1. Tests of general relativity in the solar system and a number of collaborations (details later) Séminaire CPPM 20 Feb 2012 Image : ODYSSEY Serge Reynaud (LKB Paris)

2. Gravitation ↔ geometry in space-time –the equivalence principle as a geometrical foundation –ideal (atomic) clocks measure the proper time along their trajectory –freely falling probes (test masses and light rays) follow geodesics One of the most accurately tested principles of physics : –free motions of masses with ≠ compositions coincide to an accuracy better than 10 -12 ; this accuracy is reached in the lab as well as in space (Lunar Laser Ranging) –atomic clocks working on ≠ transitions give the same time at an accuracy better than 10 -16 per year Accuracies to be improved soon : MICROSCOPE & ACES General Relativity : a metric theory

3. In General Relativity, the coupling between matter and geometry has a simple specific form, given by the Einstein equation –other forms of the coupling are possible –they may be described by other fields (scalar, vector..) –they may also be thought of as due to “radiative corrections” of GR inducing a scale dependence of the gravitational coupling –some of these forms, but not all of them, have been submitted to systematic investigation Riemannian geometry –the Einstein curvature tensor has a null divergence –the stress tensor too (conservation laws) General Relativity : a specific coupling

4. Simple model of the solar system –Sun treated as a point-like motionless source –other masses neglected in a first approach  isotropic solution (written with spatially isotropic coordinates) General Relativity in the solar system Einstein equation : solution outside the source –written here as a Taylor expansion of the Newton potential –tests : comparison of observed motions to the geodesics calculated from this metric

5. Select a vicinity of GR in the PPN family 1 0.998 1 0.9991.0011.002 1.001 0.999 0.998   Cassini ‘03 Mercury Ranging ‘93 LLR ’02 General Relativity Mars Ranging ‘76 VLBI ‘97 Living Reviews in Relativity, C.F. Will (2001 + updates) GR often tested in the PPN framework Parameterized Post Newtonian tests Courtesy : Slava Turyshev JPL NASA INPOP Ephemerides 2010 Cassini Relativity Exp. 2002

6. Search for a scale-dependent deviation of the component for example under the form of a Yukawa correction log 10  log 10 (m) Satellites Laboratory Geophysical LLR Planetary The Search for Non-Newtonian Gravity, E. Fischbach, C. Talmadge (1998) Scale dependent tests of the force law Select a vicinity of GR in the Yukawa family but windows are still open for deviations at short ranges or long ranges Courtesy : J. Coy, E. Fischbach, R. Hellings, C. Talmadge, and E. M. Standish (2003); M.T.Jaekel and S.Reynaud IJMPA (2005)

7. The largest scale gravity test ever performed (Pioneer 10 &11) failed to confirm expectations deduced from GR Interest of tests with man-made probes in the solar system Gravity law tests are in good agreement with GR but –Windows are still open for deviations –GR is a classical theory which shows inconsistencies with Quantum Field Theory –Unification models predict deviations which could be observed at short or long distances … The tests must go on ! “Dark matter” and “dark energy” are introduced to cure defects in gravitational observations at galactic and cosmic scales It is extremely important to test GR at large scales

8. The presence of the anomaly is certain, its origin still an enigma –it might be an artifact thermal issue ? drag on unknown matter ? … –as long as the problem is not solved, the status of tests of GR at the scale of the solar system remains unsteady Image courtesy : Pioneer team NASA J.D. Anderson et al, PRD 65 082004 (2002) The “Pioneer anomaly” Living Reviews in Relativity, S.G. Turyshev, V.T. Toth (2010) The largest scale gravity test ever performed failed to confirm GR predictions  Doppler tracking of the Pioneer 10/11 probes during their motions to the outer solar system

9. Several complementary strategies  Discuss the anomaly in a coherent phenomenological framework and compare it with other observations which agree with GR  Reanalyze the data to try to capture the origin of the effect  Redo the measurements with modern dedicated instruments / missions Outlook Pioneer 10 as seen recently from Arecibo (coherent signal now lost) S. Reynaud, M.-T. Jaekel Varenna lectures arXiv:0801.3407

10. A metric framework for gravity tests One preserves the metric interpretation of gravitation, with a general form for the coupling  the metric in the outer solar system may be modified  in terms of phenomenology, there are two functions to be tested M.-T. Jaekel, S. Reynaud, Ann. Physik (1995) ; Mod. Phys. Lett. (2005) They correspond to the two “sectors” of gravitation theory –there are two independent divergence-less components in the Einstein tensor (one related to the trace, the other traceless) –“radiative corrections” to GR have to accommodate two running coupling constants (two functions of momentum) –the freedom in these two running coupling constants matches the freedom in the two functions

11. Post-Einsteinian gravity (PEG) extends the PPN framework –metric and Einstein tensors show general functional dependences on r (scale dependences looked for in the two sectors, not only one of them) –gravity constant replaced by 2 running coupling constants –PPN constants  and  replaced by 2 functions of r Post-Einsteinian gravity beyond PPN PPN is a particular case with specific dependences on r  for the metric  for the Einstein tensor M.-T. Jaekel, S. Reynaud, Classical Quantum Gravity 22 (2005) 2135 M.-T. Jaekel, S. Reynaud, Classical Quantum Gravity 23 (2006) 777

12. Recent analysis of Cassini data (in the Saturn system)  modifications of the gravity force law excluded with an amplitude fitting the Pioneer anomaly at Saturn heliocentric distance PEG in the “first sector” Modifications of the temporal component  modification of the gravity force law  strongly constrained by planetary tests  deviations which would explain the Pioneer anomaly are too large to remain unnoticed on planetary tests if they correspond to a constant force or have a Yukawa form W.M. Folkner, Proceedings IAU Symposium 261 155 (2010) A. Fienga et al, Proceedings IAU Symposium 261 159 (2010) J.D. Anderson et al, PRD 65 (2002) 082004 M.-T. Jaekel, S. Reynaud, IJMPA 20 (2005) 2294 First sector

13. Modifications of the spatial component  modification of light propagation (equivalent to an Eddington parameter  with a scale dependence)  small effect on slow material motions (especially on circular or nearly circular orbits)  could have escaped detection in planetary tests more easily than deviations in the first sector PEG in the “second sector” Such modifications may produce  secular Pioneer-like anomalies for probes with escape trajectories in the outer solar system  periodic anomalies modulated by the annual and diurnal motions of the Earth M.-T. Jaekel, S. Reynaud, Classical Quantum Gravity 23 (2006) 7561 S. Reynaud, M.-T. Jaekel, IJMPD 16 (2007) 2091

14. The Doppler observable is a ratio of frequencies, it may be seen as a velocity, but takes into account all relativistic and gravitational effects Furthermore, the observable has to be corrected for propagation effects (atmosphere and solar plasma) and motions of stations…. Doppler tracking A radio signal is sent from a DSN station on Earth to the probe, received and transponded back to the Earth, and finally recorded by a DSN station (the same=2-way ; another=3-way) S Band  2,11 GHz Transponder

15. 2 Way (red) and 3 Way (blue) versus NASA Horizon ephemeris (black) Doppler tracking on Pioneer probes Data treatment : Agnès Lévy et al Motions of Earth and probe ~ 860000 Hz

16. Reanalysis of Pioneer 10 data A. Levy, B. Christophe, P. Berio, G. Metris, J.-M. Courty, S. Reynaud Advances in Space Research 43 (2009) 1538 J. Anderson et al, Phys. Rev. D 65 (2002) 082004 The presence of the anomaly is confirmed, on the same data, with an independent software ~ 3Hz Doppler velocity residuals (mm/s) Days since 1st Jan 1987

17. Anomaly = large reduction of the residuals Residuals with GR σ = 9,8 mHzσ = 35,2 mHz Periodic structures still visible in the residuals Date (year) Residuals (mHz) GR + constant acceleration Residuals = Observed – Calculated Residuals (mHz)

18. GR + constant acceleration + periodic terms Spectral analysis of the residuals σ = 5,5 mHzσ = 9,8 mHz Period (day -1 ) Significant reduction of the variance of the residuals, as well as of all spectral signatures Period (day -1 ) GR + constant acceleration A. Levy, B. Christophe, P. Berio, G. Metris, J.-M. Courty, S. Reynaud, Advances in Space Research 43 (2009) 1538

19. Modulated anomalies A. Levy et al, Advances in Space Research 43 (2009) 1538  The terms cos , sin , cos2 , sin2  are sufficient for reducing the data A single angle  is used for describing the diurnal and annual motions of the antenna on Earth Other possible interpretations for the modulated anomalies ?  solar plasma model ? … solar system ephemeris ? …  atmosphere ? … solid Earth models ? … Suggest there is an anomaly on the propagation of the radio link  if this is so, the Pioneer effect will never be explained entirely by an anomalous non-geodesic force on the probe !

20. We have an extended metric framework for testing gravity in the solar system  the metric modifications which would match Pioneer observations cannot be allowed to spoil the good agreement of GR with other gravity tests  but they can produce “correlated” anomalies to be looked for in other observations Examples of possibilities  navigation data of other planetary probes  Cassini, New Horizons …  high-quality astrometry data  GAIA  dedicated missions with improved techniques or dedicated instruments to be embarked on future planetary probes  ODYSSEY, SAGAS, OSS, GAP … Phenomenology of solar system gravity A.Hess et al arXiv:1201.5041

21. GR and PPN predict the dependence of light-deflection ω versus the angular distance  to the Sun  here written at first order in  : observer-Sun distance Testing large-angle light-deflection Idea : measure and compare with prediction  for the general metric extension, the knowledge of this function is equivalent to that of the component of the metric tensor which has a null conformal weight  this function would be sensitive to a deviation from GR in the second sector M.-T. Jaekel, S. Reynaud, Classical Quantum Gravity 22 (2005) 2135 M.-T. Jaekel, S. Reynaud, Classical Quantum Gravity 23 (2006) 777

22. GAIA will measure with a very good accuracy a large number of small deflection angles at large angular distances from the Sun Light-deflection test with GAIA Equivalent to look for a dependence of  versus    now known accurately only near grazing incidence With GAIA results, it will be possible to improve the accuracy for a mean value of  map the function by fitting  on intervals of  or trying specific dependences F. Mignard, S. Klioner, Proc. IAU Symposium 261 306 (2010)

23. Ideas for new missions Main motivations : With an accelerometer on board (none on any probe to date), we have a supplementary inertial observable and get rid of the uncertainties of models on non gravitational forces With largely improved tracking techniques and spacecraft design, we get rid of all uncertainties of Pioneers Huge interest for fundamental physics : Gravity law test performed during the cruise phases with largely improved accuracy and reliability Planetary flybys also monitored in a more precise manner Very important improvement also for the physics of the visited objects and places : Gravity field of planets, moons, Kuiper Belt objects … Environments of planets, moons and of the outer solar system

24. Ideas for new missions gravity field deduced probe with an accelerometer radio or laser link Combining tracking and accelerometry to measure the gravity force without ambiguity ODYSSEY collaboration : B. Christophe et al, Experimental Astronomy 23 (2009) 529

25. Ideas for new missions Using atomic clocks and asynchronous laser links to measure the gravity force without ambiguity and map the two sectors of gravitational theory SAGAS collaboration : P. Wolf et al, Experimental Astronomy 23 (2009) 651 up down Distance = up + down Timing = up - down probe with an atomic accelerometer and an optical clock up and down laser links

26. Outer Solar System (OSS) : Combining the ODYSSEY mission with a mission to Neptun/Triton and the Kuiper belt Ideas for new missions OSS collaboration, B. Christophe et al, arXiv:1106.0132 Fundamental physics and solar system physics objectives Collaboration ESA-NASA

27. Thank for your attention Collaborations “Pioneer Anomaly Explorer” Hansjörg Dittus et al “Pioneer Anomaly Investigation @ ISSI” Slava Turyshev et al “Deep Space Gravity Tests” Serge Reynaud et al “Solar System ODYSSEY” Bruno Christophe et al “SAGAS” Peter Wolf et al “Gravity Advanced Package” Bruno Christophe et al “Scientific Exploitation of Navigation Data” Agnès Fienga et al “Outer Solar System” Bruno Christophe et al

28. THE DEEP SPACE GRAVITY PROBE SCIENCE TEAM Nieto et al, Physics Letters B 613 (2005) 11–19 A Drag Through Dust ? Interplanetary Medium –A thinly scattered matter (neutral Hydrogen, microscopic particles) with two main contributions –Interplanetary Dust (IPD) ●Hot-wind plasma (mainly protons and electrons) distributed within the Kuiper Belt starting from 30 to 100 AU ● is a modeled density, as suggested in Man, Kimura, J. Geophys. Res. A105, 10317 (2000); –Interstellar Dust (ISD) ●Fractions of interstellar dust (characterized by greater impact velocity); ● was directly measured by the Ulysses spacecraft Effect on the Pioneers –The drag on a spacecraft is given by –One needs an axially-symmetric dust distribution within 20 and 70 AU with a constant uniform and unreasonably high density of  Dust can hardly be the origin of the Pioneer Anomaly

29. THE DEEP SPACE GRAVITY PROBE SCIENCE TEAM The thermal issue 1987 1998.8 2001  Initial analysis at JPL (PRD 2002 paper) : –Effect calculated to be small –Exponential decrease predicted and not seen Problem currently reevaluated : –New thermal models of the probe –Telemetry data recovered and analysed Status : Thermal budget is a source of concern Decrease might be present S.G. Turyshev et al PRL 107 (2011) 081103