E. Plávalová, N. A. Solovay
We investigated the motion of planets revolving in binary systems in the frame of the particular case of the three body problem. We analysed of the motion an extrasolar plant (EP) revolving in a binary system by following conditions; a) a planet in a binary system revolves around one of the components (parent star), b) the distance between the stars components is greater than between the parent star and the orbiting planet (ratio of these two distances is a small parameter), c) the mass of the planet is smaller than the mass of the star, but is not negligible. The Hamiltonian of the system without short periodic terms was used. Expanded in the terms of the Legendre polynomial and truncated after the second order term depending on the one angular variable. In this case the solution of the system was obtained and the qualitative analysis of motion was done. We have applied this theory to real EPs. Analysis of the possible regions of motion are presented. It is shown that the case of the stable and unstable motion of the EPs are possible. We applied our calculations to two binary systems hosting an EP and calculated the possible values for their insufficient orbital elements. For 16 Cyg Bb, there is a region between 44{\deg} and 46{\deg} for the inclination of the planet and the value of the ascending node between 130{\deg} and 137{\deg}, or the inclination for the planet could have a value from 134{\deg} to 136{\deg} and the ascending node from 310{\deg} to 317{\deg}. For planet HD19994 b, to have a stable system, the value for the insufficient elements should be in the region of 62{\deg} to 68{\deg} for the inclination of the planet, and the value of the ascending node between 260{\deg} and 268{\deg}. Alternatively, the inclination of the planet also could have the value of 112{\deg} to 118{\deg} and the ascending node between 80{\deg} and 88{\deg}.
View original:
http://arxiv.org/abs/1212.3843
No comments:
Post a Comment