Step 1:
We start with Kepler's third law, which states that the period of an orbit is given by the formula:
\[T = 2\pi \sqrt{\frac{r^3}{GM}}\]
where:
- \(T\) is the period,
- \(r\) is the radius of the orbit,
- \(G\) is the gravitational constant, and
- \(M\) is
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