# Kepler's Law of Planetory Motion

## Introduction :

• In our dairy life we have noticed things falling freely downwords towards earth when thrown upwards or dispped from some hight.
• Fact that all bodies irrespective of their masses are accelerated towards the earth mith a constant aceeleation was first recognized by galive (1564-1642)
• The motion of celesh'al bodies such as moon. earth plametes etc. and attrachieve of moon towards earth and arth towards sun is an interasting subject of study since long time.
• Now the question's what is the force that produces such acceleration is which earth attract all bodies      towards the centre and what is the law governing this force.
• Is this law is same for both earthly and weshal bodies.
• Answer to this question was given by Newton as he declared that "laws of nature are same for earthly and weshal Bodies".
• The force between any object falling freely towards earth and that between earth and moon are gowerned by the same laws.
• Johnaase kepler (1571-1631) Studied the planetary motion in detail and formulated his three laws of      planetary motion, which were available Universal law of grawitation.

## Kepler's Law :-

Kepler's law of planetary motion are :-

### (i)Law of orbits :-

Each planet revolues around the sun in an elliptical orbit with sun at one of the foci of the ellipse asd     shown in fig (a) below.

Fig (a) An ellipse traced by planet sevolary round the sun.

AO = a - Sewi major axis
BO = b - Sewi minor axis
P - hearest point between planet and sun k/as perihetion
A - farthest point between planet and sun apheiton.

### (ii)Law of areas :-

The line joining planet and the sun sweeps equal area in equal intervals of time" [fig b]

This law follows from the observation that when planet is nearer to the sun its velocity increases and It appears to be slower when it is farther from the sun.

### (iii)Law of periods :-

The squre of time period of any planet about the sun is propotional to the cube of the semi-major axis."
• If T is the time period of semi major axis a of elliptical orbit then.
T2 x a3                         (1)
• If T1 and T2 are time periods of any two planets and a1 and a2 being their semi major axis resp. then
T12 x a13 = a13
T22 x a23 a23                (2)
This question (2) can be used to find the time period of a planet, when the time period of the other
planet and the semi-major axis of orbits of two planets.