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(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
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