Orbit classification in the restricted three-body problem with the effect of three-body interaction

The modified circular restricted three-body problem is numerically investigated to classify the orbits of the test particle. We perform a numerical analysis on the various two-dimensional plane, i.e., (x, C)-plane, (y, C)-plane, and (x,y)-plane to classify the initial conditions on the these planes and distinguish following four types of orbits: (i) the bounded orbits, (ii) collision with the primary m(1), (iii) collision with the primary m(2), and (iv) escaping orbits. The motion of the test particle are evaluated numerically, by illustrating the color-coded diagrams (CCDs), where the starting conditions are linked to the orbit type and numerically evaluated as a function of the Jacobian constant C, the initial value of the x-co-ordinate and the Jacobian constant.. or the x,y-co-ordinates, or the y-co-ordinate and Jacobian constant. Moreover, in the mean time we have also noted the associated time for classifications of each of the starting conditions on the various 2D-planes.