The proliferation of low-Earth orbit (LEO) satellite constellations presents unprecedented opportunities for distributed machine learning (ML) applications. However, the inherent challenges of sparse connectivity, heterogeneous communication windows, and non-independent and identically distributed (non-IID) data across satellites hinder the effectiveness of conventional federated learning (FL) frameworks. To address these challenges, we propose Model Contrastive Federated Learning (MCFL), a novel framework tailored for LEO satellite constellations. MCFL introduces a two-stage approach: 1) similarity-based satellite clustering to mitigate intra-cluster data imbalance by grouping satellites with aligned data distributions, and 2) collaborative staleness-aware learning that employs semi-asynchronous model aggregation within clusters to balance convergence speed and model accuracy. The key contributions include a contrastive loss function for robust representation learning under class imbalance, gradient sparsification to minimize communication overhead, and an inter-cluster knowledge-sharing mechanism to prevent cluster-specific model bias. Extensive simulations on the EuroSAT dataset demonstrate that MCFL achieves an improvement of 15% in test accuracy and reduces training time 3× compared to state-of-the-art FL baselines while reducing communication costs by 40%. This work bridges the gap between distributed learning theory and practical satellite constraints, offering a scalable solution for real-time ML applications in dynamic space-terrestrial networks.