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