Lunar Laser Ranging A Testbed for General Relativity

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Lunar Laser Ranging A Testbed for General
Relativity
DPG Conference, Freiburg, March 4, 2008

• Jürgen Müller
• Institut für Erdmessung, Leibniz Universität
  Hannover, Germany

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Acknowledgement
Work has been supported by DFG Research Unit
FOR584 Earth Rotation and Global Dynamic
Processes (computations by Liliane
Biskupek) and the Centre of Excellence
QUEST (Quantum Engineering and Space-Time
Research)
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Contents

• Introduction
• - Motivation
• Lunar Laser Ranging
• - Data (distribution and accuracy)
• - Analysis
• Relativity Tests
• Conclusions
• - Future capabilities

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Lunar Laser Ranging (LLR)

• 38 years of observations
• Modelling so far at cm-level
• Long-term stability (e.g., orbit)
• ? Earth-Moon dynamics
• ? Relativity parameters

?
?
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Retro-Reflectors on the Moon
Apollo 11 July 1969
Apollo 14 Jan./Feb.71
Apollo 15 Jul./Aug.71
X
Luna 17 Nov.70...
Luna 21 Jan.73...
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Lunar Laser Ranging - Measurements

• Observation
• of 1019 photons per pulse from the transmitter,
• only 1 is received
• illuminated surface on the Moon about 25 km2
• (reflector surface 1 m2)
• telescope (o 70 cm), Laser power
• altitude, location, atmosphere
• - weather conditions
• - accuracy 1.5 cm t
• Identification of lunar returns Dr
• - Filtering
• spatial N
• temporal
• spectral Dr

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Observation Application of Pulse Pattern
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Observation Application of Pulse Pattern (2)
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LLR Observations per Year
Number of observations annually averaged 16 000
normal points in total, between1970 and 2007
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Distribution of Observations per Synodic Month
Observations per 100 bin
Synodic Angle (degree)
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Distribution of Observations per Synodic Month
Moon
Full Moon
New Moon
Sun
No data
No data
Earth

• - large data gaps near Full and New Moon

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Distribution of Observations per Sidereal Month
Observations per 100 bin
Sidereal Angle (degree)
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Weighted Annual Residuals
weighted residuals (observed - computed
Earth-Moon distance), annually averaged

• model?
• observations?

?
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Use of New APOLLO Data

• New site APOLLO in New Mexico (USA),
• mm accuracy
• 3,5 m telescope
• Improved receiver optics
• Local control measurements
• Software changes ? 7 stations
• 70 normal points (04.06 12.06), more in 2007
• Accuracy of observations down-weighted

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Weighted Annual Residuals (Past Years)

• only McDonald data

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LLR Observation Equation

• Relativity in LLR
• - transformation between reference
• systems (Moon, Earth, inertial)
• - transformation between time systems
• orbital motion of the solar system bodies
• rotation of Earth and Moon
• - gravitational time delay (Shapiro)
• - effect meter level

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LLR Results (Theory)

• Analysis
• - model based upon Einstein's Theory
• - least-squares adjustment
• - determination of the parameters of the
  Earth-Moon system (about 170 unknowns, without
  EOPs)
• Results of major interest
• - station coordinates and velocities (ITRF2000) -
  GGOS
• - Earth rotation, s 0.5 mas (IERS)
• - relativity parameters
• (grav. constant, equivalence principle, metric
  ...)
• - ... lunar interior ...

GGOS Global Geodetic Observing System
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Relativistic Parameters

• Strategy Newtonian effects modelled accurately
  enough or determined simultaneously
• Examples

• metric parameters (e.g. space time
  non-linearity, preferred frames)
• test of the equivalence principle (Nordtvedt
  effect, dark matter)
• time-variable Gravitational Constant
• 1/r2-law (Yukawa terms)

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Example Gravitational Constant G

• Investigation of secular and quadratic variations

Results
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Sensitivity Study for

• Separation of free and forced terms ? two orbit
  solutions
• perturbed,
• un-perturbed
• ? difference

• Sensitivity analysis via

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Corresponding Spectrum

• als Spektrum

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Example Nordtvedt Effect

• Test of the strong equivalence principle
• Shift of the lunar orbit towards the Sun?
• No! -- Realistic error below 1 cm

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Sensitivity of Relativistic Parameters (1)
Yukawa a
Equivalence principle mI/mG
Gravitational constant
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Relativistic Parameters Power Spectra (1)
Equivalence principle mG/mI
anomal
412 d anom-syn
2syn
syn
31.8d 2syn-anomal
206 d 2anom-2syn
10 d
132 d 2anom-2synann
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Relativistic Parameters Power Spectra (2)
Yukawa a
anomal
sid-2ann
2syn
10 d
204 d
131 d
409 d
1093 d
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Sensitivity of Relativistic Parameters (2)
Preferred frames a1
Preferred frames a2
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Relativistic Parameters Power Spectra (3)
Preferred-frame effect a1 (coupled with solar
system velocity)
sid, syn
sid-2ann
anom-ann
anomann
annual
2syn
204 d, 2ann
34 d
131 d
2nodal
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Relativistic Parameters Power Spectra (4)
Preferred-frame effect a2 (coupled with solar
system velocity)
2sid-anom
sid-2ann
2sid
2syn
10 d
34 d
nodal
annual
204 d
1666 d
2ann
131 d
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Relativistic Parameters Power Spectra (5)
Gravito-magnetic effect (PPN parameter a1) in the
solar system
a1(-2.8 ? 3) 10-3
Soffel et al. 2008
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Results - Relativity
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Results Relativity (2)
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Further Applications

• Reference frames
• dynamic realisation of the ICRS by the lunar
  orbit, s lt 0.01 (stable, highly accurate
  orbit, no non-conservative forces from
  atmosphere)
• Earth orientation
• Earth rotation (e.g. UT0, VOL)
• long-term nutation coefficients, precession
• Relativity
• test of further theories, Lense-Thirring effect
• Combination with other techniques
• combined EOP series and reference frames (GGOS)
• Moon as long-term stable clock

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Lunar Interior

• Lunar rotation
• libration angles, s 0.001
• numerically integrated
• Lunar tides
• - Love number k2 0.023 0.003
• Dissipation from
• - fluid core (Rc lt 354 km)
• - solid mantle, Q 33 4

Courtesy Turyshev and Williams, JPL
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Future Lunar Missions
Lunar Renaissance Orbiter (LRO)

• Deployment of transponders (6 yr lifetime) and
  new retro-reflectors on the Moon or in lunar
  orbit
• - more observatories
• - tie to VLBI (inertial reference frames)

• New high resolution photographs of reflector
  arrays
• - better lunar geodetic network
• - lunar maps

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New Ranging Measurements Why?

• New data needed to constrain lunar interior
  structure
• improve measurements of forced librations
• measure tidal distortion (amplitude and phase)
• lunar oscillations as response to large quakes or
  impacts?
• Improve on limits of relativistic effects
• time variability of the gravitational constant
• test of strong equivalence principle (Nordtvedt
  effect)
• Improve the tie between the lunar network and the
  radio reference frame (VLBI)
• Above goals require more data, more accurate
  data, and unbiased measurements!

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Conclusions

• LLR contributes to better understanding of
• - Reference frames (ITRF, dynamic ICRF)
• - Earth orientation (IERS)
• - Earth-Moon system
• - Relativity
• - Lunar interior
• -
• and supports Global Geodetic Observing System
• In future new lunar ranging experiment
• (and combination with other techniques)

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Laser on the Moon?
Selenocentric frame

• Signal has higher strength than any
  mirror-reflected signal by orders of magnitude
• energy loss r4 vs. r2
• higher measurement (mm) accuracy
• observations at Full Moon (Laser will outshine
  Moonlight)
• and at New Moon possible (pointing requ. not
  as severe)
• More measurements by orders of magnitude
• measurements from many SLR stations with light
  equipment possible
• coverage for long-period lunar variations
• identification of short-period global
  oscillations of the Moon

Dynamic inertial frame
Terrestrial frame