The efficient utilization of limited spectrum resources presents a significant challenge given the increasing demand for various services in satellite communication systems. To address this challenge, there is a growing interest in understanding and modeling the operationalization of combined geostationary (GEO) and low Earth orbit (LEO) multiorbit systems. In this letter, we investigate the potential for improving spectral efficiency in a multiorbit setup by leveraging cognitive radio. Our proposed cognitive system enables LEO satellites (SATs) to opportunistically reuse the radio resources allocated to GEO SATs. In particular, the focus of our study is on characterizing the time-varying performance of secondary LEO systems, with GEO SATs being considered as primary systems. Through comprehensive analysis and simulations, we demonstrate the significant advantages of our proposed cognitive system, particularly in terms of creating ample opportunities for LEO systems to effectively reuse the spectrum allocated to GEO systems.