It is easy to feel, on an intuitive basis, that primary cosmic rays of at least some energy range will be able to reach a satellite in earth-orbit from all directions above the local geometric horizon and from essentially no directions below the horizon. This argument suggests that directional cosmic ray detectors on board satellites may safely assume that the only particles received from earthward directions must be splash or albedo particles from the atmosphere, and that any equipment liable to possible radiation damage should be preferentially located on the earthward side of the satellite. In actual fact primary cosmic rays can have quite sharply curved trajectories in the magnetosphere, thereby enabling some particles to gain access to a satellite from a range of directions below the local geometric horizon. The present work presents recent quantitative results on this matter.