Precise Orbit Determination of Global Navigation Satellite System of ...

Chapter 5 Perturbation Models of IGSO,GEO and MEO Satellites Orbits
For actual orbit determination, the imperfect of the direct radiation model should be considered, therefore some
unmodeled direct radiation errors are estimated during orbit determination. Rewriting Eq.(5-24) as follows
��
ϖ ϖ
ϖ
A
��
2 r − rs
ad = µ �Ps
( 1+
α + α&
∆t)
as
3 �
��
m
ϖ ϖ
(5-39)
| r − rs
| ��
&α can be considered as unmodeled errors of reflection coefficient Cr which changes with time. Cr in Eq.(5-24)
can be written as
0
r
1
r
C r = C + C
(5-40)
where
0
Cr
= 1 + α
1
= α& ∆t
C r
i.e. Eq.(5-24) becomes
ϖ ϖ
ϖ A 2 r − rs
ad = µ { Ps
Cr
as
}
m
ϖ ϖ 3
| r − rs
|
ϖ ϖ
ϖ ϖ
0 A 2 r − rs
A 2 r − rs
= µ { Ps Cr
as
} { P
}
3 s t as
m
ϖ ϖ + µ & α∆
3
| r r |
m
ϖ ϖ
(5-41)
−
| r − r |
s
s
In Eq.(5-41), the first term can be calculated by mathematic model like Rock4 (Fliegel et al 1992, McCarthy
1992), the second term is solved during data processing of orbit determination.
5.3.2 Effect of Eclipses
In order to process the solar direct radiation, another problem, the sun eclipse, should be considered, i.e. how to
process the satellite orbit when satellite is inside the shadow of the Earth. The effect of the eclipse is a difficult
problem for satellite orbit determination, especially when satellite is in the penumbra. For the eclipse problem,
the simple cylinder model can be used for computation of the shadow of the Earth. According to this simple
model, for MEO (GPS) satellite, when the angle between the Sun and the +Z direction of the SV-body system of
the satellite, is less than about 14°, the Sun is eclipsed, i.e. the satellite is inside the shadow of the Earth; for
IGSO and GEO satellites with about 36000 km altitude from the surface of the Earth, the eclipse angle is about
8.6°, i.e. when the angle between the Sun and the +Z direction of the SV-body system of the satellite is less than
about 8.6°, the satellite is inside the shadow of the Earth, see Figure 5-28.
Earth
Direction of the Sun
Figure 5-28 The Eclipse Angle of IGSO and GEO Satellites
Although this simple model can be used to check if the satellite is in the shadow of the Earth, the non-continuity
of the solar radiation in force model due to the satellite entering the shadow of the earth will have problem in the
orbit integration. During an eclipse, the satellite passes continuously from sunlight to shadow of the Earth, but
60
Eclipse angle
Satellite