# Topics similar to or like Euler's three-body problem

To solve for the motion of a particle that is acted upon by the gravitational field of two other point masses that are fixed in space. Wikipedia

• To predict the motion of two massive objects which are abstractly viewed as point particles. The problem assumes that the two objects interact only with one another; the only force affecting each object arises from the other one, and all other objects are ignored. Wikipedia

• Problem of taking the initial positions and velocities of three point masses and solving for their subsequent motion according to Newton's laws of motion and Newton's law of universal gravitation. Special case of the n-body problem. Wikipedia

• Problem of predicting the individual motions of a group of celestial objects interacting with each other gravitationally. Solving this problem has been motivated by the desire to understand the motions of the Sun, Moon, planets, and visible stars. Wikipedia

• The gravitational two-body problem concerns the motion of two point particles that interact only with each other, due to gravity. This means that influences from any third body are neglected. Wikipedia

• System of point masses with the property that each mass is pulled by the combined gravitational force of the system directly towards the center of mass, with acceleration proportional to its distance from the center. Central configurations may be studied in Euclidean spaces of any dimension, although only dimensions one, two, and three are directly relevant for celestial mechanics. Wikipedia

• Angular difference between the actual position of a body in its elliptical orbit and the position it would occupy if its motion were uniform, in a circular orbit of the same period. Defined as the difference true anomaly, Wikipedia

## Sentences forEuler's three-body problem

• Gravitation from Earth and Moon dominate the spacecraft's acceleration, and since the spacecraft's own mass is negligible in comparison, the spacecraft's trajectory may be better approximated as a restricted three-body problem.
• If a planet was in a distant orbit around this star, three-body interactions during the encounter could alter the planet's path, leaving it in a stable orbit around the Sun.
• See Euler's three-body problem.
• However, this conclusion holds only when two bodies are present (the two-body problem); the motion of three bodies or more acting under their mutual gravitation (the n-body problem) remained unsolved for centuries after Newton, although solutions to a few special cases were discovered.
• In classical mechanics, Euler's three-body problem describes the motion of a particle in a plane under the influence of two fixed centers, each of which attract the particle with an inverse-square force such as Newtonian gravity or Coulomb's law.

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