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

Chapter 5 Perturbation Models of IGSO,GEO and MEO Satellites Orbits
5.2 The Solar and Lunar Attractions
Due to the great distance between the Earth and the Sun and between the Earth and Moon, it is unnecessary to
take the nospherical part of the Sun and Moon into account. For this reason, in the perturbation models the Sun
and Moon are considered as point mass. The solar and lunar attractions on the satellite may be expressed in the
inertial coordinate system as follows
(Kovalevsky 1967, Beutler 1996)
�
=
� �
2 ϖ
�
ϖ ϖ ϖ
d r µ ϖ
r − �
i r ri
= − r + µ i � −
2 3
ϖ ϖ
(5-23)
3 3
dt r i s,
m ��
| ri
− r | ri
�
where
ϖ
r
ϖ
rs ϖ
rm position vector of satellite
position vector of Sun
position vector of Moon
µ , µ s, µ m gravity constants of the Earth, Sun and Moon respectively.
In order to evaluate the influences of Sun and Moon on IGSO, GEO and MEO satellites, the accelerations
produced by the solar and lunar attractions on IGSO and GEO satellites are computed using JPL Planetary
Ephemeris DE200 and Eq.(5-23). The quantities of the accelerations and orbit errors by these two perturbation
forces are listed in Table 5-6, Table 5-7 and Table 5-8 as well as are drawn in Figures 5-24, 5-25, 5-26 and 5-27.
Table 5-6 The Effect of Solar and Lunar Attraction on IGSO Satellite
(Satellite Parameters: a=42164.174km, λ=20°, i=63°)
Perturbation Force Acceleration Orbit Errors (m)
(m/sec 2 ) One Day Ten Days
Solar Attraction 3×10 -6 945 8915
Lunar Attraction 6×10 -6 2590 77 (km)
Table 5-7 The Effect of Solar and Lunar Attraction on GEO Satellite
(Satellite Parameters: a=42164.174km, λ=20°, i=0°)
Perturbation Force Acceleration Orbit Errors (m)
(m/sec 2 ) One Day Ten Days
Solar Attraction 3×10 -6 2263 23183
Lunar Attraction 6×10 -6 2311 14 (km)
Table 5-8 The Effect of Solar and Lunar Attraction on MEO (GPS) Satellite*
Perturbation Force Acceleration Orbit Errors (m)
(m/sec 2 ) One Day Ten Days
Solar Attraction 2×10 -6 800 3500
Lunar Attraction 5×10 -6 3000 8000
*Feltens, 1991; Landau, 1988
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