A satellite has a mass of 106 kg and is located at 2.03 106 m above the surface of Earth. (a) What

Physics
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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

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

g = G M/R² 

R = Earth's radius 

At h = 2.3 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 + 2.3 10^6)² 

F = 560.80 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 = - 106 * 9.8 * 6371000 * 2.3 *10^6/(6371000 + 2.3* 10^6) 

U = - 1755.48 10^6 J 

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

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