A satellite is in a circular orbit about a planet of radius R. If the altitude of the satellite is h and its period is T, show that the density of the planet is `rho = ( 3pi )/( GT^(2)) [ 1+ ( h )/( R ) ]^(3)`

Explanation

To solve the problem, we need to derive the expression for the density of the planet in terms of the satellite's period, altitude, and the radius of the planet. Let's break it down step by step.

### Step 1: Define the orbital radius
The orbital radius \( R' \) of the satellite is the sum of the planet's radius \( R \) and the altitude \( h \) of the satellite:
\[ R' = R + h \]

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