##### A satellite has a mass of 106 kg and is located at 2.03 106 m above the surface

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A satellite has a mass of 106 kg and is located at 2.03  106 m above the surface of Earth.
(a) What is the potential energy associated with the satellite at this location?
J

(b) What is the magnitude of the gravitational force on the satellite?

N

Jun 10th, 2015

Thank you for the opportunity to help you with your question!

a) U = m g' (R + h) – m g R = m g R²/(R+h) – m g R

U = m g R (R/(R+h) – 1) = - m g R h/(R+h)

U = - 106 * 9.8 * 6371000 * 1.97 10^6/(6371000 + 1.97 10^6)

U = - 1563.1 10^6 J

b) g = G M/R²

R = Earth's radius

At h = 1.97 10^6 m of altitude:

g' = G M/(R+h)²

By dividing the equations:

g'/g = R²/(R+h)²

g' = g R²/(R+h)²

F = m g' = m g R²/(R+h)² = 106 * 9.8 * 6371000²/(6371000 + 1.97 10^6)²

F = 606.05 N

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 10th, 2015

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Jun 10th, 2015
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Jun 10th, 2015
Oct 17th, 2017
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