Consider spherical symmetric$^1$ masses of radii $R_1$ and $R_2$, with spherical symmetric density distributions $\rho_1(r_1)$ and $\rho_2(r_2)$, 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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