Kepler's Laws Of Planetary Motion

Johannes Kepler – The Story

The German astronomer, Johannes Kepler was born in the year 1571. When he was training to become a minister, he came across the work of Nicolaus Copernicus. At that time it was believed that the sun and other planets orbit the earth and not how as we know it now (everything orbits the sun!). Copernicus however, hypothesized that the earth and other planets orbit the sun. He had no proof of this though. All these theories were derided by the church in any case and as everyone knows Galileo was even thrown in jail.

With his continued work in astronomy, he impressed a Danish astronomer, Tycho Brahe, who then invited him to Prague to work with him. This wealthy Danish guy had an observatory where he kept detailed information about planetary motions. This would’ve solved the many questions Kepler had, right?

Bad luck. Brahe didn’t trust Kepler. He thought that his much smarter assistant may surpass him and become the astronomer of the age. Because of this he didn’t let Kepler access all his data. When Brahe passed away, Kepler finally had access to his data (he kind of stole it). Using this he solved the very confusing Martian problem (varying speeds and distances of the planet observed at different times) and through this formulated the Kepler’s Laws of Planetary Motion that he is famous for.

Kepler’s Laws Of Planetary Motion

  • Kepler’s First Law: Law of Orbits

The orbit of a planet about its star (the sun for our solar system), follows an elliptical path with the star occupying the position of one of the foci of the ellipse formed.

  • Kepler’s Second Law: Law of Equal Areas

If we join a planet to its star with an imaginary line, then equal areas are swept by this line in equal intervals of time.

  • Kepler’s Third Law: Law of Harmonics or Law of Periods

According to this, the square of the time period (revolution time) is proportional to the cube of the semi major axis of the elliptical orbit formed.

Write the equation \(T^{2} ~ ∝~ a^{3}\)

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Practise This Question

A sphere of mass M and radius R2 has a concentric cavity of radius R1 as shown in figure. The force F exerted by the sphere on a particle of mass m located at a distance r from the centre of sphere varies as (0r)