Stability and Fourier-Series Periodic Solution in the Binary Stellar Systems

Abstract

In this paper, we use the restricted three body problem in the binary stellar systems, taking photogravitational effects of both the stars. The aim of this study is to investigate the motion of the infinitesimal mass in the vicinity of the Lagrangian points. We have computed semi-analytical expressions for the locations of the collinear points with the help of the perturbation technique. The stability of the triangular points is studied in stellar binary systems . To investigate the stability of the triangular points, we have obtained the expressions for critical mass which depends on the radiation of both primaries. Fourier-series method is applied to obtain periodic orbits of the infinitesimal mass around triangular points in binary stellar systems. We have obtained Fourier expansions of the periodic orbits around triangular points upto third order terms. A comparison is made between periodic orbits obtained by Fourier-series method and with Runge-Kutta integration of fourth order.

Analysis of the dynamics of the resonant planetary system HD 45364

“…Now we are going to discuss the long-term variations of the eccentricities of HD 45364b and HD 45364c with the help of secular theory with MMR. For r + 1 : r MMR, the solutions for the eccentricities are given by (Mia and Kushvah, 2016c)…”

“…There are many researchers who have studied the stability of solar system and exoplanetary systems. Many researchers (Abouelmagd et al, 2013;Pal and Kushvah, 2015;Singh et al, 2016;Mia and Kushvah, 2016b;Singh et al, 2018;Yadav et al, 2021;Abouelmagd et al, 2021;Gyegwe et al, 2022) aslo studied the stability of an infinitesimal particle like asteroid, satellite, dust grain etc., in the solar and exoplanetary systems. For example Petrovich (2015) studied the stability and fates of hierarchical tow planet systems with arbitrary eccentricities and mutual inclinations.…”