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

Question

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.

Answer 1

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.