Next: The Shape Sphere Up: 3-Body Problem Configuration Simulator Previous: 3-Body Problem Configuration Simulator

# The Newtonian 3-Body Problem

A system of point masses, all of which mutually exert attractive forces on each other, will evolve in time according to Newton's second law:

where is the position of body at time , is the force exerted on body by body , and is the mass of body .

The -body problem refers to the study of the dynamical properties of the second-order system of equations (of which there are ). One needs only to specify the force law and the mass of each body to specify the system.

A common force law in the study of the -body problem is gravitation, the force of which is given by Newton' law of universal gravitation:

where is Newton's constant of universal gravitation and is a vector pointing from the position of body to that of body . Strong-force laws (those whose potential energies satisfy ) have also been used in studies of the -body problem.

This simulator applies the gravitational force law to the -body problem. All three bodies have equal masses , and Newton's gravitational constant is normalized to .

Next: The Shape Sphere Up: 3-Body Problem Configuration Simulator Previous: 3-Body Problem Configuration Simulator
Matthew Salomone 2003-07-24