Complete solution of a general problem of three bodies

Abstract

A problem investigated by C. Burrau in 1913 which may be referred to as the Pythagorean problem of three bodies is solved numerically, the solution being valid for any length of time. The solution found is neither quasi-periodic nor periodic but it assumes the form known in the recent Soviet literature as "elliptic- hyperbolic." In the final configuration two of the three participating bodies form a permanent binary while the third body is rejected to infinity. A new method of treating close approaches which allows achieving the solution is also described.