Testing the Equivalence principle with LLR

Transcription

1 Testing the Equivalence principle with LLR F. ignard(*) Observatory of the Côte d Azur, Nice, (France) (*) Thanks to J.. Torre (OCA) for providing the updated LLR documentation F. ignard icroscope ONERA, 30 January

2 Outline Principles of Lunar Laser Ranging Status of the Observations The orbit of the oon The equivalence principle testing Perspective with icroscope F. ignard icroscope ONERA, 30 January

3 LLR in eneral 3 F. ignard icroscope ONERA, 30 January 2013

4 F. ignard icroscope ONERA, 30 January

5 Short story of the LLR Apollo 11: July 1969 first reflectors on the oon surface then Apollo 14, 15, and Lunakhod 1 &2 First returns in the US σ ~ 2 m French attempts at the Pic du idi A. Orzag, O. Calame,.J. Fillol Decision to build a station in rasse (Plateau de Calern) first returns in 1981 Operational station with ruby laser in 1984 σ ~ 20 cm first upgrade to cm station σ ~ 4 cm second upgrade to mm station σ ~ 7 mm fully refurbished station with EO 2004 F. ignard icroscope ONERA, 30 January

6 Why it's difficult Photons sent per laser pulse Way to the oon beam width after atmospheric crossing 4" light on the moon spread over ~ 5 km reflector total area m 2 back to the Earth Corner Cube diffraction 12" light on the moon spread over ~ 20 km collecting area 1 to 10 m 2 Net budget : 1 photon collected every 1 to 10 shots F. ignard icroscope ONERA, 30 January

7 An array of reflectors on the oon (A 14) F. ignard icroscope ONERA, 30 January

8 Location of the reflectors on the oon L1 A15 L2 A14 A11 Not an ideal distribution for selenophysics F. ignard icroscope ONERA, 30 January

9 Observations & Age of the oon Observations as a function of the Lunar phase very important issue for the EP testing the more uniform, the better for the correlation observations at new and full oon have the much weight in the data fitting for EP testing Only 3 observations at the full oon in 1990, 1996 and 2000 during an eclipse F. ignard icroscope ONERA, 30 January

10 Normal points and detected photons Number of returns per normal points at Calern F. ignard icroscope ONERA, 30 January

11 Post fit residuals Evolution de la précision CERA CERA ,1 (2756) 3,8 (2038) 5,1 (1569) Station cdonald cdonald Haleakala ,4 (1622) 4,3 (581) 5,6 (230) 7,9 (455) CERA ,6 (1166) cdonald cdonald ,5 (992) 27,3 (1030) 43 (1487) rms (cm) Chapront et al., 2003 F. ignard icroscope ONERA, 30 January

12 Perturbations on the oon eneral Relativity TL : Earth-oon distance Tidal perturbations Perturbation type Lunar figure Earth's figure Ecliptic plane motion Planetary perturbations (D & ) ain Problem Poissson terms Periodic terms Keplerian motion 1 10^1 10^2 10^3 10^4 10^5 10^6 10^7 10^8 10^9 10^1 Amplitude (cm) 0 Chapront et al., 2003 F. ignard icroscope ONERA, 30 January

13 Where are the LLR stations Not all stations in operation simultaneously today only rasse carries out routine ranges F. ignard icroscope ONERA, 30 January

14 Targets and production Appollo 15 is the most efficient reflector Credit : J. üller et al., F. ignard icroscope ONERA, 30 January

15 Normal Points from different stations 17,000 normal points Credit : J. üller et al., F. ignard icroscope ONERA, 30 January

16 Targets and production 2010 Credit : J. üller et al., F. ignard icroscope ONERA, 30 January

17 Targets and production 2011 Credit : J. üller et al., F. ignard icroscope ONERA, 30 January

18 EO (OCA) Laser Station 18 F. ignard icroscope ONERA, 30 January 2013

19 EO telescope on the Plateau de Calern F. ignard icroscope ONERA, 30 January

20 EO Laser Station Telescope diameter 1.54 m Laser (current hardware) Nd-Yag with frequency doubling Pulse of 200 ps width Energy of 200 mj per pulse credit : J.P artin ~ 1 W!!! Firing rate: 10 Hz Detection APD (Avalanche Photo Diode) in single photon mode Timing for the two-way trip σ < 50 ps ( 1.5 cm) F. ignard icroscope ONERA, 30 January

21 Number of echoes Real restart in 2011 and routine activity in 2012 Appolo X Appolo XV Appolo XV Lunakhod 2 J. Torre et al., 2012 F. ignard icroscope ONERA, 30 January

22 Number of normal points Appolo X Appolo XV Appolo XV Lunakhod 2 J. Torre et al., 2012 F. ignard icroscope ONERA, 30 January

23 EO 2012 : Results number of echoes number of echoes per normal point months months J. Torre et al., 2012 F. ignard icroscope ONERA, 30 January

24 Heliocentric Orbit of the oon 24 F. ignard icroscope ONERA, 30 January 2013

25 Orbit of the oon Look at the oon motion from an heliocentric perspective P moon = days ; a moon = 385,000 km : sampling = 5 days a = 40 4 a moon to enhance the feature F. ignard icroscope ONERA, 30 January

26 Orbit of the oon From an heliocentric perspective P moon = days ; a moon = 385,000 km : sampling = 5 days a = 4a moon change of curvature F. ignard icroscope ONERA, 30 January

27 Orbit of the oon Heliocentric frame a = a moon orbits hardly distinguishable Earth + oon F. ignard icroscope ONERA, 30 January

28 Orbit of the oon Heliocentric frame a = a moon no change of sign of the curvature F. ignard icroscope ONERA, 30 January

29 Provisional conclusion n geocentric frame, the orbit of the oon is a ~ Keplerian motion about the Earth perturbed by the Sun n heliocentric frame, the orbit of the oon is a ~Keplerian motion about the Sun, perturbed by the Earth the oon falls on the Sun more or less as the Earth does The two conclusions seem incompatible, since the forces are identical in both cases? in fact in geocentric frame the action of the Sun is a differential (tidal) effect in 1/r 3 mplications on what is meant by a claimed 'objective' description of a physical reality! several unspoken assumptions F. ignard icroscope ONERA, 30 January

30 Equivalence Principle with LLR 30 F. ignard icroscope ONERA, 30 January 2013

31 Free fall on the oon: Hammer & Feather Painting from true images Apollo 15, David Scott F. ignard icroscope ONERA, 30 January

32 F. ignard icroscope ONERA, 30 January Equations of motion with EP violation Simplified form with Newtonian formulation and Sun-Earth-oon = * SE SE S S SE SE S S E E a E s s μ E E SE SE r E E S S r E i E s E i E s dt d dt d + = = + = = SE SE S S E E a a a E s E i i E E a E a r' E S Heliocentric equations of motions Relative acceleration of oon wrt Earth 3 SE SE a E s δ For the EP term, one has approximately:

33 δa E D λ s S δa s E SE SE 3 γ The EP perturbing force is essentially a constant force directed to/from the Sun quite similar to a radiation pressure nserting in Lagrange planetary equations one gets the observable polarisation on the Earth-oon distance (Nordvedt, 1968) δ r = δ cos D ( m) δ = E With δr to ~ 3cm level, 10 3 to 10 4 observations, one would expect δ to 2x10-14 at the best F. ignard icroscope ONERA, 30 January

34 LLR Data fitting Very complex given the detailed modelling any parameters fitted together station and reflector coordinates, motion and rotation of the oon, nutation, radiation pressure, etc. For the EP testing Primarily done by the JPL team (Williams, Turyshev, Boggs) Latest results with correction for the radiation pressure estimated by Vokrouhlicky (1997) δ = E = 1 ± Williams et al. 2009, Comments: - the uncertainty translates into ~ 4 mm in the cos D amplitude - Accuracy on δ was +/- 2x10-13 in n a presentation to the REX in 2001 said it should be +/- 5x10-14 in 2010!! F. ignard icroscope ONERA, 30 January

35 nterpretation = 1+ SEP + WEP E = 1+η + ω 2 mc WEP : Effect of nuclear composition on the free fall SEP : Coupling of self-energy with gravity E wep = (1 ± 1.4) Adelberger, 2001 then from LLR: E sep = ( 2 ± 2) Williams et al Earth : E g /mc 2 = x oon : E g /mc 2 = x Approx PPN : η = 4β γ 3 η = ± β - 1 ~ ± Williams et al (with γ to 2.3x10-5 ) F. ignard icroscope ONERA, 30 January

36 id-term perspective Very slow improvement with LLR data more observations with EO at OCA no much change regarding new oon and full oon But WEP to be tested to by icroscope LLR will give a better determination of SEP γ to 10-6 with aia from Will, 2007 will lead to better η at the end Also: Bepi Colombo will return β to 3x10-5 independent estimate of η will follow F. ignard icroscope ONERA, 30 January

37 Thanks for your attention F. ignard icroscope ONERA, 30 January