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

Step-by-step explanation:

its 99.51 im not just saying that because of the person on top of me but i have all my notes from physics and from chemistry and from biology from when i was on acellus! but the top of me is right :)

Answer 2

T = 99.51 hour

Step-by-step explanation:

Mass of Uranus,
`M=8.68* 10^(25)\ kg`

The moon Umbriel orbits Uranus at a distance of
`2.66* 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=(4\pi^2r^3)/(GM)\\\\T^2=(4\pi^2* (2.66* 10^8)^3)/(6.67* 10^(-11)* 8.68* 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.