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An artificial satellite moves in a circular orbit around the Earth and has total mechanical energy E0 (which is negative for a bound orbit). What is the ratio of its gravitational potential energy to its total mechanical energy?
- -2
- -1
- 1/2
- 2
Correct answer: 2
Solution
For a satellite in circular orbit at radius r: KE = GMm/(2r) and PE = -GMm/r = 2*KE in magnitude but opposite sign. Total energy E0 = KE + PE = -GMm/(2r) < 0. Therefore PE = -GMm/r = 2*(-GMm/(2r)) = 2*E0. Ratio PE/E0 = 2.
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