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You can write Newton's law of universal gravitation out in integral form and do the calculation as long as you know the mass density of the object over space.

Are you talking about something like a donut?There's no dough at the C of G, but the G of G is still there.

Quote from: Bored chemist on 16/02/2014 09:47:32Are you talking about something like a donut?There's no dough at the C of G, but the G of G is still there.But the forces cannot be calculated in the same way as for a sphere where the centre of gravity does contain mass. The mass distribution has to be taken into account. I am looking into numerical relativity to find a solution.

Just integrate F = GMm/r^2 over the shape and test position you have. Most standard symmetric integrals (shell, ring, torus, etc. ) are tabulated in textbooks, or you can resort to elemental analysis if you have ther time and inclination. It only gets difficult when the elements are separated and moving - i.e. astronomy.