Co-orbital transition of 2016 HO₃

In this paper, we investigate the orbital behavior of the transition between the quasi-satellite (QS) and horseshoe (HS) motions of 2016 HO ${}_3$. Based on the phase space structure in the Sun–Earth circular restricted three-body problem, we find that the surface of 2016 HO ${}_3$ in the torus space is a compound surface formed by QS and HS portions. Its co-orbital motion is therefore a QS–HS transition. 2016 HO ${}_3$ is currently located in a QS state, and its locus clings to the QS portion in the isosurface in agreement with the semi-analytical results. We provide a criterion to separate the QS and HS stages in the transition and obtain accurate incoming and outgoing epochs of the QS motion. We then propose an approximate curve to describe the locus of 2016 HO ${}_3$ in the $\omega -e$ projection. Virtual asteroids (VAs) near 2016 HO ${}_3$ in the isosurface were created to study the influence of the initial state of the QS–HS transition. We find that the duration of the QS state is mainly influenced by the loci in the $\omega -e$ projection. The VAs with large QS durations usually have longer loci across the QS region than those with shorter durations. In addition, although some VAs are close to 2016 HO ${}_3$ in the $\omega -e$ projection, their co-orbital behaviors are significantly different from that of the latter. This indicates that the QS–HS transition of 2016 HO ${}_3$ is sensitive to the $(\omega ,e)$ position.