two-body problem

The two-body problem is the problem of finding the positions and velocities of two massive bodies that attract each other gravitationally, given their masses, positions, and velocities at some initial time. It was first solved by Isaac Newton, who showed mathematically that the orbit of one body about another was either an ellipse, a parabola, or a hyperbola (see conic sections), and that the center of mass of the system moved with constant velocity.