Analytical Method for Verification of a Satellite Pass over a Region of the Earth Surface

Abstract

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.