Geometry of GSO Links Visibility : Elevation angle and azimuth angle

GSO parameters Since the GSO is the dominant orbit used for communications satellites, we will study in this section the procedures to determine the parameters required to define the GSO parameters that are used to evaluate satellite link performance and design. The three key parameters for the evaluation of the GSO link are: 1) d=range (distance) from the earth station (ES) to the satellite, in km 2)φ z =azimuth angle from the ES to the satellite, in degrees 3) θ =elevation angle from the ES to the satellite, in degrees

GSO parameters The azimuth and elevation angles are referred to as the look angles for the ES to the satellite. Figure below shows the geometry and definitions of the look angles with respect to the earth station reference. The azimuth angle φ z is measured from true north in an eastward direction to the projection of the satellite path onto the local horizontal plane

Azimuth and elevation angles

GSO parameters There are many sources available in the orbital mechanics and satellite literature that describe the detailed development of the calculations for the GSO parameters, range, elevation angle, and azimuth angle. The input parameters required to determine the GSO parameters are: l E =earth station longitude, in degrees l S =satellite longitude, in degrees L E =earth station latitude, in degrees L S =satellite latitude in degrees (assumed to be 0, i.e., inclination angle=0) H=earth station altitude above sea level, in km The point on the earth’s equator at the satellite longitude is called the subsatellite point.

GSO parameters Longitude and latitude sign values Sea level Earth station Earth station altitude

GSO parameters Additional parameters required for the calculations are: Equatorial Radius: r e = km Geostationary Radius: r S = km Geostationary Height (Altitude): h GSO =r S −r e = km Eccentricity of the earth: e = An additional parameter required for the calculation of the GSO parameters is the differential longitude, B, defined as the difference between the earth station and satellite longitudes: B = l E − l S For example, for an earth station located inWashington, DC, at the longitude of 77◦W, and a satellite located at a longitude of 110◦W: B = (−77) − (−110) = +33◦

geometry S Center of earth rsrs rere d Local horizontal θ ψ δ d=rs ( 1+(re/rs)² - 2(re/rs) cos(δ) ) 1/2 Cos(δ) =cos (Le). Cos (Ls) cos(ls-le) + sin (Le).sin (Ls)

Elevation Angle to Satellite The elevation angle is important because it determines the slant path through the earth’s atmosphere, and will be the major parameter in evaluating atmospheric degradations such as rain attenuation, gaseous attenuation, and scintillation on the path. Generally, the lower the elevation angle, the more serious the atmospheric degradations will be, because more of the atmosphere will be present to interact with the radiowave on the path to the satellite. The elevation angle from the earth station to the satellite, θ, is determined from where re =equatorial radius; h GSO = geostationary altitude; d = range, in km; B = differential longitude, in degrees; and L E =ES latitude, in degrees.

intermediate angle to Satellite The final parameter of interest is the earth station azimuth angle to the satellite. To calculate this angle an intermediate angle Ai (called also α) is found from The azimuth angle z is determined from the intermediate angle Ai from one of four possible conditions, based on the relative location of the earth station and the subsatellite point on the earth’s surface.

azimuth look angle Having found the intermidate angle α (= Ai ), the azimuth look angle φ z can be found from: Case 1: Earth station in the Northern Hemisphere with (a) Satellite to the SE of the earth station: φ z =180°- α (b) Satellite to the SW of the earth station: φ z =180°+ α Case 2: Earth station in the Southern Hemisphere with (c) Satellite to the NE of the earth station: φ z = α (d) Satellite to the NW of the earth station: φ z =360°- α

azimuth look angle

example This section presents a sample calculation for the determination of the GSO parameters described above. Consider an earth station located in Washington, DC, and a GSO satellite located at 97◦W. The input parameters, using the following sign conventions : Earth Station: Washington, DC – Latitude: LE =39◦ N=+39 – Longitude: lE =77◦ W=−77 – Altitude: H=0km Satellite: – Latitude: LS =0◦ (inclination angle=0) – Longitude: lS =97◦ W=−97 1) Find the range, d, 2) The elevation angle θ 3) The azimuth angle, φ z, to the satellite.