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To date, few-shot object detection methods have received extensive attention in the field of remote sensing, and no relevant research has been conducted using satellite videos. It is difficult to identify foreground objects in satellite videos duo to their small size and low contrast and the domain differences between base and novel classes under few-shot conditions. In this paper, we propose a few-shot aircraft detection method with a feature scale selection pyramid and proposal contrastive learning for satellite videos. Specifically, a feature scale selection pyramid network (FSSPN) is constructed to replace the traditional feature pyramid network (FPN), which alleviates the limitation of the inconsistencies in gradient computation between different layers for small-scale objects. In addition, we add proposal contrastive learning items to the loss function to achieve more robust representations of objects. Moreover, we expand the freezing parameters of the network in the fine-tuning stage to reduce the interference of visual differences between the base and novel classes. An evaluation of large-scale experimental data showed that the proposed method makes full use of the advantages of the two-stage fine-tuning strategy and the characteristics of satellite video to enhance the few-shot detection performance.