Celestia Forums

Does anyone know the formulas to compute gravitational force at a given distance for a non-spherical object? Something orbiting an oblate object will probably be pulled in a slightly different direction than the true center of mass some of the time. I imagine that the further away from the oblate object you get, the more the formula approaches that of a spherical formula (which can be treated a point mass).

Do you mean the gravitational force in the surface?
Because if you are talking the forces in the space near the celestial body, its not important its shape...
For gravity force calculations you imagine that teh celestial body is a small point in the center of gravity of that body...

El Pelado, Newton showed that you could treat a sphere as if all its mass were concentrated at the centre - that's a reasonable assumption for an irregular object when it's very far away, too, but not when you're close to it. This is why the orbits of satellites around the Earth precess so quickly, making Celestia's simple orbit models almost immediately inaccurate for things like the ISS - the orbits are being distorted from simple ellipses by the "extra" gravitation of the Earth's equatorial bulge.

Tony, I know the formulae for orbits around a single oblate body of known mass distribution, but that isn't going to help you with the general case in your gravity simulator.

Grant

This page from the Weisstein's World of Physics should be helpful:

http://scienceworld.wolfram.com/physics ... Force.html

That's more general than you need--here's the gravitational potential for an oblate spheroid:

http://scienceworld.wolfram.com/physics ... ntial.html

--Chris

Thanks, Chris and Grant. The formulas in Chris' link might do the trick for me. Grant, your formulas would be useful to check whether or not I've programmed it correctly. But that's months off since I don't have much time at the moment, so I'll ask you then.