Next-Generation Lunar Laser Ranging Tom MurphyUCSD

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

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

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 – R earth-moon = 1/400 A.U. → test motion with respect to sun at 1 A.U. via much shorter (differential) measurement

Historical Accuracy of Lunar Ranging Weighted RMS Residual (cm)

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

Why Push Further: Aristotelian Analogy Trajectory Asymmetry Trajectory Polynomial Order Newtonian Gravity Aristotelian “Gravity” Einsteinian Departures at ~10 -8 level of precision

“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

APOLLO: Next-Generation LLR recipe 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

APOLLO Goals*: One millimeter range precision Weak Equivalence Principle (WEP) to  a/a ≈ Strong Equivalence Principle (SEP) to  ≈ 3×10 -5 Gravitomegnetism (frame dragging) to dG/dt to G per year Geodetic precession (   ) to ≈ 3×10 -4 Long range forces to × 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.

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

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

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 ~40 2 = 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

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

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

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

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

Future Laser Ranging Tests of GR Interplanetary is next logical step Laser transponder on Mars measures  to 4×10 -6, and  to 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

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