Answer:
[tex]M=1.9\times 10^{27}\ kg[/tex]
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 :
[tex]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[/tex]
So, the mass of Jupiter is [tex]1.9\times 10^{27}\ kg[/tex].
Based on orbital period formula, the mass of Jupiter is 1.9 × 10^27 kg.
The period, t = 42.5 hours = 153000 seconds
The mass of Jupiter is found using the formula for orbital period given below:
Making m subject of formula
[tex]m = \frac{4 {\pi}^{2} {r}^{3} }{g {t}^{2}} [/tex]
substituting the values:
[tex]m = \frac{ 4{\pi}^{2} \times(4.22 \times {10}^{8}) ^{3} }{ {153000}^{2} \times 6.67 \times {10}^{ - 11} } [/tex]
[tex]m = 1.9 \times {10}^{27} kg[/tex]
Therefore, the mass of Jupiter is 1.9 × 10^27 kg.
Learn more about orbital period at: https://brainly.com/question/1566620
