Study of the resonant motion of a test particle inside Kepler 69 using circular restricted three body problem

Summary: Scientific researches to discover extraterrestrial life are very intense and important. For a long time, humanity has speculated about the existence of the planetary systems different from our solar system, where extraterrestrial life can be existing elsewhere in the universe. The understanding of the origin of planets and planetary systems has indeed become a major focus of research in modern Astrophysics. Exoplanet research is one of the most field developing subjects in Astrophysics and Astronomy. Today, the number of discovered exoplanets, where life is thought to exist, is large. One of the main goals of scientists is to find Earth 2, where there is possibility of extraterrestrial life. Kepler's mission was, and is very important in the field of exoplanet research. This mission has revolutionized our understanding of exoplanets. The number of discovered exoplanets has exceeded 5780 in 4314 planetary systems, with 969 systems having more than one planet [1]. Among them, one of the most interesting is Kepler 69 c, a super-Earth around Kepler 69. This exoplanet is located at the boundary between the habitable zone and the outer one. In this study let’s focus on the classical gravitational problem called Circular Restricted Three-Body Problem (CRTBP) [2, 3] and use an iterative method to perform numerical calculations through MATLAB software. Therefore, in this paper, let’s try to study the movement of a “test particle”, under the action of the gravitational field of the system Kepler 69–Kepler 69 c. The aim of this paper is to study the motion of a “test particle” (for example an extrasolar asteroid test) inside the exoplanetary system Kepler 69. Results are presented in the (x, y) plane in the rotating and inertia system. Also, some of the results are presented in the phase planes (x, vx) and (y, vy)