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