Stability Analysis of Earth Co-orbital Objects

In this paper, we investigate the stability of Earth co-orbital objects (ECOs) based on the torus structure. The Hamiltonian value is an index to evaluate co-orbital stability. According to topological characters of tadpole (TP), horseshoe (HS), quasi-satellite (QS), and critical compound surfaces in the torus space, the co-orbital area is divided into several regions in detail. We select 221 potential ECOs as representative samples. Numerical integration in the Sun-Earth system illustrates that most of objects above the collision line are short- or long-term stable ECOs in the QS-HS and QS-TP motions, and most of objects in the unstable region are unstable ones, which is in agreement with our semi-analytical conclusions. The stability of an ECO with a larger Hamiltonian value could be stronger. An efficient method to determine the long-term co-orbital stability of a potential ECO is proposed without long-term numerical integration. Numerical integration in the multiplanet model demonstrates that our stability analysis is still applicable for the real solar system. As an application of our stability analysis, two well-determined QS-HS ECOs above the collision line are identified and analyzed for the first time. For instance, the QS-HS state of 2019 VL5 can be sustained for more than 3000 yr, and its current HS state will be sustained for at least 800 yr.