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
