A satellite is in a circular Earth orbit of radius r. The area A enclosed by the orbit depends on `r^2` because `A = pi r^2`. Determine how the following properties of the satellite depend on r. (a)period, (b) kinetic energy, (c ) angular momentum, and (d) speed.

Explanation

To determine how the properties of a satellite in a circular orbit depend on the radius \( r \), we will analyze each property step by step.

### Step-by-Step Solution

**(a) Period (T)**

According to Kepler's Third Law, the square of the period \( T \) of a satellite is directly proportional to the cube of the semi-major axis (which is equal to the radius \( r \) for a circular orbit). Mathematically, this can be expressed as:

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