Accuracy and precision remains a challenge for capturing system requirements in general, space systems are no exception. Current research efforts continue to fundamentally rely on natural language (shall statements), which is inherently ambiguous, and thus unable to capture the problem space accurately and precisely. We suggest in this paper a model-based approach to requirements that avoids the use of requirements in natural language and leverages formal modeling and system-theoretic constructs instead. Specifically, the proposed approach extends behavioral and structural model elements of the Systems Modeling Language (SysML) with a system-theoretic definition of a solution space. Considering a system model to be a transformation of inputs into outputs, we model the problem space in this paper as a set of required transformations of inputs into outputs. We apply the proposed model-based approach to formulate a subset of requirements of a satellite's Telemetry, Tracking, and Command (TTC) transponder. We use an existing set of requirements for such a system in natural language as a benchmark and evaluate precision, accuracy, and completeness aspects achieved by the proposed model-based formulation.