Page 119 - Satellite Communications, Fourth Edition

The Geostationary Orbit 99

3.9 Problems

3.1. Explain what is meant by the geostationary orbit. How do the
geostationary orbit and a geosynchronous orbit differ?

3.2. (a) Explain why there is only one geostationary orbit. (b) Show that the
range d from an earth station to a geostationary satellite is given by
2
d 2sR sin Eld hs2R hd R sin El,
where R is the earth’s radius (assumed spherical), h is the height of the
geostationary orbit above the equator, and El is the elevation angle of the earth
station antenna.
3.3. Determine the latitude and longitude of the farthest north earth station
which can link with any given geostationary satellite. The longitude should be
given relative to the satellite longitude, and a minimum elevation angle of 5°
should be assumed for the earth station antenna. A spherical earth of mean
radius 6371 km may be assumed.

3.4. An earth station at latitude 30°S is in communication with an earth
station on the same longitude at 30°N, through a geostationary satellite. The
satellite longitude is 20° east of the earth stations. Calculate the antenna-look
angles for each earth station and the round-trip time, assuming this consists of
propagation delay only.

3.5. Determine the maximum possible longitudinal separation which can exist
between a geostationary satellite and an earth station while maintaining line-
of-sight communications, assuming the minimum angle of elevation of the earth
station antenna is 5°. State also the latitude of the earth station.

3.6. An earth station is located at latitude 35°N and longitude 100°W. Calculate
the antenna-look angles for a satellite at 67°W.

3.7. An earth station is located at latitude 12°S and longitude 52°W. Calculate
the antenna-look angles for a satellite at 70°W.

3.8. An earth station is located at latitude 35°N and longitude 65°E. Calculate
the antenna-look angles for a satellite at 19°E.

3.9. An earth station is located at latitude 30°S and longitude 130°E. Calculate
the antenna-look angles for a satellite at 156°E.

3.10. Calculate for your home location the look angles required to receive from
the satellite (a) immediately east and (b) immediately west of your longitude.
3.11. CONUS is the acronym used for the 48 contiguous states. Allowing for
a 5° elevation angle at earth stations, verify that the geostationary arc required
to cover CONUS is 55° to 136°W.