posted by Ruth on .
Suppose a person weighs 160 pounds on Earth. How much would that person weigh on a planet that was three times as massive as Earth and had a radius that was twice that of Earth's?
W on earth is GmM/r^2
W elsewhere = Gm(3M)/(2r)^2 = GmM/r^2 * 3/4 = 160*3/4 = 120lbs
So, even though the planet is more massive (linear), its radius has a larger (quadratic) effect on the weight.