A satellite has a mass of 94 kg and is located at 1.96 106 m above the surface

Physics
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A satellite has a mass of 94 kg and is located at 1.96 106 m above the surface of Earth.

(a) What is the potential energy associated with the satellite at this location? (b) What is the magnitude of the gravitational force on the satellite?
Jun 8th, 2015

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b) The acceleration due to gravity at sea level is: 

g = G M/R² 

R = Earth's radius 

At h = 1.96 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 = 94 * 9.8 * 6371000²/(6371000 + 1.97 10^6)² 

F = 55501.575 N 
= = = = = = = 


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 = - 94 * 9.8 * 6371000 * 1.96 10^6/(6371000 + 1.96 10^6) 

U = -442,871.24  J 
= = = = = = = = = = 

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jun 8th, 2015

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