# three-body problem

## three-body problem

A specific case of the n-body problem in which the trajectories of three mutually interacting bodies are considered. There is no general solution for the problem although solutions exist for a few special instances. Thus the orbits can be determined if one of the bodies has negligible mass, as in the case of a planetary satellite, such as the Moon, subject to perturbations by the Sun or an asteroid whose motion is perturbed by Jupiter.
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 It might be outdated or ideologically biased.

## Three-Body Problem

in astronomy, the problem of the motion of three bodies that attract each other in accordance with Newton’s law of gravitation and are regarded as mass points (seeTWO-BODY PROBLEM). The classic example of the three-body problem deals with the system consisting of the sun, the earth, and the moon.

In 1912 the Finnish astronomer K. F. Sundmann found a general solution of the three-body problem in the form of series that converge for any moment of time t. Sundmann’s series, however, turned out to be useless for practical calculations because of their extremely slow convergence.

Under certain special initial conditions it is possible to obtain very simple solutions of the three-body problem; such solutions include those found by Lagrange and are of great interest for astronomy (seeLIBRATION POINTS). A special case of the three-body problem is the elliptical restricted three-body problem, in which two bodies of finite mass move about a center of inertia in elliptical orbits, and the third body has an infinitely small mass. Various classes of periodic motions have been investigated for the restricted problem.

The properties of motion in the limit as t → +∞ and t → +∞, that is, terminal motions, have been studied in detail for the general three-body problem.

G. A. CHEBOTAREV

## three-body problem

[′thrē ¦bäd·ē ‚präb·ləm]
(mechanics)
The problem of predicting the motions of three objects obeying Newton's laws of motion and attracting each other according to Newton's law of gravitation.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
Now China counts too, and arms control becomes a 'three-body problem'.
Like its predecessor, Broken Stars features some of the most accomplished Chinese authors writing in the genre today: Xia Jia, Zhang Ran, Tang Fei, Han Song, Cheng Jingbo, Baoshu, Liu Cixin (whose The Three-Body Problem won the 2015 Hugo for Best Novel), Hao Jingfang (whose Folding Beijing won the 2016 Hugo for Best Novelette), Fei Dao, Anna Wu, Ma Boyong, Gu Shi, Regina Kanyu Wang, and Chen Qiufan.
This year Daniel LeBlanc, Aircraft Procurement for Emirates, and a regular volunteer at the festival, will moderate a session with Cixin Liu, author of The Three-Body Problem and Beyond, as well as Gerd Leonhard, author of Technology Versus Humanity.
He is particularly known for his Remembrance of Earths Past: The Three-Body Trilogy: The Three-Body Problem (*** Mar/Apr 2015), which won a Hugo Award, The Dark Forest (2015), and Death's End (*** Jan/Feb 2017).
Sundman (see [21]) succeeded in finding a general solution of the three-body problem in the form of power series in terms of some parameter.
The opening book of the series, The Three-Body Problem, became the first translated novel to win a Hugo Award, given at WorldCon each year and considered science fiction's greatest honor.
The Dark Forest provides a sequel to the Chinese science fiction best-seller The Three-Body Problem, is translated by Joel Martinsen, and continues the trilogy by telling of an Earth facing an alien invasion heading towards them--in four hundred yeas.
Many natural problems in dynamics, such as the three-body problem of celestial mechanics--for example, interactions of the sun, the moon and earth--have no exact mathematical solution.
The elliptical restricted three-body problem describes the dynamical system more accurately on account of realistic assumptions of the motion of the primaries that are subjected to move along the elliptical orbit.
To test the robustness of the method, we will study a perturbed case included in the planar restricted three-body problem, this problem includes the Earth, the Moon, and an artificial satellite with the same semiaxe that Heos II and eccentricity 0.95.
I was dissatisfied by the answer in your June Astro Q&A (page 68) to Scott Hill's question about whether moons can have moons: it seemed to dismiss the issue without giving the real physical reason for the lack of "moons of moons." A quick discussion of the three-body problem would have been more on target.

Site: Follow: Share:
Open / Close