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In the old geocentric system, in which people believed what they could OBVIOUSLY see - that the Earth was standing still and the Sun, Moon and stars traveled around the Earth - everything in the sky was fine. Well, not quite; there were five things in the sky that did not behave the way they were supposed to.

Those five things were "wanderers", or in the Greek, "planets". They did NOT move with the stars, the way the stars always moved. These five planets - which we now call Mercury, Venus, Mars, Jupiter and Saturn - "wandered" around the sky! Sometimes the moved quickly, sometimes slowly, and sometimes backwards from the way all the other stars behaved!

Aristotle, the Greek philosopher, believed that everything moved in circles, that the Earth - Athens, in fact - was the center of everything, and that everything had its own unique "nature", and that no good could come from trying to figure out any grand principles of the universe. However, by claiming this he single-handedly stunted the development of western civilization for a thousand years. For 13 centuries after him, his pronouncements were universally accepted as truth, even though he seems to have been in error about EVERYTHING he said.

So for 13 centuries after Aristotle said that EVERYTHING traveled in circles, astronomers and mathematicians tried to reconcile their observations with the Aristolean notion of circles. (Hipparchus had proposed the heliocentric concept around 130BC.) Circles within circles, or "epicycles", were one of the concepts that tried to interpret the more-and-more accurate measurements of the heavens. It finally fell to Nicolas Copernicus to broadly state the heliocentric theory, and to Johanne Keppler to propose that the planets moved in elliptical orbits rather than circular ones.

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Q: Why does the theory of heliocentrism overcome the problem of wandering stars?
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