In Karydis et al. (2021) we have introduced the method of shape continuation in order to obtain periodic orbits in the complex gravitational field of an irregularly-shaped asteroid starting from a symmetric simple model. What’s more, we map the families of periodic orbits of the simple model to families of the real asteroid model. The introduction of asymmetries in a gravitational potential may significantly affect the dynamical properties of the families. In this paper, we discuss the effect of the asymmetries in the neighborhood of vertically critical orbits, where, in the symmetric model, bifurcations of 3D periodic orbit families occur. When asymmetries are introduced, we demonstrate that two possible continuation schemes can take place in general. Numerical simulations, using an ellipsoid and a mascon model of 433-Eros, verify the existence of these schemes.
