The German mathematician, Johannes Kepler
analyzed the data resulting from the
observations of the Danish astronomer Tycho Brahe. He
summarized
his findings in three laws. 



Law 1 

Each planet orbits the sun in an elliptical path, with the sun at
one focus of the ellipse. 



The elliptical orbits are not very eccentric; they are very
nearly circular. 

To simplify calculations, we often consider them to
be circular. 



Law 2 

A line from the sun to the planet sweeps out equal areas in
equal times. 




If the planet takes the same time to go from a to b as to go
from c to d, then the areas, A (shown in blue) will be equal. 



This reminds us that the speed of a planet is greater
when it is nearer the sun. 



This law can be shown to be a direct consequence of the law of
conservation of angular momentum. 



The ellipse in this diagram is much more eccentric than
the orbits of the real planets. 



Law 3 

The square of the time period of the planet's orbital motion is
proportional to the cube of its mean distance from the sun. 



This law can be stated as 



It is (perhaps surprisingly) easy to explain this law using Newton's law of
gravitation. 
