Case studies of the circular restricted three body problem

In this thesis, the onset of instability for a planet which is part of a stellar binary system is investigated by performing numerical simulations of the circular restricted three body problem. This study also makes use of a rotating (synodic) coordinate system keeping both binary stars at rest. This allows the definition of a constant of motion (Jacobi's constant), which in turn sets a permissible region of motion for the planet. As the initial conditions are varied, the boundary of the permissible region of motion passes through each of the three collinear equilibrium points with significant changes to the orbit of the planet at or near each crossing. The synodic velocity phase space portraits are also used in order to obtain the average eccentricity of the orbit as an additional means of determining the stability. The stability limits obtained via these methods agree with other methods that were obtained with simulations over much longer time intervals.