the stable manifold.

The paper is organized as follows: In Section 2 we give a description of the model and details of methods we used. Our results are presented in the next section, Section 3. Finally, in Section 4 we summarize our findings and draw conclusions.

Model and Methods
=================

![Schema of the system configuration centred at the Earth. The position of the triangular point $L_5$, and the Moon are at the correct scale, however, the Sun’s position is indicated by an arrow. The rectangle depicts the domain $\mathcal{D}$ where initial conditions are placed. All the quantities are dimensionless, the characteristic length unit is $\mathrm{4\times10^5}$ km. The dimensionless nominal distance of the Moon from the Earth is $r_1=1$. The dashed circle $r_2=\sqrt{x^2+y^2}=1.5$ around the Earth indicates the region within which we want to keep the spacecraft.[]{data-label="fig:coosys"}](fig1){width="\columnwidth"}

Investigating the escape dynamics, we use a real planar RFBP consisting of three massive bodies, the primaries, and a mass-less test particle. To have a realistic application, the actual parameters of the massive objects in our own solar system are chosen. That is, the positions and velocities of the Sun, Earth, and Moon are taken from the freely available NASA JPL database[^2] for the 