Crater detection can provide valuable information for humans to explore the topography and understand the history of extraterrestrial planets. Due to the significantly varying scenario distributions, existing detection models trained on known labelled crater datasets are hardly effective when applied to new unlabelled planets. To address this issue, we propose a two-stage adaptive network (TAN) for semi-supervised cross-domain crater detection. Our network is built on the YOLOv5 detector, where a series of strategies are employed to enhance its cross-domain generalisation ability. In the first stage, we propose an attention-based scale-adaptive fusion (ASAF) strategy to handle objects with significant scale variances. Furthermore, we propose a smoothing hard example mining (SHEM) loss function to address the issue of overfitting on hard examples. In the second stage, we propose a sort-based pseudo-labelling fine-tuning (SPF) strategy for semi-supervised learning to mitigate the distributional differences between source and target domains. For both stages, we employ weak or strong image augmentation to suit different cross-domain tasks. Experimental results on benchmark datasets demonstrate that the proposed network can enhance domain adaptation ability for crater detection under varying scenario distributions.