Newton's law of gravity and Coulomb's law are both inverse-square laws. Consequently, there should be a "Gauss's law for gravity."

The Gauss's law for gravity: ∮g⃗ ⋅dA⃗ =−4πGMin.
A spherical planet is discovered with mass M, radius R, and a mass density that varies with radius as ρ=ρ0(1−r/2R), where ρ0 is the density at the center. Determine ρ0 in terms of M and R.

Find an expression for the gravitational field strength inside the planet at distance r < R.

Express your answer in terms of the variables G, M, r, and R.