Constellation Design for Space-Based Space Situational Awareness Applications: An Analytical Approach

Abstract

The growing number of resident space objects in Earth orbit has made effective monitoring a formidable task. Supplementing the capabilities of ground-based sensor networks with on-orbit sensing platforms would dramatically enhance the ability of such systems to detect, track, identify, and characterize resident space objects. To facilitate constellation design that promotes these goals, an optimization approach is selected, which inherently requires a predefined mathematical representation of a cost index or measure of merit. Such representations are often analytically available, but when considering optimal constellation design for space-based space situational awareness 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 certain coverage multiplicities. These analytical results are essential in validating numerical approximations that are able to simulate more complex configurations. Benefits of the cost index are also investigated by demonstrating in tradeoff studies that a significant reduction in the optimal number of satellites can be achieved compared to that predicted by the traditional streets-of-coverage technique.