Satellite Energy

Question

Total mechanical energy of satellite of mass m in circular orbit radius r is:

RankGuru · Accepted Answer

For a circular orbit:
1. Potential Energy $U = -\frac{GMm}{r}$
2. Kinetic Energy $K = \frac{1}{2} m v^2 = \frac{1}{2} m (\frac{GM}{r}) = \frac{GMm}{2r}$
3. Total Energy $E = K + U = \frac{GMm}{2r} - \frac{GMm}{r} = -\frac{GMm}{2r}$
- Note $|U| = 2K$ and $E = -K$.

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