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Question

A 200.-kg satellite is in circular orbit around the Earth and moving at a speed of $5.00 \mathrm{~km} / \mathrm{s}$. How much work must be done to move the satellite into another circular orbit that is twice as high above the surface of the Earth?

Solution

VerifiedAnswered 1 year ago

Answered 1 year ago

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- The mass of the satellite is $\color{#c34632} m=200\, \text{kg}$, and it's orbital speed is $\color{#c34632}v=5.00\, \dfrac{\text{km}}{\text{s}}=5.00\times 10^3\, \dfrac{\text{m}}{\text{s}}$.
- Also, the mass of the Earth is $\color{#c34632} M=5.97\times 10^{24}\, \text{kg}$, the radius of the Earth is $\color{#c34632} R=6.37\times 10^6\, \text{m}$ and the universal gravitational constant is $\color{#c34632} G=6.67\times 10^{-11}\, \dfrac{\text{Nm}^2}{\text{kg}^2}$
- We need to find the required work to move the satellite on a orbit of doubled altitude.

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