satellite period change

Question

If orbital radius doubles, period scales by factor?

RankGuru · Accepted Answer

1. **Kepler's Law**: $T^2 \propto r^3 \implies T \propto r^{\frac{3}{2}}$.
2. **Change**: New radius $r' = 2r$.
3. **Calculation**:
   - $\frac{T'}{T} = (\frac{2r}{r})^{\frac{3}{2}}$
   - $\frac{T'}{T} = 2^{1.5} = \sqrt{2^3} = \sqrt{8}$
   - $\frac{T'}{T} = 2 \sqrt{2}$.
4. **Conclusion**: The period increases by a factor of **$2\sqrt{2}$**.

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satellite period change

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