  Let a number, N, of particles interact classically through Newton's Laws of
Motion and Newton's inverse square Law of Gravitation. The resulting equations
of motion provide an approximate mathematical model with numerous applications
in astrophysics, including the motion of the moon and other bodies in the Solar
System (planets, asteroids, comets and meteor particles); stars in stellar
systems ranging from binary and other multiple stars to star clusters and
galaxies; and the motion of dark matter particles in cosmology. For N=1 and N=2
the equations can be solved analytically. The case N=3 provides one of the
richest of all unsolved dynamical problems -- the general three-body problem.
For problems dominated by one massive body, as in many planetary problems,
approximate methods based on perturbation expansions have been developed. In
stellar dynamics, astrophysicists have developed numerous numerical and
theoretical approaches to the problem for larger values of N, including
treatments based on the Boltzmann equation and the Fokker-Planck equation; such
N-body systems can also be modelled as self-gravitating gases, and
thermodynamic insights underpin much of our qualitative understanding.
