Look Angle Determination

Look Angle Determination:

The look angles for the ground station antenna are Azimuth and Elevation angles. They are required at the antenna so that it points directly at the satellite. Look angles are calculated by considering the elliptical orbit. These angles change in order to track the satellite.

For geostationary orbit, these angels values does not change as the satellites are stationary with respect to earth. Thus large earth stations are used for commercial communications.

For home antennas, antenna beamwidth is quite broad and hence no tracking is essential. This leads to a fixed position for these antennas.

With respect to the figure 1.8 and 1.9, the following information is needed to determine the look angles of geostationary orbit.

1. Earth Station Latitude: λ_E

2. Earth Station Longitude: Φ_E

3. Sub-Satellite Point‟s Longitude: Φ_SS

4. ES: Position of Earth Station

5. SS: Sub-Satellite Point

6. S: Satellite

7. d: Range from ES to S

8. ζ: angle to be determined

Considering figure 3.3, it‟s a spherical triangle. All sides are the arcs of a great circle. Three sides of this triangle are defined by the angles subtended by the centre of the earth.

o Side a: angle between North Pole and radius of the sub-satellite point.

o Side b: angle between radius of Earth and radius of the sub-satellite point.

o Side c: angle between radius of Earth and the North Pole.

a =90⁰ and such a spherical triangle is called quadrantal triangle. c = 90⁰ – λ

Angle B is the angle between the plane containing c and the plane containing a.

Thus, B = Φ_E-Φ_SS

Angle A is the angle between the plane containing b and the plane containing c.

Angle C is the angle between the plane containing a and the plane containing b.

Thus, a = 90⁰

c = 90⁰ - λ_E

B = Φ_E-Φ_SS

Thus, b = arcos (cos B cos λE)

And A = arcsin (sin |B| / sin b)

Applying the cosine rule for plane triangle to the triangle of figure

Applying the sine rule for plane triangles to the triangle of figure 3.3 allows the angle of elevation to be found: