  A model that combines celestial geometry and atmospheric physics is used to
calculate the dimming of artificial satellites as they enter and exit the
Earth's shadow. Refraction of sunlight by the terrestrial atmosphere can
illuminate a satellite while it is inside the eclipse region determined from
geometry alone. Meanwhile, refraction combines with atmospheric absorption to
dim the satellites for tens of km outside of that region. Spacecraft brightness
is reduced more in blue light than in red because absorption of sunlight is
stronger at shorter wavelengths. Observations from the MMT-9 robotic
observatory are consistent with the model predictions. Tables of satellite
brightness as functions of their location in the eclipse region are provided.
