Originally posted by wormwood
I don't, but I've seen it used for gravity as well.
Perhaps you can use Gauss to prove that a spherical homogenous body can be treated as a gravitational point in the center of the sphere. But any shaped object with any mass distribution inside, no...?
Even Earth is not completely spherical. It's flatter at the poles. And this alone is a reason to compensate the orbits of the satelites continuasly, especially the low polar orbits. (Asides a lot of other disturbances that the orbit is not completely stable.)
Earth is not even homogenous in mass distrubution, but as long it is symmetrical it's not a problem. But even the level of sea is not a mathematical ellipsoid, but now we ar plunging to deep of disturbances of satellite orbits.
In the mathematical sphere case, you can use Gauss, but not with other shapes and mass distributions.
I would love you to do the experiment. Compare the result between a numerical calculation and a Gauss calculation of a horse shoe body in the size and mass of that of Earth. If a difference can be explained with anything other than accumulative roundings errors, then I'm right in this. If you're right I will eat my hat (baked of pie doe and fruit filling).