In this paper, we study the privately-own IRIDIUM satellite constellation, to provide a location service that is independent of the GNSS. In particular, we apply our findings to propose a new GNSS spoofing detection solution, exploiting unencrypted IRIDIUM Ring Alert (IRA) messages that are broadcast by IRIDIUM satellites. We firstly reverse-engineer many parameters of the IRIDIUM satellite constellation, such as the satellites speed, packet interarrival times, maximum satellite coverage, satellite pass duration, and the satellite beam constellation, to name a few. Later, we adopt the aforementioned statistics to create a detailed model of the satellite network. Subsequently, we propose a solution to detect unintended deviations of a target user from his path, due to GNSS spoofing attacks. We show that our solution can be used efficiently and effectively to verify the position estimated from standard GNSS satellite constellation, and we provide constraints and parameters to fit several application scenarios. All the results reported in this paper, while showing the quality and viability of our proposal, are supported by real data. In particular, we have collected and analyzed hundreds of thousands of IRA messages, thanks to a measurement campaign lasting several days. All the collected data ($1000+$ hours) have been made available to the research community. Our solution is particularly suitable for unattended scenarios such as deserts, rural areas, or open seas, where standard spoofing detection techniques resorting to crowd-sourcing cannot be used due to deployment limitations. Moreover, contrary to competing solutions, our approach does not resort to physical-layer information, dedicated hardware, or multiple receiving stations, while exploiting only a single receiving antenna and publicly-available IRIDIUM transmissions. Finally, novel research directions are also highlighted.