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Soloha48 [4]
2 years ago
7

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 hou

rs)?
Physics
1 answer:
Whitepunk [10]2 years ago
7 0

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.

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