Stability of planetary orbits in double stars

The discovery of extra solar planets in double stars led to a growing interest of stability studies of such systems, where we distinguish between two types of motion: (a) the satellite-type or S-type motion, when the planet moves around one star and (b) the planetary-type or P-type motion when it surrounds both stars. General stability studies thereto have been carried out since 1977 by several scientists, see e.g. [6], [15], [16], [1], [2], [14], [3] and more recently by [7] [9], [10] and [11]. The fact that double and multiple star systems are more numerous than single stars and the discovery of planetary companions (moving in S-type motion) in 7 double star systems (see table 1) make such numerical investigations important. In this study we present for the two types of motion global results for a binary with mass-ratio œ = m2/(m1 + m2) = 0.5. For both investigations we used the elliptic restricted three body problem (ERTBP), that describes the motion of a mass-less planet in the gravitational field of two massive bodies (i.e. the binary) which move in Keplerian orbits around their center of mass. Finally, we give a table of all known binaries where planets were detected and report on our current studies thereto.