Overview

restricted three-body problem


'restricted three-body problem' can also refer to...

The restricted three body problem

restricted three-body problem

On motions around the collinear libration points in the elliptic restricted three-body problem

Stability chart of the triangular points in the elliptic-restricted problem of three bodies

New insights into the stability of L 4 in the spatial restricted three-body problem

Frequencies and resonances around L 4 in the elliptic restricted three-body problem

Stability and secondary resonances in the spatial restricted three-body problem for small mass ratios

On the identification of multiple close encounters in the planar circular restricted three-body problem

Comparisons of integrators on a diverse collection of restricted three‐body test problems

Energy dissipation end states of the sphere restricted planar three-body problem with collisional interaction

The Global Symplectic Integrator: an efficient tool for stability studies of dynamical systems. Application to the Kozai resonance in the restricted three-body problem

Stability of the Lagrangian point L 4 in the spatial restricted three-body problem – application to exoplanetary systems

Nekhoroshev stability at L 4 or L 5 in the elliptic-restricted three-body problem – application to Trojan asteroids

High-order analytical solutions around triangular libration points in the circular restricted three-body problem

Geometry of halo and Lissajous orbits in the circular restricted three-body problem with drag forces

Positions of equilibrium points for dust particles in the circular restricted three-body problem with radiation

 

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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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