The New Space Era and the emergence of high-bandwidth Low Earth Orbit (LEO) satellite constellations have caused a rapid change in the cyber threat landscape for industries reliant on satellite communications. One of these is the maritime sector. This work aims to analyze the threat landscape in satellite communications for maritime operations. To this end, an overview of the systems related to satellite communications in maritime operations is first provided. Then, three threat modelling methods, namely the STRIDE method, the Microsoft Threat Modelling Tool and the SPARTA framework are used to provide a holistic analysis of the threats in satellite communications at different, complementary levels. As an example, a sophisticated GPS spoofing attack that can cause major incidents for ships is analyzed in detail. The results will support the space sector towards improving the system architecture and making ship operations more secure.