Asteroids include the rocky bodies that occupy the main asteroid belt, a field occupying the region between Mars and Jupiter, and other small rocky bodies orbiting the Sun. The main asteroid belt may be the location of a planet that failed to form; certainly the largest asteroid, Ceres, orbits precisely where predicted by Bode's Law (au = 0.4 + 0.3*m, where m is 0, 1, 2, 4, 8, 16, 32, and 64). There may be as many asteroids in the Jupiter Lagrange points (Greeks and Trojans) as in the main belt, although their composition may be closer to cometary, reflecting the huge proportion of ices available so far from the Sun. Note that Neptune's Trojan point may contain ten times again as many bodies, but these are comets.

Asteroids are remnants of the process that created the planets. As the solar nebula condensed, dust and molecules clumped together into millimeter-scale chondrules, which in turn clumped into meteoroids (up to 50 meters) and planetoids (up to a few thousand meters) in diameter. These bodies collided to create planetesimals (dozens of kilometers wide), which in turn would collide and grow into planetary embryos (hundreds of kilometers wide), which in turn collided leaving the current planets in the solar system.

The largest known asteroids (Ceres, Vesta, Pallas, and Hygiea) are considered to be planetary embryos, although their histories and compositions are quite different. Ceres is rocky and may have an icy mantle over a rocky core, while Vesta has a differentiated iron core surrounded by an olivine mantle topped with a rocky crust. An enormous crater (80% of the width of the asteroid) apparently resulted in the creation of dozens of smaller asteroids (the V-types) with similar compositions, plus the HED meteorites which all appear to be fragments of Vesta's crust. Pallas and Hygiea appear to be carbonaceous chondrites.

Asteroids in the inner belt are predominately stony types including ordinary chondrites, while the outer belt is primarily occupied by carbonaceous chondrites. This is a consequence of the thermal gradient from the hot sun outward. In the inner belt, it is warm enough that ices such as water, carbon dioxide, and methane could never condense, and (much as comets boil off their ices as they approach the inner solar system) only very limited quantities (a few percent) of these volatiles could survive long enough to be incorporated into inner-belt asteroids.

In the early solar nebula, the distance from the Sun where ice can condense to form snow or stick to dust (or larger particles including chondrules) is called the snow line. It corresponds to the temperature at which water ice is stable in vacuum, about 170 K, which occurs about 2.7 au from the Sun (near the middle of the Asteroid Belt). Friction causes the gas and dust of the nebula to slowly spiral in toward the Sun. As any given body (whether a snowflake, chondrule, or meteoroid) passes sunward of the snow line, its water begins to sublimate, and the vapor is consequently blown outward by light pressure and the solar wind. This process effectively concentrates water ice at or just beyond the snow line, and large bodies may aggregate there. Indeed, we believe that thousands of icy planetary embryos (about 10 Earth masses worth) coalesced there to form the early Jupiter, whose large gravity well then captured huge quantities of hydrogen and helium which were too volatile to condense on their own.

The huge (and growing) Jupiter exerted two main effects on the solar nebula: it stopped the in spiral of gas and dust toward the inner solar system (by absorbing it), and its gravity stirred the bodies of the asteroid belt. This prevented the collapse of the belt particles into a planet, and it thinned the belt by scattering asteroids both inward (to collide with the Sun or inner planets in the Late Heavy Bombardment) or outward into the Oort Cloud, or even to escape the solar system entirely. Consequently, our Asteroid Belt contains less than a thousandth of the mass it started with. 

There are approximately 200 asteroids with a diameter of 100 kilometers or more, and in excess of 1,000,000 asteroids larger than 1 kilometer. Still, their combined mass is only about 4% of the mass of the Moon. The volume of the asteroid belt is so large that, on average, these million+ bodies are approximately a million kilometers apart (2.5 times as far apart as are the Earth and Moon). Collisions are rare. We can speculate that smaller asteroids (and meteoroids) are much more common; there may be a billion asteroids in the 100 meter up to a kilometer size range; these would have average separations of only about 100,000 kilometers (one fourth of the Moon's distance from the Earth).

Ices are still unstable in the outer belt (pure, transparent, white snow may be stable, yet dirty snow continues to absorb sunlight and warm enough to sublimate). The ice only sublimates slowly and was present long enough that it might melt (from the heat of impacts or the decay of radioactive isotopes) allowing liquid water to interact with existing minerals to form hydrates, carbonates, clays, and the other water-bearing minerals found in carbonaceous chondrites. These asteroids of the outer belt contain up to 22% water, based on actual measurements of the water content of carbonaceous chondrite meteorites.

Further out, approaching the orbit of Jupiter, even dirty ice may be stable to sublimation, and the resulting bodies are more properly called comets, as the bulk of their mass is comprised of water ice.

The C-Type asteroids (Carbonaceous chondrites) comprise about 75% of all known asteroids. Carbonaceous chondrites are very dark, with albedos ranging from 0.03 to 0.10 (darker than charcoal), approaching soot. While named for their carbon content (typically 1% to 2% by weight), they are noted for a high content of volatiles, generally reflecting a near-solar composition (minus hydrogen and helium gasses), and have a high water content (often 10%, but as high as 22%). They often contain 25% to 30% iron, of which 5% to 15% is in metallic grains, with the remainder as oxides, sulfides, or other compounds such as olivine.

The S-Type asteroids (Stony asteroids) include ordinary chondrites plus the achondrites, less primitive asteroids that were large enough to differentiate and to undergo significant thermal and/or aqueous processing (or fragments of such asteroids). All of the V-type asteroids, for example, are thought to be fragments of the large asteroid Vesta. S-types comprise about 17% of all asteroids. They have albedos ranging from 0.10 to 0.22. There are other well-known subgroups, including the E-types (Enstatite asteroids, highly differentiated, highly reduced, named for their primary mineral), and the A-Types, composed primarily of olivine, and thought to be fragments of planetary embryo mantles.

The stony asteroids (and meteorites derived from them) are primarily composed of silicates, with the actual mineral families varying according to the asteroid type. Iron content is typically 20% to 25%, but that may primarily be as metallic iron, or as oxides, or as sulfides, or as silicates, depending upon the asteroid family. Iron content may be considerably lower in asteroids derived from highly-differentiated planetary embryos.

The M-Type asteroids (Metallic or Nickel-Iron asteroids) comprise about 10% of all known asteroids. They are mostly thought to be fragments of the iron cores of planetary embryos that were disrupted due to large collisions. As such, they are highly processed/differentiated, and are igneous rocks. Some are nearly pure nickel-iron alloy, although most have significant inclusions of graphite and silicates. Note that siderophile (iron-loving) metals such as gold, platinum, iridium, and palladium leach out of crustal and mantle minerals and concentrate in the iron cores, and thus nickel-iron asteroids are a rich source of these metals. The Pallasite meteorites have such a high percentage of olivine (peridot) that they are thought to come from the core/mantle boundaries of one or more planetary embryos. Note that a significant portion of the M-types may not be metallic, although they share spectral and albedo characteristics with metallic asteroids. For example, 22 Kalliope has only about 30% of the density of an iron asteroid. Kalliope and similar asteroids may be partly metallic and partly carbonaceous, or something else entirely.

Yes, I realize that the above percentages add up to 102%, but these are the numbers my research has most consistently turned up.

See Steve's video interview about asteroid capture at Moonandback:
Part 1
Part 2
Part 3

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