  The extensive coverage offered by satellites makes them effective in
enhancing service continuity for users on dynamic airborne and maritime
platforms, such as airplanes and ships. In particular, geosynchronous Earth
orbit (GEO) satellites ensure stable connectivity for terrestrial users due to
their stationary characteristics when observed from Earth. This paper
introduces a novel approach to model and analyze GEO satellite networks using
stochastic geometry. We model the distribution of GEO satellites in the
geostationary orbit according to a binomial point process (BPP) and examine
satellite visibility depending on the terminal's latitude. Then, we identify
potential distribution cases for GEO satellites and derive case probabilities
based on the properties of the BPP. We also obtain the distance distributions
between the terminal and GEO satellites and derive the coverage probability of
the network. We further approximate the derived expressions using the Poisson
limit theorem. Monte Carlo simulations are performed to validate the analytical
findings, demonstrating a strong alignment between the analyses and
simulations. The simplified analytical results can be used to estimate the
coverage performance of GEO satellite networks by effectively modeling the
positions of GEO satellites.
