Question

planet x has one a quarter the radius of the earth and a quarter of the mass of the earth. what would be the gravitational acceleration, gx, on the surface of the planet x?

Answer 1

F = m a = G m M / R^2 gravitational force between objects of mass M and m

a = G M / R^2 gravitational acceleration due to planet of mass M

a2 / a1 = M2 R1^2 / (M1 R2^2)

given M2 = 1/4 M1 and R2 = 1/4 R1

a2 / at = (M2 / M1) * (R1 / R2)^2 = 1/4 * 4*2 = 4

a2 the acceleration on planet x would be 4 times that on earth