|MadSci Network: Astronomy|
The short answer: the planets of our Solar System move in their own circular orbits because of gravity.
The long answer involves the origin of the Solar System. Before I get into that, keep in mind that there are huge numbers involved here. The Solar System is about 15 billion kilometers across, and the Sun accounts for ninety-nine percent of the total mass of the Solar System. There's a lot of empty space between the planets. But it wasn't always like that.
The Solar System began as a nebula (a cloud of interstellar gas thousands of times larger than the current Solar System) which, beginning almost five billion years ago and continuing for about one hundred million years, collapsed into the Sun and all the planets. For another five hundred million years after that, there was a period of "bombardment"---collisions between protoplanets, asteroids, comets, and other debris flying around inside the collapsing nebula. Anything in an unstable orbit either flew off into space or destroyed itself in an impact with some other object, so the only objects left in the Solar System were those which occupied stable, unmolested orbits.
To answer why the planets move in circular orbits around the Sun, we'll need to take a closer look at how the Solar System formed.
Start with a relatively "smooth" and static nebula. Disrupt it with, for example, the shockwave from a nearby supernova (the explosion of a dying star), and the nebula starts collapsing inward upon itself.
As the nebula collapses, it compresses in the center, where a "protostar" forms---this will grow and become the Sun. Now there's a large mass at the core of the nebula, and gravity accelerates all the surrounding matter towards the core.
The nebula was already moving, rotating very slowly around its center of mass. [It's extremely unlikely that this nebula would have had exactly zero motion.] Conservation of angular momentum causes this rotation to become faster, and the omnidirectional nature of gravity pulls the gas into a roughly spherical shape, as the nebula shrinks in size. [Conservation of angular momentum is also responsible for a skater twirling faster as she pulls her arms around her.]
Because the original disruption wasn't uniform, "lumpy" local regions have developed in the collapsing nebula. These areas of higher density begin accreting matter and will later form into planets, asteroids, comets, and other objects.
Meanwhile, the competing forces associated with gravity, gas pressure, and rotation cause the nebula to flatten out---ending up like a spinning compact disc with a bulge (the protostar) in the center. So all the mass, and therefore all the planets, end up in the same "ecliptic plane" (except for Pluto, which was probably perturbed into its skewed orbit by a collision during the bombardment era).
When the dust clears (pun intended), we're left with the Solar System as we know it today.
For more information on Solar System creation:
Hope this helps!
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