ИСТИНА

We know more than 420 extrasolar planets only 15 years after the discoveries of the first extrasolar planet. More than 10 percent of planet - hosts are in binary or multiple stellar systems. We don`t know all of the orbital elements for observing extrasolar planets. To calculate the stability of the motion of the extrasolar planet in the binary stellar system, we decided to investigate this by implementing the general three-body problem where we set the three initial conditions. The first - a planet in a binary system revolves around one of the components (parent star). The second - the distance between a star’s components is greater than between the parent star and the orbiting planet (ratio of these two distances is a small parameter, less than 0.1). The third - the mass of the planet is much smaller than the mass of the star, but isn’t negligible. We can completely solve the three-body problem for these initial conditions. In this paper, we will devote some attention to the special case of a near circular orbit of an extrasolar planet. We applied these calculations to the particular specific extrasolar planet HD120136Ab (τ Boo b). For the orbital elements of the distant star we used three different sets which were derived by Hale, Popovic - Pavlovic and Kiyaeva (AMP method). This report has been updated since its presentation at the conference to reflect the new findings.