Lunar Laser Ranging LLR within LUNAR

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Lunar Laser Ranging (LLR) within LUNAR

• Tom Murphy1
• Doug Currie2
• Stephen Merkowitz3
• D. Carrier, Jan McGarry3, K. Nordtvedt, Tom
  Zagwodski3

1 UCSD 2 U Md 3 GSFC
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LLR Astrophysical Motivations

• Fundamental incompatibility of QM and GR
• Dark Energy may be misunderstanding of
  large-scale gravity
• Dvali idea replaces with leaky gravity ? lunar
  precession
• Inflation may have left residual scalar fields
  (inflaton)
• generic result is violation of EP and changing
  constants
• Dark Matter inspires alternative gravity models
  (MOND)
• test of inverse square law could reveal

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What has LLR done for us lately?

• LLR provides a comprehensive suite of
  gravitational tests
• The earth-moon system is a pristine laboratory
  for investigating gravity
• moon is massive enough to be stubborn against
  drag/pressure
• moon is far enough to be in a solar orbit (weakly
  bound)
• LLR currently provides our best tests of
• The weak equivalence principle (WEP) ?a/a lt
  1.3?10-13
• The strong equivalence principle (SEP)
  ??????????? lt 4?10?4
• Time-rate-of-change of G to lt 7?10?13 per year
• Inverse square law to 3?10?11 at 108 m scales
• Geodetic precession to 0.6
• Gravitomagnetism to 0.1
• Lunar Science
• Gravity harmonics, Love numbers, liquid core(?)

similar precision to lab experiments, though
not optimal mass pair in test
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Who Do We Put Out of Business?

• Is LLR a fishing expedition?
• well, yes, but not in a might go home empty
  sense
• if we dont catch a fish, we know something new
  about the ocean
• there are no fish big enough to chomp a hook that
  size
• thats important

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Strong Field Tests

• Weak Field tests GR to first order in v2/c2
• Strong Field does two things
• easier to see first order effects
• brings second order (v2/c2) into possibility

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LLR through the decades
Previously 200 meters
small telescope, narrow laser pulse
big telescope, fat laser pulse
APOLLO
big telescope, narrow laser pulse
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How Does LLR Work?
Short laser pulses and time-of-flight measurement
to high precision
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Apollo Reflector Design

• All three Apollo reflectors are comprised of 3.8
  cm diameter fused silica corner cubes
• work on total internal reflection
• better for solar rejection
• Diameter is a compromise
• too big and thermal distortion of corner cube is
  large
• too big and diffraction pattern smaller than
  velocity aberration offset (thus miss return)
• too small and diffraction pattern too large
  (waste light)
• Embedded in aluminum pallet
• for ameliorating thermal gradients
• recessed to shield from sun

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Extracting Science

• Ground station records photon times launch and
  return
• Build a sophisticated parameterized model to try
  to mimic time series, including
• model for gravity (equations of motion)
• solar system dynamics
• body-body interactions
• dissipative physics (tidal friction)
• crustal loading phenomena (atmosphere, ocean)
• relativistic light propagation
• atmospheric propagation delay
• Minimize residuals between obs. and model in
  least-squares fit
• result is a bunch of initial conditions, physical
  scales, gravity model
• Analysis is currently behind observation (recent
  development)

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Dominant Uncertainty
far corner
tilted reflector array
Laser Pulse
near corner
fat laser pulse return uncertainty dominated by
pulse
medium laser pulse return uncertainty dominated
by array
short laser pulse return uncertainty dominated
by pulse array irrelevant/resolved
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APOLLO Example Data
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 Array Size and Orientation
2007.10.28
2007.10.29
2007.11.19
2007.11.20
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Sparse Array Solves Problem

• A sparse (even random) array of corner cubes will
  temporally separate individual returns
• now dominated by ground station characteristics
• moderate advances in ground technology pay off
• Can either build deliberately sparse array, or
  scatter at random
• will figure out each reflectors position after
  the fact

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Next-Generation Reflector Designs

• We would do well to put arrays near the lunar
  limb
• greater leverage on lunar orientation
• Ground is sloped steeply with respect to line of
  sight, so flat pallet would work well

laser pulse
moon
to earth
laser pulse narrower than cube separation
pallet
corner cubes
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Cross Section

• LLR is a challenge, due to 1/r4 signal loss
• Large effective cross section means more ground
  stations can play
• thus better global coverage, more data, better
  science
• Apollo arrays are on the margin
• 1-m class telescope can get one photon per minute
• hard to get enough photons to beat array tilt
  uncertainty down
• Making individual cubes larger has merit
• central irradiance of return goes up as fourth
  power of diameter
• cant go too far or 5 ?rad velocity aberration
  defeats purpose
• though can intentionally spoil angles of cube to
  spread pattern
• also thermal distortions can be more significant
  on large cubes

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Our Team

• Doug Currie (UMd) was part of the original team
  that designed and built the Apollo lunar
  reflector arrays
• excellent job of thermal and optical engineering
• HST wide-field planetary camera
• Stephen Merkowitz (GSFC) has history of gravity
  research
• laboratory G measurement
• LISA
• laser ranging and transponders
• Tom Murphy (UCSD) is PI for APOLLO Apache Point
  Observatory Lunar Laser-ranging Operation
• first-hand knowledge of Apollo and Lunokhod
  reflector performance
• Ken Nordtvedt master gravitational
  phenomenologist/theorist
• David Carrier Apollo drilling expert
• Jan McGarry (GSFC) Satellite Laser Ranging
  transponders
• Tom Zagwodski (GSFC) Satellite Laser Ranging
  transponders

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Our Plan, In Overview

• Development of theoretical tools
• hone science case for sub-millimeter LLR
• develop a next-generation LLR model and use for
  science simulation
• Next-generation corner cube and array design
• optimize designs, initially following parallel
  tracks of solid cube (Currie) and hollow cube
  (Merkowitz)
• extensive thermal modeling and testing (partly at
  the Space Climatic Facility in Frascati, Italy)
• Transponder design
• develop plans for an architecture suitable for
  LLR via active transponders
• Environment/Emplacement
• develop strategies for dust mitigation
• work out emplacement scheme, aiming for 10 ?m
  stability

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Theoretical Tools

• Years 1 and 2 activities

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Part 1 New Science Paradigms

• LLR offers a classic set of tests
• EP G-dot inverse square law PPN ?, ?, ?
• But more awaits
• gravitomagnetism/torsion ideas
• brane-inspired extra dimensional modifications to
  gravity
• e.g., Dvali et al. DGP gravity
• covariant extensions of MOND
• lunar interior structure
• We will perform a detailed study of the
  sciencenew and oldthat next-generation LLR
  might accomplish
• Nordtvedt will contribute substantially, Dvali
  may participate
• This goal is intimately tied with Part 2
  analysis tools

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Part 2 Analysis Tools

• New physics ideas must be coded into an analysis
  model
• Currently, we lack an openly available and modern
  platform for LLR analysis
• JPL has best code, but the code is unavailable
• PEP is semi-functional, open to us, but needs
  modernization
• Jürgen Müller in Germany has modern code,
  unavailable
• GEODYN is used for SLR in earth-center frame, may
  be adaptable to LLR
• In year 1, we will learn enough about the options
  to decide which is worth putting our efforts into
• In year 2, we may begin to perform simulations of
  sub-millimeter LLR datasets to learn what the
  science potential might be
• At the end of year 2, we hope to be in a position
  to begin coding new physics so that we may
  simulate sensitivities

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Transponder Design

• Years 1 and 2 activities

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Years 1 2 Survey Architectures

• Transponders cut the 1/r4 LLR loss to a more
  forgiving 1/r2 law
• Lunar transponders would allow small SLR stations
  to routinely obtain quality ranges to the moon
• Transponders share many technologies in common
  with
• laser altimeters (cases in point MOLA and
  MESSENGER links)
• optical communications terminals
• We will begin with a survey of mature design
  studies
• Mars Laser Ranging (JPL Murphy PI)
• Asynchornous Laser Transponder (ALT GSFC)
• Laser Comm Terminal (GSFC)
• Tee-up for Years 3 4, when we will form a
  design plan to optimize science results from the
  moon

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Looking Forward

• where we want to be in years 3 4

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On track to

• Select optimal cube architecture and mounting
  scheme
• procure and test final version
• Look at drilling options
• work with Carrier and heat flow folks
• Investigate ground station improvements for
  sub-mm performance
• Study dust issues and mitigation strategies
• perhaps team up with other NLSI efforts

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Summary

• LLR has been a foundational technique in studying
  gravity
• Todays precision is limited by the arrays
• designed for 1970 laser
• We should design a new system that will outlive
  2010 lasers and timing systems
• passive reflectors are long-lived
• 10 ?m emplacement is an appropriate goal