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There are three laws describing the motion of planets around the Sun. Johannes Kepler was an ardent supporter and proponent of the heliocentric theory of Copernicus, while a student and collaborator of Tycho Brahe. Kepler created the three laws of planetary motion by summarising Brahe carefully collected data of positions of planets and their movements across the sky.
Kepler?s first law:
"The orbit of each planet is an ellipse and the Sun is at one focus."
The shape of an ellipse depends on the semi-major axis (a) and the eccentricity (e), which is a measure of the flatness of an ellipse (the closer e is to zero, the more circular is the ellipse). The eccentricity of an ellipse is equal to the ratio of the length between the centre section of c and one of the foci to the length of the semi-major axis:
e = c / a



Kepler?s second law:
"The line joining a planet and the Sun sweeps out equal areas during equal intervals of time."
It follows that at perihelion (near the Sun), the planet moves faster than at aphelion (far from the Sun). It means that at the same time a planet travels further (?S) near perihelion than near aphelion.
For example for the Earth's orbit (eccentricity e = 0.01672) the linear velocity of the Earth at perihelion is 30.3 km / s, while at aphelion is 29.3 km / s.

Kepler?s third law:
"The square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit."
This is its formula:



where:
T1, T2 ? orbital periods of two planets
a1, a2 ? semi-major axis of these planets

The law follows that the larger the orbit, the longer the orbital period and that the linear velocity on an orbit is inversely proportional to the root radius of the orbit (for circular orbits).



There is also the so-called "Kepler?s fourth law", binding together the rays of the orbits of the planets. Kepler discovered the link by entering and describing spheres with a radius of appropriately selected planets on individual platonic solids. However, the orbit radii measurements were not very accurate. This Kepler?s discovery is now recognized as an interesting coincidence rather than a law of nature.

Kepler's discovery that the planets in our solar system and the moons of Jupiter circle elliptical orbits around a central body was a confirmation of the Copernicus heliocentric theory, and also a break with the Pythagorean canon assuming that the movements of the planets are monotonous and run around in circles.

Kepler's laws were an inspiration and the starting point for Newton who looked for a universal law governing the motions of bodies on Earth and in Cosmos. Based on Kepler's laws and the three principles of dynamics derived from them, Newton created the law of universal gravitation.