kepler's 3rd law

Question

Kepler's third law states T² is proportional to?

RankGuru · Accepted Answer

1. **Kepler's Third Law (Law of Periods)**: The square of the time period ($T$) of revolution of a planet around the sun is proportional to the cube of the semi-major axis ($r$) of its orbit.
2. **Circular Case Derivation**: $\frac{GMm}{r^2} = m \omega^2 r = m (\frac{2\pi}{T})^2 r$.
3. **Rearrange**: $T^2 = (\frac{4\pi^2}{GM}) r^3$.
4. **Conclusion**: $T^2 \propto r^3$. This implies that planets further from the sun take longer to complete an orbit.

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kepler's 3rd law

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