Dynamics around Non-Spherical Symmetric Bodies: The case of a spherical body with mass anomaly

The continuous acquisition of data on the shape of small heliocentric bodies boosted the study of the dynamics around non-spherical bodies, mainly motivated by the development of space missions such as NEAR-Shoemaker, OSIRIS-REx, and Hayabusa (Scheeres et al., 2000; Wang et al., 2016; Winter et al., 2020; Moura et al., 2020). This class of objects characteristically have diameters of less than 1000 km and present a range of interesting irregular shapes and distinct compositions.

We are interested in the dynamics around a class of objects classified by us as Non-Spherical Symmetric Bodies (NSSBs), and here we present the results regarding a spherical object with a mass anomaly. The non-asymmetric terms of the gravitational field of the NSSBs create strong resonances between the orbital period of particles and the spin of the central body. These resonances have been proposed to be responsible for keeping the Haumea and Chariklo rings (Ortiz et al., 2017; Leiva et al., 2017).

In our study, we used the Poincaré Surface of Section technique (Borderes-Motta & Winter, 2018; Winter et al., 2019), varying the masses of the spherical and anomalous portions of the central body and its spin period. We detected the existence of an unstable region in the vicinity of the object, where the particles feel an eccentricity increase, being ejected from the system or colliding with the central body.

The instability region extends beyond the corotation radius and, therefore, mass anomaly systems do not have internal spin-orbit and corotation resonances. Beyond the unstable region, we detected on the Poincaré Surface of Sections structures remarkably similar to those of the restrict planar 3-body problem, including asymmetric periodic orbits associated with 1:1+p resonances (Winter & Murray 1997a,b). Resonance islands are immersed in regions of first-kind orbits. We detected chaotic behavior only in narrow regions in the resonances separatrix.

Since Sicardy (2020) discusses the possibility that Chariklo is a sphere with a mass anomaly, we applied our results to this object. We obtain that the 1:3 resonance is slightly displaced from the inner ring and the resonant particles have a radial range larger than the width of the rings. Therefore, this resonance should not be associated with the rings as proposed by Leiva et al. (2017). We found that the rings are probably associated with first kind orbits. The authors thank FAPESP (2016/24561-0, 2018/23568-6), CNPq (309714/2016-8, 305210/2018-1), and Capes for the financial support.