(i.e. RTBP), 0.6, and 1 solar mass, respectively. Initial velocities in both panels correspond to the velocity of the $L_5$ point in RTBP. The white cross denotes the position of the triangular Lagrangian point $L_5$.[]{data-label="fig:rtbpl5"}](fig2a "fig:"){width="\columnwidth"} ![ICMs for 1300 days. (a) Black dots represent the initial conditions ($x_{0},y_{0}$) for 90000 trajectories that do not escape the system (RTBP) until $T.$ (b) Non-escaped trajectories for the different mass of the Sun. Black, blue, and red dots correspond to 0 (i.e. RTBP), 0.6, and 1 solar mass, respectively. Initial velocities in both panels correspond to the velocity of the $L_5$ point in RTBP. The white cross denotes the position of the triangular Lagrangian point $L_5$.[]{data-label="fig:rtbpl5"}](fig2b "fig:"){width="\columnwidth"}

The Effect of the Integration Time
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In this section the size of the long-lived island is investigated for different integration times. That is, we are interested in the number (and also the position) of non-escaped trajectories, while the criterion for escape ($r>1.5$) remains the same. The mass of the Sun is set to be $1 M_{\odot}.$ In order to perform this calculation we place $N_0=10^6$ particles around the $L_5$ point, $x_0\in[-0.98;-0.88],\;y_0\in[-0.2;0.2].$

![RFBP. (a) Initial positions of non-escaped trajectories for $T=$400, 1300, and 13000 days, black, 