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There are 2 spheres. 1 is massive and the density linearly decreases, with each shell of the sphere of equal thickness having the same mass.

Density at any Radius*Volume of Layer with constant width=Constant Mass

Additionally, there is a second sphere, this time hollow, which has the same mass as a layer of the same width as before.

Assuming the second sphere can move freely through the first, and that it is centered around the others center, how would I calculate the gravitational forces acting upon it at different radii?

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    $\begingroup$ it is centered around the others center In that case, why do you think there would be any net force on it? $\endgroup$
    – G. Smith
    Commented Dec 3, 2020 at 18:24
  • $\begingroup$ Maybe I phrased that wrong. I'm not looking for a net force, I'm looking for the force of gravity pushing and pulling to or from the center point, despite the sphere not moving, there are equal forces attacking it from all sides, I'd like to calculate them. $\endgroup$
    – Mat NX
    Commented Dec 3, 2020 at 19:58

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An equivalent of Gauss's law applies to spheres of mass. The acceleration of gravity at any radius inside of your first sphere depends only on the mass which is inside of that radius. All of that included mass can be treated like a point mass located at the center of the sphere.

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