In recent years, the accumulation of space debris has become an increasingly pressing issue, and adequately monitoring it is a formidable task for designated ground-based sensors. Supplementing the capabilities of these ground-based networks with orbiting sensing platforms would dramatically enhance the ability of such systems to detect, track, identify, and characterize resident space objects -- the primary goals of modern space situational awareness (SSA). Space-based space situational awareness (SBSSA), then, is concerned with achieving the stated SSA goals through coordinated orbiting sensing platforms. To facilitate the design of satellite constellations that promote SSA goals, an optimization approach is selected, which inherently requires a pre-defined mathematical representation of a cost index or measure of merit. Such representations are often analytically available, but when considering optimal constellation design for SBSSA applications, a closed-form expression for the cost index is only available under certain assumptions. The present study focuses on a subset of cases that admit exact representations. In this case, geometrical arguments are employed to establish an analytical formulation for the coverage area provided as well as for the coverage multiplicity. These analytical results are essential in validating numerical approximations that are able to simulate more complex configurations. / text

As near-Earth space becomes increasingly crowded with spacecraft and debris, the need for improved space situational awareness has become paramount. Contemporary ground-based systems are limited in the detection of very small or dim targets. In contrast, space-based systems, above most atmospheric interference, can achieve significant improvements in dim target detection by observing targets against a clutter-free space background, i.e. targets above the horizon (ATH). In this study, numerical methods for the evaluation of ATH coverage provided by constellations of satellites are developed. Analysis of ATH coverage volume is reduced to a planar analysis of cross-sectional coverage area in the orbit plane. The coverage model performs sequences of boolean operations between polygons representing cross-sections of satellite sensor coverage regions and regions of interest, returning the coverage area at the desired multiplicity. This methodology allows investigation of any coverage multiplicity for planar constellations of any size, and use of arbitrary sensor profiles and regions of interest. The implementation is applied to several constellation design problems demonstrating the utility of the numerical ATH coverage model in a constellation design process. / text