Local: apresentação remota.
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 (Aljbaae et al., 2021a,b), we provide a preliminary realistic analysis of the orbital dynamics around the asteroid (99942) Apophis, one of the most interesting Near-Earth Asteroids due to its Earth close approach on April 13th.,2029. We used the dynamical model developed in our previous works, for which we represented the gravitational field of the asteroid by a cloud of 3996 point masses system distributed inside a polyhedral shape. In a first step, we explored the impact of the close approach with our planet on the dynamics of a spacecraft orbiting around Apophis, considering the gravitational perturbations of the planets on the Solar System and the Solar radiation pressure. We carried out a 60-days integration ranging 43 days before and 16 days after the encounter and studied the dependence of the stability of orbits with respect to the initial value of the semi-major axis. We found that in a very large majority of cases, the spacecraft undergoes a collision or escape due to the perturbation caused by the close encounter, whereas it shows in all cases a very stable orbit before. We applied the sliding mode control theory in order to solve the stabilization problem for the system. With a total ∆V of 0.495 m/s, we successfully stabilized an orbit with an initial semimajor axis of 0.5 km. Then, We included the effects of the changes of Apophis’ spin state due to the terrestrial torques during the close encounter, corresponding respectively to the minimum and maximum values of the spin variations. We applied a time series prediction with Neural Networks in Python with Keras to classify orbits based on a relationship between the difficulty in the prediction and the stability. This method can isolate the most regular orbits in the system. A good correlation was found between the Time-Series prediction approach and MEGNO (Cincotta and Sim ́o, 2000) or the Perturbation Map of type II (Sanchez and Prado, 2017, 2019).