# Celestial mechanics according to Kepler

The German astronomer and mathematician Johannes Kepler owes, in the seventeenth century, the creation of the laws on the movement of planets in their orbit around the Sun. Having studied most of the existing theories, from Pythagoras to Copernicus, passing by Ptolemy's geocentrism, Kepler developed modern laws of planetary orbits with his own physical principles.

He collaborated closely with the official astronomer of the German empire Tycho Brahe, who owned one of the best astronomical observation centers of the time. After Brahe's death, Kepler took all his writings.

It was then, from the data collected by Brahe, that Kepler had to disregard his adherence to the theories of the celestial spheres and test new geometric combinations that explained the movements of the planets, especially the retrograde movement of Mars.

After trying and rejecting all kinds of combinations with circles, he tried to explain the celestial mechanics with ovals, but it was useless. He finally opted for ellipses, which finally led him to define his three famous laws.

## Kepler's three laws

Kepler's first law ensured that "each planet moves around the Sun in an orbit that is an ellipse, in which the Sun is one of its foci." With this law Kepler got the scientific facts to precede his religious desires and prejudices about the nature of the world. From then on Kepler devoted himself solely to observing the data and drawing conclusions without preconceived ideas.

After checking the speed and movement of the planets through the orbits, he reached his second law: "A straight line that joins the Sun and a planet covers equal areas at equal times."

Kepler's third and final law makes a quantitative relationship between the orbital periods of the planets and the size of their elliptical orbits: "The squares of the periods of the planets are in direct proportion to the cubes of the semi-major axis of their orbits."

Much of the work done by Kepler would not have been possible without the contributions of Galileo, who thanks to his rudimentary telescope discovered Jupiter's satellites, the phases of Venus or sunspots, among other major milestones of Astronomy.

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