As a significant component of non-terrestrial networks, satellite communication has gradually evolved into a heterogeneous topology where the network nodes are classified as low Earth orbit (LEO) and geostationary Earth orbit (GEO) nodes. Considering the advantage of low transmission delay of LEO satellites in a heterogeneous network, ground users are arranged to access LEO satellites in the first priority. By fully understanding the equivalent channel gain difference in the beam-edge and beam-center users, we develop non-orthogonal multiple access (NOMA) in an LEO network where different users are allocated in the same resource block. As a complementary strategy, the beam-edge user has the ability to connect the GEO satellite if the LEO links are not available. That is, the two users are served cooperatively by LEO and GEO satellites in an orthogonal manner. In this paper, we provide deep insights for the uplink transmission performance of NOMA and cooperative orthogonal multiple access methods. As a general metric, the analytical expressions of outage probability are derived and the diversity orders are also provided. The simulation results show that NOMA is capable of providing remarkable performance in low signal-to-noise ratio regions and is more promising when the channels are assumed to be ordered.