Well, after (sometimes heated) debate, the International Astronomical Union has finally voted on the definition of the word "planet". From the IAU mirror site:
RESOLUTION 5AAt first glance, it seems as though extrasolar planets are no longer considered planets (as they do not orbit the Sun). However, the newly-accepted definition is for our solar system only: for planets orbiting other stars, substitute the words "a star" for "the Sun".
The IAU therefore resolves that "planets" and other bodies in our Solar System be defined into three distinct categories in the following way:
(1) A "planet" is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape, and (c) has cleared the neighbourhood around its orbit.
(2) A "dwarf planet" is a celestial body that (a) is in orbit around the Sun, (b) has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape , (c) has not cleared the neighbourhood around its orbit, and (d) is not a satellite.
(3) All other objects except satellites orbiting the Sun shall be referred to collectively as "Small Solar-System Bodies".
The important result of this definition is that Pluto is no longer considered a planet. It is now simply an important example of a "dwarf planet", along with Ceres, Charon, 2003UB313, and other largish bodies. We are left with eight planets in the solar system: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune.
Phil Plait suggested that the whole exercise was silly. I disagree - the term planet is a basic term in astronomy, and I can think of no other field of science for which the definition of a basic term would be considered "silly".
However, I don't know that it is really possible to come up with a cut-and-dried definition for the term planet. The boundaries for all the definitions of objects in space is kind of fuzzy. At the margins of any definition there are some objects that would be considered to belong to two categories (for instance, an object three times the size of Jupiter could be considered either a gas-giant planet or a brown dwarf star, and if Pluto had hurled Charon out of its orbit rather than capturing it as a moon, then Pluto would be a planet instead of a dwarf planet). I think that the IAU accepted this new definition just to get people to stop fighting over it.
Update, whoa there, not so fast, Bucko: According to Keith Cowing, under this definition Earth and Jupiter are no longer considered planets either. If Keith is right, then far from stopping the fighting over the definition, the IAU may have instead opened up a can of whupass on themselves.
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