YES, and there are even classification schemes for galaxies too!

PLANETS:

Contrary to what you might hear in science fiction programs such as 'Star Trek', astronomers don't classify planets as finely as what the fictional universe suggests. We just don't have enough different examples to require that level of sorting out. In our solar system, we recognize the 'Outer Planets' which are Jupiter, Saturn, Uranus, Neptune and Pluto. We recognize the 'Inner Planets' which are Mercury, Venus, Earth and Mars. There are also various distinctions made on the basis of whether the planets are mostly gaseous like Jupiter, Saturn, Uranus and Neptune. Rocky like Mercury, Venus, Earth and Mars. Some also add the satellites of the major planets to this list and then further distinguish the primarily icy bodies such as Pluto, Ganymede, Callisto and so on. The problem is that ALL of the major bodies are different from each other in important ways so that each body would be its own unique classification.

As for the minor bodies in the solar system such as asteroids, they do have a slightly more complicated classification scheme according to their composition and place of origin. There are Iron, Stoney and Carbonaceous asteroids ( and meteors!). Some are even identified according to place of origin such as Lunar or Martian ( yes, a very few of the meteors found in antarctica have been identified as originating on the surface of Mars!). Of all the astronomical bodies, stars have by far the most complex classification scheme.

STARS:

For almost a century, astronomers have classified stars on the basis of their temperatures according to the scheme. They began with the 26 letters of the alphabet, but then discovered that many of these categories were duplicative, or made better sense in a diffeent order. The result is:

O....B....A....F....G....K....M

With O-type stars being the hottest with temperatures above 20,000 K and M- type stars being the coolest with temperatures near 2500 K. In most introductory astronomy courses, students are asked to find a pithy mnemonic to remember this sequence such as 'Of Berkeley Astronomers, Few Give Kind Marks".

There are also three other major classifications added to this: R...N...S. Once astronomers began to use spectroscopy to study stars, they decided to add 'sub-types' to this list running from 0 to 9 so that the sun became a 'G2' star. In addition to their temperature, stars differ in their luminosity so astronomers add a Roman numeral luminosity classification to each spectral classification:

I.....Supergiant Stars...like the bright star Betelgeuse in Orion (M2 I)

II.....Bright Giant Stars...like the star Beta Centauri ( B1 II)

III...Giants...like Pollux in Gemini (K0 III)

IV....Sub-giants...like Menkent in Centaurus (K0 IV)

V.....Main Sequence...like our own Sun (G2 V)

VI....Sub-dwarfs...like Tau Ceti (G8 VI)

VII...White dwarfs...like Sirius B

Some stars are also indicated by additional sub-classifications such as, for example, 'e' = emission line star, 'p' = peculiar spectrum, 'm' = metallic line star or 'n' = nebulous lines. As an example, the star Saiph in Orion is a B0.5e I star meaning it looks like a regular B0.5 I supergiant but has emission lines of certain elements in its spectrum.

There are also many different classifications for white dwarfs, variable stars and other kinds of objects in addition to spectral type.

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