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How many planetoids have been discovered that are, say, 50% the size of Pluto or larger? Where are they?

Incidentally, what is the difference between a planet, a planetoid, and an asteroid?

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How many planetoids have been discovered that are, say, 50% the size of Pluto or larger?

At least three, though it's hard to compare their exact sizes (including Pluto's) due to the distances involved - Haumea, Makemake and Eris. Ceres (the largest asteroid) comes close to the 50% cutoff, too. There are also several candidate dwarf planets that may also qualify: Orcus, Quaoar, 2007 OR10 and Sedna.

Where are they?

All of them, except Ceres, are Trans-Neptunian Objects (TNOs) - their orbits are beyond the one of Neptune. Pluto, Haumea and Makemake are considered to be in the Kuiper Belt. Sedna's orbit takes it so far away from the Sun that it is speculated that it is an Oort Cloud object.

Incidentally, what is the difference between a planet, a planetoid, and an asteroid?

"Asteroid" and "planetoid" are somewhat synonymous - "planetoid" is used for the larger, "planet-like" asteroids. An asteroid is any Sun-orbiting body that is too small to be considered a dwarf planet (see below), too big to be a meteoroid (roughly less than a few meters across), and not a comet.

The definition of "planet" is somewhat fuzzy. The term itself comes from the Greek "planetes" - "wanderer", because the ancients recognized the fact that the planets "wander" relative to the "fixed" stars. Traditionally, it came to mean something like "any large roughly spherical body orbiting the Sun". So when Pluto was discovered in the 1930s, it got called a "planet". In the 2000s, though, the discovery of more bodies with roughly the same size (especially Eris) made the International Astronomical Union adopt the first official definition of a planet and create a new category for bodies like Pluto that didn't fulfill all requirements - dwarf planets. There are still debates whether this was the right move.

So, by "planetoid" you may mean "dwarf planet". Wikipedia has a list of the "official" ones and the known candidates: http://en.wikipedia.org/wiki/Dwarf_planet

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Thanks for the good answer! –  xpda Dec 11 '11 at 16:07
    
Suggestion: Add the IAU definitions of "planet" and "dwarf planet" to your answer. –  Keith Thompson Dec 11 '11 at 16:38
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