Systems of planets

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á The paths of the planets

"Kepler's law of areas is the first mathematical description of planetary motions that does not use uniform circular motion as building blocks." (1)

Kepler, frustrated with the behaviour of Mars, eventually concluded that its orbit was not a circle but an ellipse, with the Sun at one focus. Newton showed that elliptical orbits were a consequence of the inverse square law of gravitation. On this point, David Layzer remarks:

"If the orbit of a planet is not a circle, the force exerted by the Sun varies from point to point [along the orbit]. One of the few force laws for which all bound orbits are periodic is the inverse-square law, in which the Sun's pull diminishes as the inverse square of the distance Newton proved that for this law, and only for this law, the orbits are ellipses with the Sun at one focus." (2)

Layzer then goes on to prove this statement mathematically, and to derive Newton's form of Kepler's third law. (3)

Much later, perturbations to the calculated orbits of planets in our Solar system would be used as the basis for predicting the existence of 'new' planets, Neptune and Pluto.
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New planets

'New' planets have now been discovered outside our Solar system too á­ most of them through their gravitational effects on their parent stars. The first, and probably most bizarre, were the planets orbiting a pulsar (http://www.astro.psu.edu/users/pspm/arecibo/planets/planets.html).

However, the ones that have attracted more attention have been giant planets found from 1996 onward. One comprehensive site on extrasolar planets, regularly updated, is the Extrasolar Planets Encyclopedia (http://www.obspm.fr/encycl/encycl.html): this contains a catalogue of planet candidates, an overview of the various methods of searching, and a contact list for a number of search teams.

The new planets are interesting because of the light they can throw on the general processes of planetary system formation. So far, most of the planets found seem to be in systems quite different from our own Solar system. Comments on the implications of some of these differences can be found in this early (1996) media release from MIT - but of course this field is changing all the time.
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(1) David Layzer, "Constructing the Universe", Scientific American Books, Inc. 1984, ISBN 0 7167 5003 1, p. 51

(2) Ibid, p. 79

(3) Ibid, pp. 80-83
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