# Geocentric Spherical Surfaces Emulating the Geostationary Orbit at Any Latitude with Zenith Links

## Abstract

**:**

## 1. Satellite Constellations: Many Architectures and Many Problems

## 2. Geocentric Spherical Surfaces Emulating the Geostationary Orbit

## 3. Geometrical and Radio Electrical Parameters

^{3}s

^{−2}.

## 4. Discussion and Conclusions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Geometry for finding the relationship between the geocentric angle $\phi $ and aperture angle $\theta $ (the main antenna lobe, e.g., at $-3$dB gain) of the downlink and uplink antennas of the GeoSurf. This situation, with no overlapping of the service areas, is found only at the equator. O is the center of the Earth; AB is the approximate diameter of the service area. $R$ is the Earth radius, the segment CD gives the (approximate) height $h$of the orbit from the surface. The connected satellite is at C. The triangles at left and right give the position and service area of the adjacent satellites in the same orbit plane in the North−South direction, or in adjacent orbit planes in West−East direction but only at the equator (no overlapping).

**Figure 2.**Total number of satellites in the design of the GeoSurf constellation. This number is independent of the altitude of the GeoSurf constellation. $N$ ranges from 2592 for $\phi =5\xb0$ to 288 for for $\phi =15\xb0$.

**Figure 3.**Up−link, down−link and service area angle ($-3$ dB) of the GeoSurf constellation design, as a function of the geocentric angle $\phi $.

**A**refers to $h=35,876$ km;

**B**to $h=20,000$ km;

**C**to $h=10,000$ km,

**D**to $h=1500$ km.

**Figure 4.**Satellite service-area time as a function of the service area diameter for the GeoSurf Constellation.

**A**refers to $h=35,876$ km;

**B**to $h=20,000$ km;

**C**to $h=10,000$ km,

**D**to $h=1500$ km.

**Figure 5.**Antenna gain as a function of the service area diameter for the GeoSurf constellation. Antenna efficiency is 0.6.

**A**refers to $h=35,876$ km;

**B**to $h=20,000$ km;

**C**to $h=10,000$ km,

**D**to $h=1500$ km.

**Figure 6.**Antenna diameter as a function of the service area diameter, at 20 GHz for the GeoSurf constellation.

**A**refers to $h=35,876$ km;

**B**to $h=20,000$ km;

**C**to $h=10,000$ km,

**D**to $h=1500$ km.

**Figure 7.**Antenna diameter as a function of the service area diameter, at 30 GHz for the GeoSurf constellation.

**A**refers to h = 35,876 km;

**B**to h = 20,000 km;

**C**to h = 10,000 km,

**D**to h = 1500 km.

**Figure 8.**Antenna diameter as a function of the service area diameter, at 40 GHz for the GeoSurf constellation.

**A**refers to h = 35,876 km;

**B**to h = 20,000 km;

**C**to h = 10,000 km,

**D**to h = 1500 km.

**Figure 9.**Antenna diameter as a function of the service area diameter, at 50 GHz for the GeoSurf constellation.

**A**refers to h = 35,876 km;

**B**to h = 20,000 km;

**C**to h = 10,000 km,

**D**to h = 1500 km.

**Table 1.**General characteristics (advantages and disadvantages) of the most popular constellations (identified by their altitude above the Earth surface) compared to the GeoSurf constellation. It is assumed that the frequency band and worldwide communication service type are the same for all systems.

Parameter | GEO (35,876 km) | MEO (20,000 km) | LEO (1500 km) | GeoSurf (35,876 to 1500 km, or Lower) |
---|---|---|---|---|

Number of satellites | few | several | many, up to 12,000 | many, up to 2592 |

Free−space attenuation | large | medium | low | minimum (zenith path); 6 dBs extra loss when the satellite enters or leaves the local −3 dB service area |

Antenna steering | fixed | moderate | large | fixed (zenith) |

Minimum (zenith path for all) two−way latency due to propagation (ms) | 238.7 | 133.4 | 10.1 | from 238.7 to 10.1 |

Link elevation angle | fixed | variable | largely variable | fixed 90° (zenith) |

High latitude service | no service | service | service | equal service for any latitude |

Satellite footprint | fixed | almost fixed | changes very much | fixed, large moderate to large overlapping at high latitudes |

Tropospheric attenuation (no rain) | stationary, easy to estimate. Fade countermeasures “easy” to implement. | can be smaller than GEO, easy to estimate. Fade countermeasures relatively “easy” to implement. | can be much larger than GEO, difficult to estimate. Fade countermeasures very difficult to implement. | minimum (zenith path), very easy to estimate. Fade countermeasures “easy” to implement. |

Scintillation | moderate or large, depends on elevation angle and antenna size, easy to estimate | can be smaller than GEO, easy to estimate | can be much larger than GEO, difficult to estimate | minimum (zenith path), very easy to estimate |

Rain attenuation | can be large, depends on site, easy to estimate | can be smaller than GEO, easy to estimate | can be much larger than GEO, difficult to estimate | minimum (zenith path), very easy to estimate |

Switchovers in a given time interval | none or very few | few | many | few to many |

Inter-satellite links | none or very few | few | many | few to many |

Doppler phenomena | negligible | small | large or very large | negligible to very small |

Frequency plan and complexity | moderate | moderate | large to very large | from moderate to very large |

Interference with GEO satellites | small | moderate | large | only for sites very close to the equator |

Orbit capacity | moderate | moderate | large | from moderate to large |

Launching sites for minimizing fuel | close to equator | medium latitudes | medium latitudes | any latitude |

Control and maintenance | minimum | moderate | large | from moderate to large |

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**MDPI and ACS Style**

Matricciani, E.
Geocentric Spherical Surfaces Emulating the Geostationary Orbit at Any Latitude with Zenith Links. *Future Internet* **2020**, *12*, 16.
https://doi.org/10.3390/fi12010016

**AMA Style**

Matricciani E.
Geocentric Spherical Surfaces Emulating the Geostationary Orbit at Any Latitude with Zenith Links. *Future Internet*. 2020; 12(1):16.
https://doi.org/10.3390/fi12010016

**Chicago/Turabian Style**

Matricciani, Emilio.
2020. "Geocentric Spherical Surfaces Emulating the Geostationary Orbit at Any Latitude with Zenith Links" *Future Internet* 12, no. 1: 16.
https://doi.org/10.3390/fi12010016