  In this paper we consider satellite trajectories in central force field with
quadratic drag using two formalisms. The first using polar coordinates in which
the angular momentum plays a dominant role. The second is in Levi-Civita
coordinates in which the energy plays a central role. We then unify these two
formalisms by introducing polar coordinates in Levi-Civita space and derive a
new equation for satellite orbits in which energy and and angular momentum are
on equal footing {and thus characterize the orbit by its two invariants}. In
the second part of the paper we derive in Levi-Civita coordinates a linearized
equation for the relative motion of two satellites whose trajectories are in
the same plane. We carry out also a numerical verification of these equations.
