Newton’s law of gravity and Coulomb’s law are both inverse square laws. Consequently, there should be a “Gauss’s law for gravity.”
a. The electric field was defined as E = F _{on q}/q, and we used this to find the electric field of a point charge. Using analogous reasoning, what is the gravitational field g of a point mass?

Write your answer using the unit vector r̂, but be careful with signs; the gravitational force between two “like masses” is attractive, not repulsive.
b. What is Gauss’s law for gravity, the gravitational equivalent of Equation 24.18? Use Φ_G for the gravitational flux, g for the gravitational field, and M_in for the enclosed mass.
c. 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.
d. Find an expression for the gravitational field strength inside the planet at distance r < R.