Question

Ganymede is one of the many moons of Jupiter. Ganymede's period of revolution around Jupiter is 7.16 Earth days and an orbital radius about 1.07x10^9 meter. Find the mass of the Jupiter

Answer 1

Given:

$T=7.16\:\rm days$

$r=1.07*10^9\:\rm m$

The third Kepler's law says

$$T^2=\frac{4\pi^2 r^3}{GM}$$

Hence, the mass of Jupiter

$$M=\frac{4\pi^2 r^3}{GT^2}$$

$$M=\frac{4\pi^2 (1.07*10^9)^3}{6.67*10^{-11}*(7.16*24*3600)^2}=1.89*10^{27}\:\rm kg$$