The geostationary orbit is a special and important spatial orbital resource. However, space resident objects in this orbit pose potential threats to space security, characterized as dim and small targets in imaging features. To solve the problem of detecting dim and small targets in geostationary orbit, we propose a multi-frame temporal dense nested attention method, which consists of a uniform linear motion constraint module and a dense nested attention module. The dense nested attention module adopts a multi-layer U-shaped structure and channel spatial attention mechanism, which can preserve the deep features of small targets, extract and fuse features from different scales of feature maps, and finally obtain the preliminary detection results of single-frame images. The uniform linear motion constraint module uses the prior information of the target motion in the image sequence, removes false positives and supplements false negatives, and improves the detection performance. Experiments were conducted on the SpotGEO dataset publicly released by the European Space Agency. The results of our experiments indicate that our method outperforms the state-of-the-art approach, showing a 12.83% reduction in Mean Squared Error compared to the current leading method. Our method, characterized by its minimal parameter requirement and independence from extensive dataset pre-training, is ideally suited for integration into small satellite devices, enabling efficient monitoring and mitigation of resident space objects.