Analytical Effective Method for Verification of a Satellite Pass over a Region of the Earth Surface Atanas Marinov Atanassov Solar Terrestrial Influences Institute, Bulgarian Academy of Sciences, Stara Zagora Department, P.O. Box 73, 6000 Stara Zagora, Bulgaria 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. 1. Introduction. A number of cases exist when, during space experiments, it is necessary to know the time of a satellite pass over a definite region of the earth surface. Thus, for example, in synchronous satellite and ground-based measurements, it is important when the satellite passes over a definite territory where the ground-based station is located. When problems of meteorological character are solved on the basis of satellite information, it is significant when the satellite is going to pass over a definite territory or a meteorological structure (cyclone centre, front). The solution of many other problems, connected with the study of the earth surface from space is connected with the determination of the temporal interval pass over a specific region. This is necessary in some of the cases for experiments planning. In other cases, the analysis is needed to schedule the seances for receiving satellite information. In both cases this is important for the quality of the conducted experiments, and from economical point of view. The problem for determining a satellite pass over a definite geographic region has a standard solution. It is obtained on the basis of the imitation modelling by selecting a proper geometrical model for region V which determines the situational condition. The discretization of the solution of the artificial earth satellite motion equation and the respective analysis, as concerns the model of the region, allow to determine whether the satellite passes over the region as well as the moments of crossing its borders. For the equation of the artificial earth satellite motion in geo-equatorial co- ordinate system (GeCS) we have: (1) , f t d r d m k 2 2  - = → →