Transcript Folie 1

Impact of Albedo Radiation
on GNSS Satellites
Carlos Javier Rodriguez Solano*), Urs Hugentobler,
Peter Steigenberger
Institute for Astronomical and Physical Geodesy
Technische Universität München
IAG Scientific Assembly 2009, Buenos Aires, Argentina
August 31, 2009
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
1
Content
•
Motivation
•
Earth albedo modeling
•
Albedo acceleration at GNSS altitude
•
Impact on GNSS orbits
•
Conclusions
*)
Master's Thesis in progress in the International Master's Course ESPACE
(Earth Oriented Space Science and Technology) at Technische Universität
München.
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
2
SLR Residuals of GNSS Orbits
•
β0
SLR residuals for GPS satellites in a sun-fixed coordinate system show a
peculiar pattern
Δu
Urschl, 2006
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
3
Earth Albedo Radiation
•
Visible light reflected from the Earth and infrared radiation emitted by the
Earth cause an acceleration on satellites pointing away from the Earth.
•
Order of magnitude for GNSS satellites is 10−9ms−2
•
Impact on the orbit thus is of similar
magnitude as, e.g., y-bias
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
4
Earth Albedo Radiation
•
The acceleration acting on a GNSS satellite depends on
– relative geometry of satellite, Sun and Earth
– shape and size of the satellite as well as attitude
– optical properties of satellite surfaces
– reflectivity and emissivity of the Earth surface
– scattering properties of the Earth surface
•
satellite model
Earth radiation model
What are the most important elements of an Earth albedo model?
– solar panels?
– optical properties of surfaces?
– modeling of reflectivity and emissivity of Earth's surface as a function
of geographical location and time?
– ...?
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
5
Earth Radiation Models
•
Models:
– Earth scattering properties approximated as a Lambertian sphere
– emitted and reflected radiation  infrared and visible radiation
•
Types of solutions:
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
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
6
Earth Radiation Models
•
CERES
(Clouds and the
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
IAG 2009, Buenos Aires, Argentina
7
Comparison of Models
•
Analytical and numerical models for constant albedo:
– Different albedos of the Earth
only emission
only reflection
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
8
Comparison of Models
•
Analytical and numerical models for constant albedo:
– Different satellite altitudes
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
9
Comparison of Models
•
•
•
•
CERES data,
August 2007
Min.
Diff.:
Max.
Diff.:
Latitude
dependency
-3.2%
+3.7%
Numerical,
constant albedo
-6.7%
+10.8%
Analytical,
constant albedo
-7.4%
+14.0%
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
10
GPS Satellite Model
•
•
•
Box-wing model
Three main satellite surfaces:
– +Z side, pointing always to the Earth
– Front-side of solar panels, pointing always to the Sun
– Back-side of solar panels
Main dependency on angle ψ satellite – Earth – Sun
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
11
GPS Satellite Model
•
•
•
Acceleration caused by infrared radiation (albedo=0)
Variations with impact angle dominated by solar panels
Different GPS satellite types: 10% differences
solar panels oriented
perpendicular to Earth
direction
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
12
Acceleration on GPS Satellites
•
Cannon-ball model
PRN 05 (β0=55.5°)
Institute for Astronomical
and Physical Geodesy
PRN 06 (β0=20.2°)
IAG 2009, Buenos Aires, Argentina
13
Acceleration on GPS Satellites
•
Box-wing model
PRN 05 (β0=55.5°)
Institute for Astronomical
and Physical Geodesy
PRN 06 (β0=20.2°)
IAG 2009, Buenos Aires, Argentina
14
Acceleration on GPS Satellites
•
•
•
Cannon-ball model: radial acceleration as a function of β0 and ∆u
Minimum at dark side of the Earth (β0 = 0° and ∆u = 180°)
Maximum at daylight side of the Earth (β0 = 0° and ∆u = 0°)
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
15
Acceleration on GPS Satellites
•
•
•
•
Box-wing model: radial acceleration as a function of β0 and ∆u
Local maximum at dark side of the Earth (β0 = 0° and ∆u = 180°)
Caused by infrared albedo radiation acting on solar panels
Compare with pattern of SLR residuals
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
16
Orbit Determination Including Albedo Acceleration
•
•
Analysis of one year (Jan-Dec 2007) of tracking data from 190 IGS sites
Orbit determination using the same analysis strategy as the CODE (Center
for Orbit Determination in Europe) Analysis Center
•
Five tests have been performed for GPS satellites:
(1) Cannon-ball, analytical (constant albedo)
(2) Cannon-ball, numerical (constant albedo)
(3) Box-wing, numerical (constant albedo)
(4) Box-wing, latitude-dependent reflectivity and emissivity
(5) Box-wing, monthly CERES data for 2007
•
Result: Orbit differences = orbit with albedo – orbit without albedo
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
17
Orbit Differences to Non-albedo Orbits
PRN 5
PRN 6
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
18
SLR Validation of GNSS Orbits
•
SLR residuals = SLR measurements – computed orbit distance
PRN 05
PRN 06
Mean [m]
RMS [m]
Sigma [m]
CODE,
No albedo
-0.0219
-0.0239
0.0359
0.0420
0.0285
0.0346
Cannon-ball,
Numerical (constant albedo)
-0.0069
-0.0091
0.0292
0.0358
0.0284
0.0346
Box-wing,
CERES data 2007
-0.0102
-0.0138
0.0292
0.0350
0.0274
0.0322
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
19
Orbits with Albedo Acceleration
•
•
•
Cannon-ball model, orbit residuals as function of β0 and ∆u
Reduction of orbital radius by 1-2 cm
Most pronounced in direction of Sun (β0 = 0°, ∆u = 180°)
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
20
Orbits with Albedo Acceleration
•
Cannon-ball model: Reduction of orbit radius by about 1 cm, more
pronounced in direction of Sun
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
21
Orbits with Albedo Acceleration
•
•
•
Cannon-ball model, orbit residuals as function of β0 and ∆u
Reduction of orbital radius by 1-2 cm
Most pronounced in direction of Sun (β0 = 0°, ∆u = 180°)
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
22
Orbits with Albedo Acceleration
•
•
•
Box-wing model, orbit residuals as function of β0 and ∆u
Additional orbit height reduction at dark side of Earth (β0 = 0°, ∆u = 180°)
Caused by Earth infrared radiation acting on solar panels
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
23
Orbits with Albedo Acceleration
•
Box-wing model: Reduction of orbit height also at night-side of the Earth
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
24
Orbits with Albedo Acceleration
•
•
•
Box-wing model, orbit residuals as function of β0 and ∆u
Additional orbit reduction at dark side of Earth (β0 = 0°, ∆u = 180°)
Caused by Earth infrared radiation acting on solar panels
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
25
SLR Residuals of GNSS Orbits
•
Residuals for GPS satellites PRN 5 and 6 in the sun-fixed coordinate
system show a similar pronounced pattern
Urschl, 2006
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
26
Conclusions
•
The aim of the study was not to construct the perfect albedo model but to find
the best but simplest model.
•
Accelerations due to Earth albedo have a similar magnitude as the y-bias.
•
Impact of albedo model components on GNSS orbits:
(1)
Albedo causes a mean reduction of the orbit radius of about 1 cm
(2)
The largest impact in periodic variations is caused by the solar panels

(3)
•
Use of a box-wing satellite model is a must
Different Earth albedo models as well as satellite model details have a
small impact on the orbits
Earth albedo has the potential to explain the peculiar pattern observed in
SLR residuals.
Institute for Astronomical
and Physical Geodesy
IAG 2009, Buenos Aires, Argentina
27