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I have looked in several astronomy texts, and they pretty much agree
that the asteroids are material that never quite got together to form a planet.
Many astronomers believe that the early solar system was a swirling cloud of
dust and gas. Sometimes particles of dust would collide and stick together; even tually, through many
such chance collisions, some of these clumps would be big enough to
gravitationally attract other nearby bits of dust, getting bigger yet. These
clumps are called planetesimals, and the process I've described is called accret ion. You can imagine that
eventually some of the planetesimals would get big enough to absorb most of the
other stuff in their orbit, finally leaving perhaps only one (maybe some smaller
ones survive as moons). But in the case of the asteroids, Jupiter's gravity prev ented this
accumulation from going to completion, leaving several small bodies instead of
one big one. That's the theory, anyway.
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