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

Institute for Astronomical and Physical Geodesy 1

Newcastle, 30.06.2010

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



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)l

Angle satellite – Earth – Sun:

.coscoscos 0 u



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)

● Geocenter position.

Also pointed out by:

Hugentobler et al. (2006)

● 9 years of tracking data: 2000.0 – 2009.0

13.65 ± 0.02 daysPenna et al. (2007):13.66 days



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:

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

r

hR

EAhE

E

sunEAERM ˆ

4

1sincos

3

2,

22

AE = πRE2, RE = 6378 km, ESUN = 1367 W/m2, h = satellite altitude, α = albedo (≈ 0.3)



● 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/




Min.

Diff.:

Max.

Diff.:

-3.2% +3.7%

-6.7% +10.8%

-7.4% +14.0%

E4: CERES data(August 2007)

E3: Latitude dependency

E2: Numerical, constant albedo

E1: Analytical, constant albedo




3 GPS Satellite Model

● Box-wing model

● Three main satellite surfaces:1) +Z side, pointing always to the Earth2) Front-side of solar panels, pointing always to the Sun3) 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 complexityfor PRN06 and β0 = 20.2°

Along track acceleration [m/s2]

Cross track acceleration [m/s2]Radial acceleration [m/s2]



● 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 orientationEarth radiation pressure bus is fixed, solar panels change orientation

● Comparable to Y-bias effect (1x10-9 m/s2)




● 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)

● Simplest model

● Earth radiation:

- Analytical

● GPS satellite:

- Cannon-ball

PRN05

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


● Most complex model

● Earth radiation:

- CERES data

● GPS satellite:

- Num. Box-Wing

- Block specific

- Antenna thrust

PRN05

PRN06





● Comparable with SLR – GPS residuals in a Sun-fixed reference frame (β0 and ∆u)


Urschl et al. (2008)



● 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?



● 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

6 Impact on the Ground Stations …and Orbits



7 Impact on the LOD

● Change of Length of Day (LOD) due to Earth radiation pressure around 10 µs

● Effect on other geodetic parametersimportance of orbit modeling



● 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

8 Conclusions



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



only reflection

only emission

● Comparison of analytical and numerical models for constant albedo:

- Different albedos of the Earth




● Comparison of analytical and numerical models for constant albedo:

- Different satellite altitudes




E3 – E4

E2 – E4

E1 – E4




● 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

,13

21

c

E

M

Af r

2coscos1

3

21cos

c

E

M

Af r

.2sinsin13

2cos

c

E

M

Af r

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



● 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)





● Earth radiation and satellite models of increasing complexityfor PRN06 and β0 = 20.2°

Along track acceleration [m/s2]

Cross track acceleration [m/s2]Radial acceleration [m/s2]



● 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




● Acceleration over one year in a sun-fixed coordinate system, E1-S1 and E1-S2

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




● 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




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





-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




● Orbit differences effect of different models, PRN05


Num. (const. albedo) model

Box-wing analytical model

Latitude dependent albedo

CERES data




● Orbit differences effect of different models, PRN05

Block specific properties

Box-wing numerical model

Antenna thrust



● SLR validation: SLR measurements – GPS orbits

● SLR-GPS orbit anomaly mean reduction of 16 mm - 11 mm albedo - 5 mm antenna thrust

● Scale parameter: 0.00163 +/- 0.00160 mm/KmComparison SLRF2005 and ITRF05RS

Red: with a priori ROCK model

Blue: no a priori ROCK model


ITRF05















6 Impact

Documents

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