Question

Find Jupiter's mass from the fact that its moon Io orbits every 42.5 hours at an average distance of 422,000 kilometers.

Answer 1

Answer:

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

Explanation:

Given that,

Orbital period, T = 42.5 hours = 153000 seconds

The average distance of Jupiter's mass, r = 422,000 km

We need to find Jupiter's mass. The formula for the orbital period is given by :

$T^2=\dfrac{4\pi^2}{GM}r^3\\\\T^2GM=4\pi^2 r^3\\\\M=\dfrac{4\pi^2 r^3}{T^2 G}\\\\M=\dfrac{4\pi^2 \times (422000 \times 10^3)^3}{(153000 )^2 \times 6.67\times 10^{-11}}\\\\M=1.9\times 10^{27}\ kg$

So, the mass of Jupiter is $1.9\times 10^{27}\ kg$.