[frayesto]

So we can determine the orbit using only line of sight measurements of the object relative to the Earth.

This is a problem originally solved by Gauss for Ceres.

https://en.wikipedia.org/wiki/Gauss%27s_method

More generally given sufficient observations one can use many similar methods of orbit determination to get a relatively accurate orbit of the body. All of this is standard stuff in astrodynamics and happens on a near constant basis for both man made and natural objects.

A good introduction is the classic BMW

https://www.amazon.com/Fundamentals-Astrodynamics-Dover-Aero...

None of this requires the shape or material of the object, just some fuzzy measurements of the position

[jimhefferon]

But surely it can be affected if the body outgasses because of some solar effect? I don't believe that applies to Ceres, or to satelites around the Earth, etc.

[sandworm101]

Outgassing should be seen. If it is close enough to the sun to melt anything, it is close enough that we should see the resulting tail. Once it is far away from the sun again, outgassing should stop as everything freezes up.

[russdill]

That depends quite highly on the object's mass.