ESPACE Porto, June 2009 MODELLING OF EARTH’S RADIATION FOR GPS SATELLITE ORBITS Carlos Javier Rodriguez Solano Technische Universität München 3 a Conferencia Alβan – Porto 2009

ESPACE Porto, June 2009 ESPACE International Master‘s Program ESPACE – Earth Oriented Space Science and Technology

ESPACE Porto, June 2009 ESPACE combines elements of engineering and science in one single interdisciplinary program Remote Sensing Satellite Technology Navigation Earth System ESPACE

ESPACE Porto, 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

ESPACE Porto, 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

ESPACE Porto, 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

ESPACE Porto, June 2009  Compute irradiance at satellite altitude due to emitted and reflected radiation, using: - Albedo of the Earth (α ≈ 0.3) - Satellite altitude (h ≈ km) - Angle ψ, formed by satellite, Earth and Sun Earth radiation model

ESPACE Porto, 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 Earth radiation model

ESPACE Porto, 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

ESPACE Porto, 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]EccentricityInclination [deg]RAAN [deg]Argument of Perigee [deg] Position in the RTN frame, perturbed – unperturbed (reference) orbit RTN frame

ESPACE Porto, June 2009 Numerical orbit integration Keplerian elements, perturbed – unperturbed (reference) orbit Important  drift in: Argument of Perigee + True Anomaly = T-component of position

ESPACE Porto, 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

ESPACE Porto, June 2009 Results and Discusion Also very interesting, plot of radial residuals as a function of: Sun elevation angle β 0 and angle ∆u Strong dependency with position of Sun Twice per revolution and twice per year perturbation

ESPACE Porto, 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

ESPACE Porto, June 2009 THANK YOU! ANY QUESTIONS?