**Motion Under Central forces (series List)**

Introduction

Equation of motion under central forces

Law of conservation of angular momentum

Law of conservation of energy

Equation of motion (equation of path of moving particle)

Form of motion under the effect of 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., $a^3$

$$\Rightarrow \quad t^2 \propto a^3$$

## Newton’s Conclusion from Kepler’s Law