Modeling Earth radiation pressure Carlos Rodriguez-Solano and its impact on GPS orbits and ground tracking stations Carlos Rodriguez-Solano Urs Hugentobler Peter Steigenberger Tim Springer Bernese GPS Software NAPEOS Software

1 Motivation GPS – SLR orbit anomaly: 4 – 5 cm SLR residuals for GPS satellites (mean subtracted) in a Sun-fixed reference frame show a peculiar pattern: l Angle satellite – Earth – Sun: Urschl et al. (2008)

1 Motivation More recently … SLR range residuals based on reprocessed ESOC orbit series 1995.0 – 2009.0 SLR and GPS agree very well! Only a small bias (~1.8 cm) and eclipse season (attitude) effects remain

1 Motivation Orbit-related frequencies on geodetic time series  GPS draconitic year Station coordinates (> 200 IGS sites). Also computed by: Ray et al. (2009) 13.65 ± 0.02 days Penna et al. (2007): 13.66 days 9 years of tracking data: 2000.0 – 2009.0 Geocenter position. Also pointed out by: Hugentobler et al. (2006)

2 Earth Radiation Model Computation of Irradiance [W/m2] at satellite position, assuming: Earth scattering properties approximated as a Lambertian sphere emitted and reflected radiation  infrared and visible radiation Types of models: Analytical: Constant albedo, Earth as point source  only radial acceleration: Numerical: Constant albedo, finite Earth radius Latitude-dependent reflectivity and emissivity Latitude-, longitude- and time-dependent reflectivity and emissivity from NASA CERES project AE = πRE2, RE = 6378 km, ESUN = 1367 W/m2, h = satellite altitude, α = albedo (≈ 0.3)

2 Earth Radiation Model CERES (Clouds and Earth's Radiant Energy System) NASA EOS project Reflectivity  Emissivity  CERES data, monthly averages, July 2007 http://science.larc.nasa.gov/ceres/

2 Earth Radiation Model Min. Diff.: Max. -3.2% +3.7% -6.7% +10.8% E4: CERES data (August 2007) E3: Latitude dependency E2: Numerical, constant albedo E1: Analytical, constant albedo Min. Diff.: Max. -3.2% +3.7% -6.7% +10.8% -7.4% +14.0%

3 GPS Satellite Model Box-wing model Three main satellite surfaces: 1) +Z side, pointing always to the Earth 2) Front-side of solar panels, pointing always to the Sun 3) Back-side of solar panels Main dependency on angle ψ satellite – Earth – Sun

4 Acceleration on the Satellites Earth radiation and satellite models of increasing complexity for PRN06 and β0 = 20.2° Along track acceleration [m/s2] Radial acceleration [m/s2] Cross track acceleration [m/s2]

4 Acceleration on the Satellites Key factors can be already identified: - No large differences between Earth radiation models - Analytical box-wing model with block specific optical properties and with antenna thrust Most important factor  box-wing (solar panels change drastically w.r.t. the Earth over one revolution) Magnitude of acceleration compared to solar radiation pressure is just 1-2 % But if the change of acceleration (minimum to maximum) is compared  the effect is up to 20% of the solar radiation pressure Solar radiation pressure  solar panels are fixed, bus changes orientation Earth radiation pressure  bus is fixed, solar panels change orientation Comparable to Y-bias effect (1x10-9 m/s2)

5 Impact on the Orbits Implementation of a priori acceleration in the Bernese GPS Software Computation of GPS orbits as done by CODE for one year (2007) of tracking data Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo) PRN05 Simplest model Earth radiation: Analytical GPS satellite: Cannon-ball PRN06

5 Impact on the Orbits Implementation of apriori acceleration in the Bernese GPS Software Computation of GPS orbits as done by CODE for one year (2007) of tracking data Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo) PRN05 Most complex model Earth radiation: CERES data GPS satellite: Num. Box-Wing Block specific Antenna thrust PRN06

5 Impact on the Orbits Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo) Comparable with SLR – GPS residuals in a Sun-fixed reference frame (β0 and ∆u) Urschl et al. (2008)

5 Impact on the Orbits SLR validation: SLR measurements – GPS orbits SLR-GPS orbit anomaly  mean reduction of 16 mm - 1.1 cm  albedo (TUM, ESA) - 0.5 cm  antenna thrust (TUM) TUM: ESA:

6 Impact on the Ground Stations

6 Impact on the Ground Stations Change of spectra for the North coordinates, > 200 IGS sites and 9 years of tracking data Main reduction on the sixth peak Where the other peaks come from?  Solar radiation pressure? Why this pattern on the North stations residuals?

6 Impact on the Ground Stations …and Orbits Orbit residuals  (NORTH) as a function of latitude and DOY Mainly effect of cross-track component  orientation of solar panel Almost direct effect of the orbits (cross-track) on the ground stations positions Systematic “deformation” of the Earth

7 Impact on the LOD Change of Length of Day (LOD) due to Earth radiation pressure  around 10 µs Effect on other geodetic parameters importance of orbit modeling

8 Conclusions Earth radiation pressure has a non-negligible effect  on GPS orbits (1x10-9 m/s2) comparable to Y-bias  on ground stations (mainly North) at the submillimeter level Albedo causes a mean reduction of the orbit radius of about 1 cm The largest impact in periodic variations is caused by the solar panels  Use of a box-wing satellite model is a must Different Earth radiation models as well as satellite model details have a small impact on the orbits Albedo can partially explain the peculiar pattern observed in SLR residuals Recommendation for an adequate but simple modelling:  Earth radiation model with CERES data (or alternatively the analytical model for constant albedo)  Analytical box-wing model with block specific optical properties and with antenna thrust

9 References Fliegel H, Gallini T, Swift E (1992) Global Positioning System Radiation Force Model for Geodetic Applications. Journal of Geophysical Research 97(B1): 559-568 Fliegel H, Gallini T (1996) Solar Force Modelling of Block IIR Global Positioning System satellites. Journal of Spacecraft and Rockets 33(6): 863-866 Hugentobler U, van der Marel, Springer T (2006) Identification and mitigation of GNSS errors. Position Paper, IGS 2006 Workshop Proceedings Knocke PC, Ries JC, Tapley BD (1988) Earth radiation pressure effects on satellites. Proceedings of AIAA/AAS Astrodynamics Conference: 577-587 Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical Recipes in Fortran 77, 2nd edn. Cambridge University Press Ray J, Altamimi Z, Collilieux X, van Dam T (2008) Anomalous harmonics in the spectra of GPS position estimates. GPS Solutions 12: 55-64 Rodriguez-Solano CJ, Hugentobler U, Steigenberger P (2010) Impact of Albedo Radiation on GPS Satellites. IAG Symposium – Geodesy for Planet Earth, accepted Urschl C, Beutler G, Gurtner W, Hugentobler U, Schaer S (2008) Calibrating GNSS orbits with SLR tracking data. Proceedings of the 15th International Workshop on Laser Ranging: 23-26 Ziebart M, Sibthorpe A, Cross P (2007) Cracking the GPS – SLR Orbit Anomaly. Proceedings of ION- GNSS-2007: 2033-2038

1 Motivation Consistent bias of 4 – 5 cm  The GPS – SLR Orbit Anomaly. Ziebart et al. (2007)

1 Motivation Power Spectrum Estimation Using the FFT Use of Discrete FFT instead of Lomb-Scargle periodogram Why? Data has the same time spacing (1 day) but problem with data missing FFT still appropiate if data is missing and e.g. set to zero Lomb-Scargle periodogram robust if time spacing is not the same, e.g. in astronomical measurements As expected results are very similar using both methods  but Power Spectrum using FFT is much faster and simpler Press et al. (1992)

1 Motivation

1 Motivation Period: 27.6 +/- 0.1 days

2 Earth Radiation Model Comparison of analytical and numerical models for constant albedo: - Different albedos of the Earth only emission only reflection

2 Earth Radiation Model Comparison of analytical and numerical models for constant albedo: - Different satellite altitudes

2 Earth Radiation Model E3 – E4 E2 – E4 E1 – E4

3 GPS Satellite Model General radiation pressure model from Fliegel et al. (1992,1996) Analytical model assuming Earth radiation to be purely radial  Acceleration acting on the satellites Satellite Bus Solar Panels A: area of satellite surface ψ: angle satellite – Earth – Sun M: mass of satellite μ: specularity, 0 diffuse to 1 specular E: Earth‘s irradiance ν: reflectivity, 0 black to 1 white c: velocity of light in vacuum

4 Acceleration on the Satellites Simpler model: cannon-ball model (no solar panels)  average over ψ More sophisticated model: Numerical box-wing model  considering the full disc of the Earth (not purely radial radiation) In total three GPS satellite models: - S1: cannon-ball - S2: analytical box-wing - S3: numerical box-wing Additionally consideration of: - B: block specific dimensions and optical properties - A: thrust due to navigation antennas Many possibilities: 4 Earth radiation models 3 GPS satellite models 2 extras (turn on/off)

4 Acceleration on the Satellites Earth radiation and satellite models of increasing complexity for PRN06 and β0 = 20.2° Along track acceleration [m/s2] Radial acceleration [m/s2] Cross track acceleration [m/s2]

4 Acceleration on the Satellites Earth Radiation Models: E1: analytical, constant albedo E2: numerical, constant albedo E3: numerical, latitude dependent albedo E4: numerical, CERES data Other options: B: block specific dimensions and optical properties A: thrust due to navigation antennas R: a priori solar radiation pressure (ROCK) model GPS Satellite Models: S1: cannon-ball S2: analytical box-wing S3: numerical box-wing

4 Acceleration on the Satellites Cannon-ball: radial acceleration Box-wing: radial acceleration 4 Acceleration on the Satellites Acceleration over one year in a sun-fixed coordinate system, E1-S1 and E1-S2 Minimum at dark side of the Earth Maximum at dark side of the Earth  Caused by infrared radiation acting on solar panels

4 Acceleration on the Satellites Acceleration over one year in a sun-fixed coordinate system, E1-S2 Box-wing: along track acceleration Twice per revolution Box-wing: cross track acceleration Once per revolution

4 Acceleration on the Satellites Earth radiation pressure [m/s2] From 0.5x10-9 to 2.5x10-9 Solar radiation pressure [m/s2] From 9.5x10-8 to 10.5x10-8

5 Impact on the Orbits Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo) -0.0165 +/- 0.0017 0.0005 +/- 0.0023 0.0001 +/- 0.0010 -0.0164 +/- 0.0016 0.0006 +/- 0.0023 0.0002 +/- 0.0009 -0.0186 +/- 0.0036 -0.0001 +/- 0.0062 -0.0004 +/- 0.0074 -0.0179 +/- 0.0037 -0.0000 +/- 0.0056 -0.0002 +/- 0.0075

5 Impact on the Orbits Orbit differences  effect of different models, PRN05 Num. (const. albedo) model Box-wing analytical model Latitude dependent albedo CERES data

5 Impact on the Orbits Orbit differences  effect of different models, PRN05 Block specific properties Box-wing numerical model Antenna thrust

5 Impact on the Orbits SLR validation: SLR measurements – GPS orbits SLR-GPS orbit anomaly  mean reduction of 16 mm - 11 mm  albedo - 5 mm  antenna thrust ITRF05 Scale parameter: 0.00163 +/- 0.00160 mm/Km Comparison SLRF2005 and ITRF05RS Red: with a priori ROCK model Blue: no a priori ROCK model

5 Impact on the Orbits

5 Impact on the Orbits

6 Impact on the Orbits

6 Impact on the Orbits

6 Impact