Page 87 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 67

North
celestial pole

P
Sun

0
a p
a
s
Celestial
equator

Figure 2.14 Sun-synchronous orbit.

sphere is centered on the geocentric-equatorial coordinate system
(see Sec. 2.9.6). What this means is that the celestial equatorial plane
coincides with the earth’s equatorial plane, and the direction of the
north celestial pole coincides with the earth’s polar axis. For clarity the
IJK frame is not shown, but from the definition of the line of Aries in
Sec. 2.9.6, the point for Aries lies on the celestial equator where this is
cut by the x-axis, and the z-axis passes through the north celestial pole.
Also shown in Fig. 2.14 is the sun’s meridian. The angular distance
along the celestial equator, measured eastward from the point of Aries
to the sun’s meridian is the right ascension of the sun, denoted by a . In
s
general, the right ascension of a point P, is the angle, measured east-
ward along the celestial equator from the point of Aries to the meridian
passing through P. This is shown as a in Fig. 2.14. The hour angle of
P
a star is the angle measured westward along the celestial equator from
the meridian to meridian of the star. Thus for point P the hour angle of
the sun is (a − a ) measured westward (the hour angle is measured in
s
p
the opposite direction to the right ascension).
Now the apparent solar time of point P is the local hour angle of the
sun, expressed in hours, plus 12 h. The 12 h is added because zero hour
angle corresponds to midday, when the P meridian coincides with the
sun’s meridian. Because the earth’s path around the sun is elliptical
rather than circular, and also because the plane containing the path of
the earth’s orbit around the sun (the ecliptic plane) is inclined at an angle
of approximately 23.44°, the apparent solar time does not measure out