What is a scientific definition for a planet?

Answer 1

The official definition decided by the International Astronomical Union (IAU): a planet is a body that orbits the Sun, is large enough for its own gravity to make it round, and has "cleared its neighbourhood" of smaller objects.
This definition only applies to our solar system, not extra-solar systems.

Answer 2

Well, there's the thing... there really isn't one, which is why all the Pluto hoo-haa.

I saw Dava Sobel speak (she was on the "Pluto committee"), and she explained what a mess it was. The accepted definition USED to be something equal to or bigger than the size of Pluto but smaller than Jupiter, but then they found half a dozen lumps of debris floating around the sun that weren't known when they decided that but which met that criterion. She was hilarious.

Answer 3

The International Astronomical Union defines "planet" as a celestial body that, within the Solar System,[1]

(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 neighborhood around its orbit;

or within another system,[2]

(i) is in orbit around a star or stellar remnants;
(ii) has a mass below the limiting mass for thermonuclear fusion of deuterium; and
(iii) is above the minimum mass/size requirement for planetary status in the Solar System.

also
In 2003, The International Astronomical Union (IAU) Working Group on Extrasolar Planets made a position statement on the definition of a planet that incorporated a working definition:[2]

1) Objects with true masses below the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 Jupiter masses for objects of solar metallicity) that orbit stars or stellar remnants are "planets" (no matter how they formed). The minimum mass/size required for an extrasolar object to be considered a planet should be the same as that used in our Solar System.
2) Substellar objects with true masses above the limiting mass for thermonuclear fusion of deuterium are "brown dwarfs", no matter how they formed nor where they are located.
3) Free-floating objects in young star clusters with masses below the limiting mass for thermonuclear fusion of deuterium are not "planets", but are "sub-brown dwarfs" (or whatever name is most appropriate).