Consider spherical symmetric1 masses of radii R1 and R2, with spherical symmetric density distributions ρ1(r1) and ρ2(r2), and with a distance between the centers of the spheres d. What is the exact force between them? I know point masses are a good approximation, but I'm looking for an exact formula. This would be useful for a gravity-simulation toy software.
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1 Assume for simplicity the idealization where tidal or centrifugal forces do not deform the spherical symmetric, i.e., the various mass parts are held in place by infinitely strong and rigid bonds.
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