  The nearby space surrounding the Earth is densely populated by artificial
satellites and instruments, whose orbits are distributed within the
Low-Earth-Orbit region (LEO), ranging between 90 and 2 000 $km$ of altitude. As
a consequence of collisions and fragmentations, many space debris of different
sizes are left in the LEO region. Given the threat raised by the possible
damages which a collision of debris can provoke with operational or manned
satellites, the study of their dynamics is nowadays mandatory. This work is
focused on the existence of equilibria and the dynamics of resonances in LEO.
We base our results on a simplified model which includes the geopotential and
the atmospheric drag. Using such model, we make a qualitative study of the
resonances and the equilibrium positions, including their location and
stability. The dissipative effect due to the atmosphere provokes a tidal decay,
but we give examples of different behaviors, precisely a straightforward
passage through the resonance or rather a temporary capture. We also
investigate the effect of the solar cycle which is responsible of fluctuations
of the atmospheric density and we analyze the influence of Sun and Moon on LEO
objects.
