Coverage regions are important considerations in the design and use of
many space systems. Applications include ground-to-space and space-to
-space communications, sensor coverage, and weapon reach. The ''covera
ge region'' umbrella includes ''constraint regions,'' e.g., eclipse re
gions for satellite visibility issues. The fundamental building blocks
are circular regions on a sphere. These are combined to form more com
plex regions. Equations, based on spherical trigonometry, are develope
d to compute the boundaries of coverage regions in both geographic and
satellite orbit coordinates. Emphasis is placed on circular satellite
orbits, but extensions to elliptical orbits are addressed. For the la
tter, approaches to derive quartic solutions for satellite umbra and p
enumbra entrance and exit times, and for tangents to coverage regions,
are indicated. Various applications are illustrated.