  An analytical method is proposed in this work for verification whether an
artificial earth satellite during its orbital motion passes over a region of
the earth surface. The method is based on undisturbed Keppler's approximation
of the orbit and approximation of the region by a circular segment S. In order
to define the situational condition, a conic surface is used with apex in the
earth centre, cutting out the circular segment. The tangents of the conical
surface with Keppler's plane determine the time intervals in which the
satellite trace on the earth surface occurs inside the segment S. The
transformation of these tangents in the plane of Keppler's orbit and the
determination of their crossing points with Keppler's ellipse lies in the basis
of the examined method.
