Using dimensional analysis, show that the planets obey Kepler's th

Question

Using dimensional analysis, show that the planets obey Kepler's third law.

18 Feb 2025

Answer :

Word Count : 197

To demonstrate that planets obey Kepler's third law using dimensional analysis, we start with the gravitational force between a planet and the Sun, given by Newton’s law of gravitation:

\[
F = G \frac{M m}{r^2}
\]

where \(F\) is the gravitational force, \(G\) is the gravitational constant, _____ ____ ___ _______ ____ _________ _______.
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