We discuss the effects of taking into account the Earth's
polar flattening when modelling the solar radiation force which
perturbs the orbit of Earth satellites during their penumbra
transitions. For this purpose, we generalize our previous theory for
these perturbations (Vokrouhlick\'y et~al. 1993b), which assumed a
spherical Earth. The new theory is then applied to two satellites for
which the penumbra perturbations may produce detectable effects. The
main changes with respect to the case with a spherical Earth appear
in the timing of the transition phases leading from sunlight to
shadow and {\it vice versa}, and in the overall duration of the
eclipse intervals. These changes can cause
short--periodic dynamical effects, and might be directly observable
through {\it in situ} microaccelerometric measurements with good time
resolution. On the other hand, we show that no additional long--term
orbital effect on LAGEOS--type satellites is expected as a consequence
of the Earth's polar flattening, owing to a symmetry in the shadow
entry/exit phases, which causes the perturbations to average out along
one satellite revolution.
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