Using a gravitational field truncated at the 4th degree and order, the 1:1 ground-track resonance is studied. To address the main properties of this resonance, a 1-degree of freedom (1-DOF) system is firstly studied. Equilibrium points (EPs), stability and resonance width are obtained. Different from previous studies, the inclusion of non-spherical terms higher than degree and order 2 introduces new phenomena. For a further study about this resonance, a 2-DOF model which includes a main resonance term (the 1-DOF system) and a perturbing resonance term is studied. With the aid of Poincaré sections, the generation of chaos in the phase space is studied in detail by addressing the overlap process of these two resonances with arbitrary combinations of eccentricity (e) and inclination (i). Retrograde orbits, near circular orbits and near polar orbits are found to have better stability against the perturbation of the second resonance. The situations of complete chaos are estimated in the e- i plane. By applying the maximum Lyapunov Characteristic Exponent (LCE), chaos is characterized quantitatively and similar conclusions can be achieved. This study is applied to three asteroids 1996 HW1, Vesta and Betulia, but the conclusions are not restricted to them.

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The general orbital motion around a contact binary asteroid system is investigated in this study. System 1996 HW1 is explored in detail, as it is the mostly bifurcated asteroid known to date. The location of its equilibrium points (EPs) is obtained and their linear stability is studied. Families of Lyapunov, Halo and vertical periodic orbits (POs) in the vicinity of these EPs as well as their stability are found and examined, respectively. The influence of the relative size of each lobe and the shape of the ellipsoidal lobe and the rotation rate of the asteroid on the location and stability of the EPs are studied. Additionally, two families of equatorial orbits are obtained at a wide range of distances: from far away to nearby. Their stability is examined against the distance to the asteroid and the rotation rate of the asteroid, to uncover the influence of highly non-spherical gravitational field and the rotation of the asteroid on the orbital motion. Finally, resonant orbits in N commensurability with the rotation of the asteroid are found and their stability is discussed. The fast rotation of the asteroid has a stabilizing effect on the equatorial orbital motion.@en