SATELLITE SYSTEMS - GPS Satellite Surveying - page 69

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3.1.4.2 Acceleration due to the Sun and the Moon The lunar and solar

accelerations on the satellites are (Escobal, 1965, p. 37)

X m −

X m = µ

m m
m e

X X m

3 −

(3.77)

3

X m X m − X

X s −

X s = µ

m s
m e

X X s

3 −

(3.78)

3

X s − X X s

The commonly used values for the mass ratios are m m /m e = 0 . 0123002 and m s /m e

= 332,946. Mathematical expressions for the geocentric positions of the moon X m

and the sun X s are given, for example, in van Flandern and Pulkkinen (1979).

[69

3.1.4.3 Solar Radiation Pressure Solar radiation pressure (SRP) is a result
of the impact of light photons emitted from the sun on the satellite's surface. The basic
parameters of the SRP are the effective area (surface normal to the incident radiation),
the surface reflectivity, thermal state of the surface, luminosity of the sun, and the dis-
tance to the sun. Computing SRP requires the evaluation of surface integrals over the
illuminated regions, taking shadowed components into account. Even if these regions
are known, the evaluation of the surface integrals can still be difficult because of the
complex shape of the satellite. The ROCK4 and ROCK42 models represent early
attempts to take most of these complex relations and properties into consideration
for GPS Block I, Block II, and Block IIa satellites, respectively (Fliegel et al., 1985;
Fliegel and Gallini, 1989). Fliegel et al. (1992) describe an SRP force model for
geodetic applications. Springer et al. (1999) report on SRP model parameter estima-
tion on a satellite-by-satellite basis, as part of orbital determinations from heavily
overdetermined global networks. Ziebart et al. (2002) discuss a pixel array method
in connection with finite analysis, in order to delineate even better the illuminated
satellite surfaces and surface temperature distribution.
One of the earliest and simplest SRP models uses merely two parameters. Consider
the body-fixed coordinate system of Figure 3.5. The z axis is aligned with the antenna
and points toward the center of the earth. The satellite finds this direction and remains
locked to it with the help of an earth limb sensor. The x axis is positive toward the half
plane that contains the sun. The y axis completes the right-handed coordinate system
and points along the solar panel axis. The satellites are always oriented such that the
y axis remains perpendicular to the earth-satellite-sun plane. The only motion of the
spacecraft in this body-fixed frame is the rotation of the solar panels around the y
axis to make the surface of the solar panels perpendicular to the direction of the sun.
The direction of the sun is denoted by e in Figure 3.5.
In reference to this body-fixed coordinate system, a simple SRP model formula-
tion is

Lin
—
1 ——
No
PgE

[69

X sun − X X sun × X

X SRP =−

p

+

Y (3.79)

X sun − X X sun × X