Planet - This 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 nearly round shape (due to a hydrostatic equilibrium);
and
(c) has cleared the neighborhood around its orbit. As now defined, the
Solar System has eight planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn,
Uranus, and Neptune.
Dwarf Planet - This is a celestial body that: (a) is in orbit around the
Sun; and (b) has sufficient mass for its self-gravity to overcome rigid body
forces so that it assumes a nearly round shape (due to a hydrostatic
equilibrium); but (c) has not cleared the neighborhood around its orbit; and
(d) is not a satellite of another planet. As defined, the Solar System has
probably has at least one dwarf planet in the Main Asteroid Belt (Ceres),
Edgeworth-Kuiper Belt (Pluto and Eris); and Oort Cloud (possibly Sedna).
In addition, the "dwarf planet" Pluto is recognized as a prototype of a new
class of trans-Neptunian objects.
Smaller Solar System Bodies - This category collectively refers to all
other celestial bodies orbiting our Sun, Sol (including asteroids, comets,
and satellites).
Currently, the International Astronomical Union (IAU) has
recognized five
dwarf planets,
Ceres, the trans-Neptunian object
Eris (2003 UB313), Pluto, Haumea, and Makemake.