  As low Earth orbit (LEO) satellite communication systems are gaining
increasing popularity, new theoretical methodologies are required to
investigate such networks' performance at large. This is because deterministic
and location-based models that have previously been applied to analyze
satellite systems are typically restricted to support simulations only. In this
paper, we derive analytical expressions for the downlink coverage probability
and average data rate of generic LEO networks, regardless of the actual
satellites' locality and their service area geometry. Our solution stems from
stochastic geometry, which abstracts the generic networks into uniform binomial
point processes. Applying the proposed model, we then study the performance of
the networks as a function of key constellation design parameters. Finally, to
fit the theoretical modeling more precisely to real deterministic
constellations, we introduce the effective number of satellites as a parameter
to compensate for the practical uneven distribution of satellites on different
latitudes. In addition to deriving exact network performance metrics, the study
reveals several guidelines for selecting the design parameters for future
massive LEO constellations, e.g., the number of frequency channels and
altitude.
