Page 111 - Satellite Communications, Fourth Edition

The Geostationary Orbit 91

rotation from the Greenwich meridian. The Greenwich sidereal time
(GST) gives the eastward position of the Greenwich meridian relative
to the line of Aries, and hence the subsatellite point is at longitude

SS GST (3.20)

and the mean longitude of the satellite is given by
M GST (3.21)
SSmean
Equation (2.31) can be used to calculate the true anomaly, and because
of the small eccentricity, this can be approximated as

M 2e sin M (3.22)

The two-line elements for the Intelsat series, obtained from
Celestrak at http://celestrak.com/NORAD/elements/intelsat.txt are
shown in Fig. 3.7.

Example 3.5 Using the data given in Fig. 3.7, calculate the longitude for INTELSAT
10-02.
Solution From Fig. 3.7 the inclination is seen to be 0.0079°, which makes the
orbit almost equatorial. Also the revolutions per day are 1.00271159, or approxi-
mately geosynchronous. Other values taken from Fig. 3.7 are:
epoch day 124.94126775 days; year 2005; Ω 311.0487°; w
59.4312°; M 190.2817°; e 0.0000613
From Table 2.2 the Julian day for Jan 0.0 2005 is JD 00 2453370.5 days. The Julian
day for epoch is JD 2453370.5 124.94126775 2453495.44126775 days. The ref-
erence value is (see Eq. 2.20) JD ref 2415020 days. Hence T in Julian centuries is:

JD JD ref
T
36525
38475.442

36525
1.05340017
The decimal fraction of the epoch gives the UT as a fraction of a day, and in
degrees this is:

UT° 0.94126775 360°
338.85637°
Substituting these values in Eq. (2.34) gives, for the GST:
GST 99.9610° 36000.7689° T 0.0004° T UT°
2
201.764° (mod 360°)