Question

Ganymede is one of the moons of Jupiter. Ganymede’s period of revolution around Jupiter is 7.16 Earth days and an orbital radius of about 1.07x10^9. What is the mass of Jupiter?

Answer 1

$$m\frac{v^2}R=G\frac{Mm}{R^2},\\\space\\ M=\frac{v^2R}{G}=\frac{(2\pi R/T)^2R}{G}=\frac{4\pi^2 R^3}{GT^2}=1.89·10^{27}\text{ kg}.$$