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Where are these asteroids you speak of?

There are three large groupings of asteroids in our Solar system, one of which can be further subdivided into three families. The first is the Near Earth Asteroids. As their name would suggest, these are close to the Earth, astronomically speaking, ranging from 0.3 to 1.3 AU (approximately 50 to 200 million kilometers) away from us. Their orbital periods further divide them into the Atens, Amors, and Apollos. The remaining asteroids can be found in a large belt between the orbits of Mars and Jupiter, and in two groups that lie along the Jovian orbital path, at the LaGrangian points.

Here we have a basic map of the Solar System out to Jupiter, showing the orbital regions of the Asteroids. The Trojan asteroids seen at two equidistant points along the Jovian orbital path proved the existence of LaGrangian points, sets of 5 locations in every two body system where the opposing gravitational attractions balance out, and objects are able to maintain a steady position with little energy input.

Near Earth Asteroids

This is an illustration of the three families of Near Earth Asteroids. The Apollos have highly eccentric, near Solar, Earth-crossing orbits. The Amors have orbits that cross that of Mars, but not Earth, and are believed to have originally been Apollos whose orbits were altered by Mars' gravity. The Atens orbits lie largely within the orbit of the Earth, and may be Earth-crossing.

Near Earth Asteroids

There is one more group of asteroids in our solar system; the Centaurs. They were named such due to their "half comet, half asteroid" nature. They orbit in the space between Jupiter and Neptune, and their orbits cross those of the gas giants. Because of this, their orbital characteristics change frequently. Their composition is thought to be more like the Kuiper Belt objects (chunks of frozen methane and other gasses), than that of the asteroids of the inner Solar system. In the picture, the Centaurs are represented by the orange dots.