Abstract: Two-body problems are very common in physics, especially in collision and celestial body problems. When the perturbation force of the multi-body problem is far less than the interaction force between two bodies, it can be approximated as a two-body system. In this paper, koenig^,s theorem is derived from two perspectives of transformation of reference frame and conservation of energy, which leads to the two-body modification of the problem by reduced mass, and puts forward the idea of equivalent integration to deal with the problem, which simplifies the discussion of the two-body problem. At the same time, the degenerate ellipse time method is introduced to solve the time problem from relative rest to collision of two bodies under inverse square force. Finally, we discuss and improve the multi-solution method of the two-body problem, and use the conclusion of the two-body problem of the celestial system to compare the two-body problem with the two-point charge problem, so as to avoid the complicated integration in the book, and highlight the superiority of the equivalent integration treatment of the problem.

Key words: two-body problem, reduced mass, two-body correction, equivalent integration