Third Body Perturbations of Double Stars

We report on the different results concerning the stability of the hierarchical triple systems where a close binary is accompanied by a third star. There are different possible approaches to answer the question of the stability limits for such triple stars: the most direct investigations can be undertaken in integrating numerically the respective equations of motion for many different initial conditions. It is then difficult to take into account all the important parameters like eccentricities, inclination, phases and masses. Analytical approaches and qualitative methods are more approriate to deal with this problem; the respective results confirm the numerically found results that: 1. for prograde orbits the ratio semimajor axis of the inner orbits to the periastron position of the outer orbit is approximately 3.2 2. for retrograde orbits this ratio is just some 10 percents smaller 3. the results are not sensitive in what concerns the masses involved 4. There is a tendency that the inclinations and eccentricities change slightly the stability limits mentioned above. This revised version was published online in August 2006 with corrections to the Cover Date.