The many-body problem is 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.