modelling of earth’s radiation for gps satellite orbits
DESCRIPTION
MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS. Carlos Javier Rodriguez Solano Technische Universität München [email protected] 3 a Conferencia Al β an – Porto 2009. ESPACE. International Master‘s Program. ESPACE – Earth Oriented Space Science and Technology. - PowerPoint PPT PresentationTRANSCRIPT
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ESPACEPorto, June 2009
MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS
Carlos Javier Rodriguez Solano
Technische Universität München [email protected]
3a Conferencia Alβan – Porto 2009
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ESPACEPorto, June 2009
ESPACE
International Master‘s Program
ESPACE – Earth Oriented Space Science and Technology
www.espace-tum.de
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ESPACEPorto, June 2009
ESPACE combines elements of engineering and science in one single interdisciplinary program
Remote Sensing
Satellite Technology
Navigation
Earth System
ESPACE
www.espace-tum.de
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ESPACEPorto, June 2009
“The NAVSTAR GPS ( NAVigation System with Time And Ranging Global Positioning System) is a satellite-based radio navigation system providing precise three dimensional position, navigation and time information to suitably equipped users.”
Seeber (2003)
Introduction
Positions of at least 4 satellites
+
Travelled distance of the signal from the satellite’s antenna to the receiver
=Position on Earth and synchronization
of the receiver
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ESPACEPorto, June 2009
The better the positions of the satellites are known
the higher precision that can be achieved on Earth for positioning
The International GNSS Service provides: Final Orbits with accuracy of 5 cm
Final Orbits are computed using:
1) Direct observations from the satellites to reference stations on Earth
2) Force models that include the principal perturbations to the orbit:
- Low terms of Geopotential
- Attraction of Sun and Moon
- Solar Radiation Pressure
- Solid Earth and Ocean Tides
- General Relativity
Introduction
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ESPACEPorto, June 2009
An independent way to test the accuracy of Final Orbits is using:
Satellite Laser Ranging (SLR)
Accuracy of SLR measurements is 5 – 6 mm
NERC
This bias could come from the Earth radiation that arrives to the satellites
Not included in the modelling of Final Orbits
But there is a consistent bias of 4 – 5 cm
The GPS – SLR Orbit Anomaly.
Ziebart et al. (2007)
Introduction
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ESPACEPorto, June 2009
Compute irradiance at satellite altitude due to emitted and reflected radiation, using:
- Albedo of the Earth (α ≈ 0.3)
- Satellite altitude (h ≈ 20000 km)
- Angle ψ, formed by satellite, Earth and Sun
Earth radiation model
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ESPACEPorto, June 2009
After integration of and over the part of the sphere visible to the satellite,we get the total Earth´s irradiance model, which is plotted as function of ψ
emitId
reflId
Earth radiation model
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ESPACEPorto, June 2009
GPS satellite model
The radiation coming from the Earth that impacts a satellite accelerates it due to the momentum transfer between the photons and the surface of the satellite.
GPS satellite model spherical bus + solar panel pointing to the Sun
100 times smaller as acceleration due to direct solar radiation
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ESPACEPorto, June 2009
Numerical orbit integration
Numerical integration over one year of:
Unperturbed keplerian orbit + perturbing acceleration
Initial conditions for PRN06, one of the GPS satellites with laser retroreflectors
Semimajor axis [km] Eccentricity Inclination [deg] RAAN [deg] Argument of Perigee [deg]
26560.699 0.0062068 53.5060 155.9994 282.1291
Position in the RTN frame, perturbed – unperturbed (reference) orbit
RTN frame
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ESPACEPorto, June 2009
Numerical orbit integration
Keplerian elements, perturbed – unperturbed (reference) orbit
Important drift in: Argument of Perigee + True Anomaly = T-component of position
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ESPACEPorto, June 2009
Results and Discusion
Definition of different reference orbit:
- Mean keplerian elements over one revolution
- Same true anomaly as perturbed orbit
- Star of it at ∆u = 0
Possible to compare just in radial direction!
Position in the RTN frame, perturbed – reference orbit
Shift of 2 – 4 cm in radial direction, comparable with GPS – SLR Orbit Anomaly
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ESPACEPorto, June 2009
Results and Discusion
Also very interesting, plot of radial residuals as a function of:
Sun elevation angle β0 and angle ∆u
Strong dependency with position of Sun
Twice per revolution and twice per year perturbation
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ESPACEPorto, June 2009
Conclusions
- A not negligible effect of the Earth radiation on satellite orbits has been found
- Key factors for final results are
1) Earth radiation model with dependency on the relative position of satellite, Earth and Sun
2) Satellite model: bus, solar panel and orientation to the Sun
3) Reference orbit, suitable for the comparison in radial direction
Next steps of the Master Thesis:
- Include models in the computation of GPS orbits
- Use of real GPS and SLR data in the Bernese GPS Software
Better understanding of the GPS – SLR Orbit Anomaly,
a current limit of GPS orbits
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ESPACEPorto, June 2009
THANK YOU!
ANY QUESTIONS?