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

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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

Hello friend...Thank you for the opportunity to help you with your question :-)

(a) What is the potential energy associated with the satellite at this location?

               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 * 1.97 10^6/(6371000 + 1.97 10^6) 

               U = - 1386.1 x 10^6 J


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

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

F = 537.44 N 


Hello once more! Here is the complete answer! Please let me know if you need any clarification. Please best with a 5* as soon as you can Thank you and Godbless!!
Jun 8th, 2015

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