Spatial Temporary Capture in the Sun-Planet Three-Body System

Temporary object capture in the Sun-planet three-body system is essential for understanding the origin of planetary moons. This paper extends existing research on planar Temporary Capture (TC) motion to spatial TC motion, utilizing Poincaré maps and parameter scanning methods. The primary contributions are as follows: first, a method is introduced to construct the feasible set of spatial TC motion within the Sun-planet circular restricted three-body problem framework, revealing a significant number of spatial TC trajectories. Second, an approach is proposed to define the spatial TC domain in the heliocentric inertial frame, identifying a critical region through which heliocentric objects can be temporarily captured by a planet. Third, a novel technique is presented for identifying spatial TC objects using the constructed TC domain, demonstrated through the Sun-Jupiter system. This method successfully identifies all previously reported comets and asteroids that can be temporarily captured by Jupiter. Additionally, a comet and an asteroid are newly discovered, both exhibiting large orbital inclinations in the heliocentric system, which may experience temporary capture events around Jupiter in the future. This work provides a novel framework for investigating the origin of planetary moons, particularly irregular moons with large orbital inclinations.