# How do we define geographical coordinates on non-spheroid celestial bodies?

On Earth, we can use latitude and longitude to fairly accurately describe a single point on the surface of the earth. This works because the earth is, for all intents and purposes, a sphere. It got me thinking about what kind of system, if any, we would use to describe a single point on the surface of a non-spheroid body, like a large asteroid or an oblong moon.

I suppose you could just "wrap" the object's topology to a spherical projection, though this would result in massive distortions. More importantly, it also raises the question of what the 'fixed points' are of the system (i.e. where are geographical north and south poles)? We've recently witnessed large asteroids and moons tumbling chaotically in their orbits with no discernible rotation axis.

• Earth is not for all intents and purposes a sphere. For GPS, the reference ellipsoid WGS84 is used, a spherical model would not fit for the precision of GPS. Latitude and longitude may be used for an ellipsoid too, not only for a sphere.
– Uwe
Apr 28, 2017 at 8:07
• Any coordinate system with three parameters would fit to such an irregular body. Polar coordinates with two angles and one distance to center, cartesian coordinates or a cylindrical system with one angle and two distances. Of course there is no mean sea level to be used as height reference. The well known Mercator projection of Earth is also massively distorted close to the poles. But today we may use a computer model enabling us to turn, shift, zoom or pan the virtual body in any direction or axis. Or we may use the data to print a model using a 3D printer.
– Uwe
Dec 3, 2018 at 12:32

All projections will have some kind of distortion, even on Earth. Spherical projections may not be ideal for such bowling pin shaped asteroids. In fact, a cylindrical projection may be applied or even new custom projections.

Much has been written on the subject including "Morphographic Projections for Maps of Non-Spherical Worlds" and "Map Projections for Non-spherical Worlds / The Variable-Radius Map Projections" (paywall). The latter describing an interesting concept applied to Saturn's moon Epimetheus.

This page has a collection of maps of small solar system bodies prepared by Phil Stooke of the University of Western Ontario. Many of the bodies have maps created using a variety of projections.

This cylindrical projection of Eros is highly distorted, especially at the poles, but also in the centre. It's clear that no projection is perfect.

• Half of external links no longer work.
– Pere
Dec 2, 2018 at 9:25
• Thanks for the heads up. It appears that they have been archived to a different server. I've repaired the links. Dec 2, 2018 at 22:56
• This is still a link-only answer. 1st link is a short, 32 year old conference abstract, 2nd link is paywalled and therefore unreadable, 3rd is just a list of large downloads, 4th is an uncredited and unexplained image I don't understand, but could at least be included here. From my perspective this does not really answer How do we define geographical coordinates on non-spheroid celestial bodies? Is it possible to take a minute and briefly explain how this is done in some generalized way? Perhaps just add a basic discussion of what a reference surface is, how altitude is defined from it, etc.
– uhoh
Dec 3, 2018 at 0:36
• I've added a bounty to sweeten the pot a bit. Thanks! (btw this GIS-like question could use another answer as well: Shape and dimensions of the Moon's reference surface for selenographic latitude/longitude?)
– uhoh
Dec 3, 2018 at 0:44