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# Satellite Communications

## 5.1 SPACE GEOMETRY OF SATELLITE SYSTEM

### 5.1.1 Introduction

This chapter provides useful indications for determination of satellite orbits, such as the period of revolution, the distance with respect to the center of Earth or to an Earth station, and the travel speed of the satellite on its orbit. It is devoted, essentially, to the systems of telecommunication using a geostationary satellite, but the principles remain valid for the systems comprising a moving satellite.

### 5.1.2 General Characteristics of Orbits

Calculation of a satellite orbit rests, on the one hand, on Kepler's laws and, on the other hand, on universal gravitation, Newton's law. Figure 5.1 presents the relative positions of Earth and the satellite in its orbit with the following notations:

 r Distance between centers of gravity of Earth and satellite a Half large axis of ellipse c Distance between center of Earth and that of ellipse M Mass of Earth m Mass of satellite α Angular distance of satellite relative to perigee

5.1.2.1 Kepler's Laws

1. The trajectory of a planet in space, called its orbit, is an ellipse described in a plane which contains the center of the sun placed at one of the focus (1602).
2. The vector which connects the sun to the planet sweeps equal surfaces ...

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