INPOP planetary ephemeridesÊ: Recent results in testing...
Transcript of INPOP planetary ephemeridesÊ: Recent results in testing...
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INPOP planetary ephemerides: Recent results intesting gravity
A. Fienga1
J. Laskar2 P. Exertier1 H. Manche2 M. Gastineau2
1GéoAzur, Observatoire de la Côte d’Azur, France
3IMCCE, Observatoire de Paris, France
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The planetary ephemerides today
DE430,EPM2011, INPOP13c: what they have in common ...
Numerical integration of the (Einstein-Imfeld-Hoffmann, c−4 PPN approximation)equations of motion.
ẍPlanet =∑A6=B
µBrAB‖rAB‖3
+ ẍGR(β, γ, c−4) + ẍAST ,300 + ẍJ�2
Adams-Cowell in extended precision
8 planets + Pluto + Moon + asteroids (point-mass, ring),GR, J�2 , Earth rotation (Euler angles, specific INPOP)
Moon: orbit and librations
Simultaneous numerical integration TT-TDB, TCG-TCB
Fit to observations in ICRF over 1 cy (1914-2014)
GAIA ESA planetary ephemerides, Asteroid physics,Tests of gravity
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The Solar system and the tests of gravity
With such accuracy, the solar system is still the ideal lab for testinggravity
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1970 1975 1980 1985 1990 1995 2000 2005 2010Year
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LLR WRMS based on INPOP10a
5 cm
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and the modified gravity comes ...!
For example,
Theories Phenomenology Object
Standard Model violation of EP Moon-LLR
MOND d$̇supp, dΩ̇supp planets
Scalar field theories Ġ/G Moon-LLR, planetsvariation of β, γ planets
Dark Energy Ġ/G Moon-LLR, planetsAWE/chameleons variation of β, γ planetsDark Matter linear drift of AU planets
asupp Moon-LLR,planets
d$̇supp, dΩ̇supp planetsISL d$̇supp planets,Moon-LLRf(r) asupp planets
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INPOP and gravity tests
In Planetary and Lunar ephemerides (like INPOP), GR plays a role in
∆tSHAP = (1 + γ)GM�(t)lnl0 + l1 + t
l0 + l1 − t
∆$̇PLA =2π(2γ − β + 2)GM�(t)
a(1− e2)c2+
3πJ2R2�
a2(1− e2)c2+ ∆$̇AST
∆$̇Moon =2π(2γ − β + 2)GM�(t)
a(1− e2)c2+ ∆$̇GEO + ∆$̇SEL + ∆$̇S,PLA
GR tests are then limited by
Contributions by J�2 , Asteroids, 2γ − β + 2Lunar and Earth physics
BUTDecorrelation with all the planetsBenefit of PE global fit versus single space mission
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Specific INPOP developments for testing gravity
Variations/Estimations of PPN β, γ, Sun J�2 (Fienga et al. 2011)
Simulation of a Pioneer anomaly type of acceleration → ẍconstant (Fienga et al. 2011)
Supplementary advance of perihelia $̇ and nodes Ω̇ → R($(ti ),Ω(ti )) → MONDconstraints (Fienga et al. 2011)
Equivalence Principle @ astronomical scale
→ ẍj =mGj
mIjF (xi , ẋi ,m
Gi , ...) = (1 + η)F (xi , ẋi ,m
Gi , ...)
With µ� = GM�, µj = GMj for planet j
Ṁ�M�
and ĠG with˙µ�µ�
= ĠG +Ṁ�M�
andµ̇jµj
= ĠG
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more than 1 century of data
Mercury: independent analysis ofMESSENGER data (Verma et al. 2014)
Saturn: Cassini VLBI and radio tracking
Jupiter: Galileo VLBI and 5 s/c flybys
Venus, Mars: VEX, MEX, MGS, MRO,MO, ...
α δ ρS/C VLBI 1990-2010 V, Ma, J, S 1/10 mas 1/10 mas
S/C Flybys 1976-2014 Me, J, S, U, N 0.1/1 mas 0.1/1 mas 1/30 m
S/C Range 1976-2014 Me, V, Ma 2/30 m
Direct range 1965-1997 Me,V 1 km
Optical 1914-2014 J, S, U, N, P 300 mas 300 mas
LLR 1980-2014 Moon 1cm
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INPOP13C accuracy versus to DE, EPM (I)
Name # Perturbers # fitted masses Ring GM�
TNO Main belt TNO Main belt TNO Main belt
INPOP13c 0 150 0 150 0 F F
DE430 0 343 0 343 0 0 F
EPM2011 21 301 0 21 + 3 density classes F F
Differences in dynamical modeling and adjustments
INPOP13c data sets ≈ DE430 data sets BUT
2 specific data analysis for MESSENGER
new JPL analysis for CASSINI → Independent analysis in progress
EPM2011 older data sets without MESSENGER data and recently published
Cassini VLBI
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INPOP13C accuracy versus to DE, EPM (II)
Differences in angles [mas] Differences in range [m]
(INPOP13c - DE430)
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Tests of gravity
ẍPlanet =∑A6=B
µBrAB‖rAB‖3
+ ẍGR(β, γ, c−4) + ẍAST ,300 + ẍJ�2
With µ� = GM�, µj = GMj for planet j
Ṁ�M�
and ĠG with˙µ�µ�
= ĠG +Ṁ�M�
andµ̇jµj
= ĠG
∀ti ,M�(ti ) andG (ti )→µ(ti ), µ�(ti ) → ẍPlanet , ẍAst , ẍMoon
What values of ˙µ�µ� (and thenṀ�M�
or ĠG ) BUT also PPN β, γ and
J�2 are acceptable / INPOP13c accuracy ?
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2 approaches based on INPOP13c
1 - Global fit including ˙µ�µ� , PPN β, γ and J�2
Planet CI, 290 GMast ,GMring , GM�, EMRAT + GRFull data samples including Messenger and Cassini data
Correlations between parameters
Correlated datasets
2 - Monte Carlo simulation
about 36000 runs
optimized by a genetic algorithm
With Ṁ�M� = (−0.92± 0.46)× 10−13 yr−1 → ĠG (Pinto et al. 2013),(Pitjeva et al. 2012)
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GR Global fit
Correlations between parameters (Ashby et al. 2007), (Fienga et al. 2009), (Iorio et al.2011)
∆$̇ = 2π(2γ−β+2)µ�(t)a(1−e2)c2 +
3πJ�2 R2�
a2(1−e2)c2 + ∆$̇AST
→ Full modeling with 290 GMast and Limited modeling with 60 GMast
Correlated datasets (Konopliv et al. 2011), (Kuchynka et al. 2012)
S/C electronic delay → bias by s/cJPL data analysis (MO,MRO) →Mis-calibration per station → bias bystation DSS
Independant analysis (MEX, VEX,MGS, MESSENGER): mean rangeper station and per data arc
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GR Global fit: results
Method PPN β − 1 PPN γ − 1 Ġ/G J�2× 105 × 105 × 1013 yr−1 × 107
Limited -12.8 ± 5.4 10.2 ± 6.6 1.12 ± 0.40 2.23 ± 0.2Limited + SC + DSS -4.45 ± 9.1 10.1 ± 2.4 1.12 ± 0.34 2.23 ± 0.2Full -4.9 ± 5.1 -2.0 ± 5.1 -0.54± 0.51 2.27 ± 0.3Full + SC + DSS -4.4 ± 5.3 -0.81 ± 4.5 0.42 ± 0.53 2.27 ± 0.25INPOP13a (Verma et al. 2014) 0.2 ± 2.5 -0.3 ± 2.5 0.0 2.40 ± 0.20
First INPOP Full fit of the 4 GR parameters all together
Stable estimation for J�2
Greater uncertainties for β and γ vs (Verma et al. 2014)
Sensivity of 3 GR β, γ and Ġ/G to dynamical modeling
∆χ2 ≈ 1%
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MC simulations”Real” uncertainty/LS estimations + ”my theory proposes this violation of GR. Is it compatible with INPOP ?”
Grid of sensitivity for GRP determinations(Fienga et al. 2009, 2011), (Verma et al. 2014)
GRP: PPN β,γ, $̇, Ω̇, asupp, Ġ/G , J�2
Construction of different INPOP for different values of GRP
For each value of GRP , all parameters (IC planets, GMAst ,GM�) of INPOP are fitted.
Iteration = all correlations are taken into account2 selection criteria
1 C1 = Postfit residuals /INPOP → GRP intervals with ∆residuals < 50%
2 C2 = ∆χ2 < 3%
What values of GRP are acceptable at the level of data accuracy ?
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INPOP13a and tests of GR: PPN β and γ
INPOP13a (Verma et al. 2014):
(β − 1)× 105 = 0.2± 2.5 , (γ − 1)× 105 = −0.3± 2.5 , J�2 × 107 = 2.40± 0.20
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Direct Monte Carlo of µ̇/µ, J�2 , β, γ
4000 INPOP runs with random
selection of (µ̇/µ, J�2 , β, γ)
1 run = 4 iterations (1hr/iteration@ 16 itanium processors)
Selection of INPOP(µ̇/µ, J�2 , β, γ)
inducing differences to INPOP13a
residuals < 50 %
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Direct Monte Carlo of µ̇/µ, J�2 , β, γ
Only 15 % INPOP(µ̇/µ,J�2 , β, γ) < 50 %1.4% for INPOP() < 25 %
No clear gaussiandistribution especiallyfor β and γ
→ Optimisation of the MCby a genetic algorithm
< J�2 > (2.21 ± 0.29) × 10−7
W-test = 0.984
< β − 1 > (-0.8 ± 8.2)× 10−5 ?0.969
< γ − 1 > (0.2± 8.2)× 10−5 ?0.968
< Ġ/G > (0.04± 2.46)*× 1013 yr−1 (0.27± 1.66)**
0.987
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Simple Genetic Algorithm with mutation (SGAM)
1 individual = INPOP (µ̇/µ, J�2 , β, γ)
1 chromosome = a set of (µ̇/µ, J�2 , β, γ)
2 crossovers + 1/10 mutation (= new random value each over 10)
2 selection criteria : (O-C) < 50% and ∆χ2 < 3%
35 800 runs with 4000 MC simulation as population 0
set i [(µ̇/µ)i , (J�2 )i , βi , γi ]
set j [(µ̇/µ)j , (J�2 )j , βj , γj ]
1 crossover [(µ̇/µ)i , (J�2 )i ,βj , γj ]
[(µ̇/µ)j , (J�2 )j ,βi , γi ]
2 crossovers [(µ̇/µ)i , (J�2 )j ,βi , γj ]
[(µ̇/µ)j , (J�2 )i ,βj , γi ]
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35 800 runs with SGAM
@ PSL mesocentre : NEC 1472 kernels on 92 nodes2 nodes allocated for INPOP12 runs (= 12 x 4 iterations) @ 1hr / node4000 MC simulation = population 0 @ SGAM30 generationsC1 convergency reached @ 18th (12125 runs)C2 convergency reached @ 25th
C1 C2
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Improvement of gaussianity
C1 C2
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Improvement of gaussianity
→ Proper definitionof mean and 1-σ
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Decrease of σ of the GRP distribution with thenumber of runs
C1 C2
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PPN β, γ, µ̇/µ, J�2
Method PPN β − 1 PPN γ − 1 Ġ/G J�2× 10−5 × 10−5 × 1013 yr−1 × 107
LS -4.4 ± 5.5 -0.81 ± 4.5 0.42 ± 0.53 2.27 ± 0.3MC -0.8 ± 8.2 0.2 ± 8.2 0.04 ± 2.46 2.21 ± 0.29MC + SGAM C1 -0.5 ± 6.3 -1.2 ± 4.4 0.4 ± 1.4 2.26 ± 0.11MC + SGAM C2 -0.01 ± 7.1 -1.7 ± 5.2 0.5 ± 1.6 2.22 ± 0.14MC + SGAM C1,C2 -0.25 ± 6.7 -1.5 ± 4.8 0.5 ± 1.6 2.24 ± 0.125
Ġ/G ≈ 2 ×10−13 yr−1 β − 1 ≈ 7 ×10−5 γ − 1 ≈ 5 ×10−5EP η = 4β − γ − 3≈ 2×10−4
J�2 = (2.24± 0.15)× 10−7
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PPN β, γ, µ̇/µ, J�2Method PPN β − 1 PPN γ − 1 Ġ/G J�2
× 10−5 × 10−5 × 1013 yr−1 × 107LS -4.4 ± 5.5 -0.81 ± 4.5 0.42 ± 0.53 2.27 ± 0.3MC + SGAM C1 -0.5 ± 6.3 -1.2 ± 4.4 0.4 ± 1.4 2.26 ± 0.11MC + SGAM C2 -0.01 ± 7.1 -1.7 ± 5.2 0.5 ± 1.6 2.22 ± 0.14MC + SGAM C1,C2 -0.25 ± 6.7 -1.5 ± 4.8 0.5 ± 1.6 2.24 ± 0.125K11-DE 4 ± 24 18 ± 26 1.0 ± 2.4 fixed to 1.8P13-EMP -2 ± 3 4 ± 6 0.29 ± 1.25 2.0 ± 0.2INPOP13a 0.2 ± 2.5 -0.3 ± 2.5 0.0 2.4 ± 0.2F13-DE 0.0 0.0 0.0 2.1 ± 0.70W09-LLR 12 ± 11 fixed 0.0 fixedM05-LLR 15 ± 18 fixed 6 ± 8 fixedB03-Cass 0.0 2.1 ± 2.3 0.0L11-VLB 0.0 -8 ± 12 0.0 fixedPlanck +WP+BAO -1.42± 2.48Heliosismo. 2.206 ± 0.05
Ġ/G ≈ 2 ×10−13 yr−1 β − 1 ≈ 7 ×10−5 γ − 1 ≈ 5 ×10−5J�2 = (2.24± 0.15)× 10−7 EP η = 4β − γ − 3≈ 2×10−4
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Conclusions
β − 1 ≈ 7 ×10−5 γ − 1 ≈ 5 ×10−5EP η = 4β − γ − 3≈ 2×10−4
Ġ/G ≈ 2 ×10−13 yr−1 J�2 = (2.24± 0.15)× 10−7
Short term improvement:
Saturn: Full reprocessing of Cassini 10 years data
Jupiter: JUNO mission in 2015/2016
Mars: MO,MEX,MRO
In the coming years: GAIA, Bepi-Colombo, JUICE
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