Massive machine-type communication in satellite networks presents significant challenges for random access systems, particularly due to the limited number of terminals that can successfully access the network concurrently. To address this issue, this paper proposes a novel binary circular polarization modulation based non-orthogonal multiple access slotted ALOHA (BCPM-NOMA-SA) scheme that fully exploits the polarization characteristics of satellite transmission. The proposed approach first achieves orthogonal signal separation in the polarization domain through BCPM. Subsequently, an equivalent noise model is established by analyzing the Cramér-Rao lower bound (CRLB) of channel estimation errors. Finally, the upper bound of system throughput is derived, providing a theoretical foundation for the synergistic gains of polarization and power domain multiplexing. Simulation results demonstrate that the proposed scheme achieves 20-35% throughput improvement compared to conventional NOMA-SA and BCPM-SA schemes, showing significant performance advantages.