Despite their well-known energy advantages, spiking neural networks (SNNs) still fall short of conventional artificial neural networks in detection accuracy for on-orbit remote sensing, limiting their use on power-constrained satellites. To address this gap, we present SpikeYOLO-C2TCA, an improved SNN detector built upon the SpikeYOLO backbone. The core of our method is a new attention module, SpikeTCA, which operates directly on membrane potentials. It combines three complementary descriptors—direction-aware pooling, multi-scale depthwise convolution, and temporal convolution—and fuses them through cross-temporal self-attention and a lightweight channel MLP to enhance feature discriminability and suppress background clutter. In addition, we introduce a SpikeC2fCIB module that employs a five-layer depthwise-separable bottleneck following a split–process–merge structure, leading to better feature reuse, gradient flow, and computational efficiency. On the RSOD dataset, SpikeYOLO-C2TCA reaches an mAP50 of 96.7% and an mAP50-95 of 63.7%, exceeding the SpikeYOLO baseline by 6.6 and 1.2 percentage points, respectively. Overall, SpikeYOLO-C2TCA delivers better detection accuracy than the baseline while consuming less energy, offering a practical lightweight solution for edge platforms such as on-orbit satellites and long-endurance unmanned aerial vehicles.