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)
2
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
3
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)
4
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
5
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
6
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&
7
∫ −−
=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
8
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)
9
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
10
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)
11
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)
12
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
13
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)
14
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
15
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
16
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
17
Criteria for the rejection ofpoints depending on their
elevation
Validation tests: robustness of the results (1/2)
% of rejected points
18
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)
19
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
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