## General Knowledge on Kepler Laws of Planetary Motion

Kepler was a great astronomer and physicist from Germany. His theory about planetary motion open a new revolutionary direction in the field of physics.

He formulated three famous laws on the motion of any planetary object.

The laws are –

`1.>`

All planets in our solar system revolve around the sun in elliptical orbits. The sun will remain rest at one of the foci of the elliptical orbit.

`2.>`

The line joining a planet to the sun i.e., the position vector or radius vector traces out equal areas in equal times. In other words the areal velocity of the radial vector is constant.

`3.>`

The square of the period of revolution of the planet round the sun is directly proportional to the cube of the major axis of the ellipse which the planet describes.

### Explanation of Three Kepler’s Laws :

The revolution of planets occurs due to the gravitational force between the sun and planets. Though we assume that all the planets move around the sun along a circular path for simple calculation, it is not practically correct. Actually all the paths are elliptical. For ellipse there are two axes, one is semi-major axis and the other is the semi-minor axis.

From the above figure, we can see that the red line (a) is semi-major axis and the yellow (b) line is the semi-minor axis. F_{1} and F_{2} are two foci. The sun is situated on one of its focus (F_{1}).

The radius vector (the blue line from the figure) swipe out equal area in equal time. Let the planet moves from point P to point Q in a fixed interval of time and The amount of area is swiped out. Again it moves from point R to point S in that fixed interval of time, and B amount of area is swiped out by it. Then from Kepler’s law of motion the area A will be equal to area B.

If T is the time period of the planet i.e., time is taken to complete one revolution, and R is the radius vector (the line joining sun and planet) then, according to Kepler’s third law of motion, we can express as –

T^{2}∞ R^{3}

From the above expression it is clear that, when the planet is located far from the sun, the time period is smaller. This means that the planet will move with less velocity. And when the planet is near to the sun, the velocity is greater.

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