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

Engineering
Tutor: None Selected Time limit: 1 Day

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 




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Jun 10th, 2015

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