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Originally Posted by Peter Wilson
How does that not define planets around other stars?
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What you've quoted is not what the IAU has decided.
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RESOLUTION 5A
The IAU therefore resolves that "planets" and other bodies in our Solar System, except satellites, be defined into three distinct categories in the following way:
(1) A "planet"1 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.
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Sun with a capital S is
our sun. The definition only applies to objects in our solar system.