Suppose a light planet is revolving around a heavy star in a circular orbit of radius r and period of revolution T. The gravitational force of attraction between the star and the planet is proportional to `(1)/(r^(3//2))`. Derive the relation between T and r.

Explanation

To derive the relation between the period of revolution \( T \) and the radius \( r \) for a light planet revolving around a heavy star, we will follow these steps:

### Step 1: Understand the Forces Involved
The gravitational force of attraction between the star and the planet provides the necessary centripetal force for the planet's circular motion.

### Step 2: Write the Expression for Gravitational Force
According to the problem, the gravitational force \( F_g \) is proportional to \( \frac{1}{r^{3/2}} \):
\[
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