Modeling Earth radiation pressure
and its impact on
GPS orbits and ground tracking stations
Carlos Rodriguez-Solano
Tim Springer
Urs Hugentobler
Peter Steigenberger
Bernese GPS Software
Institute for Astronomical
and Physical Geodesy
NAPEOS Software
Newcastle, 30.06.2010
1
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:
cos  cos 0 cos u.
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
2
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
3
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)
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
4
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:

A E
EERM  A  , h   E sun 2
RE  h
AE = πRE2,
1    rˆ
 2







cos


sin


 3 2
4 
RE = 6378 km,
ESUN = 1367 W/m2,
h = satellite altitude,
α = albedo (≈ 0.3)
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
5
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/
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
6
2 Earth Radiation Model
E4: CERES data
(August 2007)
Min.
Diff.:
Max.
Diff.:
E3: Latitude
dependency
-3.2%
+3.7%
E2: Numerical,
constant albedo
-6.7%
+10.8%
E1: Analytical,
constant albedo
-7.4%
+14.0%
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
7
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
8
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]
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
9
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)
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
10
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
Institute for Astronomical
and Physical Geodesy
PRN06
Newcastle, 30.06.2010
11
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
PRN06
- Block specific
- Antenna thrust
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
12
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)
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
13
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:
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
14
6 Impact on the Ground Stations
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
15
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?
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
16
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
17
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
18
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
19
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 IONGNSS-2007: 2033-2038
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
20
1 Motivation
● Consistent bias of 4 – 5 cm
 The GPS – SLR Orbit Anomaly.
Ziebart et al. (2007)
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
21
1 Motivation
Power Spectrum Estimation Using the FFT
Press et al. (1992)
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
22
1 Motivation
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
23
1 Motivation
● Period:
27.6 +/- 0.1 days
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
24
2 Earth Radiation Model
● Comparison of analytical and numerical models for constant albedo:
- Different albedos of the Earth
only emission
only reflection
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
25
2 Earth Radiation Model
● Comparison of analytical and numerical models for constant albedo:
- Different satellite altitudes
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
26
2 Earth Radiation Model
E3 – E4
E2 – E4
E1 – E4
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
27
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
f r 
A E
2

 1      1   ,
M c
3

f r 
A E
 2

cos 1   1    cos   cos 2 
M c
 3

Solar Panels
f r 
A E
2
cos   1   sin    sin 2
M c
3

.

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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
28
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)
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
29
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]
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
30
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
● GPS Satellite Models:
S1: cannon-ball
S2: analytical box-wing
S3: numerical box-wing
● Other options:
B: block specific dimensions and optical properties
A: thrust due to navigation antennas
R: a priori solar radiation pressure (ROCK) model
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
31
4 Acceleration on the Satellites
● Acceleration over one year in a sun-fixed coordinate system, E1-S1 and E1-S2
Cannon-ball: radial acceleration
Minimum at dark side of the Earth
Box-wing: radial acceleration
Maximum at dark side of the Earth
 Caused by infrared radiation
acting on solar panels
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
32
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
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
33
4 Acceleration on the Satellites
Earth radiation pressure [m/s2]
Solar radiation pressure [m/s2]
From 0.5x10-9 to 2.5x10-9
From 9.5x10-8 to 10.5x10-8
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
34
5 Impact on the Orbits
● Orbit differences = perturbed orbit (with albedo) – reference orbit (without albedo)
-0.0165
-0.0186 +/- 0.0017
0.0036 -0.0001
0.0005 +/+/- 0.0023
0.0062 -0.0004
0.0001 +/+/- 0.0010
0.0074
-0.0164
-0.0179 +/- 0.0016
0.0037 -0.0000
0.0006 +/+/- 0.0023
0.0056 -0.0002
0.0002 +/+/- 0.0009
0.0075
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
35
5 Impact on the Orbits
● Orbit differences  effect of different models, PRN05
Num. (const. albedo)
model
Latitude dependent
albedo
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
36
Box-wing
analytical model
CERES data
5 Impact on the Orbits
● Orbit differences  effect of different models, PRN05
Block specific
properties
Box-wing
numerical model
Antenna thrust
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
37
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
● Scale parameter: 0.00163 +/- 0.00160 mm/Km
Comparison SLRF2005 and ITRF05RS
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
38
ITRF05
Red: with a priori ROCK model
Blue: no a priori ROCK model
5 Impact on the Orbits
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
39
5 Impact on the Orbits
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
40
6 Impact on the Orbits
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
41
6 Impact on the Orbits
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
42
6 Impact
Institute for Astronomical
and Physical Geodesy
Newcastle, 30.06.2010
43