A STUDY OF THE LINEAR AND NONLINEARDYNAMICS OF A TROJAN ASTROPHYSICAL OBJECTWITHIN EXOPLANETARY SYSTEM HD 126053

In many exoplanetary systems asteroids, planets, or moons can be found near Lagrange points L4 and L5. Described as many-body problems, planetary systems are fundamentally chaotic with high sensitivity from initial conditions. However, for various ranges of the mass parameter, there are observed specific regimes that defy chaoticity. Of particular relevance is the mass ratio parameter with critical value μc=0.0385. For this critical value, the stability of the Lagrange points L4 and L5 changes followed by a bifurcation of the system. The present paper focuses on analysing the motion of a test astrophysical objects within the exoplanetary system HD 126053. We aim to find a stable trajectory around the Lagrange points of an astrophysical object with application to the mentioned exoplanetary system. In the initial phase of the study we consider a body with utterly small mass (for example, the mass of a Trojan asteroid, Trojan exomoon, or the mass of a Trojan Earth planet) that begins it motion near one of the Lagrange points of the binary star system, HD 126053. In the second phase of the study we increase this mass until the critical value of the system’s mass ratio is reached. We predict that an astrophysical object (or a cluster of astrophysical objects) with mass at most 6.365 MJ can orbit in a stable configuration around the Lagrange points within the HD 126053 system. The analytical calculations are performed under the framework of the Planar Circular Restricted Three-Body Problem. The studies about this problem and the results of this study are of great importance, especially in Physics, Astronomy, and the field of Mechanics of Celestial Bodies. On the other hand, they expand the applications of the theory of dynamical systems to better understand the dynamics of the interactions of celestial bodies in different exoplanetary systems.