Question

Io and Europa are two of Jupiter's many moons. The mean distance of Europa from Jupiter is about twice as far as that for Io and Jupiter. By what factor is the period of Europa's orbit longer than that of Io's?
TEu/TIo =

I know that Europa's period is twice Io's but I'm struggling in how to present it properly.

Answer 1

whats your awnser

Answer 2

I know that orbital period equation is T^2=4pi^2r^3/GM and that Europa's period is twice Io's but otherwise I'm pretty stumped.

Answer 3

since T^2 is proportional to r^3,
T is proportional to √(r^3)
so if r is doubled, T grows by a factor of √8