Answer to Question #275513 in Physics for physics

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

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