Answer to Question #295673 in Astronomy | Astrophysics for Ayena

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 1.07  m. Find the mass of Jupiter.

Answer 1

Explanation & Calculation

• Apply Newton's gravitational law for the planet and its moon.

$\qquad\qquad \begin{aligned} \small G\frac{Mm}{r^2}&=\small mr\omega^2\\&=\small mr\frac{4\pi^2}{T^2}\\ \small M&=\small \frac{1}{G}.\frac{4\pi^2.r^3}{T^2}\\ &=\small \frac{1}{6.67\times10^{-11}\,Nm^2kg^{-2}}.\frac{4\pi^2.(1.07\times10^6\times10^3\,m)^3}{(7.16\times24\times3600\,s)^2}\\ &=\small 1.89\times10^{27}\,kg \end{aligned}$