Answer:
T = 99.51 hour
Explanation:
Mass of Uranus, [tex]M=8.68\times 10^{25}\ kg[/tex]
The moon Umbriel orbits Uranus at a distance of [tex]2.66\times 10^8\ m[/tex]
We need to find Umbriel's orbital period. Let it is T. Using Kepler's third law of motion to find it.
[tex]T^2\propto r^3\\\\T^2=\dfrac{4\pi^2r^3}{GM}\\\\T^2=\dfrac{4\pi^2\times (2.66\times 10^8)^3}{6.67\times 10^{-11}\times 8.68\times 10^{25}}\\\\T=358244.51\ s[/tex]
As 1 hour = 3600 s
358244.51 s = 99.51 hour
Hence, Umbriel's orbital period is 99.51 hour.
