Question

The moon Umbriel orbits Uranus (mass = 8.68 x 10^25 kg) at a distance of 2.66 x 10^8 m. What is Umbriel's orbital period (in hours)?

Answer 1

Answer:

T = 99.51 hour

Explanation:

Mass of Uranus, $M=8.68\times 10^{25}\ kg$

The moon Umbriel orbits Uranus at a distance of $2.66\times 10^8\ m$

We need to find Umbriel's orbital period. Let it is T. Using Kepler's third law of motion to find it.

$T^2\propto r^3\\\\T^2=\dfrac{4\pi^2r^3}{GM}\\\\T^2=\dfrac{4\pi^2\times (2.66\times 10^8)^3}{6.67\times 10^{-11}\times 8.68\times 10^{25}}\\\\T=358244.51\ s$

As 1 hour = 3600 s

358244.51 s = 99.51 hour

Hence, Umbriel's orbital period is 99.51 hour.