What is the official difference between a planet and a dwarf planet? I'm trying to understand how objects are classified as planets, moons, or dwarf planets. Can someone please explain the differences between them? I'm really curious about why Pluto is a dwarf planet, for example. 
 A: Planets are define as gravitationally round bodies that orbit the sun and have cleared their orbital region. In other words, the only bodies that will cross a planet's orbit are temporary transits (i.e. comets) or bodies that are gravitationally controlled by the planet (moons & smaller bodies in orbital resonance with the planet). This resonance requirement includes trojan asteroids, so the previous answer is incorrect in this regard.
Pluto is locked into a 3:2 orbital resonance with the far more massive Neptune, as are other nearby objects in the Kuiper Belt.
This is why Pluto is not classified as a planet, but rather as a dwarf planet.
Please note that the IAU classification of planets applies only to our Solar System as not enough information was known in 2005 about the orbital dynamics of other planetary systems.
A: 
The definition of planet set in 2006 by the International Astronomical Union (IAU) states that, in the Solar System, a planet is a celestial body which:
  
  
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*Is in orbit around the Sun,
  
*Has sufficient mass to assume hydrostatic equilibrium (a nearly round shape), and
  
*Has "cleared the neighbourhood" around its orbit.
  
  
  A non-satellite body fulfilling only the first two of these criteria is classified as a "dwarf planet". 

(from http://en.wikipedia.org/wiki/IAU_definition_of_planet)
The IAU has come up with this definition. It probably won't be revised for quite some time. The reason that Pluto fails as a major planet is because it has not "cleared its neighborhood."  Pluto's orbit crosses that of Neptune, a vastly larger body. Pluto also shares its orbit with the Kuiper belt, a swath of small icy bodies beyond Neptune.
A moon is usually understood to be a natural body that orbits a planet, be it major (e.g. Earth), minor (e.g. Pluto), or extra-solar (although no extra-solar moons have been detected at the time of this posting).  However, the IAU has not yet formally defined a moon.
Sticky situations and possible future revisions/extensions for the definition of a planet-


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*Binary planets- Pluto and Charon are so close in mass that it is more accurate to say that they both more orbit a point in space between them, rather than Charon strictly orbiting Pluto. Put more technically, the barycenter of the Pluto/Charon system lies outside the most massive body. The term binary planet is now informal, but could become official some time in the future.

*How round? The second bullet point in the IAU definition of a planet is that a planet must be in hydrostatic equilibrium, but at the smallest end of the planet spectrum, this gets a little bit blurry. They may have to attach some kind of number to it someday.

*Exoplanets As of right now, this only applies to our own Solar system, with "exoplanet" being an entirely separate category. Aside from human prejudice for good ol' Sol, this is silly. There should be one, universal definition. (IMHO)

*Brown dwarfs New observations are making it clear that objects may exist ranging smoothly from Jupiter, an undisputed planet, right on up to objects that are indisputably stars. Where do we draw the line? Nowhere is that mentioned. Transitional objects are fuzzily known as brown dwarfs.

*Trojan asteroids If you want to get really finicky about it, even Earth, Mars, Jupiter, and Neptune might not qualify as major planets, either. They all have a significant number of asteroids orbiting the Sun locked into orbital resonances at their orbital radii- they may be dominant at their radii, but some people grumble at the wording of the "cleared their neighborhood" criterion.
[Note: a previous edit cited the 3:2 resonance between Pluto and Neptune as evidence for why Pluto is not a planet; however, the IAU definition does not list a secular orbit (i.e. lack of resonance) as a criterion for being a major planet, so an orbital resonance per se is not disqualifying.  In fact, many known planets and other bodies in our solar system are in or have been in similar orbital resonances. Jupiter and Saturn are thought to have been in resonance in the past, and Jupiter's Galilean moons are in a 1:2:4 resonance.  Additionally, we know of extra-solar planets in multiple systems, such as the Kepler-11 system, that are in resonance.]
A: A dwarf planet is a minor planet that is round, so it does not dominate its orbit like a real planets do. If an object is more massive than other objects near its orbit and it is gravitationally dominating, then it is called a planet. Otherwise it is a minor planet, if it is not a comet (comets do follow orbits that make their surface ices sublimate when they are close their stars). Round non-dominant objects orbiting a star are called dwarf planets. Actually a dwarf planet is any minor planet or comet that is round. It can also be said that a dwarf planet is any round object that is less massive than other objects near its orbit combined. Round moons are not dwarf planets, because they do not orbit star directly. IAU only wrote about objects orbiting the Sun, but I'm trying to write more generally.
