alleryThe total mechanical energy of a satellite of mass m in a circular orbit of radius r around the Earth (mass M) is:
A+G M m / (2 r)
B−G M m / (2 r)
C−G M m / r
D+G M m / r
Answer & Solution
Correct answer: B. −G M m / (2 r)
1. KE of the satellite = ½ m v² = ½ m (G M / r) = G M m / (2 r).
2. Gravitational PE = − G M m / r (zero reference at infinity).
3. Total E = KE + PE = G M m / (2 r) − G M m / r = − G M m / (2 r).
4. The negative sign means the satellite is bound — energy must be added to escape.
5. |Total E| = ½ |PE| = KE — the virial relation for an inverse-square central force.
_Source: syllabus Physics Ch 7 "Gravitation", §7.10 Energy of an Orbiting Satellite_
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