An increase in availability of Software Defined Radios (SDRs) has caused a dramatic shift in the threat landscape of legacy satellite systems, opening them up to easy spoofing attacks by low-budget adversaries. Physical-layer authentication methods can help improve the security of these systems by providing additional validation without modifying the space segment. This paper extends previous research on Radio Frequency Fingerprinting (RFF) of satellite communication to the Orbcomm satellite formation. The GPS and Iridium constellations are already well covered in prior research, but the feasibility of transferring techniques to other formations has not yet been examined, and raises previously undiscussed challenges. In this paper, we collect a novel dataset containing 8992474 packets from the Orbcom satellite constellation using different SDRs and locations. We use this dataset to train RFF systems based on convolutional neural networks. We achieve an ROC AUC score of 0.53 when distinguishing different satellites within the constellation, and 0.98 when distinguishing legitimate satellites from SDRs in a spoofing scenario. We also demonstrate the possibility of mixing datasets using different SDRs in different physical locations.