Question

A hypothetical planet has a mass of one-half that of the earth and a radius of twice that of the earth. what is the acceleration due to gravity on the planet in terms of g, the acceleration due to gravity at the surface of the earth?

Answer 1

Let m = mass of earth 
let r = radius of earth 
let a = acceleration due to gravity on earth 
G = constant (it doesn't change) 

If you plug in the mass and radius of the new planet, you get 

a = G (.5m)/(2r)^2 
a = 1/8 (Gm/r^2) 

so the acceleration on the new planet is 1/8 what it is here.