  Low Earth orbit (LEO) satellites are being considered for expanding legacy
terrestrial cellular networks. The end users may not be able to optimize
satellite orbits and constellations, however, they can optimize locations of
ground stations which aggregate terrestrial traffic and inter-connect with
over-passing satellites. Such optimization requires a model of satellite
visibility to decide when the satellite becomes visible to the ground station
in a given geographical location. Our model assumes ideal Kepler orbits
parameterized by six orbital elements to describe the satellite movements. The
steps of Kepler orbit modeling are presented in detail to enable other studies
requiring geometric representation of satellite trajectories in the 3D space or
their 2D footprint on the Earth surface. The long-term mean time satellite
visibility (MTSV) metric is defined to measure satellite visibility at a given
ground station. Numerical results reveal that efficiency of optimizing the
ground station locations is dependent on the satellite orbit and other
satellite visibility constraints. The ground station location optimization is
especially important when MTSV is improved by orthogonal time sharing schemes
using multiple satellites on the same or different orbits. Similar conclusions
can be drawn assuming other performance metrics such as the capacity of links
between the ground station and the satellites.
