Page 70 - Satellite Communications, Fourth Edition
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50 Chapter Two
The sidereal day is defined as one complete rotation of the earth rel-
ative to the fixed stars. One sidereal day has 24 sidereal hours, 1 side-
real hour has 60 sidereal minutes, and 1 sidereal minute has 60 sidereal
seconds. Care must be taken to distinguish between sidereal times and
mean solar times, which use the same basic subdivisions. The relation-
ships between the two systems, given in Bate et al. (1971), are
1 mean solar day 1.0027379093 mean sidereal days
24 h 3 m 56.55536 s sidereal time (2.21)
86,636.55536 mean sidereal seconds
1 mean sidereal day 0.9972695664 mean solar days
23 h 56 m 04.09054 s mean solar time (2.22)
86,164.09054 mean solar seconds
Measurements of longitude on the earth’s surface require the use of
sidereal time (discussed further in Sec. 2.9.7). The use of 23 h, 56 min
as an approximation for the mean sidereal day will be used later in
determining the height of the geostationary orbit.
2.9.5 The orbital plane
In the orbital plane, the position vector r and the velocity vector v spec-
ify the motion of the satellite, as shown in Fig. 2.8. For present purposes,
Figure 2.8 Perifocal coordinate system (PQW frame).
