Question

Kepler's third law of planetary motion when stated for circular orbits, has the form (v = orbital velocity of a planet and r = distance from the sun)

Answer 1

Kepler's third law is the square of its period of revolution around the sun is directly proportional to the cube of mean distance of a planet from the sun

Answer 2

Answer:

v²∝1/R

Explanation:

Given:

Orbital velocity of the planet = v

Distance from the Sun = R

We have to find the relation between v and R from Kepler's third law of planetary motion for circular orbits.

For circular orbits, Kepler's third law states that square of time period of the planet is proportional to the cube of the radius of circular orbit (with Sun at centre).

T²∝R³

T²=4π²R³/GM -------------> 1

where,T²=4π²R³/GM  is proportionality constant.

As the planet is revolving in a circular path, time period can be written as

T=2πR/V -------> 2

From 1 and 2,

4π²R²/V² = 4π²R³/GM

Solve it, you'll get my answer. v²∝1/R

Hope my explanation is clear.