AAS 97-620
AN ANALYTIC APPROACH TO CALCULATING EARTH COVERAGE
B. Kantsiper and S. Weiss - MIT
Abstract
The recent proliferation of satellite networks for personal communication systems has led to an increase in interest in understanding the dynamics of constellations of satellites. One of the primary metrics used to describe a constellation is its percent coverage, i.e. what percent of the earth's surface can be seen by the satellites at any given time. This parameter is typically calculated computationally, requiring the creation of a grid containing large numbers of points. When there are a large number of satellites or fine precision requirements, this method can be rather slow and becomes even slower if one is interested in multiple satellite coverage instead of only single satellite coverage.
This paper discusses an alternative approach. This new approach is an analytical method utilizing the inclusion-exclusion principle. It is found that the area of the region on a sphere defined by the overlap of circles on that sphere is integrable analytically. The overlap regions are integrated analytically, and inclusion-exclusion is used to calculate the total area covered. The only assumptions which are made are a spherical earth and nadir-pointing satellites. The new method shows a significant increase in speed over traditional numerical integrations.
The first section of this paper details the integration of the overlap regions. The second section discusses how to use the result from section one to implement a code to calculate the coverage for a given constellation of satellites. It also compares the speed of the resulting code to that for a typical grid-based method. The third section discusses possible applications for this new approach to coverage calculations, focusing on its application to developing control requirements for the constellation.