The mathematical problem of finding the positions and velocities of any
number of massive bodies that interact with each other gravitationally,
at any point in the future or the past, given their present positions, masses,
and velocities. The problem can only be solved precisely for all cases of
the two-body problem and for special
cases of the three-body problem.
High-speed computers enable approximate solutions to be found for general
cases of the many-problem, but because of chaos and rounding errors, these
solutions decline in accuracy as the period over which the behavior is calculated
increases. Two broad principles govern the overall behavior of a many-body
system: the center of mass of the system moves with constant velocity, and
the total energy and total angular momentum of the system remains constant.
| Many-body simulation of star cluster.
Credit: Adam Block