
                                – MttJocy
                                2 days ago













                              up vote
                              0
                              down vote










                              up vote
                              0
                              down vote









                              Expanding a bit on LDutch's answer and MttJocy's comment on it. Take a page from pre-GPS aerial and nautical navigation systems.



                              Aviation commonly uses (fading as GPS is taking over, but still present) the VOR system and ADFs to figure positions and navigate. Essentially the various beacons all broadcast at a different frequency, with a directional pulse that varies in phase with the base signal. By calculating the phase difference between the primary and secondary phases your ADF provides your bearing from the station. Getting a bearing from two different stations gives you a very precise location. There are also some things that can be done in terms of phasing and signal strength to give an approximate distance from a single station, allowing for a rough position fix off of a single signal, but I am not aware of it being done in practice as the two bearing option is much more reliable. The major drawback for this system as currently implemented, and your intended use is that it is line of site and relatively short range (~200 miles). If you are too far from a station, or a pesky mountain (or the horizon of your asteroid) happens to be between you and it, you are not going to be able to pick up the signals. Meaning this system is not commonly used for surface travel.



                              The LORAN system was developed in WW2 and used until fairly recently for nautical navigation. It again works by using a series of fixed position transmitters, but in this case they come in paired units. Each member of the pairing is separated by a known distance, and they pulse out synchronized signals. The receiver compares the time difference in receiving the two pulses and from that difference you can plot a line of your relative distance from the two. Grab readings from an alternate pair to plot your location. The major advantage this system has over the other is range (~1500 miles) and being much less sensitive to LoS issues, though it is also somewhat less accurate. With the sensitivity and precision of modern electronics, it is conceivable that someone could build a 3+ point LORAN system and pinpoint their location pretty accurately off of one reading, the challenge being keeping the signals synchronized across the additional broadcast stations.



                              Now the range and LOS issues are primarily a function of the frequencies that are used in broadcasting the signals. So you could theoretically implement a VOR system in the frequency bands used by LORAN and have better performance in that respect, but it will also change the timing and phase calculations for determining direction. These would be engineering problems and may impact how quickly and reliably you could find you position. (Way too long since I studies this stuff to remember that level of detail)



                              Once the beacon network is established your coordinates become a range and bearing to a convenient beacon. "10 klicks from beacon XYZ bearing 175".



                              Note, I would advise against trying to establish a GPS network around an asteroid. That system is dependent on known orbits & timing for the satellites, and I suspect it would be very difficult to maintain such with the irregular shape and weak gravity of an asteroid.






                              share|improve this answer












                              Expanding a bit on LDutch's answer and MttJocy's comment on it. Take a page from pre-GPS aerial and nautical navigation systems.



                              Aviation commonly uses (fading as GPS is taking over, but still present) the VOR system and ADFs to figure positions and navigate. Essentially the various beacons all broadcast at a different frequency, with a directional pulse that varies in phase with the base signal. By calculating the phase difference between the primary and secondary phases your ADF provides your bearing from the station. Getting a bearing from two different stations gives you a very precise location. There are also some things that can be done in terms of phasing and signal strength to give an approximate distance from a single station, allowing for a rough position fix off of a single signal, but I am not aware of it being done in practice as the two bearing option is much more reliable. The major drawback for this system as currently implemented, and your intended use is that it is line of site and relatively short range (~200 miles). If you are too far from a station, or a pesky mountain (or the horizon of your asteroid) happens to be between you and it, you are not going to be able to pick up the signals. Meaning this system is not commonly used for surface travel.



                              The LORAN system was developed in WW2 and used until fairly recently for nautical navigation. It again works by using a series of fixed position transmitters, but in this case they come in paired units. Each member of the pairing is separated by a known distance, and they pulse out synchronized signals. The receiver compares the time difference in receiving the two pulses and from that difference you can plot a line of your relative distance from the two. Grab readings from an alternate pair to plot your location. The major advantage this system has over the other is range (~1500 miles) and being much less sensitive to LoS issues, though it is also somewhat less accurate. With the sensitivity and precision of modern electronics, it is conceivable that someone could build a 3+ point LORAN system and pinpoint their location pretty accurately off of one reading, the challenge being keeping the signals synchronized across the additional broadcast stations.



                              Now the range and LOS issues are primarily a function of the frequencies that are used in broadcasting the signals. So you could theoretically implement a VOR system in the frequency bands used by LORAN and have better performance in that respect, but it will also change the timing and phase calculations for determining direction. These would be engineering problems and may impact how quickly and reliably you could find you position. (Way too long since I studies this stuff to remember that level of detail)



                              Once the beacon network is established your coordinates become a range and bearing to a convenient beacon. "10 klicks from beacon XYZ bearing 175".



                              Note, I would advise against trying to establish a GPS network around an asteroid. That system is dependent on known orbits & timing for the satellites, and I suspect it would be very difficult to maintain such with the irregular shape and weak gravity of an asteroid.







                              share|improve this answer












                              share|improve this answer



                              share|improve this answer










                              answered 2 days ago









                              Rozwel

                              1,290511




                              1,290511












                              • Distance measurement using a single station these days is generally done using DME instead which basically works like secondary radar but with the roles reversed as the interrogator is on the aircraft and the transponder is on the ground. Those are more often found co-located with VOR/NDB/LNAV stations used in non precision approach procedures at airports though but there is no real reason why you couldn't have this on all your beacons on the asteroid if you wanted it. Could be useful especially if the asteroid is a very irregular shape where LoS to two or more stations might be an issue.
                                – MttJocy
                                2 days ago


















                              • Distance measurement using a single station these days is generally done using DME instead which basically works like secondary radar but with the roles reversed as the interrogator is on the aircraft and the transponder is on the ground. Those are more often found co-located with VOR/NDB/LNAV stations used in non precision approach procedures at airports though but there is no real reason why you couldn't have this on all your beacons on the asteroid if you wanted it. Could be useful especially if the asteroid is a very irregular shape where LoS to two or more stations might be an issue.
                                – MttJocy
                                2 days ago
















                              Distance measurement using a single station these days is generally done using DME instead which basically works like secondary radar but with the roles reversed as the interrogator is on the aircraft and the transponder is on the ground. Those are more often found co-located with VOR/NDB/LNAV stations used in non precision approach procedures at airports though but there is no real reason why you couldn't have this on all your beacons on the asteroid if you wanted it. Could be useful especially if the asteroid is a very irregular shape where LoS to two or more stations might be an issue.
                              – MttJocy
                              2 days ago




                              Distance measurement using a single station these days is generally done using DME instead which basically works like secondary radar but with the roles reversed as the interrogator is on the aircraft and the transponder is on the ground. Those are more often found co-located with VOR/NDB/LNAV stations used in non precision approach procedures at airports though but there is no real reason why you couldn't have this on all your beacons on the asteroid if you wanted it. Could be useful especially if the asteroid is a very irregular shape where LoS to two or more stations might be an issue.
                              – MttJocy
                              2 days ago










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                              Assuming a sufficiently advanced society, what about artificial poles, magnetic or otherwise?






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                                Assuming a sufficiently advanced society, what about artificial poles, magnetic or otherwise?






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                                  up vote
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                                  up vote
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                                  Assuming a sufficiently advanced society, what about artificial poles, magnetic or otherwise?






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                                  New contributor




                                  Buns Glazing is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
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                                  Assuming a sufficiently advanced society, what about artificial poles, magnetic or otherwise?







                                  share|improve this answer








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                                  answered yesterday









                                  Buns Glazing

                                  1012




                                  1012




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                                      up vote
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                                      down vote













                                      A map with landmarks



                                      The asteroid would be mapped out and photographed to generate a 3d model with landmarks



                                      Like a pirate's map, directions would be given from the nearest landmark.






                                      share|improve this answer

























                                        up vote
                                        0
                                        down vote













                                        A map with landmarks



                                        The asteroid would be mapped out and photographed to generate a 3d model with landmarks



                                        Like a pirate's map, directions would be given from the nearest landmark.






                                        share|improve this answer























                                          up vote
                                          0
                                          down vote










                                          up vote
                                          0
                                          down vote









                                          A map with landmarks



                                          The asteroid would be mapped out and photographed to generate a 3d model with landmarks



                                          Like a pirate's map, directions would be given from the nearest landmark.






                                          share|improve this answer












                                          A map with landmarks



                                          The asteroid would be mapped out and photographed to generate a 3d model with landmarks



                                          Like a pirate's map, directions would be given from the nearest landmark.







                                          share|improve this answer












                                          share|improve this answer



                                          share|improve this answer










                                          answered 22 hours ago









                                          Thorne

                                          13.9k42040




                                          13.9k42040






















                                              up vote
                                              0
                                              down vote













                                              Use Peaks and Valleys, and polar coordinates



                                              In the old days, prior to GPS, cartography and mapping were major and necessary fields of study. Obviously without a magnetic pole you would be unable to create universal direction, but you could still create a 'map' by using surveying techniques found mainly in triangulation of mountain peaks.



                                              Basically, you identify the highest point in a field of view, triangulate this with others to determine its distance and height, allowing you to build up an accurate map of peaks.



                                              As it is an asteroid, it has a centre of mass, and should be relatively easy to determine which peak is the highest - this would be your reference point. The second tallest peak would be your reference base line, from which you could measure polar coordinates in a consistent anticlockwise direction from centre of gravity (z-axis) for all peaks thereon.



                                              Often, when exploring Australia, Charles Sturt would have to 'artificially' create mini-piles of rocks to serve as references to determine coordinates. If your asteroid is flat, this could be used to create artificial reference points too.






                                              share|improve this answer

























                                                up vote
                                                0
                                                down vote













                                                Use Peaks and Valleys, and polar coordinates



                                                In the old days, prior to GPS, cartography and mapping were major and necessary fields of study. Obviously without a magnetic pole you would be unable to create universal direction, but you could still create a 'map' by using surveying techniques found mainly in triangulation of mountain peaks.



                                                Basically, you identify the highest point in a field of view, triangulate this with others to determine its distance and height, allowing you to build up an accurate map of peaks.



                                                As it is an asteroid, it has a centre of mass, and should be relatively easy to determine which peak is the highest - this would be your reference point. The second tallest peak would be your reference base line, from which you could measure polar coordinates in a consistent anticlockwise direction from centre of gravity (z-axis) for all peaks thereon.



                                                Often, when exploring Australia, Charles Sturt would have to 'artificially' create mini-piles of rocks to serve as references to determine coordinates. If your asteroid is flat, this could be used to create artificial reference points too.






                                                share|improve this answer























                                                  up vote
                                                  0
                                                  down vote










                                                  up vote
                                                  0
                                                  down vote









                                                  Use Peaks and Valleys, and polar coordinates



                                                  In the old days, prior to GPS, cartography and mapping were major and necessary fields of study. Obviously without a magnetic pole you would be unable to create universal direction, but you could still create a 'map' by using surveying techniques found mainly in triangulation of mountain peaks.



                                                  Basically, you identify the highest point in a field of view, triangulate this with others to determine its distance and height, allowing you to build up an accurate map of peaks.



                                                  As it is an asteroid, it has a centre of mass, and should be relatively easy to determine which peak is the highest - this would be your reference point. The second tallest peak would be your reference base line, from which you could measure polar coordinates in a consistent anticlockwise direction from centre of gravity (z-axis) for all peaks thereon.



                                                  Often, when exploring Australia, Charles Sturt would have to 'artificially' create mini-piles of rocks to serve as references to determine coordinates. If your asteroid is flat, this could be used to create artificial reference points too.






                                                  share|improve this answer












                                                  Use Peaks and Valleys, and polar coordinates



                                                  In the old days, prior to GPS, cartography and mapping were major and necessary fields of study. Obviously without a magnetic pole you would be unable to create universal direction, but you could still create a 'map' by using surveying techniques found mainly in triangulation of mountain peaks.



                                                  Basically, you identify the highest point in a field of view, triangulate this with others to determine its distance and height, allowing you to build up an accurate map of peaks.



                                                  As it is an asteroid, it has a centre of mass, and should be relatively easy to determine which peak is the highest - this would be your reference point. The second tallest peak would be your reference base line, from which you could measure polar coordinates in a consistent anticlockwise direction from centre of gravity (z-axis) for all peaks thereon.



                                                  Often, when exploring Australia, Charles Sturt would have to 'artificially' create mini-piles of rocks to serve as references to determine coordinates. If your asteroid is flat, this could be used to create artificial reference points too.







                                                  share|improve this answer












                                                  share|improve this answer



                                                  share|improve this answer










                                                  answered 3 hours ago









                                                  flox

                                                  6,508422




                                                  6,508422






















                                                      up vote
                                                      0
                                                      down vote














                                                      1. enter image description here


                                                      You can apply a graph to your asteroid and find the distances of each point. From one another with this equation.



                                                      AB^2=(Bx-Ax)^2+(By-Ay)^2…………………^2=squared



                                                      If you make the same graph on four sided sections of asteroid you will have a rough grid.
                                                      Next




                                                      1. enter image description here


                                                      This is a better way to make a three dimensional coordinate site system labeling each point from the center as a distance with the equation:



                                                      The root of [(x2-x1)+(y2-y1)+(z2-z1)] where each point is a labeled coordinate at the surface of the asteroid.
                                                      Next




                                                      1. enter image description here


                                                      Use a circle grid to plot points from center with meters or kilometers or centimeters.



                                                      enter image description here



                                                      Then you find the angle degree of the point with this type of equation. Remember your circle grid always has a 90 degree angle already.



                                                      enter image description here



                                                      One can also find angle this way



                                                      enter image description here



                                                      Now apply the equation.
                                                      X^2 + y^2=(r cos @)^2. + (r sin @)^2 Where @ is a Greek representational letter for degrees or radians.



                                                      And this gives a unique coordinate for any point and it’s distamce from center of asteroid. You can put a stake or pin at any point and create a grid by stretching a bright colored string from one to the other. And use these shapes to find area.
                                                      Next




                                                      1. Another way is calculus if the asteroid is spinning you can find sections of surface area as zones of the asteroid.


                                                      enter image description here



                                                      And use integration.



                                                      enter image description here



                                                      For this you need the radius or diameter at each given integrated section. It if one can imagine a large amount of sections and each having a sub measure of length sections to each sliced section it also makes a grid.



                                                      There are few more possibilities and I will add if asked.



                                                      This is a rough idea and I am a little rusty and just woke up. Will edit later. I had a better presentation but the pictures would not copy here.






                                                      share|improve this answer



























                                                        up vote
                                                        0
                                                        down vote














                                                        1. enter image description here


                                                        You can apply a graph to your asteroid and find the distances of each point. From one another with this equation.



                                                        AB^2=(Bx-Ax)^2+(By-Ay)^2…………………^2=squared



                                                        If you make the same graph on four sided sections of asteroid you will have a rough grid.
                                                        Next




                                                        1. enter image description here


                                                        This is a better way to make a three dimensional coordinate site system labeling each point from the center as a distance with the equation:



                                                        The root of [(x2-x1)+(y2-y1)+(z2-z1)] where each point is a labeled coordinate at the surface of the asteroid.
                                                        Next




                                                        1. enter image description here


                                                        Use a circle grid to plot points from center with meters or kilometers or centimeters.



                                                        enter image description here



                                                        Then you find the angle degree of the point with this type of equation. Remember your circle grid always has a 90 degree angle already.



                                                        enter image description here



                                                        One can also find angle this way



                                                        enter image description here



                                                        Now apply the equation.
                                                        X^2 + y^2=(r cos @)^2. + (r sin @)^2 Where @ is a Greek representational letter for degrees or radians.



                                                        And this gives a unique coordinate for any point and it’s distamce from center of asteroid. You can put a stake or pin at any point and create a grid by stretching a bright colored string from one to the other. And use these shapes to find area.
                                                        Next




                                                        1. Another way is calculus if the asteroid is spinning you can find sections of surface area as zones of the asteroid.


                                                        enter image description here



                                                        And use integration.



                                                        enter image description here



                                                        For this you need the radius or diameter at each given integrated section. It if one can imagine a large amount of sections and each having a sub measure of length sections to each sliced section it also makes a grid.



                                                        There are few more possibilities and I will add if asked.



                                                        This is a rough idea and I am a little rusty and just woke up. Will edit later. I had a better presentation but the pictures would not copy here.






                                                        share|improve this answer

























                                                          up vote
                                                          0
                                                          down vote










                                                          up vote
                                                          0
                                                          down vote










                                                          1. enter image description here


                                                          You can apply a graph to your asteroid and find the distances of each point. From one another with this equation.



                                                          AB^2=(Bx-Ax)^2+(By-Ay)^2…………………^2=squared



                                                          If you make the same graph on four sided sections of asteroid you will have a rough grid.
                                                          Next




                                                          1. enter image description here


                                                          This is a better way to make a three dimensional coordinate site system labeling each point from the center as a distance with the equation:



                                                          The root of [(x2-x1)+(y2-y1)+(z2-z1)] where each point is a labeled coordinate at the surface of the asteroid.
                                                          Next




                                                          1. enter image description here


                                                          Use a circle grid to plot points from center with meters or kilometers or centimeters.



                                                          enter image description here



                                                          Then you find the angle degree of the point with this type of equation. Remember your circle grid always has a 90 degree angle already.



                                                          enter image description here



                                                          One can also find angle this way



                                                          enter image description here



                                                          Now apply the equation.
                                                          X^2 + y^2=(r cos @)^2. + (r sin @)^2 Where @ is a Greek representational letter for degrees or radians.



                                                          And this gives a unique coordinate for any point and it’s distamce from center of asteroid. You can put a stake or pin at any point and create a grid by stretching a bright colored string from one to the other. And use these shapes to find area.
                                                          Next




                                                          1. Another way is calculus if the asteroid is spinning you can find sections of surface area as zones of the asteroid.


                                                          enter image description here



                                                          And use integration.



                                                          enter image description here



                                                          For this you need the radius or diameter at each given integrated section. It if one can imagine a large amount of sections and each having a sub measure of length sections to each sliced section it also makes a grid.



                                                          There are few more possibilities and I will add if asked.



                                                          This is a rough idea and I am a little rusty and just woke up. Will edit later. I had a better presentation but the pictures would not copy here.






                                                          share|improve this answer















                                                          1. enter image description here


                                                          You can apply a graph to your asteroid and find the distances of each point. From one another with this equation.



                                                          AB^2=(Bx-Ax)^2+(By-Ay)^2…………………^2=squared



                                                          If you make the same graph on four sided sections of asteroid you will have a rough grid.
                                                          Next




                                                          1. enter image description here


                                                          This is a better way to make a three dimensional coordinate site system labeling each point from the center as a distance with the equation:



                                                          The root of [(x2-x1)+(y2-y1)+(z2-z1)] where each point is a labeled coordinate at the surface of the asteroid.
                                                          Next




                                                          1. enter image description here


                                                          Use a circle grid to plot points from center with meters or kilometers or centimeters.



                                                          enter image description here



                                                          Then you find the angle degree of the point with this type of equation. Remember your circle grid always has a 90 degree angle already.



                                                          enter image description here



                                                          One can also find angle this way



                                                          enter image description here



                                                          Now apply the equation.
                                                          X^2 + y^2=(r cos @)^2. + (r sin @)^2 Where @ is a Greek representational letter for degrees or radians.



                                                          And this gives a unique coordinate for any point and it’s distamce from center of asteroid. You can put a stake or pin at any point and create a grid by stretching a bright colored string from one to the other. And use these shapes to find area.
                                                          Next




                                                          1. Another way is calculus if the asteroid is spinning you can find sections of surface area as zones of the asteroid.


                                                          enter image description here



                                                          And use integration.



                                                          enter image description here



                                                          For this you need the radius or diameter at each given integrated section. It if one can imagine a large amount of sections and each having a sub measure of length sections to each sliced section it also makes a grid.



                                                          There are few more possibilities and I will add if asked.



                                                          This is a rough idea and I am a little rusty and just woke up. Will edit later. I had a better presentation but the pictures would not copy here.







                                                          share|improve this answer














                                                          share|improve this answer



                                                          share|improve this answer








                                                          edited 3 hours ago

























                                                          answered 3 hours ago









                                                          Robus

                                                          1046




                                                          1046

















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