APOLLO

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APOLLO

• Testing Gravity
• via
• Laser Ranging to the Moon

Tom Murphy (UCSD)
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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.

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Simplified (Conservative) PPN Equations of Motion
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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 lt 10?12 per year
• geodetic precession
• to ? 0.5
• 1/r2 force law
• to 10?10 times the strength of gravity at 108 m
  scales
• gravitomagnetism (origin of frame-dragging)
• to 0.1 (from motions of point massesnot
  systemic rotation)
• APOLLO effort will improve by 10? access new
  physics

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Aside on Gravitomagnetism

• Stems from motional term in equation of motion
• If earth has velocity V, and moon is Vu, two
  terms of consequence emerge
• One proportional to V2 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 lt 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, 071102

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LLR through the decades
Previously 200 meters
APOLLO
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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

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The APOLLO Collaboration
UCSD Tom Murphy (PI) Eric Michelsen
U Washington Eric Adelberger Erik Swanson
Apache Point Obs. Russet McMillan
Harvard Chris Stubbs James Battat
Northwest Analysis Ken Nordtvedt
Humboldt State C. D. Hoyle
JPL Jim Williams Slava Turyshev Dale Boggs
Lincoln Lab Brian Aull Bob Reich
CfA/SAO Bob Reasenberg Irwin Shapiro John
Chandler
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Photo by NASA
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Lunar Retroreflector Arrays
Corner cubes
Apollo 11 retroreflector array
Apollo 14 retroreflector array
Apollo 15 retroreflector array
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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)
• gt1017 loss considering other optical/detection
  losses

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APOLLOs Secret Weapon Aperture

• The Apache Point Observatorys 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 810 lt 1 hour sessions per lunar
  month
• 7-university consortium (UW NMSU, U Chicago,
  Princeton, Johns Hopkins, Colorado, Virginia)

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APOLLO Laser

• NdYAG 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

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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

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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

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APOLLO Random Error Budget
Error Source Time Uncert. (ps) (round trip) Range error (mm) (one way)
Retro Array Orient. 100300 1545
APD Illumination 60 9
APD Intrinsic lt60 lt 9
Laser Pulse Width 50 7.5
Timing Electronics 30 4.5
GPS-slaved Clock 7 1
Total Random Uncert 143317 2248
Ignoring retro array, APOLLO system has 104 ps
(16 mm) error per photon
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Laser Mounted on Telescope
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Laser Illumination of Telescope
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Gigantic Laser Pointer
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Out the Barn Door
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Blasting the Moon
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Breaking All Records
Reflector prev. max photons/run APOLLO max photons/run prev. max photons/5-min APOLLO max photons/5-min
Apollo 11 172 4288 83 2812
Apollo 14 213 5100 131 3060
Apollo 15 603 8937 280 7950
Lunokhod 2 70 310 29 372

• 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 cant (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

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Killer Returns
Apollo 11
Apollo 15
2007.11.19
red curves are theoretical profiles get
convolved with fiducial to make lunar return
which array is physically smaller?
represents system capability laser detector
timing electronics etc.
RMS 120 ps (18 mm)

• 6624 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

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Sensing the Array Size Orientation
2007.10.28
2007.10.29
2007.11.19
2007.11.20
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Reaching the Millimeter Goal?

• 1 millimeter quality data is frequently achieved
• especially since Sept. 2007
• represents combined performance for single (lt 1
  hour) observing session
• random uncertainty only
• Virtually all nights deliver better than 4 mm,
  and 2 mm is typical

median 1.8 mm 1.1 mm recent
shaded ? recent results
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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

15 mm
individual error bars ? ? ?1.5 mm
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Residuals Run-to-Run
We can get 1 mm range precision in single runs
(lt10-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
1.16 mm 2269 photons 3k shots
Apollo 15 reflector 2008.02.18
1.73 mm 901 photons 2k shots
0.66 mm 8457 photons 10k shots
1.45 mm 1483 photons 3k shots
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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
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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 orientationas 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
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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