Modeling Earth radiation pressure and its impact on GPS orbits and ground tracking stations

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

2. l Angle satellite – Earth – Sun: 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: Urschl et al. (2008)

3. 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

4. 13.65 ± 0.02 days Penna et al. (2007): 13.66 days 1 Motivation • Orbit-related frequencies on geodetic time series  GPS draconitic year • Station coordinates (> 200 IGS sites). Also computed by: Ray et al. (2009) • 9 years of tracking data: 2000.0 – 2009.0 • Geocenter position. Also pointed out by: Hugentobler et al. (2006)

5. 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)

6. 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/

7. 2 Earth Radiation Model E4: CERES data (August 2007) E3: Latitude dependency E2: Numerical, constant albedo E1: Analytical, constant albedo

8. 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

9. 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]

10. 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)

11. 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

12. 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

13. Urschl et al. (2008) 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)

14. 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:

15. 6 Impact on the Ground Stations

16. Why this pattern on the North stations residuals? 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?

17. 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

18. 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

19. 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

20. 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

21. 1 Motivation • Consistent bias of 4 – 5 cm •  The GPS – SLR Orbit Anomaly. Ziebart et al. (2007)

22. 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)

23. 1 Motivation

24. 1 Motivation • Period: 27.6 +/- 0.1 days

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

26. 2 Earth Radiation Model • Comparison of analytical and numerical models for constant albedo: - Different satellite altitudes

27. 2 Earth Radiation Model E3 – E4 E2 – E4 E1 – E4

28. 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 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

29. 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)

30. 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]

31. 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

32. Cannon-ball: radial acceleration Box-wing: radial acceleration 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-S1 and E1-S2

33. 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

34. 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

35. -0.0165 +/- 0.00170.0005 +/- 0.00230.0001 +/- 0.0010 -0.0186 +/- 0.0036-0.0001 +/- 0.0062-0.0004 +/- 0.0074 -0.0164 +/- 0.00160.0006 +/- 0.00230.0002 +/- 0.0009 -0.0179 +/- 0.0037-0.0000 +/- 0.0056-0.0002 +/- 0.0075 5 Impact on the Orbits • Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo)

36. 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

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

38. 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 Red: with a priori ROCK model Blue: no a priori ROCK model • Scale parameter: 0.00163 +/- 0.00160 mm/Km Comparison SLRF2005 and ITRF05RS

39. 5 Impact on the Orbits

40. 5 Impact on the Orbits

41. 6 Impact on the Orbits

42. 6 Impact on the Orbits

43. 6 Impact