# 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.

## 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

## two-body problem

[′tü ¦bäd·ē ′präb·ləm]
(mechanics)
The problem of predicting the motions of two objects obeying Newton's laws of motion and exerting forces on each other according to some specified law such as Newton's law of gravitation, given their masses and their positions and velocities at some initial time.
References in periodicals archive ?
Laplace supposed such a speed as a result of his soltion of the gravitational two-body problem, which concerns the motion of two point particles that interact only with each other, due to gravity.
Each of these interactions is considered a two-body problem because it asks how two objects--such as Earth and a spacecraft--behave if the only forces acting on them are each other's gravity.
Physics has a long history of reducing many-body problems to one-or two-body problems in order to find more powerful solutions, and Alder and his colleagues have high hopes of doing it for this one.

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