Answer to Question #273934 in Mechanics | Relativity for Lhen

Question

Ganymede is one of the moons of Jupiter.Ganymede's period of revolution around Jupiter is 7.16 earth days and orbital radius about 1.7x10^9m.Find the mass of Jupiter.

Answer 1

Explanations & Calculations

• Apply Newton's gravitation law to Saturn and its moon.
• An earth day is $\small 86400$ seconds.
• Then,

$\qquad\qquad \begin{aligned} \small G\frac{M_S.m_G}{r^2}&=\small m_Gr\omega^2\\ \small M_S&=\small \frac{r^3}{G}.\frac{4\pi^2}{T^2}\\ &=\small \frac{(1.7\times10^9\,m)^3}{6.67\times10^{-11}m^3kg^{-1}s^{-2}}.\frac{4\pi^2}{(7.16\times86400\,s)^2}\\ &=\small 7.60\times10^{27} \,kg\end{aligned}$