Optimization processes rely on the availability of a pre-defined cost function. Generally, such representations are often analytically available. However, when considering optimal constellation design for space-based space situational awareness applications, a closed-form representation of the cost index is only available under certain assumptions. The present investigation 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.
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