# Geometric Spherical Surfaces Emulating the Geostationary Orbit at Any Latitude with Zenith Links
## 1 Satellite Constellations: Many Architectures and Many Problems
Recently, new systems are being deployed, such as OneWeb, Telesat, and Starlink. OneWeb aims at establishing a global network with 720 satellites at 1200 km for providing Internet services at Ku and Ka bands, with latency of about 30 ms. Telesat aims at establishing a global network with 120 satellites at about 1200 km using V band, with latency in the range from 30 to 50 ms. Starlink will eventually deploy a very large number of satellites, up to about 12,000. First, 4425 satellites at about 1200 km with latency in the range from 25 to 35 ms. Later, 7518 satellites at 340 km with latency 10 to 15 ms. The satellites will use Ku and Ka bands. Although LEO satellite systems have several advantages, such as shorter propagation delay, fast deployment and lower development costs, there are still many issues to cope with. First, it is necessary to study a system architecture that must integrate with terrestrial networks to offer continuous coverage worldwide. Of course, for this purpose satellite constellation design and coverage schemes are fundamental. LEO systems can be affected by interference from GEO and MEO satellite systems, and therefore interference coordination techniques are required. When inter-satellite links are necessary, the relative movement of the satellites can lead to unstable links, and therefore dynamic network topology and frequent routing updates must be taken into account. The radius of the footprint of a communications satellite in LEO varies significantly. A global communications system using this type of orbit requires a large number of satellites in a number of different orbits. LEO satellite constellations can minimize power in satellites and user terminals, satellite antenna size, time delay for a two-way signal, and maximize the angle of elevation. Compared to MEO satellites, the speed of LEO satellites is high, so that a user can only be connected to a single satellite for few minutes before switching to another. The large number of switchovers must not affect the continuous service. The large speed of LEO satellites results, of course, in very large Doppler shift and Doppler frequency rate of change, which therefore require to be compensated (not an easy task), and the satellites need to be tracked (steering antennas). The large speed and the rapid changes of the satellite footprint and elevation angle make it difficult to estimate the tropospheric fading due to water vapor, oxygen [9] and, especially, rain attenuation [10; 11]. Compared to GEO systems, fade countermeasures (e.g., modulation and coding, site diversity) are very difficult to adopt in LEO systems because of the very fast change in channel transfer function and the small interval of time of its passage. The design of a satellite constellation is one of the critical factors that determine the performance of MEO and, especially, LEO satellite communication systems. The fundamental parameters of a satellite constellation are the type of orbit, the altitude of the orbital plane, the number of orbital planes, the number of satellites in each orbital plane, and the satellite phase factor between different orbit planes. Currently, two LEO satellite constellations are mostly studied and used, the Walker Delta constellation with circular orbits and the Walker star constellation with circular near\(-\)polar orbits [1; 12]. The Walker Delta constellation can adjust the inclination of the orbit according to the desired overlapping coverage of service areas. For example, the overlapping coverage at poles can be reduced, while the overlapping at the Equator can be increased. However, one of its disadvantages is that it cannot establish a stable inter-satellite link with any other satellite on adjacent orbit planes because the relative distance and position of the satellites change continuously [13]. In contrast, in the Walker star constellation, all satellites move regularly from the South Pole to the North Pole, or all in the opposite direction.