# Kepler’s Law of Planetary motion (Central Forces)

## Kepler’s Law of Planetary motion

This article is about Kepler's Law of Planetary motion. This article is for B.Sc. physics first year students under the subject Mechanics.

### Kepler’s First Law

Each planet revolves round sun in an elliptical orbit such that sun is situated at one of its focus.

### Kepler’s Second Law

Area swept by line joining sun and planet per second is constant i.e., areal velocity of planet is constant.
$$\Rightarrow \quad \farc{1}{2}r^2 \frac{d\theta}{dt}=const.$$

### Kepler’s Third Law

Square of time taken by planet to revolve in the orbital motion i.e., $T^2$ is proportional to the cube of semi major axis of their elliptical orbit i.e., $a^3$
$$\Rightarrow \quad t^2 \propto a^3$$