Answer to Question #275938 in Physics for physics

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

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

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