  We consider a nearly free falling Earth satellite where atomic wave
interferometers are tied to a telescope pointing towards a faraway star. They
measure the acceleration and the rotation relatively to the local inertial
frame.
  We calculate the rotation of the telescope due to the aberrations and the
deflection of the light in the gravitational field of the Earth. We show that
the deflection due to the quadrupolar momentum of the gravity is not negligible
if one wants to observe the Lense-Thirring effect of the Earth.
  We consider some perturbation to the ideal device and we discuss the orders
of magnitude of the phase shifts due to the residual tidal gravitational field
in the satellite and we exhibit the terms which must be taken into account to
calculate and interpret the full signal.
  Within the framework of a geometric model, we calculate the various periodic
components of the signal which must be analyzed to detect the Lense-Tirring
effect. We discuss the results which support a reasonable optimism.
  As a conclusion we put forward the necessity of a more complete, realistic
and powerful model in order to obtain a final conclusion on the theoretical
feasibility of the experiment as far as the observation of the Lense-Thirring
effect is involved.
