# two-body problem

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## two-body problem

A special case of the n-body problem in which a general solution can be found for the orbits of two bodies under the influence of their mutual gravitational attraction. The motion of a planet around the Sun is an example as long as the attractive forces of other planets are assumed to be negligible. A solution of the two-body problem is often acceptably realistic. Most theories of celestial motion thus use functions and principles, such as orbital elements and Kepler's laws, that have been derived by consideration of a two-body problem.
Collins Dictionary of Astronomy © Market House Books Ltd, 2006
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Two-Body Problem

(in astronomy), the problem of the motion of two bodies that are mutually attracting in accordance with Newton’s law of gravitation. In the two-body problem attracting bodies are taken to be material points, which is valid if they are spherical in structure or if the distances between them are very great compared to their size. This requirement is largely met for the sun and each of the planets. In solving the two-body problem the motion of one body in relation to the other is usually considered. The motion in this problem occurs in conic sections—a circle, ellipse, parabola, hyperbola, or straight line—in accordance with Kepler’s laws. The two-body law, describing so-called unperturbed motion, is the first approximation in studying the true motion of celestial bodies.

N. P. ERPLYLEV