epoch JD = 2455999.5 (2012 March 13 00:00 UT), see Table \[table:epoch\]. Since we investigate the Earth - Moon Lagrangian points, for the sake of better understanding we used a 2D geocentric model. A coordinate transformation is performed to have the originally in inertial frame described equations of motion in the geocentric system (Fig. \[fig:coosys\]). The equations are implemented in dimensionless form where the characteristic length unit is $\mathrm{4\times10^5}$ km, and the time unit is 1 day. The computation method is an adaptive step size Runge-Kutta-Fehlberg 7(8) integrator (Fehlberg 1968) in which the actual step size is determined according to the desired accuracy, $\epsilon=10^{-16}.$ We also set the mass of the test particle at 1 kg in order to be able to compute the energy consumption with a real spacecraft (Section 3.4). The reason for the choice the RFBP is to illustrate the Sun’s effect to the size, position and essentially the escape dynamics from the regular domain around the $L_5$ Lagrangian point. Since the Sun is included as a perturber to the Earth–Moon–test particle three body problem, the escape from the vicinity of a triangular Lagrangian point is more probable than in the case without the Sun.

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