Homoclinic/heteroclinic connections of equilibria and periodic orbits of contact binary asteroids

In this paper, homoclinic/heteroclinic connections of equilibrium points of two different types (that is, equilibrium points with one-dimensional unstable/stable manifolds together with two-dimensional center manifolds and those with two-dimensional unstable/stable manifolds and zero-dimensional center manifolds) are constructed and a control strategy for low-cost transfer orbits between them is proposed. These two types of equilibrium points are called the 1+1 + 2 type and 2 + 2 + 0 type, respectively. First, asteroid 1996 HW1 is modeled as a contact binary asteroid consisting of a sphere and an ellipsoid. Analytical results show that two collinear equilibrium points are of the 1 + 1 + 2 type and the noncollinear ones are of the 2 + 2 + 0 type. Then, a preliminary investigation on the phasespace structure near the equilibrium points of the 2 + 2 + 0 type is carried out. Subsequently, homoclinic/heteroclinic connections of equilibrium points of two types are yielded by four common Poincaré sections and one adjustable Poincaré section parameterized by the phase angle. Finally, the control strategy for low-cost transfer orbits visiting each equilibrium point and circling near them is proposed. Among all the low-cost trajectories near 1996 HW1, the lowest fuel consumption is about 0.13 ms with a duration of 28.96 h.