Planar low-energy asteroid and comet transit analysis using isolating blocks

Abstract

Asteroids and comets often capture and sometimes transit near a planet by traveling through the $$\hbox {L}_1$$ and $$\hbox {L}_2$$ libration point gateways, and these regions are therefore key to understanding the mechanism by which captures, transits, and some potential impacts of these bodies occur. Isolating blocks have recently been used to provide a theoretically rigorous method for computing the invariant manifolds of libration point periodic orbits in the circular restricted three-body problem (CRTBP), and for an appropriate energy range, they can allow us to compute all possible transit trajectories at a particular Jacobi constant in the CRTBP. In this study, both $$\hbox {L}_1$$ and $$\hbox {L}_2$$ isolating blocks are found for the Sun–Earth and Sun–Jupiter CRTBP systems to rigorously compute trajectories transiting near the Earth and Jupiter in the low-energy regime common for asteroids and comets. The characteristics of these transit trajectories are explored, and individual trajectory solutions are analyzed in more detail. The transit trajectories are also characterized using their orbital elements and compared to known comets and asteroids.