Federated learning (FL) has recently become a promising solution for analyzing remote sensing satellite imagery (RSSI). However, the large scale and inherent data heterogeneity of images collected from multiple satellites, where the local data distribution of each satellite differs from the global one, present significant challenges to effective model training. To address this issue, we propose a Geometric Knowledge-Guided Federated Dual Knowledge Distillation (GK-FedDKD) framework for RSSI analysis. In our approach, each local client first distills a teacher encoder (TE) from multiple student encoders (SEs) trained with unlabeled augmented data. The TE is then connected with a shared classifier to form a teacher network (TN) that supervises the training of a new student network (SN). The intermediate representations of the TN are used to compute local covariance matrices, which are aggregated at the server to generate global geometric knowledge (GGK). This GGK is subsequently employed for local embedding augmentation to further guide SN training. We also design a novel loss function and a multi-prototype generation pipeline to stabilize the training process. Evaluation over multiple datasets showcases that the proposed GK-FedDKD approach is superior to the considered state-of-the-art baselines, e.g., the proposed approach with the Swin-T backbone surpasses previous SOTA approaches by an average 68.89% on the EuroSAT dataset.