Lunar Laser Ranging - A Science Tool for Geodesy and General Relativity

Lunar Laser Ranging - A Science Tool for Geodesy and General Relativity

Jürgen Müller

Institut für Erdmessung, Leibniz Universität Hannover, Germany

16th International Workshop on Laser Ranging, Poznan, October 13, 2008

Acknowledgement 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)

Contents Contents

Introduction

- Motivation

Lunar Laser Ranging

- Data (distribution and accuracy)

- Analysis

Relativity Tests

Conclusions

- Future capabilities

Lunar Laser Ranging (LLR)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

McDonald

Wettzell

Hawaii

Grasse

Orroral

MateraApollo

? ?

4

Retro-Reflectors on the MoonRetro-Reflectors on the Moon

Apollo 11July 1969

Apollo 14Jan./Feb.`71

Apollo 15Jul./Aug.`71

Luna 21Jan.`73...

Luna 17Nov.`70...

Apollo11

Luna 21

Apollo14

Apollo15Luna 17X

LLR Observations per YearLLR Observations per Year

L L R 2000UNAR ASER ANGINGA S G T G RPACE EODETIC ECHNIQUE FOR EODESY AND ELATIVITYDieter Egger, Markus Rothacher,Manfred Schneider, Ulrich SchreiberResearch Facility for Space GeodesyTechnische Universität München80290 MunichGermanyJürgen Müllerjxmx@bv.tum.deInstitute for Astronomical and Physical GeodesyTechnische Universität München80290 MunichGermany

RMS Residuals (Observed - Computed Earth-Moon Distance)0510152025301970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000YearResiduals (RMS) [cm] Mean Annual Error of UT100,050,10,150,20,250,30,350,40,451970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000YearError [ms]

Lunar Observations (Normal Points) per Year0200400600800100012001970 1972 1974 1976 1978 1980 1982 1984 1986 1988 1990 1992 1994 1996 1998 2000YearNumber of Observations

Determination of Relativistic ParametersMost relativistic effects cause periodic perturbations of the lunar orbit (some also secular ones). The typical periods (e.g. synodic, sidereal, annual, anomalistic, ...) are used to identify/separate the effects and to derive realistic errors. LLR is the most important tool of relativity checks in the solar system.

The unevenly distributed observations with respect to the synodic month (data gaps at full and new moon and asymmetry wrt. quarter moon) affect the parameter determination.More observations near new moon would be very helpful to improve e.g. the determination of the equivalence principle parameter . The unevenly distributed observations with respect to the sidereal month are caused by the absence of observatories at the southern hemisphere. Again the parameter determination is affected.One should aspire to establish a site in the southern hemisphere or try to improve some mobile/transportable laser systems to observe the moon.As optical technique, LLR is strongly dependent of weather conditions which leads to a further inhomogeneity in the distribution of the measurements.Because of the relatively large distance the energy balance for each laser observation looks very bad: only one photon out of transmitted ones finds its way back to the receiver.On the other hand, LLR benefits from the very long period of observations (more than 30 years) which allows to solve for the largest periods in the nutation series (the nodal drift of the lunar orbit:18.6 years) or to determine even secular quantities like G/G with high accuracy.The curve on the left indicates the enormous increase of the measurement precision corresponding with the high degree of accuracy of the analysis model. In recent years the 2.5 cm-level (RMS of the residuals) has been achieved.The figure on the right shows the time evolution of the accuracy of the UT1-determination. Today LLR can still compete with the other space geodetic techniques.In the Seventies LLR was the only space technique (besides optical ones) which was able to determine EOP parameters. 18

FGS

(shape of G / G

Number of observations; annually averaged; 16 300 normal points in total,

between1970 and 2008

- large data gaps near Full and New Moon

Distribution of Observations per Synodic MonthDistribution of Observations per Synodic Month

No data No data

Sun

Moon

Earth

Full Moon

New Moon

?

model?

observations?

Weighted Annual ResidualsWeighted Annual Residuals

weighted residuals (observed - computed

Earth-Moon distance), annually averaged

LLR Results (Theory)LLR Results (Theory)

Analysis

- model based upon Einstein's Theory

- least-squares adjustment

- determination of the parameters of the Earth-Moon system (about 180 unknowns, without EOPs)

Results of major interest

- station coordinates and velocities (ITRF2000) - GGOS

- Earth rotation, = 0.5 mas (IERS)

- relativity parameters

(grav. constant, equivalence principle, metric ...)

- ... lunar interior ...

GGOS – Global Geodetic Observing System

Example: Gravitational Constant GExample: Gravitational Constant G

Investigation of secular and quadratic variations

2

0 tG

G

2

1t

G

G1GG

113 yr1072GG

215 yr1054GG

Results

Sensitivity Study forSensitivity Study for

Sensitivity analysis via Separation of free and forced terms two orbit solutions: 1)perturbed, 2)un-perturbed

difference

G

GG

rGr

emem

)(

als Spektrum

ano

mal

syn

sid-

2an

n

ann

ual

2an

om-2

syn

2an

om-2

syn+

ann

2syn

10d

=3

syn

Corresponding SpectrumCorresponding Spectrum

Example: Nordtvedt EffectExample: Nordtvedt Effect

rS

EI

EGEG e

r

M

m

mGa

2

,

,,

rS

MI

MGMG e

r

M

m

mGa

2

,

,,

Test of the strong equivalence principle: Shift of the lunar orbit towards the Sun?

No! -- Realistic error: below 1 cm

Relativistic Parameters – Power Spectra (1)Relativistic Parameters – Power Spectra (1)

Equivalence principle mG/mI

41

2 d

= a

no

m-s

yn

20

6 d

= 2

an

om

-2sy

n

an

om

al

13

2 d

= 2

an

om

-2sy

n+

an

n

syn

2sy

n

~1

0 d

31

.8d

= 2

syn

-an

om

al

Relativistic Parameters – Power Spectra (2)Relativistic Parameters – Power Spectra (2)

Gravito-magnetic effect (PPN parameter ) in the solar system

=(1.6 4) · 10-3

Soffel et al. 2008, PRD

Results - RelativityResults - Relativity

Parameter Results

Nordtvedt parameter (violation of the strong equivalence principle)

(6 7) · 10-4

time variable gravitational constant

( unification of the fundamental interactions)

(2 7) · 10-13

(4 5) · 10-15

difference of geodetic precession GP - deSit [/cy]

(1.92 /cy predicted by Einstein’s theory of gravitation)

(6 10) · 10-3

metric parameter - 1 (space curvature; = 1 in Einstein)

(4 5) · 10-3

metric parameter - 1 (non-linearity; = 1)

or using = 4 - Cassini - 3 with Cassini-1 (~10-5)

(-2 4) · 10-3

(1.5 1.8) ·10-

4

][/

][/2

1

yrGG

yrGG

Results – Relativity (2)Results – Relativity (2)

Parameter Results

Yukawa coupling constant =400 000 km

(test of Newton’s inverse square law for the Earth-Moon distance)

(3 2) · 10-11

special relativity 1 - 0 - 1

(search for a preferred frame within special relativity)

(-5 12) · 10-5

influence of dark matter gc [cm/s2]

(in the center of the galaxy; test of strong equivalence principle)

(4 4) · 10-14

preferred frame effects 1

2

(coupled with velocity of the solar system)

(-4 9) · 10-5

(2 2) ·10-5

preferred frame effect 1

(coupled with dynamics within the solar system)

(1.6 3) · 10-3

Further ApplicationsFurther Applications

Reference frames- dynamic realisation of the ICRS by the lunar orbit,

< 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

see Biskupek/Müller, session 6, Tuesday

New Combined ProductsNew Combined Products

Earth orientation UT0 (VLBI) Long-periodic nutation, precession (VLBI, GPS, SLR)

Celestial reference frame Dynamic realisation of ICRS, ephemeris tie between the lunar network and the radio reference

frame (VLBI)

Gravitational physics parameters Space curvature (VLBI) Lense-Thirring precession (SLR) Others (Grav. constant, equivalence principle metric)

Lunar interior

ConclusionsConclusions

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)

Future Lunar MissionsFuture Lunar Missions

New high resolution photographs of reflector arrays

- better lunar geodetic network

- lunar maps

Lunar Reconnaissance 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 Ranging Measurements – Why?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!