Monday, March 21, 2011

Kepler's laws of planetary motion


From ancient times, humans have observed the movements of the planets, stars, and other celestial objects. In ancient history, these observations led scientists to regard Earth as the center of the Universe because of the movement of the rotation of the earth. This geocentric model was elaborated and formalized by the Greek astronomer Claudius Ptolemy(100 AD  - 170 AD) in the second century and was accepted for another 1400 years.
Ptolemy's law of planetary motion



 In 1543, Polish astronomer Nicolaus Copernicus (1473-1543) suggested that that the Earth and other planets revolved in circular orbits around the Sun(heliocentric theory). But no one believed him. The King was so angry with him that he killed Copernicus by slow poisoning.
Nicolaus Copernicus


German astronomer Johannes Kepler, who was Brahe's assistant for a short while, before his death,spent 16 years trying to deduce a mathematical model for the motion of the planets. Such data were difficult to sort out because the moving planets are observed from the moving Earth. After many laborious calculations, Kepler found that Brahe's data of the revolution of Mars around the Sun, led to a successful model.

Johannes Kepler


Kepler completed his analysis and summarized into three parts known as ''Kepler's laws of planetary motion''.
They are: 



  1.       All planets move in elliptical orbits around the Sun at one Focus.


  2.       The radius vector drawn from the Sun to a planet sweeps out equal areas in equal time intervals.

  3. The square of the orbital period of any planet is proportional to the cube of the semi-major axis  of the elliptical orbit.






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