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The aim of this work is to explore the escape process of three-dimensionalorbits in a star cluster rotating around its parent galaxy in a circular orbit.The gravitational field of the cluster is represented by a smooth, sphericallysymmetric Plummer potential, while the tidal approximation was used to modelthe steady tidal field of the galaxy. We conduct a thorough numerical analysisdistinguishing between regular and chaotic orbits as well as between trappedand escaping orbits, considering only unbounded motion for several energylevels. It is of particular interest to locate the escape basins towards thetwo exit channels and relate them with the corresponding escape times of theorbits. For this purpose, we split our investigation into three cases dependingon the initial value of the $z$ coordinate which was used for launching thestars. The most noticeable finding is that the majority of stars initiated veryclose to the primary $(x,y)$ plane move in chaotic orbits and they remaintrapped for vast time intervals, while orbits with relatively high values of$z_0$ on the other hand, form well-defined basins of escape. It was alsoobserved, that for energy levels close to the critical escape energy the escaperates of orbits are large, while for much higher values of energy most of theorbits have low escape periods or they escape immediately to infinity. We hopeour outcomes to be useful for a further understanding of the dissolutionprocess and the escape mechanism in open star clusters.

Revealing the escape mechanism of three-dimensional orbits in a tidally limited star cluster