Stability and Fourier-series periodic solution in the binary stellar systems

TL;DR

This paper analyzes the motion and stability of infinitesimal masses near Lagrangian points in binary stellar systems, incorporating photogravitational effects and using Fourier-series to find periodic orbits, validated by numerical integration.

Contribution

It introduces a semi-analytical approach for locating collinear points and applies Fourier-series to derive periodic orbits in binary systems with photogravitational effects.

Findings

Stability conditions depend on the radiation of both stars.

Fourier-series method effectively computes periodic orbits.

Comparison shows good agreement with numerical integration.

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 Kepler-34, Kepler-35, Kepler-413 and Kepler-16. 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.