infinity, or specifically in our case $r>$1.5 (white region in Figure \[fig:rtbpl5\]). Consequently, the disjointed set of this basin of attraction (black structure in Fig. \[fig:rtbpl5\]) yields the trajectories in the ICM not escaping before time $T.$ Therefore, if we wait to keep the test particle at least until $T$ in the system, we should move it away from the infinity’s basin boundary.

Results
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[*Lissauer & Chambers (2008); Slíz , Süli & Kovács (2015); Páez & Efthymiopoulos (2015)*]{} showed that particles relative close to the $L_5$ Lagrangian point may leave the system both in RTBP and RFBP. The dynamics of the escaping trajectories can be described by the well-known formalism of transient chaos (Lai & Tél 2011).

 The Effect of the Sun’s Mass
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First we demonstrate the effect of the Sun’s gravitational perturbation on the size and position of the domain containing non-escaping trajectories for $T=1300$ days ( $\sim 6.5\tau$), see Fig. \[fig:rtbpl5\]. Panel (a) depicts the (ICM) ($x_0,y_0$) for RTBP in region $x_0\in[-0.95;-0.85],$ $y_0\in[-0.2;0.2].$ Initial velocities for all trajectories equal to the Keplerian velocity of the $L_5$ point, see Table \[table:epoch\]. As is expected from classical celestial mechanics, the triangular Lagrangian point (white cross) is situated deep 