  To model existing or future low Earth orbit (LEO) satellite networks
leveraging multiple constellations, we propose a simple analytical approach to
represent the clustering of satellites on orbits. More precisely, we develop a
variable-altitude Poisson orbit process that effectively captures the geometric
fact that satellites are always positioned on orbits, and these orbits may vary
in altitude. Conditionally on the orbit process, satellites situated on these
orbits are modeled as linear Poisson point processes, thereby forming a Cox
point process. For this model, we derive useful statistics, including the
distribution of the distance from the typical user to its nearest visible
satellite, the outage probability, the Laplace functional of the proposed Cox
satellite point process, and the Laplace transform of the interference power
from the Cox-distributed satellites under general fading. The derived
statistics enable the evaluation of the performance of such LEO satellite
communication systems as functions of network parameters.
