ssrs 2014 barcode A geostationary satellite is located at 90 W. Calculate the azimuth in Software

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Example 3.1 A geostationary satellite is located at 90 W. Calculate the azimuth
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angle for an earth-station antenna at latitude 35 N and longitude 100 W.
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The given quantities are 90 100 lE E B
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(c) Figure 3.3
Azimuth angles related to angle A (see Table 3.1).
TABLE 3.1
Azimuth Angles Az from Fig. 3.3 lE <0 <0 >0 >0 B <0 >0 <0 >0 Az, degrees A 360 180 180 A A A
Fig. 3.3 a b c d
The Geostationary Orbit
From Eq. (3.8): b arccos(cos B cos lE) 36.23 From Eq. (3.9): A 5 arcsina 17.1 By inspection, lE > 0 and B < 0. Therefore, Fig. 3.3c applies, and Az 180 162.9 A sin Z B Z sin b b
Applying the cosine rule for plane triangles to the triangle of Fig. 3.2b allows the range d to be found to a close approximation: d 2R
a2 GSO
2RaGSO cos b
(3.11)
Applying the sine rule for plane triangles to the triangle of Fig. 3.2b allows the angle of elevation to be found: El
Example 3.2
arccosa
aGSO d
sin bb
(3.12)
Find the range and antenna elevation angle for the situation specified in Example 3.1. R 6371 km; aGSO Equation (3.11) gives: d 26371
Solution
42164 km, and from Example 3.1, b
36.23 .
cos 36.23
> 37215 km Equation (3.11) gives: El arccosa > 48 42164 37215 sin 36.23 b
Figure 3.4 shows the look angles for Ku-band satellites as seen from Thunder Bay, Ontario, Canada.
Three
Figure 3.4 Azimuth-elevation angles for an earth-station location of 48.42 N, 89.26 W (Thunder Bay, Ontario). Ku-band satellites are shown.
The preceding results do not take into account the case when the earth station is on the equator. Obviously, when the earth station is directly under the satellite, the elevation is 90 , and the azimuth is irrelevant. When the subsatellite point is east of the equatorial earth station (B < 0), the azimuth is 90 , and when west (B > 0), the azimuth is 270 . Also, the range as determined by Eq. (3.11) is approximate, and where more accurate values are required, as, for example, where propagation times need to be known accurately, the range is determined by measurement. For a typical home installation, practical adjustments will be made to align the antenna to a known satellite for maximum signal. Thus the look angles need not be determined with great precision but are calculated
The Geostationary Orbit
to give the expected values for a satellite the longitude of which is close to the earth-station longitude. In some cases, especially with direct broadcast satellites (DBS), the home antenna is aligned to one particular cluster of satellites, as described in Chap. 16, and no further adjustments are necessary. 3.3 The Polar Mount Antenna Where the home antenna has to be steerable, expense usually precludes the use of separate azimuth and elevation actuators. Instead, a single actuator is used which moves the antenna in a circular arc. This is known as a polar mount antenna. The antenna pointing can only be accurate for one satellite, and some pointing error must be accepted for satellites on either side of this. With the polar mount antenna, the dish is mounted on an axis termed the polar axis such that the antenna boresight is normal to this axis, as shown in Fig. 3.5a. The polar mount is aligned along a true north line, as shown in Fig. 3.5, with the boresight pointing due south. The angle between the polar mount and the local horizontal plane is set equal to the earth-station latitude lE; simple geometry shows that this makes the boresight lie parallel to the equatorial plane. Next, the dish is tilted at an angle relative to the polar mount until the boresight is pointing at a satellite position due south of the earth station. Note that there does not need to be an actual satellite at this position. (The angle of tilt is often referred to as the declination, which must not be confused with the magnetic declination used in correcting compass readings. The term angle of tilt will be used for in this text.) The required angle of tilt is found as follows: From the geometry of Fig. 3.5b, 90o El0 lE (3.13)
where El0 is the angle of elevation required for the satellite position due south of the earth station. But for the due south situation, angle B in Eq. (3.8) is equal to zero; hence, from Eq. (3.9), b lE. Hence, from Eq. (3.12), or Fig 3.5c. cos El0 aGSO d sin lE (3.14)
Combining Eqs. (3.13) and (3.14) gives the required angle of tilt as 90 arccosa aGSO d b sin lE lE (3.15)
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