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

TL;DR

This paper introduces an analytical method to verify if a satellite passes over a specific Earth surface region using Kepler's approximation and geometric constructions, enabling precise orbit-region intersection analysis.

Contribution

The work presents a novel analytical approach combining Kepler's orbit approximation with geometric methods to verify satellite passes over designated Earth regions.

Findings

Method accurately determines satellite passes over regions.

Uses geometric and Kepler's approximation for analysis.

Applicable for satellite orbit verification tasks.

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.