Orbital analysis of small bodies in co-orbital motion with Jupiter through the torus structure

In this paper, based on the torus structure, we investigate the orbital characteristics of Jupiter Trojans and Jupiter-family comets (JFCs) in co-orbital motion with Jupiter. The motivation of this paper is to test whether the semi-analytical approach and conclusions of the torus structure proposed in the circular restricted three-body problem are still valid for real small bodies in the ephemeris model, and how long they follow the prediction of the semi-analytical approach. Based on the topological structure of the co-orbital motion in the torus space, we propose a method for estimating the libration amplitude for Trojans. 873 Jupiter Trojans with well-determined orbits are picked as examples to demonstrate the validity of our estimation method. Numerical analysis reveals that the difference between the osculating semimajor axes of the Trojan and Jupiter can influence the accuracy of our estimation method significantly. Based on the semi-analytical approach, we predict orbital behaviours of three JFCs, 85P/Boethin, P/2012 US27 (Siding Spring), and P/2019 A1 (PANSTARRS). Numerical integration in the ephemeris model indicates that their real orbital behaviours are consistent with our predictions. In particular, we find that the current quasi-satellite state of P/2012 US27 (Siding Spring) can remain for about 1.5 × 105 yr, much longer than those that correspond to other previously reported QS companions of Jupiter.