Dynamics of a Particle in 3:1 Tesseral Resonance with the Dwarf Planet Haumea

The dynamics of a particle in 3:1 tesseral resonance with the dwarf planet Haumea is analysed. This resonance, three rotations of the primary per orbital period of the particle, is located inside the region where Haumea's ring was observed. Thus, determining the effect of this resonance on a particle's orbit reveals its relationship to the orbits that follow the particles of the ring. To analyse the effect, we propose four models of anisotropy; two of them are a reduced representation of the distribution of the mass of Haumea that we use to determine the centre of the resonance by means of the Hamiltonian formulation. After this, we analyse the effects of the four models on the resonance orbit by using the Lagrange planetary equations technique. The results show that the resonance centre has a high eccentricity value, meaning that a particle in 3:1 resonance with Haumea does not remain confined to the region that we consider to be the ring region.