Geostationary Satellite

Question

What is the approximate height of a geostationary satellite above Earth's surface? (R = 6400 km, T = 24 hours, g = 10 m/s²)

RankGuru · Accepted Answer

1. **Orbital Condition**: A geostationary satellite must stay over the same spot, meaning its period $T = 24$ hours ($86,400$ s).
2. **Radius Calculation**: From $T = 2\pi \sqrt{\frac{r^3}{GM}}$:
   - $r = \left( \frac{gR^2 T^2}{4\pi^2} ight)^{1/3}$.
3. **Constants Applied**: $r \approx 4.22 	imes 10^7$ m or $42,200$ km from the center.
4. **Height from Surface**: $h = r - R_{Earth}$.
5. **Final Computation**: $42,200 - 6,400 \approx 35,800$ km. The standard value used is **36,000 km**.

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