Page 85 - Satellite Communications, Fourth Edition

Orbits and Launching Methods 65

S
z

h SS h
r
H SS

ψ SS λ SS

Figure 2.13 Geometry for determining the subsatellite point.

satellite above the reference ellipsoid is

h H SS h SS (2.50)
Now the components of the radius vector r in the IJK frame are given
by Eq. (2.33). Figure 2.13 is seen to be similar to Fig. 2.11, with the dif-
ference that r replaces R, the height to the point of interest is h rather
than H, and the subsatellite latitude l SS is used. Thus Eqs. (2.39)
through (2.42) may be written for this situation as
a E (2.51)
N
2
2
21 e sin l SS
E
r (N h) cos l SS cos LST (2.52)
I
r (N h) cos l SS sin LST (2.53)
J
(2.54)
2
SNQ1 e R hT sin l
r K E SS
We now have three equations in three unknowns, LST, l , and h,
E
which can be solved. In addition, by analogy with the situation shown
in Fig. 2.10, the east longitude is obtained from Eq. (2.35) as
EL LST GST (2.55)
where GST is the Greenwich sidereal time.