Some aspects of the dynamics of fictitious Earthʹs satellites

In this work we study the dynamics of fictitious satellites of the Earth. In the first part we do not consider the effect of the Moon and study the dynamics in the restrict three–body model, i.e., a massless satellite under the effect of the gravitational force of an oblate Earth and that of the Sun. We show that a satellite starting with an almost circular orbit suffers very large variations of eccentricity, depending on the initial inclination of the orbit with respect to the reference plane. As the eccentricity may be driven to very large values (≈0.9), mutual collisions between satellites or collisions with the planet may occur. In the second part, we include the gravitational effect of the Moon. In this case, we find two regions with large variations of eccentricity due to the presence of the Moon. Consequently, in both scenarios, we find some large regions of the phase space where the long-term stability of some fictitious Earthʹs satellites is not possible.