# Kepler

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Vectorial Calculus Project
Juan Camilo Carrillo,Daniel Eduardo Ram´ ırez, Fabi´n S´nchez Garc´ a a ıa,Daniel Woodcock Guerrero Laws of Kepler’s Vectorial Calculus Department of Basic Sciences St.Thomas University Bogot´ a
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Kepler’s Laws Of Planetary Motion
Posted in: Guide to Space by Jerry Coﬀey (Comments Oﬀ)

Figura 1: Kepler’s Laws

Kepler’s Laws Of Planetary Motion werewritten by Johannes Kepler between 1609 and 1619. He based his ﬁrst two laws(published in 1609) on the observations of Danish astronomer Tycho Brahe. All of these laws give approximate descriptionsof the motion of the planets around the Sun. There are three Kepler laws: The orbit of every planet is an ellipse with the Sun at one of the two foci, A line joining a planet and the Sun sweeps outequal areas during equal intervals of time, and the square of the orbital period of a planet is directly proportional to the cube of the semi-major axis of its orbit(this last was published in 1619).Kepler’s laws challenged the two major theories of the day. First, it challenged geocentrism by proving that the Earth orbited the Sun. Secondly, it challenged the theories of Copernicus. WhileCopernicus favored the heliocentric view, he thought that orbits were circular and had epicycles. These laws combined with the mathematical equations of Sir Isaac Newton are the foundation of modern astronomy.Kepler was considered to be quite the radical. He challenged the notion that orbits were circles, yet a circle is a form of ellipse. Most of the planets follow orbits of low eccentricity, so they can2

Vectorial Calculus Project: Laws of Kepler’s

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be closely approximated to a circle. The result is that it is not immediately evident that orbits are elliptical. Detailed calculations byKepler, for the orbit of the planet Mars, indicated its elliptical shape. From that work he inferred that other heavenly bodies have elliptical orbits, also. In this way he allowed for highly...