The development and application of the "one-star multi-purpose, multi-star networking, multi-network collaboration" concept is bringing challenges and imposing higher requirements for the identification of satellite internet key nodes. To solve the problem of inaccurate node evaluation in dynamic satellite networks, an enhanced supra-adjacency matrix (SAM)-based model was proposed. Additionally, taking into account the inherent topological and communicative characteristics of satellite nodes, a comprehensive index system for evaluating node importance was established through the selection of indices such as betweenness centrality, closeness centrality, eigenvector centrality, transmission delay, rate, and capacity. By entropy-weighted technique for order preference by similarity to an ideal solution(TOPSIS) and time-weight matrices, an evaluation algorithm for the determination of the significance of satellite Internet nodes was designed. Simulation results from ARPANET and the Iridium constellation are shown to demonstrate that the proposed model and method not only can sequence the satellite nodes accurately from both local and global perspectives, but also can identify the potential key nodes effectively. These findings are considered to hold significant reference value for the future research of the identification of satellite Internet key nodes.