We have studied the perturbative effect of the force due
to direct solar radiation pressure on the dynamics of artificial
satellites in a more comprehensive way than has been done so far. We
have included a general model for the atmospheric refraction and
extinction and have computed the illumination of a satellite for any
geometric arrangement between it, the Earth and the Sun. This allowed
us to investigate in detail the transition between the full sunlight
and the shadow. We have considered separately the influence of the
atmospheric refraction (treated according to geometrical optics) and
the various physical processes in the atmosphere (absorption and
scattering), to conclude that in general the flux attenuation during
penumbra is most easily interpreted as due to a compression of the
solar disk when viewed from the satellite through the Earth's
atmosphere. The eclipsing of the finite--size solar disk by the
solid Earth plays a minor role, whereas the refraction in the Earth
atmosphere's produces an extended tail in the radiation force.
However, the magnitude and duration of this tail depends upon the
atmospheric conditions over a limited region of the Earth's surface.
Several consequences of the theory have been exemplified by
computing the perturbing force during penumbra on LAGEOS and other
satellites.
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