1. Testing Gravity with Lunar Laser Ranging DoE Site Visit James Battat August 21, 2006

2. Testing Gravity with Lunar Laser Ranging New Mexico, near White Sands. Note SDSS 3.5 m

3. APOLLO UCSD: Tom Murphy - PI Eric Michelsen Adam Orin Harvard: Christopher Stubbs James Battat U. Washington: Eric Adelberger Erik Swanson C. D. Hoyle Larry Carey JPL: Jim Williams Jean Dickey Slava Turyshev Lincoln Lab: Brian Aull Bernie Kosicki Bob Reich Northwest Analysis: Ken Nordtvedt Mapping the lunar orbit to 1 millimeter APD detectors Ephemeris

4. Why Push Gravity Tests Further? Order of magnitude in constraints Dark energy, w Scalar field modifications to GR –Predict non-GR effects Brane-world cosmology –Gravitons leaking into bulk modify gravity at large scales

5. LLR is a Powerful Test of Gravity With one millimeter range precision: Weak EP  a/a 10 -14 Strong EP  3×10 -5 Gravitomagnetism 10 -4 dG/dt 10 -13 G/year Geodetic precession 3×10 -4 Long range forces 10 -11 × the strength of gravity * In each case, LLR currently provides the best limit.

6. LLR is a Powerful Test of Gravity With one millimeter range precision: Weak EP  a/a 10 -14 Strong EP  3×10 -5 Gravitomagnetism 10 -4 dG/dt 10 -13 G/year Geodetic precession 3×10 -4 Long range forces 10 -11 × the strength of gravity * In each case, LLR currently provides the best limit.

7. Nordtvedt Effect Nordtvedt, Phys Rev, 169, 1014, 1968 Nordtvedt, Phys Rev, 169, 1017, 1968 Nordtvedt, Phys Rev, 170, 1186, 1968 Synodic period = 29.35 days  r = 13  cos(D) meters

8. Avalanche Photodiode Array  = 30  m -Courtesy of MIT Lincoln Lab 3.5 meter telescope Good seeing APOLLO: Reaching 1 mm

9. Laser Ranging Apparatus: Transmit 2.3 Watt NdYAG laser 20 Hz, = 530 nm < 100 ps pulse width 110 mJ per pulse APD array START 3.5m primary LASER Corner cube

10. Laser Ranging Apparatus: Receive 2.3 Watt NdYAG laser 20 Hz, = 530 nm < 100 ps pulse width 110 mJ per pulse APD array STOP 3.5m primary LASER

11. 25 km 4 km ~10 17 attenuation MOONMOON

12. Interpretation Requires Sophisticated Modeling Measure telescope-to-reflector distanceWant center-to-center separationThrough the atmosphereNeed precise ephemeris information – JPL collaboration

13. MLRS: The Old Way 28 photons in 42 minutes

14. Enter APOLLO 1,500 photons in 13 minutes 1 mm statistical uncertainty

15. Current Status Millimeter precision data Returns from all 3 Apollo arrays Remote operations Enter campaign mode (October) 1-2 hours every 2-3 nights Improve site coordinates New constraints on gravitational params

16. The End

17. THE END

18. EXTRA SLIDES

19. APOLLO: Reaching 1 mm Large-aperture, good seeing –Figure of merit goes like (D/  ) 2 Incorporate modern technology –Detectors, precision timing, laser Re-couple data collection to analysis/science

20. LLR Targets

21. Gravitational Self-Energy + SEP Objectm SE /m 1 kg sphere, 6” diam5 x 10 -27 Moon0.2 x 10 -10 Earth5 x 10 -10

22. APOLLO Random Error Budget Expected Statistical ErrorRMS Error (ps)One-way Error (mm) Laser Pulse (95 ps FWHM)406 APD Jitter507 TDC Jitter152.2 50 MHz Freq. Reference71 APOLLO System Total6610 Lunar Retroreflector Array80–23012–35 Total Error per Photon105–24016–37

23. Nordtvedt, Class. Quantum Grav., 15, 3363, 1998 Lunar Phase Coverage EP violation has a null at Quarter moon and maxima at Full and New Moons Same data, uniform coverage gives tighter  No measurements at max signal

24. Current PPN Constraints 1 0.998 1 0.9991.0011.002 1.001 0.999 0.998   Lunar Laser Ranging Mercury Perihelion Shift Mars Radar Ranging VLBI & combined planetary data Spacecraft range & Doppler Basic phenomenology:  measures curvature of Spacetime  measures nonlinearity of gravity  = (2.1 § 2.3) x 10 -5  = (1.2 § 1.1) x 10 -4  = (4.4 § 4.5) x 10 -4

25. Solar System Parameters Separation –Moon-Earth 0.38 million km –Sun-Earth 150 million km Mass –Sun 2 x 10^30 kg –Earth 6.0 x 10^24 kg –Moon 0.073 x 10^24 kg Radius –Sun695,000 km –Earth6380 km –Moon1740 km Gravitational Constant 6.67 x 10^-11 m^3 kg^-1 s^-2

26. Testing Gravity with Lunar Laser Ranging

27. Historical Accuracy of LLR Data 30 cm 0 cm 1970present

28. Laser Ranging Apparatus 2.3 Watt NdYAG laser 20 Hz, = 530 nm < 100 ps pulse width 110 mJ per pulse APD array START 3.5m primary LASER Corner cube

29. 2.3 Watt NdYAG laser 20 Hz, = 530 nm < 100 ps pulse width 110 mJ per pulse APD array 3.5m primary Laser Ranging Apparatus LASER STOP