State and prove kepler's third law of planetary motion by assuming the orbit to be circular

**Kepler’s third law of planetary motion** (Law of periods) states that the square of the time period of revolution of a planet around the sun is directly proportional to the cube of the semi major axis of its elliptical orbit i.e.

Where, T= time taken by the planet to revolve once around the sun.

R= semi major axis of the elliptical orbit.

Suppose a planet of mass 'm' revolves around Sun of mass 'M' in semi major axis 'R' then the centripetal force on planet around the Sun is provided by Gravitational force between Sun and the planet to revolve in circular orbit, i.e.

Now we know velocity of planet is,

Third law of planetary motion is proved.

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