Answer:
M_J = 1.875 x 10²⁷ Kg
Explanation:
given,
orbital radius of the moon of Jupiter(r) = 4.22 ✕ 10⁸ m
Period of the moon(T) = 1.77 days
= 1.77 x 24 x 60 x 60
= 152928 s
using Kepler's formula top calculate mass of the Jupiter
[tex]T^2 = \dfrac{4\pi^2}{GM_J}r^3[/tex]
where M_J is the mass of the Jupiter
and G is gravitational constant
[tex]152928^2 = \dfrac{4\pi^2}{6.67 \times 10^{-11}\times M_J}(4.22 \times 10^8)^3[/tex]
[tex]M_J = \dfrac{4\pi^2}{6.67 \times 10^{-11}\times 152928^2}(4.22 \times 10^8)^3[/tex]
M_J = 1875.028 x 10²⁴
M_J = 1.875 x 10²⁷ Kg
Mass of Jupiter is equal to M_J = 1.875 x 10²⁷ Kg
