N-body problem
The n-body problem' is the problem of finding, given the initial positions, masses, and velocities of n bodies, their subsequent motions as determined by classical mechanics, i.e. Newton's laws of motion and Newton's law of gravity.
The two-body problem is simple; its solution is that each body travels along a conic section which has a focus at the centre of mass of the system.
The three-body problem is much more complicated; its solution can be chaotic. The general three-body problem has not been solved analytically,
although approximate solutions can be calculated by numerical methods or perturbation methods.
A restricted three-body problem, in which two of the bodies are in circular orbits and the third is of negligible mass (approximated by the Sun - Earth - Moon system) was solved analytically by Lagrange in the 18th century. The points where the smallest object can orbit the other two with the same period are called Lagrangian points.
See also: many-body problem
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Referenced By
Appel | Henri Poincare | Henri Poincaré | Joseph-Louis Lagrange | Joseph-Louis de Lagrange | Joseph Louis Lagrange | Jules-Henri Poincaré | Jules Henri Poincaré | Jules Poincare | Kenneth Appel | List of astronomical topics | List of astronomical topics (N-Z) | List of dynamical system and differential equation topics | List of dynamical system topics | List of mathematical topics (M-O) | List of physics topics M-Q | Poincaré
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