Satellite modems are critical components in satellite communication networks. Especially, they determine the entire communication regime in traditional systems where the satellites only act as transparent relays. However, unlike satellites that are usually more isolated and better protected, satellite modems are accessible and susceptible to lower-cost attacks, potentially serving as a weak link in the chain of satellite communication security. We make the first attempt to shed light on satellite modem security. We first physically disassemble commodity satellite modems and systematically examine hardware and software modules. We perform a measurement study on the satellite modems that are exposed to the Internet. We identify 16 security vulnerabilities across three attack surfaces: satellite communication interface, ground network interface, and hardware. We further introduce AirSecAnalyzer, an automated security analyzer/fuzzer for the modems' satellite communication interface. Through comprehensive analysis and extensive experiments on 9 real-world satellite modems, we report 18 novel attacks that exploit the identified vulnerabilities. Our findings are expected to contribute as a valuable foundation for future research on the security of satellite modems and satellite communication networks.