  We aim at providing a preliminary approach on the dynamics of a spacecraft in
orbit about the asteroid (99942) Apophis during its Earth close approach. The
physical properties from the polyhedral shape of the target are derived
assigning each tetrahedron to a point mass in its center. That considerably
reduces the computation processing time compared to previous methods to
evaluate the gravitational potential. The surfaces of section close to Apophis
are build considering or not the gravitational perturbations of the Sun, the
planets, and the SRP. The Earth is the one that most affects the invisticated
region making the vast majority of the orbits to collide or escape from the
system. Moreover, from numerical analysis of orbits started on March 1, 2029,
the less perturbed region is characterized by the variation of the semimajor
axis of 40-days orbits, which do not exceed 2 km very close to the central body
($a < 4$ km, $e < 0.4$). However, no regions investigated could be a possible
option for inserting a spacecraft into natural orbits around Apophis during the
close approach with our planet. Finally, to solve the stabilization problem in
the system, we apply a robust path following control law to control the orbital
geometry of a spacecraft. At last, we present an example of successful
operation of our orbit control with a total $\bigtriangleup v$ of 0.495 m/s for
60 days. All our results are gathered in the CPM-ASTEROID database, which will
be regularly updated by considering other asteroids.
