We analyze a narrow-beam low earth orbit (NB LEO) terrestrial-satellite uplink from the perspective of the typical satellite base station. The user equipment (UEs) are located on the earth's surface according to a homogeneous Poisson point process (PPP). We present a simplified planar system model and focus on the point process of the approximate antenna gains of each UE in the satellite base station's antenna pattern and analyze the signal-to-interference ratio (SIR), the SIR meta distribution (MD), the signal-to-interference-plus-noise ratio (SINR) and the throughput. We present simple analytical results, some in closed form, for the performance metrics. We validate the approximate system model by comparing the results to the Monte Carlo simulated performance metrics using the more accurate system model incorporating the earth's curvature. The paper includes insightful results that help to understand the quantitative and qualitative nature of the NB LEO satellite uplink.