In practice, low Earth orbit (LEO) and medium Earth orbit (MEO) satellite networks consist of multiple orbits, each populated with many satellites. A widely used spatial architecture for satellites is the Walker constellation, where the longitudes of orbits are equally spaced and the satellites are periodically distributed along the orbits. In this paper, we develop a stochastic geometry model for Walker constellations by constructing orbits that are invariant with respect to (w.r.t.) Earth's spin and satellites that are invariant w.r.t. orbit-wise rotation. This model enables an analysis based on dynamical systems, which allows one to address structural properties such as periodicity and ergodicity. It also enables a stochastic geometry analysis where, for a typical user at a given latitude, we derive the performance of downlink communications as a function of key constellation parameters, including orbit inclination and altitude, the number of orbits, the number of satellites, and the user latitude.

翻译：在实践中，低地球轨道（LEO）和中地球轨道（MEO）卫星网络由多个轨道组成，每个轨道上部署着多颗卫星。Walker星座是一种广泛采用的卫星空间构型，其轨道经度等间距分布，卫星沿轨道周期性排列。本文通过构建相对于地球自转不变的轨道以及相对于轨道旋转不变的卫星，建立了一个Walker星座的随机几何模型。该模型支持基于动力系统的分析，从而能够研究周期性、遍历性等结构特性。同时，该模型也支持随机几何分析：对于给定纬度的一个典型用户，我们推导了下行链路通信性能与关键星座参数（包括轨道倾角与高度、轨道数量、卫星数量以及用户纬度）的函数关系。