This is the Greek model. With the earth in the centre, each planet labeled P will revolve in a perfect circle around a Centre which will in turn revolve in a perfect circle around the Earth, as shown below. My guess for their idea of a perfect circle was to make the orbit, well, ‘perfect’.

While this theory was in only in thought at that time, Ptolemy solidified this theory in his massive treatise Almagest in the second century A.D., calling this theory the Ptolemaic system.

It was only much later in 1543 that Polish astronomer Copernicus came in and abolished this theory and proposed that the sun was in the centre of the solar system with the earth revolving around it, a heliocentric system. Since this reasoning redefined the idea of the Earth being in the centre and of celestial bodies in general, Copernicus was under fire from the church. Nevertheless, after much perseverance he managed to publish his work On the Revolution of the Celestial Spheres which paved the way for further scientist and astronomers to develop on this heliocentric system. Copernicus formed the ground for the today’s understanding of astronomy.

ERRATA: In the video, I mentioned Ptolemy was the one who thought of the heliocentric system. I was wrong. It was Copernicus, not Ptolemy. Please accept my sincere apologies.

And now comes our famous hero Johannes Kepler. A student of Tycho Brahe, he took great masses of data they collected, worked on them for 20 years to formulate three elegant laws which govern planetary motion:

1. The orbit of each planet is an ellipse with the sun at one focus.
2. The line segment joining a planet to the sun sweeps out equal areas in equal times.
3. The square of the period of the revolution of a planet is proportional to the cube of the semimajor axis of the planet’s elliptical orbit. That is, if T is the time required for a planet to make one complete revolution about the sun and a is the semimajor axis, then the ratio  is the same for all planets in the solar system.

When Kepler created these laws, they were simply statements that fitted in the data he had with no way of finding the theory or principle that could explain such laws.

Then came Sir Issac Newton and his theory of universal gravitation which briefly put is that two particles of matter in the universe attract each other with a force directed along a line between them of the magnitude

,

This one law provided an understanding to Kepler’s law. Newton published this theory of his in this treatise Principia Mathematica which is perhaps the greatest of all scientific treatises and sparked development on the science of physics and astronomy to what we have now.

We at Gaussian Math will attempt to use Newton’s universal law of gravitation, with the help of Calculus, to prove Kepler’s Laws, which is by no means an easy feat. I hope you participate with us in this exciting ride.