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Strange Orbits

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Author:Ivars Peterson (MathTrek)
Description: Newton's laws provide a precise answer to the problem of determining the motion of two bodies under the influence of gravity. If the solar system consisted of the sun and a single planet, for example, the planet would follow an elliptical orbit. When the system consists of more than two bodies, solving the relevant equations of motion gets very tricky. For three interacting bodies (described as the three-body problem), mathematicians have found a small number of special cases in which the orbits of the three masses are periodic. In 1765, Leonhard Euler (1707-1783) discovered an example in which three masses start in a line and rotate so that they stay in line. Such a set of orbits is unstable, however, and it would not be found anywhere in the solar system.

Levels: High School (9-12), College
Languages: English
Resource Types: Articles
Math Topics: Conic Sections and Circles, Astronomy

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