Investigating temporary capture in the Sun-Jupiter three-body system via Lagrangian coherent structures

The temporary capture (TC) of Jupiter-family objects has long been a pivotal focus in celestial mechanics research. This study investigates the temporary capture of objects near Jupiter within the context of the planar circular restricted three-body problem (PCRTBP), employing Lagrangian coherent structures (LCSs) and periapsis Poincaré maps. Initially, LCSs are identified via periapsis Poincaré maps and applied to segment the phase space. Parameter scanning enables a detailed analysis, classifying the orbital behaviors of objects in the proximity of Jupiter into three distinct categories: temporary capture, low-energy flyby, and collision, each designating specific regions in phase space. Subsequently, a novel method for screening potential TC objects within the Jupiter system is proposed and validated, informed by the dynamic characteristics of TC motions. The efficacy of this method is illustrated by the reidentification of six known TC comets and the prediction of a prospective TC asteroid, 2002 GV28. Within the framework of the PCRTBP, analogous TC trajectories for these comets and asteroids are identified, offering novel insights into the dynamics of temporary capture events.