The period of revolution (T) of a planet around the sun depends upon (i) radius (r ) of obit (ii) mass M of the sun and (iii) gravi-tational constant G. Prove that `T^2 prop r^3`

Explanation

To prove that \( T^2 \propto r^3 \), we will start with Newton's law of gravitation and the concept of centripetal force. Here’s the step-by-step solution:

### Step 1: Understand the forces acting on the planet
The gravitational force acting on the planet provides the necessary centripetal force for its circular motion around the Sun. The gravitational force \( F \) between the Sun and the planet is given by Newton's law of gravitation:

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