Third-order and tidal effects in the stellar three-body problem

A stable three-body system is characterized by two orbital periods P₁ and P₂. For P₂/P₁ greater than some 50:1, the point-mass problem has a well-known second-order analytical solution. It is shown how this solution can be modified to take tidal deformation into account. As expected, the motion becomes qualitatively different when the apsidal advance due to deformation becomes larger than that due to the third body. In particular, there is no longer a "critical" relative inclination, and circular close orbits are allowed at all inclinations. For large period-ratios, even a small deformation may have this effect. For small period-ratios, the previously neglected third-order terms become important. The tidal forces have important evolutionary consequences and as a first step towards better understading, a "classification" of triple stars is introduced.