Enhancing Temporary Capture of Small Bodies via Planetary Moon Flybys in Sun-Planet Systems

Abstract

Spatial temporary capture (TC) within Sun-planet systems is essential for elucidating the transport pathways of small bodies and the dynamical origins of planetary moons. While planetary moon flybys (PMFs) play a pivotal role in the formation of spatial TC, the underlying chaotic dynamical environment poses significant challenges in identifying the initial conditions that trigger such events. To address this, we propose an identification methodology within the framework of the circular restricted three-body problem (CRTBP) to determine the feasible initial states of TC involving PMFs. The primary contributions of this work are three-fold: First, analytical formulas are derived to quantify the influence of close PMFs on the object’s three-body energy. Second, a systematic method is introduced to construct the feasible set of spatial TC motions with PMF. By leveraging Poincaré sections and the derived energy-variation formulas, this approach reduces the coupled 12-dimensional state space, formed by the three position and three velocity components of the small body and those of the planetary moon at the flyby epoch, to a six-dimensional space. This reduction enables the identification of all possible post-flyby motion types, including TC, at a significantly reduced computational cost. Finally, a strategy is developed to transition spatial TC trajectories from the CRTBP framework to high-fidelity ephemeris models. Taking the Sun-Jupiter system as a case study, the analytical energy variations demonstrate an error of less than 2 % compared to high-fidelity numerical solutions. Furthermore, the inclusion of PMFs is found to enhance the spatial TC probability by several factors to an order of magnitude, offering a novel pathway for investigating the dynamics of spatial temporary capture.