A planet has a mass of M1, a radius of R1, and a density of 1. A second planet h

Question

A planet has a mass of M1, a radius of R1, and a density of 1. A second planet has a mass of M2, a radius of R2, and a density of 2. This problem will explore the relationships between the surface gravities (g1 and g2) of the planets depending on the relative sizes of their masses, radii, and densities. Assume that planet 2 has X times the mass of planet 1, or M2 = XM1. The densities of both planets are the same. Write an expression for the ratio of the surface gravity of planet 2 to planet 1 in terms of X.

Explanation / Answer

the accleration due to gravity is

g = GM/r^2

relation between mass and density and volume

M = V

= ( 4/3 * pi r^3)

g = 4/3 * pi G * r

for planet M1

g 1= 4/3 * pi G * 1 R1

g 2= 4/3 * pi G * 2 R2

g2/g1 =  4/3 * pi G * 2 R2/4/3 * pi G * 1 R1

=2 R1/1 R1

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