

Johannes Kepler: the laws of planetary motion 
The planets' orbits
around the Sun are described by three laws first formulated by
Johannes Kepler (15711630), a great astronomer of the sixteenth
century. These empirical laws have been initially formulated on
the basis of astronomical observations of Mars' orbit, made by
Tycho Brahe (15461601).
Later, Isaac Newton
(16421727) demonstrated that these three laws can be obtained as
an application of the law of universal gravitation in an
approximated case (a 2body problem where the
bodies are pointlike, the Sun is still and the planets don't
interact ). To formulate this demonstration, Newton invented
the infinitesimal calculus.
Here are Kepler's three laws
and their main consequences:
Kepler's
first law : 
The picture is just an illustration, but in reality, the planets' orbits are ellipses much less eccentric (much more similar to a circle). Some important consequences of this law need to be enumerated:

Kepler's
second law: 
A very important consequence of this second law is that the planet's speed will not be constant during the orbit. In fact, due to the elliptical shape of the orbit (first law) the line joining the Sun and the planet will not be a constant distance. Since, as the second law says, the area swept by this line must be constant, this means that the speed of the motion will vary during the orbit. So, as a consequence of the first and second Kepler's laws, the planet will go faster near the perihelion and slow down when it comes near the aphelion. 

This third law implies that the period of a planet increases rapidly with the radius of its orbit: the more the planet is distant from the sun, the bigger is its major semiaxis, and the longer is its period P. This means that the farther planets of the solar system are much slower than the inner planets, and therefore have much longer years (the time it takes them to make a complete orbit around the Sun). 