Determination method of co-orbital objects in the solar system

In this paper, based on two-dimensional maps from the semi-analytical Hamiltonian approach, we proposed an improved determination method to classify co-orbital objects in the solar system without numerical integration. Taking advantage of a simple pattern analysis, we present two certainty conditions to recognize co-orbital objects with uncertain orbital parameters. Then, our determination method is applied to classify potential co-orbital objects (PCOs) of Mars, Jupiter, Saturn, Uranus, and Neptune, and then their results are verified through numerical integration in the multiplanet model, respectively. Through our method, we identify 11 new co-orbital objects for the first time, including four Mars trojans i.e. tadpole (TP) objects, one short-term Mars quasi-satellite (QS), one Mars horseshoe (HS), one Jupiter QS, one short-term Uranus trojan, one Uranus PCO, and one Neptune PCO with short-term transitions between QS and HS, and one Neptune PCO with short-term transition between QS and TP. Numerical computation shows that except Saturn PCOs significantly perturbed by Jupiter, our determination method for co-orbital objects in the solar system is effective, but it cannot deal with the classification of PCOs near the boundary of different co-orbital regions. Since our method does not rely on time-consuming numerical integration, it is efficient and suitable for a large amount of screening for numerous co-orbital objects in the solar system.