  Satellite networks are recognized as an effective solution to ensure seamless
connectivity worldwide, catering to a diverse range of applications. However,
the broad coverage and broadcasting nature of satellite networks also expose
them to security challenges. Despite these challenges, there is a lack of
analytical understanding addressing the secrecy performance of these networks.
This paper presents a secrecy rate analysis for downlink low Earth orbit (LEO)
satellite networks by modeling the spatial distribution of satellites, users,
and potential eavesdroppers as homogeneous Poisson point processes on
concentric spheres. Specifically, we provide an analytical expression for the
ergodic secrecy rate of a typical downlink user in terms of the satellite
network parameters, fading parameters, and path-loss exponent. Simulation
results show the exactness of the provided expressions and we find that optimal
satellite altitude increases with eavesdropper density.
