Next-Generation Lunar Laser Ranging

1. Next-Generation Lunar Laser Ranging Tom Murphy UCSD

2. Designing the Perfect Gravity Test • Gravity must be the dominant influence • Negligible frictional, electrostatic, radiation forces • Make test bodies large • Gravity dominates • Test Strong Equivalence Principle (SEP) by having appreciable “self-energy”: how does gravity pull on gravity? • Place in vacuum environment

3. Precision Requirements • Order-of-Magnitude improvement over current measurements/tests of gravity • ~10-5 test of General Relativity • ~10-14 measurement precision needed • Good clocks are 10-12 • Need leverage somehow

4. Earth-Moon System Fits the Bill • Earth “self-energy” is ~0.5×10-9 of total mass • Moon is large, but only 0.02×10-9 in grav. energy • Non-gravitational forces very small • Self-energy small compared to that of earth • Sun dominates for both bodies • Can test differential motion/acceleration to Sun • Leverage from proximity of moon to earth • Rearth-moon = 1/400 A.U. → test motion with respect to sun at 1 A.U. via much shorter (differential) measurement

5. 30 25 20 15 10 5 0 1970 1975 1980 1985 1990 1995 2000 2005 Historical Accuracy of Lunar Ranging Weighted RMS Residual (cm)

6.  Lunar Laser Ranging Mercury Perihelion Shift 1.002 Mars Radar Ranging 1.001 VLBI & combined planetary data 1 Spacecraft range & Doppler 0.999 0.998  1 0.998 0.999 1.001 1.002 Current PPN Constraints on GR • Is the Parameterized Post-Newtonian (PPN) formalism still relevant? • Basic phenomenology: • measures curvature of spacetime,  measures nonlinearity of gravity • What fool would want to push this further? Isn’t GR obviously right?

7. Newtonian Gravity 2.5 2.0 Aristotelian “Gravity” 1.5 Trajectory Polynomial Order 1.0 0.5 0.0 0 -1.0 -0.5 0.5 1.0 Trajectory Asymmetry Why Push Further: Aristotelian Analogy Einsteinian Departures at ~10-8 level of precision

8. “Real” Rationale for Pushing Further • Gravity is incompatible with the Standard Model • Cosmological departures from old GR model • Acceleration of expansion of Universe • Fine structure constant, , possibly varying? • What about gravitational constant, Equivalence Principle • Scalar Field modifications to GR • Predictions of PPN departures from GR • Brane-world cosmological models • Gravitons leaking into bulk, modifying gravity at large scales

9. APOLLO: Next-Generation LLRrecipe for success: • Move LLR back to a large-aperture telescope • 3.5-meter: more photons! • Incorporate modern technology • Detectors, precision timing, laser • Re-couple data collection to analysis/science • Scientific enthusiasm drives progress • Devise brilliant acronym: • Apache Point Observatory Lunar Laser-ranging Operation

10. APOLLO Goals*: • One millimeter range precision • Weak Equivalence Principle (WEP) to a/a ≈ 10-14 • Strong Equivalence Principle (SEP) to  ≈ 3×10-5 • Gravitomegnetism (frame dragging) to 10-4 • dG/dt to 10-13•G per year • Geodetic precession ( ) to ≈ 3×10-4 • Long range forces to 10-11 × the strength of gravity * These 1 errors are simply ~10 times better than current LLR limits. In each case, LLR currently provides the best limits. Timescales to achieve stated results vary according to the nature of the signal.

11. The APOLLO Apparatus • Uses 3.5-meter telescope at 9200-ft Apache Point, NM • Excellent atmospheric “seeing” • 532 nm Nd:YAG, 100 ps, 115 mJ/pulse, 20 Hz laser • Integrated avalanche photodiode (APD) arrays • Multi-photon capability • Daylight/full-moon capability

12. APD Arrays • We have a working prototype courtesy MIT Lincoln Labs • 4×4 format (LL has made much larger) • 30m diameters on 100m centers • Fill-factor recovered by lenslet array • ~30 ps jitter at 532 nm, ~50% photon detection eff. • Multiple “buckets” for photon bundle

13. Millimeter Range?!! • Seven picosecond round-trip travel time error • Half-meter lunar reflectors at ±7° tilt → up to 35 mm RMS uncertainty per photon • 95 ps FWHM laser pulse → 6 mm RMS • Need ~402 = 1600 photons to beat down error • Calculate ~5 photon/pulse return for APOLLO • “Realistic” 1 photon/pulse → 20 photons/sec → millimeter statistics achieved on few-minute timescales

14. APOLLO Random Error Budget

15. APOLLO Systematic Errors • Various contributions to systematic error: • Atmospheric refractive delay (2-meter signal) • Ocean, atmosphere, and ground-water loading • Thermal expansion of telescope & reflectors • Will implement supplemental metrology on-site • Barometric transducer array • Superconducting gravimeter (<1 mm vertical displacements) • Precision GPS (0.5 mm horz., 2.3 mm vert. in 24 hr) • IMPORTANT: Science signals are narrow-band • Environmental factors will not mimic new physics

16. Laser Mounted on Telescope Mounted June 2003 In thermal enclosure (“fridge”)

17. Timing Electronics Built/Verified Timing System in Operation CAMAC Crate Inhabitants Calibration/Frequency Board APOLLO Command Module Timing/APD control, CPU interface

19. Future Laser Ranging Tests of GR • Interplanetary is next logical step • Laser transponder on Mars measures  to 4×10-6, and  to 10-5 • Mercury orbiter (Messenger: launched) could be used to measure perihelion shift →  • May perform test-ranging from Apache Point this summer • LATOR (stay tuned for Turyshev talk) uses inter-spacecraft laser ranging to measure curvature of spacetime to unprecedented precision:  to 10-8

20. APOLLO Collaboration UCSD: Tom Murphy John Goodkind Eric Michelsen U. Washington: Eric Adelberger Jana Strasburg Larry Carey Northwest Analysis: Ken Nordtvedt JPL: Jim Williams Jean Dickey Slava Turyshev Lincoln Labs: Brian Aull Bernie Kosicki Bob Reich Harvard: Chris Stubbs Joint NASA/NSF funding