Orbital Velocity

Question

A satellite orbits Earth at a height equal to Earth's radius R. What is the orbital velocity? (g = 10 m/s², R = 6.4 × 10⁶ m)

RankGuru · Accepted Answer

1. **Orbital Speed Formula**: $v_o = \sqrt{\frac{GM}{r}}$, where $r$ is distance from center.
2. **Distance Calculation**: Radius of orbit $r = R + h$. Since $h=R$, $r = 2R$.
3. **Using g at Surface**: $GM = gR^2$.
4. **Substitution**:
   - $v_o = \sqrt{\frac{gR^2}{2R}} = \sqrt{\frac{gR}{2}}$.
5. **Computation**:
   - $v_o = \sqrt{\frac{10 	imes 6.4 	imes 10^6}{2}} = \sqrt{32 	imes 10^6}$ m/s.
   - $v_o \approx 5656 	ext{ m/s} = 5.66 	ext{ km/s}$.

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