Orbital Velocity (near Earth)

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Satellite in circular orbit near Earth surface speed?

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1. **Centripetal Requirement**: For a satellite of mass $m$ in orbit, the gravitational force provides the necessary centripetal force.
2. **Force Equivalence**: $\frac{G M m}{r^2} = \frac{m v_o^2}{r} \implies v_o = \sqrt{\frac{GM}{r}}$.
3. **Near Surface Condition**: For $r \approx R$, $v_o = \sqrt{\frac{GM}{R}}$.
4. **Using g**: Substitute $GM = g R^2$:
   - $v_o = \sqrt{\frac{gR^2}{R}} = \sqrt{gR}$.
5. **Comparison**: Note that $v_{escape} = \sqrt{2} v_{orbital}$. For Earth, $v_o \approx 7.9$ km/s.

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Orbital Velocity (near Earth)

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