  Tumbling asteroids belong to a small group of objects, whose angular velocity
vector is unaligned with any of its principal axes of inertia. This leads to
challenging efforts to model the trajectory of any spacecraft designed to orbit
these bodies. In this work, we deepen a previous study on this topic,
concerning the asteroid (99942) Apophis during its close encounter with the
Earth in 2029. We analyze the orbital behaviour of a spacecraft orbiting the
asteroid during this event, by including the effects of the changes of
orientation of the spin axis of the asteroid, depending on two sets of initial
conditions. The global dynamics of the spacecraft around the target are
analyzed using three approaches, MEGNO, PMap, and Time-Series prediction. We
confirm that no spacecraft with natural orbits could survive the high
perturbations caused by the close encounter with our planet.
