pioneer 10 data analysis
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Groupe Anomalie Pioneer - FRANCE
Pioneer 10 Data Analysis
A. Levy, B. Christophe (ONERA)P. Berio, G. Metris (OCA)
J-M. Courty, S. Reynaud (LKB)
GPhyS(21/10/2009)
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The Pioneer 10 and 11 space missions
Very high navigation precision:
Spin stabilization, simple design � 0.1 nms-2
Agency: NASA Pioneer 10 Pioneer 11
Launch 2 march 1972 5 april 1973
Fly-bys Jupiter: 4 dec. 1973 Jupiter: 2 dec. 1974 Saturn: 1 sep. 1979
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Obs
erva
ble
(Hz)
X 105
∝vantenna ≈0.5km/s
Date (year)1993.94 1994
The Doppler observable
f1(t1)
f2(t2)f3(t3)
• Doppler shift: f1(t1) – f3(t3)
≈2.11 GHz
∝vEarth ≈30 km/s
∝vPio≈12 km/s
Relative velocity of the S/C wrtground station
Date (year)
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The Pioneer anomaly
)tt(avv 0Pobservedcomputed −−≅−
2P /nm 13.087.0a s±≅
Hypothesis: � Assymetric radiation of the RTG, gas leak, ... ?� Drag force in the outer solar system ?� Deviation of the gravity law ?
3000
Days from 1 January 1987
400
-400
300
200
0
-100
-200
-300
0 500 1000 1500 2000 2500
100
J. Anderson et al,Phys. Rev. D 65 (2002) 082004
Dop
pler
vel
ocity
(mm
/s)
3000
200 mm/s 3 Hz
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Available data
f1(t1)
f2(t2)f3(t3)
ODF P10 : 26/11/1986 to 20/07/1998(analysed by Anderson et al, 2002)
Before processing After Processing
≈2.11 GHz
Observable corresponds to the difference of Doppler count� averaged doppler shift
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Initial conditions: ,
maneuvers…
Development of a trajectography software: ODYSSEY (OCA+Onera)
EdE
dOOO th
thmes δ=−
End
E=E0 Initial Value
Computation of NumericalIntegration
Computation of Model of themeasurement
Computation of Least-squaresestimation
Stability Test
E
)X,X(),X,X(
∂∂ &
&
E
O,
)X,X(
O,O thth
th ∂∂
∂∂
&
Eδ
EEE δ+=
Yes
NoItera
tion
)X,X( 00&
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∫ −−
=j
i
t
tijth
dttftftt
O 33311 ))()(221
240(
1
Computation of the observable in ODYSSEY (1/2)
f1(t1)
f2(t2)f3(t3)
pertfδ+
Ionosphere (IRI)+ Troposphere (GMF)
Shapiro delay+solar corona (JPL model)
221
240×
: information provided in the ODF
Iterative resolution of thelight travel time equation
(accuracy of 1 µs)
Simpson methodaccuracy: 0.4 mHz
Depends on the trajectory
Objective of accuracy : 1mHz
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State vector of the S/C (2)
� Dynamics
• Gravitational pull by theSun and planets
• Solar radiation pressure: JPL model
• Maneuvers as instantaneous incrementsof velocity
DE 405 Ephemeris (JPL)
State vector of the antenna (1, 3)
� Position of the antenna wrt thecentre of the Earth
� Position of the centre of the Earth
)221
2401()(
221
240)( 23121133 cfctftf spin
+−=
Links between time and space references: IERS conventions
222
212
112
221
12/1
/1
/1
/1
cv
cvu
cvu
cvc
−
⋅+⋅+
−=
rr
rr
Computation of the observable in ODYSSEY (2/2)
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Test conditions
• Estimated parameters: • Initial conditions
• 3D components of maneuvers
• Parameters of anomalous models
• Minimal elevation: 20°
• Criteria for outliers: � residuals > 100 Hz at first iteration� residuals > 6σ at following iterations
• GPT+GMF model for tropo. corrections
• IRI 2007 model for iono. corrections
IERS recommendations
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Constant anomaly: independant confirmation
J. Anderson et al
ap= -0.83 ±±±± 0.05 nms-2
Plots correspond to : Omeasured-Otheoretical(Ciopt, manopt, ap=0)
ap= -0.87 ±±±± 0.13 nms-2
A. Levy et al
Days from 1 January 19873000
400
300
200
0
-100
-200
-300
500 1000 1500 2000 2500
100
J. Anderson et al,Phys. Rev. D 65 (2002) 082004
Dop
pler
vel
ocity
(mm
/s)
0-400
Quasi identical results for thedirections: SSB, Earth, Sun
A. Levy et al, Advances in Space Research
43 (2009) 1538–1544
Days from 1 January 1987
Dop
pler
vel
ocity
(mm
/s)
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Residuals analysis
σ = 9.8 mHzap= 0.83 ±±±± 0,05 nms-2
σ = 35.2 mHz
Estimation: initial conditions, maneuvers, ap
Without anomalous acceleration With anomalous acceleration
Date (year) Date (year)R
esid
uals
(mH
z)
Res
idua
ls(m
Hz)
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O. Olsen, A&A 463 (2007)
Days since July 12th 1992
Validation tests
Solar Corona effect
Nσ criteria
Sol
ar in
dex
Nr of rejected points
Low activity High activity
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Qualitative study of the residuals
Annual variation Daily variation
Days since the 1st of november 1996Date (year)
Res
idua
ls(m
Hz)
Res
idua
ls(m
Hz)
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Detection of periodic variations in the residuals
Detection of variations at6 months, 1 day and 0.5
sidereal day
Spectral analysis with the SparSpec software
(SparSpec software avalaible at http://www.ast.obs-mip.fr/Softwares )
Period (solar day)
0.9974±0.0004 sol. day= 1 sidereal day
½(0.9972±0.0004) sol. day=1/2 sidereal day
6 months
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ϕ = ϕA- ϕP
Difference of azimuthal angles
)]sin()[sin(')]cos()[cos(2
1rectrirectr
ii iiiif ϕϕνϕϕν +++=∆ ∑
=
ϕ describes the daily and annualmotion of the Earth antenna
Periodic model in ODYSSEY
Projection of the Spacecraft and the Earthantenna motions in the ecliptic plane
ϕ
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Without periodic model
Improvement of the results with the periodicmodel
Reduction of the whole spectrum
With periodic model ϕ, 2 ϕσ = 9.8 mHz σ = 5.5 mHz
Period (solar day) Period (solar day)
6 months1 sideral day
1/2 sideral day
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Criteria for the rejection ofpoints depending on their
elevation
Validation tests: robustness of the results (1/2)
% of rejected points
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IRI 2007, PIM or Cnes model
Ionospheric delaymodel
2if)Esin(
TEC28,40)E( =∆
Validation tests: robustness of the results (2/2)
ReferenceDate (year)D
iffer
ence
betw
een
mod
els
(mH
z)
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Summary
mHz 7.1137.123 1 ±=ν
mHz 9.153.123'1 ±−=ν
mHz 6.17.22 ±=νmHz 5.08.4'2 ±−=ν
nm/s² 05.083.0 ±−=Pa
φ 2φ
• Independant confirmation of the existence of a constant anomaly:
• Detection of periodic terms:
� the periodic anomaly cannot beexplained by a S/C technical artefact