Page 78 - Satellite Communications, Fourth Edition

58 Chapter Two

Here, UT° is universal time expressed in degrees, as given by Eq. (2.19).
T is the time in Julian centuries, given by Eq. (2.20).
Once GST is known, the local sidereal time (LST) is found by adding
the east longitude of the station in degrees. East longitude for the earth
station will be denoted as EL. Recall that previously longitude was
expressed in positive degrees east and negative degrees west. For east
longitudes, EL f , while for west longitudes, EL 360° f . For
E
E
example, for an earth station at east longitude 40°, EL 40°. For an
earth station at west longitude 40°, EL 360 ( 40) 320°. Thus the
LST in degrees is given by

LST GST EL (2.35)
The procedure is illustrated in the following examples

Example 2.17 Find the GST for 13 h UT on 18 December 2000.

Solution From Example 2.11: T 1.00963838 . The individual terms of Eq. (2.34)
are:
X 36000.7689° T 347.7578° (mod 360°)
2
Y 0.0004° T 0.00041° (mod 360°)
13
UT 5 360 195
24
GST 99.6910° X Y UT
282.4493° (mod 360°)

Example 2.18 Find the LST for Thunder Bay, longitude 89.26°W for 13 h UT on
December 18, 2000.
Solution Expressing the longitude in degrees west: WL 89.26°
In degrees east this is EL 360° ( 89.26°) 270.74°
LST GST EL
282.449 270.74
93.189° (mod 360°)

Knowing the LST enables the position vector R of the earth station
to be located with reference to the IJK frame as shown in Fig. 2.10.
However, when R is resolved into its rectangular components, account
must be taken of the oblateness of the earth. The earth may be modeled
as an oblate spheroid, in which the equatorial plane is circular, and any