APOLLOAPOLLO Testing Gravity via Laser Ranging to the Moon Testing Gravity via Laser Ranging to the Moon Tom Murphy (UCSD)

Q2C32 The Full Parameterized Post Newtonian (PPN) Metric Generalized metric abandoning many fundamental assumptions GR is a special case Allows violations of conservations, Lorentz invariance, etc. Generalized metric abandoning many fundamental assumptions GR is a special case Allows violations of conservations, Lorentz invariance, etc.

Q2C33 Simplified (Conservative) PPN Equations of Motion Newtonian piece

Q2C34 Relativistic Observables in the Lunar Range Lunar Laser Ranging provides a comprehensive probe of gravity, currently boasting the best tests of: Equivalence Principle (mainly strong version, but check on weak)  a/a  10  13 ; SEP to 4  10  4 time-rate-of-change of G fractional change < 10  12 per year geodetic precession to  0.5% 1/r 2 force law to 10  10 times the strength of gravity at 10 8 m scales gravitomagnetism (origin of frame-dragging) to 0.1% (from motions of point masses—not systemic rotation) APOLLO effort will improve by 10  ; access new physics Lunar Laser Ranging provides a comprehensive probe of gravity, currently boasting the best tests of: Equivalence Principle (mainly strong version, but check on weak)  a/a  10  13 ; SEP to 4  10  4 time-rate-of-change of G fractional change < 10  12 per year geodetic precession to  0.5% 1/r 2 force law to 10  10 times the strength of gravity at 10 8 m scales gravitomagnetism (origin of frame-dragging) to 0.1% (from motions of point masses—not systemic rotation) APOLLO effort will improve by 10  ; access new physics

Q2C35 Aside on Gravitomagnetism Stems from “motional” term in equation of motion: If earth has velocity V, and moon is V+u, two terms of consequence emerge: One proportional to V 2 with 6.5 meter cos2D signal One proportional to Vu with 6.1 meter cosD signal LLR determines cosD to 4 mm precision and cos2D to < 8 mm Constitutes a  0.1% measurement of effect The same exact v  v  g term can be used to derive the precession of a gyroscope in the presence of a spinning mass recovers the full effect sought by GPB see Murphy et al. 2007, PRL 98, Stems from “motional” term in equation of motion: If earth has velocity V, and moon is V+u, two terms of consequence emerge: One proportional to V 2 with 6.5 meter cos2D signal One proportional to Vu with 6.1 meter cosD signal LLR determines cosD to 4 mm precision and cos2D to < 8 mm Constitutes a  0.1% measurement of effect The same exact v  v  g term can be used to derive the precession of a gyroscope in the presence of a spinning mass recovers the full effect sought by GPB see Murphy et al. 2007, PRL 98,

Q2C36 LLR through the decades Previously 200 meters APOLLO

Q2C37 APOLLO: the next big thing in LLR APOLLO offers order-of-magnitude improvements to LLR by: Using a 3.5 meter telescope Operating at 20 pulses/sec Using advanced detector technology Gathering multiple photons/shot Achieving millimeter range precision Tightly integrating experiment and analysis Having the best acronym funded by NASA & NSF

Q2C38 The APOLLO Collaboration UCSD: Tom Murphy (PI) Eric Michelsen U Washington: Eric Adelberger Erik Swanson Harvard: Chris Stubbs James Battat JPL: Jim Williams Slava Turyshev Dale Boggs Lincoln Lab: Brian Aull Bob Reich Northwest Analysis: Ken Nordtvedt Apache Point Obs. Russet McMillan Humboldt State: C. D. Hoyle CfA/SAO: Bob Reasenberg Irwin Shapiro John Chandler

Q2C39 Photo by NASA

Q2C310 Lunar Retroreflector Arrays Corner cubes Apollo 14 retroreflector array Apollo 11 retroreflector array Apollo 15 retroreflector array

Q2C311 The Reflector Positions Three Apollo missions left reflectors Apollo 11: 100-element Apollo 14: 100-element Apollo 15: 300-element Two French-built, Soviet-landed reflectors were placed on rovers Luna 17 (lost!) Luna 21 similar in size to A11, A14 Signal loss is huge:  10  8 of photons launched find reflector (atmospheric seeing)  10  8 of returned photons find telescope (corner cube diffraction) >10 17 loss considering other optical/detection losses

Q2C312 APOLLO’s Secret Weapon: Aperture The Apache Point Observatory’s 3.5 meter telescope Southern NM (Sunspot) 9,200 ft (2800 m) elevation Great “seeing”: 1 arcsec Flexibly scheduled, high-class research telescope APOLLO gets 8–10 < 1 hour sessions per lunar month 7-university consortium (UW NMSU, U Chicago, Princeton, Johns Hopkins, Colorado, Virginia)

Q2C313 APOLLO Laser Nd:YAG; flashlamp-pumped; mode-locked; cavity-dumped Frequency-doubled to 532 nm 57% conversion efficiency 90 ps pulse width (FWHM) 115 mJ (green) per pulse after double-pass amplifier 20 Hz pulse repetition rate 2.3 Watt average power GW peak power!! Beam is expanded to 3.5 meter aperture Less of an eye hazard Less damaging to optics

Q2C314 Catching All the Photons Several photons per pulse necessitates multiple “buckets” to time-tag each one Avalanche Photodiodes (APDs) respond only to first photon Lincoln Lab prototype APD arrays are perfect for APOLLO 4  4 array of 30  m elements on 100  m centers Lenslet array in front recovers full fill factor Resultant field is 1.4 arcsec on a side Focused image is formed at lenslet 2-D tracking capability facilitates optimal efficiency

Q2C315 Differential Measurement Scheme Corner Cube at telescope exit returns fiducial pulse Same optical path, attenuated by 10 O.D. Same APD detector, electronics, TDC range Diffused to present identical illumination on detector elements Result is differential over 2.5 seconds Must correct for distance between telescope axis intersection and corner cube

Q2C316 APOLLO Random Error Budget Error SourceTime Uncert. (ps) (round trip) Range error (mm) (one way) Retro Array Orient.100–30015–45 APD Illumination609 APD Intrinsic<60< 9 Laser Pulse Width507.5 Timing Electronics304.5 GPS-slaved Clock71 Total Random Uncert143–31722–48 Ignoring retro array, APOLLO system has 104 ps (16 mm) error per photon

Q2C317 Laser Mounted on Telescope

Q2C318 Laser Illumination of Telescope

Q2C319 Gigantic Laser Pointer

Q2C320 Out the Barn Door

Q2C321 Blasting the Moon

Q2C322 Breaking All Records Reflector prev. max photons/run APOLLO max photons/run prev. max photons/5-min APOLLO max photons/5-min Apollo Apollo Apollo Lunokhod APOLLO has seen rates higher than 2 photons per pulse for brief periods max rates for French and Texas stations about 0.1 and 0.02, respectively APOLLO has collected more return photons in 100 seconds than these other stations typically collect in months or years APOLLO can operate at full moon other stations can’t (except during eclipse), though EP signal is max at full moon! Often a majority of APOLLO returns are multiple-photon events record is 11 photons in one shot (out of 12 functioning APD elements) APD array (many buckets) is crucial APOLLO has seen rates higher than 2 photons per pulse for brief periods max rates for French and Texas stations about 0.1 and 0.02, respectively APOLLO has collected more return photons in 100 seconds than these other stations typically collect in months or years APOLLO can operate at full moon other stations can’t (except during eclipse), though EP signal is max at full moon! Often a majority of APOLLO returns are multiple-photon events record is 11 photons in one shot (out of 12 functioning APD elements) APD array (many buckets) is crucial

Q2C323 Killer Returns Apollo 15 Apollo photons in 5000 shots 369,840,578,287.4  0.8 mm 4 detections with 10 photons 2344 photons in 5000 shots 369,817,674,951.1  0.7 mm 1 detection with 8 photons which array is physically smaller? red curves are theoretical profiles: get convolved with fiducial to make lunar return represents system capability: laser; detector; timing electronics; etc. RMS = 120 ps (18 mm)

Q2C324 Sensing the Array Size & Orientation

Q2C325 Reaching the Millimeter Goal? 1 millimeter quality data is frequently achieved especially since Sept represents combined performance for single (< 1 hour) observing session random uncertainty only Virtually all nights deliver better than 4 mm, and 2 mm is typical 1 millimeter quality data is frequently achieved especially since Sept represents combined performance for single (< 1 hour) observing session random uncertainty only Virtually all nights deliver better than 4 mm, and 2 mm is typical shaded  recent results median = 1.8 mm 1.1 mm recent

Q2C326 Residuals During a Contiguous Run Breaking 10,000-shot run into 5 chunks, we can evaluate the stability of our measurement Comparison is against imperfect prediction, which can leave linear drift No scatter beyond that expected statistically Breaking 10,000-shot run into 5 chunks, we can evaluate the stability of our measurement Comparison is against imperfect prediction, which can leave linear drift No scatter beyond that expected statistically 15 mm individual error bars:    1.5 mm

Q2C327 Residuals Run-to-Run We can get 1 mm range precision in single “runs” (<10- minutes) The scatter about a linear fit is small: consistent with estimated random error 0.5 mm effective data point for Apollo 15 reflector on this night 1.45 mm 1483 photons; 3k shots 0.66 mm 8457 photons; 10k shots 1.73 mm 901 photons; 2k shots 1.16 mm 2269 photons; 3k shots Apollo 15 reflector

Q2C328 Residuals Against JPL Model APOLLO data points processed together with 16,000 ranges over 38 years shows consistency with model orbit Fit is not yet perfect, but this is expected when the model sees high-quality data for the first time, and APOLLO data reduction is still evolving as well Weighted RMS is about 8 mm   3 for this fit plot redacted: no agreement from JPL to make public

Q2C329 APOLLO Impact on Model If APOLLO data is down-weighted to 15 mm, we see what the model would do without APOLLO- quality data Answer: large (40 mm) adjustments to lunar orientation—as seen via reflector offsets (e.g., arrowed sessions) May lead to improved understanding of lunar interior, but also sharpens the picture for elucidating grav. physics phenomena plot redacted: no agreement from JPL to make public

Q2C330 Summary & Next Steps APOLLO is a millimeter-capable lunar ranging station with unprecedented performance Given the order-of-magnitude gains in range precision, we expect order-of-magnitude gains in a variety of tests of fundamental gravity Our steady-state campaign is not quite 2 years old began October 2006, one year after first light Now grappling with analysis in the face of vastly better data much new stuff to learn, with concomitant refinements to data reduction and to the analytical model Modest improvements in gravity seen already with APOLLO data; more to follow in the upcoming months and years Next BIG step: interplanetary laser ranging (e.g., Mars) see talk by Hamid Hemmati later in this session APOLLO is a millimeter-capable lunar ranging station with unprecedented performance Given the order-of-magnitude gains in range precision, we expect order-of-magnitude gains in a variety of tests of fundamental gravity Our steady-state campaign is not quite 2 years old began October 2006, one year after first light Now grappling with analysis in the face of vastly better data much new stuff to learn, with concomitant refinements to data reduction and to the analytical model Modest improvements in gravity seen already with APOLLO data; more to follow in the upcoming months and years Next BIG step: interplanetary laser ranging (e.g., Mars) see talk by Hamid Hemmati later in this session