A Study about the Secular Evolution of the Hierarchical Three-body Problem Using the Numerical Integrator TIDES

The hierarchical three-body problem is one of the classical issues of celestial mechanics, but recently it has regained importance due to its applications to new scenarios, like compact objects and exoplanets. In this paper we realize a computational study of this problem using the TIDES software package, which is applied not only to a set of theoretical cases but also to actual stellar systems. The characteristics of the Taylor series integration method, used by TIDES, permit the confirmation of the appearance of the Lidov–Kozai cycles in the case of high mutual inclinations. In addition, a historical review of this problem is included.