The IAU defines a Planet and Dwarf Planet thusly:
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.
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.
So interestingly, it is not its mass that makes it a “dwarf” but rather whether it shares its orbit with other objects.
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