## Quick Reference

A version of the three-body problem in which one of the bodies is taken to be essentially massless and so does not affect the relative orbit of the other two massive bodies. The problem is thus simplified to finding the behaviour (position and velocity) of the massless body at any time in the combined gravitational field of the two other bodies. In the *circular restricted three-body problem* the two massive bodies follow circular orbits about their common centre of mass; in the *elliptical restricted three-body problem* they follow elliptical orbits about the centre of mass. Other variations include the *coplanar restricted three-body problem*, in which the massless body moves entirely in the plane of the two massive bodies' orbits; and the *three-dimensional restricted three-body problem*, in which the massless body is free to move in all three dimensions. Practical applications include three-body systems such as the Sun, a planet, and a small planetary satellite; the Sun, Jupiter, and an asteroid; the Sun, a planet, and a comet; the Earth, the Moon, and an artificial satellite; and a binary star with a planet.

*Subjects:*
Astronomy and Astrophysics.

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