the planet jupiter is more than 300 times more massive than earth. However,an object scarcley weighs 3 times as much on the surface of jupiter as it does on the surface of the earth. how can that be? Determine the radius of jupiter in terms of earth radii

1 answer

The value of the acceleration of gravity at the surface of a planet is G M/R^2, where G is a universal constant.
If "1" denotes Earth and "2" denotes Jupiter, and Jupiter has 300 times the Earth's mass,

g2 = 3 g1
M2/R2^2 = 3 M1/R1^2
(R2/R1)^2 = 3 M1/M2 = 3/300 = 1/100
R2/R1 = 10