In the context of terrestrial space missions, thanks to the recent development of micro and nanotechnologies, nanosatellites are becoming increasingly popular for their lower cost and ease of deployment. The NIMPH (Nanosatellite to Investigate Microwave Photonics Hardware) mission is an ongoing academic project aimed at developing and launching such a nanosatellite. The onboard resources on these missions are often very limited, and in our study case, a single onboard computer is responsible for orchestrating the science and avionic tasks of the nanosatellite. These tasks are subject to various constraints, such as frequency, minimum/maximum delay between the execution of the same type of task and strict precedences. This makes the scheduling of the onboard tasks a challenging problem, which is critical for the mission success. In this paper, we tackle the problem of scheduling NIMPH onboard tasks using Constraint Programming methods. Our scheduler demonstrates its performance by generating optimal or near-optimal schedules for the NIMPH nanosatellite.