Is Gravitational Interaction Affected by Different Shapes of Bodies?

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paweld
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I wonder about gravitational interaction between two bodies of any shape (not necessarly symmetrical).
I would like to predict the motion of their centers of mas if they don't interact with any other bodies. Can I assume that mass of each body is located only in the center and compute the gravitational force as if the bodies were punctual? (In fact I should compute double vector integral over volume of each body.)

I know that it's true in case of bodies with spherical symmetry (one can prove this using e.g. Gauss theorem). Is it always true for all shapes of bodies.
 
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paweld said:
Can I assume that mass of each body is located only in the center and compute the gravitational force as if the bodies were punctual?
No.
I know that it's true in case of bodies with spherical symmetry (one can prove this using e.g. Gauss theorem). Is it always true for all shapes of bodies.
No, it's not true in general.
 
Thanks.

I've just devised a simple counterexample.
Consider three points of equal masses m lying on the line in the distance a from each other.
One body consists of two points lying side by side and other of one point. The real interaction between bodies is up to multiplicative constant 1/a^2 +1/(2a)^2 while according to my assumption about the center of masses it would be 2/(3/2 a)^2.