Page 88 - Satellite Communications, Fourth Edition

68 Chapter Two

uniform intervals along the celestial equator, in other words, the length
of a solar day depends on the position of the earth relative to the sun.
To overcome this difficulty a fictitious mean sun is introduced, which
travels in uniform circular motion around the sun (this is similar in
many ways to the mean anomaly defined in Sec. 2.5). The time deter-
mined in this way is the mean solar time. Tables are available in vari-
ous almanacs which give the relationship between mean solar time and
apparent solar time through the equation of time.
The relevance of this to a satellite orbit is illustrated in Fig. 2.15. This
shows the trace of a satellite orbit on the celestial sphere, (again keep-
ing in mind that directions and not distances are shown). Point A cor-
responds to the ascending node. The hour angle of the sun from the
ascending node of the satellite is Ω a measured westward. The hour
s
angle of the sun from the satellite (projected to S on the celestial sphere)
is Ω a b and thus the local mean (solar) time is
s
1
) 12 (2.56)
t SAT ( s
15
To find b requires solving the spherical triangle defined by the points
ASB. This is a right spherical triangle because the angle between the
meridian plane through S and the equatorial plane is a right angle.
The triangle also contains the inclination i (the angle between the orbital
plane and the equatorial plane) and the latitude l (the angle measured
at the center of the sphere going north along the meridian through S). The
inclination i and the latitude l are the same angles already introduced
in connection with orbits. The solution of the right spherical triangle

S

0
r
Ω i
a s
B
A
Figure 2.15 The condition for sun syn-
chronicity is that the local solar time
should be constant.