Nonlinear dynamics of the Trappist-1-Trappist-1e exoplanetary system

I addition to the various methods on the study of exoplanetary systems, the case of the circular restricted three body problem can be used, among others, to determine the character of the orbits of an astronomical body which moves under the action of the gravitational field of two massive bodies such as star-planets or binary star systems. In this paper we will first present some general information on the Trappist-1 exoplanetary system. Then we will determine the position of the Lagrange points for the Trappist-1-Trappist-1e system as well as the values of the Jacoby constant for each positions of the Lagrange points. We will than construct trajectories for zero velocity, studying the motion of a particle in this system. Also, in this paper we will try to do a numerical analysis on the phase plane for different initial conditions, building in MATLAB® 2020, different orbits for the exoplanetary system Trappist-1-Trappist-1e, distinguishing between the types of body motion of the third body in this exoplanetary system. So, for this we will perform some numerical experiments in MATLAB® 2020. Finaly, we will also study the possibility of the existence of an exomoon in this very impressive exoplanetary system.