Studies of the stellar three-body problem

The motions in point-mass triple star systems are studied by analytical and numerical methods. The existing analytical theories are found to be quite accurate as long as the ratio of orbital periods P2/P1 is above some 50:1. The theory for the secular motions is given in detail, with the elliptical functions expanded in more tractable Fourier series. A key feature of this solution is the variation of the eccentricity of the close orbit with a typical period T3 = P(2)2/P1. The amplitude of this variation is coupled to the relative inclination, and tidal interaction in the close pair may tend to diminish both the eccentricity and the relative inclination. Further work with the tidal forces taken into account is required.