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

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Chapter 5 Perturbation Models of IGSO,GEO and MEO Satellites Orbits Difference (kilometer) 15 10 5 0 -5 -10 -15 dx dy dz 0 24 48 72 96 120 Tim e (hour) 144 168 192 216 240 Figure 5-27 The Effect of the Lunar Attraction on GEO Satellite 5.3 The Solar Radiation Pressure Model The effect of solar radiation pressure on satellite orbit can be divided into two categories, i.e. direct radiation and earth albedo radiation. Because IGSO, GEO and MEO satellites are much far away from the earth surface, the earth albedo radiation has small influence on these types of satellites and can be neglected. Therefore only the direct radiation pressure should be considered in the satellite dynamic models. 5.3.1 Direct Radiation Pressure For the direct radiation it means the satellite absorbs the entire solar radiation. If assuming the satellite is a perfect sphere, the perturbing acceleration of direct radiation pressure may be written by (Beutler 1996) �� ϖ ϖ ϖ A 2 r − r �� s ad = µ �Ps Cr as ϖ ϖ 3 � (5-24) �� m | r − rs | �� where ϖ ad acceleration due to the direct radiation pressure, µ eclipse factor (=1 if the satellite is in sunlight, =0 if the satellite is in the Earth shadow, 0< µ
Chapter 5 Perturbation Models of IGSO,GEO and MEO Satellites Orbits 2 E F1, D = − ( A ) ν ( 1− µ ) cosθ 3 c where ν reflectivity, ranging from 0 (black) to 1 (white), µ specularity, ranging from 0 (diffuse) to 1 (specular), θ angle between the incoming solar ray and the normal to the flat surface, other symbols are the same as Eq.(5-24). For the cylindrical surfaces the component of the acceleration due to radiation pressure can be written by Normal E µν 2 F2, N = −( A )( 1+ ) cos θ c 3 Shear E F2, S = −( A )( 1− µν ) sinθ cosθ c Diffuse π E F2, D = − ( A ) ν ( 1− µ ) cosθ 6 c For total acceleration, the accelerations from each surface are summed as F F F Σ � = = K N, i 1 Σ � = = K S, i 1 Σ � = = K D, i 1 F F N , i S, i F D, i 59 (5-27) (5-28) (5-29) (5-30) (5-31) (5-32) (5-33) The parameters in Eq.(5-28) to Eq.(5-30) are dependent on satellite profile. Fliegel et al (1992) give a simple formula for GPS components of total radiation accelerations in SV-body coordinate system, i.e. X =− 455 . sin( B) + 008 . sin( 2B+ 09 . ) − 006 . cos( 4B+ 008 . ) + 008 . � � Z =− 454 . cos( B) + 020 . sin( 2B−03 . ) −003 . sin( 4B) � where B the angle between the Sun and +Z axis. (5-34) All above formulas must be divided by satellite mass ms. SV-body coordinate system is defined as follows: the +Z direction is toward the Earth and therefore along the SV antennas. The +X direction is positive toward the half plane that contains the Sun, and +Y completes a right-handed system and points along one of the solar panel center beams. Assuming ϖ r represents a position vector of the satellite in the inertial system, ϖ rs a position vector of the Sun, also in the inertial system, then SV-body unit vector in the inertial system can be written as ϖ ϖ ϖ ϖ r × ( r − rs ) u y = ϖ ϖ ϖ (5-35) | r × ( r − rs ) | ϖ ϖ r uz = − ϖ (5-36) | r | ϖ ϖ ϖ u = u × u (5-37) x y z The acceleration due to direct radiation pressure according to Fliegel model which is also in the inertial coordinate system may be written by 2 ϖ as ϖ ϖ −5 ad = µ ϖ ϖ ( Xu + ) × 10 2 x Zu z (5-38) | r − rs | m
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PRECISE ORBIT DETERMINATION OF GLOB
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Summary GNSS-2 (Global Navigation S
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3.2.2.1 Principle..................
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9.3.3 The Effect of Distribution of
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Chapter 1 Introduction 1.2 Developm
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Chapter 2 Observations of Orbit Det
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Chapter 2 Observations of Orbit Det
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Page 26 and 27: Chapter 3 Orbit Tracking System and
Page 40 and 41: Chapter 4 Major Error Sources of Sa
Page 52 and 53: Chapter 5 Perturbation Models of IG
Page 74 and 75: Chapter 6 Algorithms of Orbit Deter
Page 94 and 95: Chapter 7 Orbit Determination Using
Page 104 and 105: Chapter 8 Geostationary Orbit Deter
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Chapter 8 Geostationary Orbit Deter
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Chapter 9 Software and Simulation R
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Conclusion 144
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References Carpino M. (1995): SAEG
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References Klobuchar, J. A.(1996):
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References Traquilla, J. M. and J.
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Acknowledgments 152
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