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  1. Impact of Albedo Radiation on GNSS SatellitesCarlos Javier Rodriguez Solano*), Urs Hugentobler, Peter SteigenbergerInstitute for Astronomical and Physical GeodesyTechnische Universität MünchenIAG Scientific Assembly 2009, Buenos Aires, ArgentinaAugust 31, 2009 Institute for Astronomical and Physical Geodesy

  2. Content • Motivation • Earth albedo modeling • Albedo acceleration at GNSS altitude • Impact on GNSS orbits • Conclusions *)Master's Thesis in progress in the International Master's Course ESPACE (Earth Oriented Space Science and Technology) at Technische Universität München. Institute for Astronomical and Physical Geodesy

  3. ☼ β0 Δu SLR Residuals of GNSS Orbits • SLR residuals for GPS satellites in a sun-fixed coordinate system show a peculiar pattern Urschl, 2006 Institute for Astronomical and Physical Geodesy

  4. Earth Albedo Radiation • Visible light reflected from the Earth and infrared radiation emitted by the Earth cause an acceleration on satellites pointing away from the Earth. • Order of magnitude for GNSS satellites is 10−9ms−2 • Impact on the orbit thus is of similar magnitude as, e.g., y-bias Institute for Astronomical and Physical Geodesy

  5. satellite model Earth radiation model Earth Albedo Radiation • The acceleration acting on a GNSS satellite depends on • relative geometry of satellite, Sun and Earth • shape and size of the satellite as well as attitude • optical properties of satellite surfaces • reflectivity and emissivity of the Earth surface • scattering properties of the Earth surface • What are the most important elements of an Earth albedo model? • solar panels? • optical properties of surfaces? • modeling of reflectivity and emissivity of Earth's surface as a function of geographical location and time? • ...? Institute for Astronomical and Physical Geodesy

  6. Earth Radiation Models • Models: • Earth scattering properties approximated as a Lambertian sphere • emitted and reflected radiation  infrared and visible radiation • Types of solutions: 1) Analytical: Constant albedo, Earth as point source  only radial acceleration 2) Numerical: Constant albedo, finite Earth radius 3) Latitude-dependent reflectivity and emissivity 4) Latitude-, longitude- and time-dependent reflectivity and emissivity from NASA CERES project Institute for Astronomical and Physical Geodesy

  7. Earth Radiation Models • CERES (Clouds and the Earth's Radiant Energy System) NASA EOS project Reflectivity  Emissivity  • CERES data, monthly averages, July 2007 http://science.larc.nasa.gov/ceres/ Institute for Astronomical and Physical Geodesy

  8. only emission only reflection Comparison of Models • Analytical and numerical models for constant albedo: • Different albedos of the Earth Institute for Astronomical and Physical Geodesy

  9. Comparison of Models • Analytical and numerical models for constant albedo: • Different satellite altitudes Institute for Astronomical and Physical Geodesy

  10. Comparison of Models • CERES data, August 2007 • Latitude dependency • Numerical, constant albedo • Analytical, constant albedo Institute for Astronomical and Physical Geodesy

  11. GPS Satellite Model • Box-wing model • Three main satellite surfaces: • +Z side, pointing always to the Earth • Front-side of solar panels, pointing always to the Sun • Back-side of solar panels • Main dependency on angle ψ satellite – Earth – Sun Institute for Astronomical and Physical Geodesy

  12. solar panels oriented perpendicular to Earth direction GPS Satellite Model • Acceleration caused by infrared radiation (albedo=0) • Variations with impact angle dominated by solar panels • Different GPS satellite types: 10% differences Institute for Astronomical and Physical Geodesy

  13. Acceleration onGPS Satellites • Cannon-ball model PRN 05 (β0=55.5°) PRN 06 (β0=20.2°) Institute for Astronomical and Physical Geodesy

  14. Acceleration onGPS Satellites • Box-wing model PRN 05 (β0=55.5°) PRN 06 (β0=20.2°) Institute for Astronomical and Physical Geodesy

  15. Acceleration onGPS Satellites • Cannon-ball model: radial acceleration as a function of β0 and ∆u • Minimum at dark side of the Earth (β0 = 0° and ∆u = 180°) • Maximum at daylight side of the Earth (β0 = 0° and ∆u = 0°) Institute for Astronomical and Physical Geodesy

  16. Acceleration onGPS Satellites • Box-wing model: radial acceleration as a function of β0 and ∆u • Local maximum at dark side of the Earth (β0 = 0° and ∆u = 180°) • Caused by infrared albedo radiation acting on solar panels • Compare with pattern of SLR residuals Institute for Astronomical and Physical Geodesy

  17. Orbit Determination Including Albedo Acceleration • Analysis of one year (Jan-Dec 2007) of tracking data from 190 IGS sites • Orbit determination using the same analysis strategy as the CODE (Center for Orbit Determination in Europe) Analysis Center • Five tests have been performed for GPS satellites: (1) Cannon-ball, analytical (constant albedo) (2) Cannon-ball, numerical (constant albedo) (3) Box-wing, numerical (constant albedo) (4) Box-wing, latitude-dependent reflectivity and emissivity (5) Box-wing, monthly CERES data for 2007 • Result: Orbit differences = orbit with albedo – orbit without albedo Institute for Astronomical and Physical Geodesy

  18. Orbit Differences to Non-albedo Orbits PRN 5 PRN 6 Institute for Astronomical and Physical Geodesy

  19. SLR Validation of GNSS Orbits • SLR residuals = SLR measurements – computed orbit distance PRN 05 PRN 06 Institute for Astronomical and Physical Geodesy

  20. Cannon-ball model, orbit residuals as function of β0 and ∆u • Reduction of orbital radius by 1-2 cm • Most pronounced in direction of Sun (β0 = 0°, ∆u = 180°) Orbits with Albedo Acceleration Institute for Astronomical and Physical Geodesy

  21. Orbits with Albedo Acceleration • Cannon-ball model: Reduction of orbit radius by about 1 cm, more pronounced in direction of Sun Institute for Astronomical and Physical Geodesy

  22. Cannon-ball model, orbit residuals as function of β0 and ∆u • Reduction of orbital radius by 1-2 cm • Most pronounced in direction of Sun (β0 = 0°, ∆u = 180°) Orbits with Albedo Acceleration Institute for Astronomical and Physical Geodesy

  23. Box-wing model, orbit residuals as function of β0 and ∆u • Additional orbit height reduction at dark side of Earth (β0 = 0°, ∆u = 180°) • Caused by Earth infrared radiation acting on solar panels Orbits with Albedo Acceleration Institute for Astronomical and Physical Geodesy

  24. Orbits with Albedo Acceleration • Box-wing model: Reduction of orbit height also at night-side of the Earth Institute for Astronomical and Physical Geodesy

  25. Box-wing model, orbit residuals as function of β0 and ∆u • Additional orbit reduction at dark side of Earth (β0 = 0°, ∆u = 180°) • Caused by Earth infrared radiation acting on solar panels Orbits with Albedo Acceleration Institute for Astronomical and Physical Geodesy

  26. SLR Residuals of GNSS Orbits • Residuals for GPS satellites PRN 5 and 6 in the sun-fixed coordinate system show a similar pronounced pattern Urschl, 2006 Urschl, 2006 Institute for Astronomical and Physical Geodesy

  27. Conclusions • The aim of the study was not to construct the perfect albedo model but to find the best but simplest model. • Accelerations due to Earth albedo have a similar magnitude as the y-bias. • Impact of albedo model components on GNSS orbits: (1) Albedo causes a mean reduction of the orbit radius of about 1 cm (2) The largest impact in periodic variations is caused by the solar panels  Use of a box-wing satellite model is a must (3) Different Earth albedo models as well as satellite model details have a small impact on the orbits • Earth albedo has the potential to explain the peculiar pattern observed in SLR residuals. Institute for Astronomical and Physical Geodesy

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