**15 May is reserved to Johannes Kepler**On this day 1618 Johannes Kepler rediscovered his 3rd Law of Planetary Motion.

*After I had discovered true intervals of the orbits by ceaseless labor over a very long time and with the help of Brahe’s observations, finally the true proportion of the orbits showed itself to me. On the 8th of March of this year 1618, if exact information about the time is desired, it appeared in my head. But I was unlucky when I inserted it into the calculation, and rejected it as false. Finally, on May 15, it came again and with a new onset conquered the darkness of my mind, whereat there followed such an excellent agreement between my seventeen years of work at the Tychonic observations and my present deliberation that I at first believed that I had dreamed and assumed the sought for in the supporting proofs. But it is entirely certain and exact that the proportion between the periodic times of any two planets is precisely one and a half times the proportion of the mean distances.”* With these words Johannes Kepler announced, in his usual overblown flowery style, his third law of planetary motion in the fifth book of his Harmonices Mundi.

While Kepler published his first two laws in 1609, the third law was published ten years later in 1619. Now it was known that the orbital period, the time taken by the planet to make one complete orbit around the sun, was lower for the planets closer to the sun than those farther away from the sun. Planet mercury, for example, is named after the Roman God Mercury who was the messenger of the Gods. Mercury circles around the sun in a mere 88 (Earth) days. Pluto, on the other hand, revolves around the sun in 246 years!

Kepler's third law finds the underlying pattern in these orbital periods and states:

*The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit.*In other words, if T is the orbital period of the planet and D be its distance, T2 ∝ D3.

To explain simply, consider Earth. Earth is at a distance of 1 a.u. (1 a.u. = roughly 150 million km) from the sun and revolves in 1 year around the sun. Jupiter is about 5.2 a.u. from the sun.

If T is the orbital period of Jupiter, then...

T2 should be close to the 5.23 ≈ 140.

And what number squared is roughly 140? 11.8. And sure enough, Jupiter's orbital time is 11.8 years.

References:

http://www.physicsclassroom.com/class/circles/Lesson-4/Kepler-s-Three-Lawshttp://www.mayankacademy.com/sci101/keplers_laws_of_planetary_motion/http://csep10.phys.utk.edu/astr161/lect/history/kepler.html #history #physics #astronomy #kepler #lawsofplanetarymotion