Question

One of the satellites of Jupiter has an orbital period of 1.769 days and the radius of the orbit is $4.22\times {10}^{8}m$. Show that the mass of Jupiter is about one-thousandth that of the sun.

Answer 1

$\text{Gravitational force = Centripetal Force}$

$\frac{G{M}_p{M}_J}{R_p^2}=\frac{M_p{v}_p^2}{R_p}...............\left(1\right)$

Also, $v_p=\frac{2\pi R_p}{T_p}...............\left(2\right)$

Substituting (2) in (1),

$M_J=\frac{4{\pi }^2{R}_P^3}{G{T}_P^2}$

$=1.9\times {10}^{27}kg$

$M_J/M_S=\frac{1.9\times {10}^{27}}{2\times {10}^{30}}\approx {10}^{-3}$