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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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