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Kepler's Laws

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Kepler's Laws - Lesson Summary

The configuration and motion of the earth, the sun and the other planets in the solar system was debated for ages till Ptolemy, a Greek scientist, put forward his geocentric theory. His theory stated that the earth is at the centre of the universe, and that the planets, stars and the sun revolve around the earth in circular orbits. Later, Copernicus, a Polish monk, put forward his heliocentric theory,  which stated that sun is at the centre of the solar system, and that all the planets, including the earth, revolve around it in circular orbits. And then Johannes Kepler, building on the work by Tyco Brahe, formulated the three famous laws of planetary motion that have been named after him. They are the Law of Orbits, the Law of Areas and the Law of Period


Kepler’s first law, the ‘ law of orbits’, states that all the planets revolve in elliptical orbits with the sun at one of the focii of the ellipse (path of the planets).
 
Observe the figure of ellipse. Points F 1 and F 2 are called the focii, and ‘O,’ is the centre of the ellipse. For any point ‘P’ on the ellipse, the sum of the lengths PF 1 and PF 2 is constant. So, as per the first law, the sun is at one of the focii of the ellipse and the planets rotate around it in elliptical orbits. Also the sum of the lengths PF 1 and PF 2 is always constant.


Kepler’s second law of planetary motion is the ‘ law of areas’. According to this law, the line joining the sun and a planet, sweeps equal areas in equal intervals of time. Consider a planet revolving around the sun.
 
Let ‘P 1’ and ‘P 2’ represent its positions at the start and end of 30-day duration. Let A 1 represent the area swept during this period. Similarly, let ‘P 3’ and ‘P 4’ represent two positions of the planet during its revolution for a 30-day duration represented by A 2. According to Kepler’s second law of planetary motion, area A 1 equals area A 2. The concept of Kepler’s second law can be understood by the fact that the angular momentum of the planet revolving in its orbit remains constant. This is because it is under the influence of a central force.
 
The force of attraction pulls the planet towards the sun and the magnitude depends on the distance between them. For a body under the action of a central force, the angular momentum, ‘L’, which is the product of ‘mvr,’ remains constant. Where, ‘r’ is the radius vector; ‘v’ is the velocity vector and ‘m’ the mass of the body.
 
 
 
 
 
 
 
 
 
Kepler’s third law



Kepler’s third law of planetary motion is called the ‘ law of periods’ According to this law, the square of the time period of a planet is directly proportional to the cube of the semi-major axis of its elliptical orbit. That is, T squared is proportional to R cubed, where T is the time taken by the planet for one rotation and R is the length of the semi-major axis of its elliptical orbit. Kepler’s laws revolutionised the field of astronomy and have helped people understand the configuration and movement of planets better.

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