Energies of an Orbiting Satellite

For a satellite of mass $m$ in a circular orbit of radius $r$ around mass $M$:

Concept

$\text{KE} = \tfrac{1}{2}mv_{\rm orb}^2 = \frac{GMm}{2r}$ $\text{PE} = -\frac{GMm}{r}$ $\text{Total } E = \text{KE}+\text{PE} = -\frac{GMm}{2r}$

Binding energy = $|E| = \frac{GMm}{2r}$ (energy to send to infinity at rest).

Common Confusions

• Total energy is NEGATIVE for bound orbits.
• |PE| = 2 × KE (virial theorem for inverse-square).
• Binding energy is positive.

Key Takeaways

• KE = $-E$, PE = $2E$, total = $E < 0$.
• To raise orbit, must add energy (paradoxically, increases r but decreases speed).