Kepler's Laws

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Culture & Science - Science
Wednesday, 20 October 2010 03:28

The discovery of the reality of the orbital motions of the planets and the evolution of his theory was made in the sixteenth and seventeenth centuries, and was one of the most fascinating in the history of the development of human thought.


The first to set out the exact scenario of planetary orbits was Johannes Kepler. As a starting point meant that the Sun was the center of the system. Kepler determined the orbit of the planet Mars and found the solution step by step: the planets move on circular orbits as they all insisted on hold, but in elliptical orbits.

Kepler summarized his findings in three fundamental laws of celestial mechanics and orbital movements of celestial bodies:

1) Kepler's First Law: Planetary orbits are ellipses in which the Sun occupies one focus.

The difficulty in reaching this conclusion comes mainly from that, in general, the orbits of the planets have very small eccentricities, ie are almost circular. The only exceptions are the orbits of Mercury and Pluto, which at the time of Kepler, were unknown. The distance from Earth to the Sun never changes by more than 2 million kilometers above the 150 million km away form the media.

The eccentricity of the orbit of Mars is slightly higher than this value: distance from the Sun ranges from 204 million km when the planet is at perihelion and about 250 million miles when it is at aphelion. This feature on Mars was the one that favored the discovery of Kepler.


2) Kepler's Second Law: The areas described by the radius vector in equal times are equal.

Vector radio means the imaginary line connecting the center of the Sun with the planet's center. For a planet that describes an elliptical orbit, it does mean that the orbital speed will vary with the position of the planet in orbit: the velocity is maximum at perihelion, ie when the planet is closer to the Sun and more influenced by attraction, and minimum at aphelion, when the planet is farthest removed from the Sun

An extreme case to illustrate this law is what gives us the orbit of a comet long period, highly eccentric orbits. At perihelion, the comet gets close to 500,000 km from the Sun, its velocity is then maximum and the order of 500 km / sec (!), Which allows you to describe an arc of 180 degrees around the sun in a few hours while he needs a million years to go the other side of its orbit from the Sun, when, at aphelion, its speed would fall to the 1 cm / sec, ie 36 m / hour.


3) Kepler's Third Law: The square of time of revolution of a planet around the Sun is inversely proportional to the cube of the semi-major axis of the elliptical orbit.

This law allows be a representation of the solar system if you know the times of revolution of the planets. As a unit of distance is used the average distance between Earth and the Sun, ie the astronomical unit. This representation is only a model of the system at a given scale until it has determined the unit of length in kilometers.

Astronomers have made great efforts, since the laws of Kepler were accepted unanimously, to determine accurately the astronomical unit , which is about 149,597,870 km.

Beyond the great discoveries of Kepler, who opened the doors to a new astronomy , it took Newton's subsequent findings to completely determine the orbits of the planets.

Sources: The orbs of heaven, or, The planetary and stellar worlds , National Illustrated Library, 1851 / Focus, Technique and Material, Editorial Argos, Barcelona / Cornelius, G.: Manual of the heavens and their myths, Blume, 1998

Images: Kalipedia