MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS

1. MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS Carlos Javier Rodriguez Solano Technische Universität München carlos.rodriguez@mytum.de 3a Conferencia Alβan – Porto 2009

2. ESPACE International Master‘s Program ESPACE – Earth Oriented Space Science and Technology www.espace-tum.de

3. Earth System Satellite Technology Remote Sensing Navigation ESPACE ESPACE combines elements of engineering and science in one single interdisciplinary program www.espace-tum.de

4. 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 Introduction “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)

5. Introduction 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

6. But there is a consistent bias of 4 – 5 cm  The GPS – SLR Orbit Anomaly. Ziebart et al. (2007) Introduction 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

7. Earth radiation model •  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

8. Earth radiation model After integration of and over the part of the sphere visible to the satellite, we getthe total Earth´s irradiance model, which is plotted as function of ψ

9. 100 times smaller as acceleration due to direct solar radiation 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

10. Position in the RTN frame, perturbed – unperturbed (reference) orbit RTN frame 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

11. Important  drift in: Argument of Perigee + True Anomaly = T-component of position Numerical orbit integration Keplerian elements, perturbed – unperturbed (reference) orbit

12.  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 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

13. 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

14. 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

15. THANK YOU! ANY QUESTIONS?