Tests of Gravity Using Lunar Laser Ranging

Stephen :V!. :'IIerkowitz :\ASA Goddard Space Flight Center

Greenbelt, >ID 20771 email: St ephen.;\I .l'vIerkowi tz@nasa.gov

http://asd.gsfc.nasa.gov/Stephen.Merkowitz/

Abstract

Lunar laser ranging (LLR) has been a workhorse for testing general relativitv over the pa~t four decades. The three retrorefiector arrays put on the Moon by the Apollo astronauts and the French built array on the second Soviet Lunokhod rover continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point :3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly. it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retrorefiectors are limiting the precision of the range measurements. In this article. we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.

1 Introduction

On J nly 20. 1969. humans landed on 1 he :\Iooll for the first time. The d(1~·. t ht'\ pullo 1 I astronHuts deployed t he first Laser Rdroreflect OJ' (LRFtH. or LH;j). \Yit hill a lllOllt Ii, ret Ulil

photon:; \vere detected at s(~\'('ral observatories '7' Two 1l10l't' rctrorell{'cto]' illT1i\',' \\'('l'('

011 the :'\[oon the !\pullo 11 ,mel I;) missions, III ddditl()l1, t\\U Frelic', dl'r"\~ \\(1< ul,

Russian LUllokhod rovers carried 011 LUlla IlllHlns, hOl\,('\'('l'. unh t 1](, 1ilTil\ Oil Lllllukliod 2 ilil~ 1)«('11

a viable target. These four retroreflector arrays relliain visible and the 1m.;,,]' rdllging (btlii collected over the past 40 years has dramatically and continually increased our understc1llding 01 gravitational physics along with Earth and Moon geophysics, geodesy, and dynamics, They remain the only operating lunar experiment from the Apollo era, and more incredibly, only has the ground station technology advanced to the point where uncertainties associated with the lunar arrays are limiting the range measurement precision.

The Apollo 11 and 14 arrays consist of 100 fused silica circular opening cubes (:l.Ii Clll didllll'tn each) with a total estimat.ed lidar cross-Sc:UiOll (bill:ied un the illt of till' diffillctioll Pitll(':l, of the array at the position of the receiver in the far field) of 0.5 billion sq W)j'(-' lllC'l ers, A polio i .-) has 300 of these cubes and therefore about 3 times the lidar cross-sectio]] c\!lel is the Illllilr ilHill

with the highest response. The diffraction pattern of the Apollo arrays has a central lobe at the center with six surrounding lobes with an effective tophat function 1\ arcsec ill diilllwter for small incidence [3, Tbey produce 1H1 approximately 20 klll diallleter spot on Eelrt Ii This is suliicient to cover the velocity alwrriltioll due to the \!OOIl'S lllot iOll S() tile (111)(' ~

refiect ive relet' were 1101 intent i()llidh ,spuil('d I ilill ir()lll (!()

Figure 1: From left to , (he Apollo l1. 14. and 15 retrordiector alTaI'S,

The' two Lunukhod alTC1\'S COllsi:-;( of I .. } ( ('ub(·,;, fCCIl'll ;-;ick llcllL Shurt j\ ,1:t(,1 landing, the Lunokhod 1 array ceased to be a \'idble target no st8tion:s han' "im:(' beel] able to get returns from it. It is also very difficult to get returns from Lunokhod :2 the lunar

The silver size of the Lunokhod cubes makes them less stable which performance when sunlit,

is perfornwd the round trip light (ran;] (ime twt\\'('f'll a ground transmitter and the retroreflector. LLR measurements had i1 of :tbout :2U ern, Since 1969, multiple stations have tot he lunar ret roreilect or", howt'v('J two stations have dominated LLR data .\lcDonald Laser Ranging III

Texas (since 1969) [62] and Observatoire de la Cote d'Azur (OCA) in Grasse, France [56]. The vast majority of their lunar data comes from the array with the highest Ii dar cross section: Apollo 15. These stations have increased the range precision a factor of 10 oyer the years to

:2

Figure 2: The Russian Lunokhod 1 lander with the Frellch built retroreiJ(,clor illTm SI Uill

the left side<

the level of about two centimeters. Recently. the Apache Point Observatory Lunar Laser-ranging Operation (APOLLO) has begun contributing high-quality data at the millimeter level 42.39].

Poor detection rates are a major limiting factor in past LLR. Taking into account velocity aberrations. optical performance of the ground station. and other systelllatic effect~. the O\'('nl1l round-trip loss is of order 10- 21 . mostly due to the {A loss from the EMth-'dUOIl disUlII((' BIT;)::sl'

of this loss of light. not every laser pulse sent to the 1\loon results ill it delect(,d ret IlII) photoll. leading to poor measurement stat istics. l\lLRS typically collects less thilll tOO pliot Oll::;

per range measurement with a scatter of about 2 cm. However. the !lew APOLLO illst r1l111(,lIt III

Apache Point has overcome this limitation. The area of the Apache Point :\.5 m diameter telescope lilld t Iw eifici('ll:

avalanche photodiode arrays used in APOLLO wsu]t in thousands of detectiolls lIm]1 i det('cti()n~ per pulse) to ij s\<!ristinli 1111("("1"I,li]11 of ahemt 1 lllill. Till' d(JlJlill<'lli 1",llIdlilli

llllCl'rl per photo)] ill :\l'OLLO S\(·!II.~ fro II 1 Ilj(' Uriell1!11iOli ()r 1he I·e-Iln·tol" dl',I\ "lid 1]·(

sDeiated spread of return tillles Additiollil errors ilSS()ci!lthi \\ilh itillill" arrays. such as regolith motion and thermal expansion of the array. start to becOIllt' sigllificanl ill the millimeter level of precision.

Each ground station records the single-photon reffection events. which are then combined in1 () normal points that are adjusted for station-specific corrections. A typical normal point is generated from 5 to 20 minutes of ranging. The normal points are then submitted to a central archiw with the International Laser Ranging Service [551 which Inakes them available to the public. measurements. such as environmental conditions pressure. etc.) are also record!,!!. as these are required to further correct the data for atmospheric effects. A detailed model of t I1\" solar system is then used to to estimate various lllodel

parameters from the measured data , the most fruitful

tivistic effects show up elt thelll from most other parallleters.

hora of UI lwr effeci Wil h the n!(lill le';l" of C; H

Vilfiiilion of thl' illiollill COIlSIlllli. I ile ill\'«r:ov squilre lit\\'.

disc~l~:3 the current state of LLl{ data (tll(lh·si~. \\.C' describe thE' Hext g(,llCf(lliull or' !lll){lr

Illode'ed post-fit residuals

APOLLO :~'ed,an uncert.

1q09';-7:;"0--;-1:;"9 ::c7S;:----,1:-:9:-::S:"::0---,--::1"""9:-;;S-;:S--;-1:;"9-;::'90-;::'J ---:;c19;:-:9;:-:5,----:2:"::O:"::O"""O---:2"""O-;:O';:-5--;-20~·10 year

Figure 3: Improvelllents in the ground station over thE' pa::;t :10 Vetar" hilve illcredsec1 t Ii, range 2 orders of Uncertainties associated with the retroreflectms are now becoming a limitation.

laser instnullents and discuss the possibilities that the future of IUllilr clnd pLlIl(,tilr\' Illsn lllay hold.

2 Equivalence Principle

The gravitational acceleration of massive bodies toward other bodies is dependent on the non-linear properties of gravity within metric theories of gravity [48]. Tracking this acceleration provides a measurement of how gravity pulls on the gravitational binding energy and how gravitational energy affects illertia. This probe of nOll-linear IS out in 1l1l'aSllrt'1l1l'1l\ s oj

the Parameterized Po,;\-:\ewtolliall parallletlT ,j discussed iwlow. hut i\ IS Idso Illlpiicli II ([Jill ill"('(j

within the Einstein Equivalence The Equivalence Principle (EP), which state,.; thE' equality of ilnd illert iiI! Illll:iS.

is central to the theory of General Relativity. The EP comes in two flavors: the weak (WE!') and the strong (SEP). The \VEP to non-gravitational contributions to mass: Standard :\Iodel contributions of lluclear and energy plus quark nwsses «lid 1 heir kinetic :\ucieons of fnl('tiullid elect ro-wt'llk and uuclear exhibIt dilfereIll to ii,l'il\'it\ III the Lise 0111 \\'1-:1' \iola\IOll. rlj( Sl':l' ('Xl('lld~ IiI< \\1:1' to llh'luclc graviL-lllUil<:d ul (j < (lddr('~:r:llg (he qll('~tlUJl ullll.}\\' ,~L:\\lt\ t>L d

allcL t berefol'e. the lloll-linear Ilsl)('('\ oj \Vhile the EP must hold true in GR. all altel'llativE' theories of it Yiuiatiull

of the EP at some level. Efforts to formulate a quantum description of introdu(,c new scalar or vector fields that violate the EP These violations manifest t helllselves in \ he equations of motion for massive bodies. as well as location effects on the GR may be the only metric IS on the SEP it from all other theories of Therefore. the the EP is one of \ he strongest ways of

4

is often considered one of the most powerful ways to search for new jWHmd the st,]ll(brc! model [13].

Precision tests of the EP generally test the Universality of Free Fall (CFF): all test bodies have the same gravitational acceleration in a uniform gravitational field. Tests of the CFF an' performed by compaTing the gravitational accelerations al and a2 of different test bodies:

(lHG) JIr ;

(I)

where !I is the jOllal su t itt' class]( al E(lt nis tY[J(' ('XI)(,lI]llelll~ \\'11](11

compare the acceleration of test bodies with differc'lIt COlllpositiollS only probe thl' \rEI' ''''1 In the late 1960's. Nordtvedt recogllized that the SEt' could be tested 1 11(

itational acceleration of two massive bodies For each body. the 1 t () inert liil mass ratio can be written as:

where C is t.he

f; =

-- = I +1; JfI

of t.he \('sl bock:

G j' p(,r)p 2 , 'I' r/:

is the body's total mass energy, and 7) is a dimensionless constant that is the EP holds true,

zero if

For a uniform sphere ofradius R, -3G AI/5Rc2, however due to their complex interior

structure, the self-energy for astronomical bodies is comput.ed llUlllericalh', !\n Earl h Illodel based 011 of I!:

( I;

while a }\loon with a 20% iron core

I I ) \ II ,I [O()!

1 ,')() X [O-i!, I.»)

:\ordt \Iedt l'f'alized Iba t " \'iolario11 llf 1 be El-' would CClllse the Eml h ilnd }\lO(JlI 10 bll II t di ri'(,],(111

rates toward the Sun result ing in a polarization of t be lunar orbit Tb is ion shu\\'> up in LLR as a the Earth-Sun line with a 29.53 solutions to the equations of motion for the Earth-1\loon-Sun system find that the ladi,d perturbation of the Earth-Moon distance due to an EP violation is

5'1' = - 2,9427 X 1010 r ( JIe;) , L " Earth

(-) cos D (6)

where D is the between the mean longitude of the 1\Ioon dnd the mean longitude of t lw SUll

as obseI'\!ed from the Earth (synodic Eq, with the estimated for the Earth and i\Ioon, we find that

Hen'lll soillt iOllS LLH dilUl illl 1:P 1 esl

linlit ill a part III 10::) 1 Sillce the L\l', I!

but also have differcllt compusit iOllS t hl' LLH llIE'<lSllH'llH'llts aloue do Ilot p]'()\'icli' it

punc Lest of SEP [49], To separate the \VEP and SEP effects and eliminate the ()f a conspiratorial cancellation. the Eot- 'vVash group at the of performed il

torsion balance experiment using test masses of similar composition to the Earth and :.\10011

Combining the torsion balance results with the latest LLR analyses produced the best test of t IlP

SEP to date 75]:

.0.. (1\10) = (-2,0 ± 2,0) x lO-B • jll/ ,'-iEI'

ri')

'/ = (1. 1 ~. )i) x III I

Because Earth's of 0049;',

cOlltribute::) 4.0 x lO-ilJ of its totallllilss. this tnlllslates to;1 SEt' tlst

3 Variation of the strength of gravity

III GH the slrength of \' is tdkl'll ;IS <l CUllSlilll!. G, h()\H'W'l'. UOI ;111 theories

SllCh;1 comllraillt \\'ithill sc;,j;lr-t(,ll.sor tl]('orics 1111' gr;\\ildliull<li c()llplillg Cill' \W«()IJ'I'" IIIIIl·I)lll.

of a dynamical scalar field. Thtl vmiillioll of tlte gUlvitatiollal ccmstml1 t1Wll Oil thl' cosmological evolution of the scalar field. The exact form of the variation will depend OJ] t hc specific cosmological scenario being proposed [67, 26, 43].

A time variation of G will show up as an anomalous evolution of the orbital periods oj astro­nomical bodies. This is easily seen fronl the Newtonian limit plus post Newtonian corrections to

the two body orbital period:

p= (10)

where t is the angular momentum per unit mass. P 1S the orbital and III is " 1 ill'u]'\ mass parameter of the two bodies the tillle deri\'atin' ,\lld igllorillg till'

order terms we f1nd }) I (,' iii

= :1- -,- ') - :2--I' - (,' fJl

( II·

For sohn' systelll bodies. \\'(' ('(Ill :'(1 \ lH' llli\;-::--, \('l'l1L except I(»)" (I ~Ill;dl 1";',1(' U\ ~l :():1:-

the Sun (for COlllpact objects like llC\ltrOll ,,,ti1rS thi,~ term li('COllle" :llIportillll j(j), The il'l'Il>

account for t he effects of t.orque act on the orbit and must be scparat c'd frulll 111(' time evolution of C.

The radial size of the :.\10011',; orbit is also aff,,(\ecl

[ D :2

G r / 11

Both tidal-friction and a G influence the ::;emirnajor axis. However, one can separat Ie'

the effects by taking into account their different proportional contributions to the orbital period. Combining Eqs. (11) and (12) one can solve for the momentum in terms of quantities measurable LLR:

r 2-

which call t hell lw used 10 n\lclll1lI.(' (:.(;, Th:s linear wit h tim\' t bid Will' ll~\'d rur 11,1\\('\, I, .I l

!l

G atkcts both the lllomblv lunar orbit illld the illlllliid blrtlt-.\!oOIl urbit ilrtllllld lLI' :-lUll S()I,d

perturbations on the lunar orbit are also large. G accumulat.es as an orbital longitude effect 011 the of t he solar

LLI{ datn 1)\ tile .Jl'L gro\lp ~('h ,I lil11il Oil () 'C; c (()::" 71 x III ('t ,d. filld C;,C; (1T7) x I() IS\·(·m ,111<1 (,'(:'~ ( ~:)I x J()

lilllits translate to less thall il 1'/ \'ari,lliull or G on'!' tlte 13.7 lJillioll \'('i!r ii!',(' ul 11](' universe. Beca\lse the dOlllimmt effect for II vmiati()ll in G is in tilllC'. COllt ill\lI'ri LLI{ measurements will significantly improve this limit. Additionally. a Hlore opt lillal meaSUl'CIlJ('lll

schedule throughout the lunar month. now possibk with APOLLO, will also put better cOllstnlillh

on a possible time variation of G

4 Inverse square law

The inverse square law (18L) of gravity has been meaningfully tested over length scales spanning 20 orders of magnitude, eliminating Yukawa-like couplings competitive with the strength of from 1O~4 to 1016 meter length scales. The deepest probe of the I8L is from LLR at a scale of ~ 108 meters, where any new force must be weaker than more t hall t en orders-of~

tests of the ISL havE' recenl Iv beell pm!ll])t eel t ill' ('I In;>,\' ~(,d(· of

the acceleratloll which sllggest iw]()w J Illill 1 :\iocierll tests of \Jc'\\'ton's Ii,\\, ()f gnl\'il\ ()h(,II~('ilr('h 1m IIIl addIIIOi"l! 'iltkd\\,i

cOlltrlbution to tlw atiulwl pute'nll,,]!

(j j)

where Cl' is the dilllensicmless strength IlJld A is the length scale. Such II potent Ill! wOllld gelJenilc a precessioll of the :\!OOll'" with freqUl'llC'v (50 1

(\ (11\2

2\):) ( , J ,-,

where a is the mean radius of the Moon's orbit. The agreement of geodetic precession with C H described below leads to a limit on an anomalous precession of 5w/w < 1.6 X 10-11 This translates into a limit on the strength of a new Yukawa potential of Cl' < 5,9 X 1O~1l at A where the

lunar test is most sensitive. Recent of LLR data includes specifically fitting for YukaWH perturb,ltioll \erriLS ill 1]11'

equations of motion leading to a meaS1ll'emellt of Cl = (:l 2) x 10- 11 at A =1 x 10" km. \\'llil,'

int this !lOlI-!lull result llclS H't \() bl' I hurollghh' iJl\'('~l iglll('<1 -:r;-'

5 The nature of spacetime

The recent ewd new lllOt ivatiull

llleaSUH'llWlll. uf the a('c('lenll the Ililt ur(' of ,~PilC('t 1111(. :\Iodcls I lUll

(1\ clistdllCC':'"I, S1h,h rrS brtHle-\Y\)1'ld It!odt'l~, h(l\'I' ]"('('('ld lv 1H'CU1;1('

exhil);t strong tlkd l:ldkcs Ill{ g!'i\\il(;l

t ileorit':-i be(,OlIIl' t.('slaI.Jk ill "lion,,:' d!Sli'Il(,('~ \\'1,1'1'1' 'Ii" a t C'iOt bC'te! for in \'('sl

of the Ullin'l'se hilS

1l1otii IiUll IOI! Di

11 {'j' ~\}' {;--. , '"

The Earth-:\loOll Systt'lll

system scales. For that it gyroscope curved

will precess with respect The Earth-Moon

to a rest frarne. This is referred to as geodetic or de Sitter behaves as a gyroscope with a

This is obst'l'ved lilllit on the cleviat iOll of t he Ie (I.D::;::G.-1) x 10-:; This IlJeaSUrell]('llt (:,111 also be llsed to set il limit Oil ,) possible

~'2 constant: /\. < which ha.s illlplicat iOlls for our lllldnslililciin:d, of dmk ('IH,)"!',\"

It is also useful to look ,ll. violatiolls of GR ill t he context of lllctric tlH'ories or Y. I'l\-ramet erized Post-Newtoniall (PPN) rOr!lwlislYl prm'icles a COll\'('lliellt Wil\' t () desni he II (LIS::; ,

deviations from GR [53]. The most often com:iidered PI'", parameters are i aud ~. illdicill"~ how much spacetime curvature is produced per unit mass, while (3 indicates how nonlinear is (self-interaction). rand (3 are identically one in GR. Also of interest are the parameters 0;1 and 0;2 which are identically zero in GR [69,

Limits on can be set from geodetic precession measurements , but. the best limits come from measurements of the time of i.e. the Doppler measurements (0 the Cilssini set tile current limit on ,,: l~' I)

TIl<' EquivalencE'

'I 4{:i -~. (](i;

Combining the Cassini value for '\ wit h the LLH valuE' for 'I provides (he best lilllit OIl i: ( j - j)

(1.2::': 1.1) x 10-.1 Sc:ctlm tensor theories with il1trl1Ctor.S for thE' cosmic SCilj,I!'-lil,ld predict ,1 re::;idulli - 1111\(1 j I. of order lO---IO--' lorim \\'ililil! ),hl(li

of iHh'illlCtcc! ttl{ 1 illlc-<i"i;ll 1l]('ll."lll'('II]('llt:-/\ non-zero frcUll(' \\'ol11d :-1h()\\' ;q) (t~ ;-lll {)scilLltion of 1he IUlld]' ntllgc dl t:1(\ ,~llJj; ill

the difference of the illlOntalistic and (he annual period )(j, uJ LLH data sets the current limit on the PPN parameter CVl = 9) x LLR has also been used to set a limit on 0;2 = (1.8 ± 2.5) x 10-5 [37], however. the close solar spin axis aliglllllell1 with the total solar system angular momentum produces a much tighter constraint on 0;2 of order 10-7

Lunar laser ranging also places limits on the gravitomagnetic interaction. the same physical interaction that leads to the Lense-Thirring and Schiff precession phenomena as tested b\' of the LAGEOS orbital and by the of a gyroscope ill Gravity Probe-B respect

In the case of the lunar orbit. rotation is not involved, but rat her trall~Ii1(i()Jl of t he Lin Ii "Ill! \loon point-masses in the solar system signatures at both t.he

barycenter frame that produce G llleter Cllllplit wl(' rllL!',,' alld twice the frequency. Tht' illllplit udes of t hi's(

the deep connection ollugllet ism has wit l ill'

covariant propert.y of rellltivistic dvnlllllics. Sofrel ('I. al. showed the lll'cd for the :d,l'C'\'iiOIl]cl:d,i\('j i( (,erm in tilt: LLH eqmltiol1s of 1l1otioll III (he leVid ()f O.l:)'/c. whether cu!!filled to ,I PI'\; context ell

,dlowC'd to \'iHY h- If llll0( hel' 1'IIIil1\('11 I' gril\·itlllllll:';lIe'1 il (),. ,!l(-

un' from C]{ itt ('\'('11 tlie 1 1,,\(,1. 1.1.1\ dilli! w()llld "'lilid iii (UllliIl: III

6 Modeling and Analysis

The c! model of t he solar svstelll I hill 1l1.S()

includes all the effects that contribute to the range between the Earth statio!!s ilnd Ih,' lunar retrorefiectors. These models comput.e a range and tbe deriViltiv('s of rallge

with to each model parameter at the of eetCh normal lOllS take into account orbital paTameters, attraction t.o the Sun and s. relativistic cOlTecti()ll~, as well as tidal distortions, mot.ion, and other that affect the of the

retroreflector and ground station relatin: to the centers of mass of the Earth and :\Ioon SOlllC'

of these parameters are measured ot ber means, but most are est ima( eel frolll the L L H. rid l.il.

The range measurements are corrected for atmospheric delay and a least square is performed to estimate the ~ 170 parameters in the model [37,34]' most of which are initial conditions and masses of solar system bodies. LLR data is often combined with other and planetary tracking data to further constrain the estimates or remove

A number of models have been over the past 40 .years. The model deveicmed i1i (.1PL1 was oue or the tirst programs for LLH ?() ill)(1

continues to be was recently used to produCt· lilllit.s OIl llie SEI' V]()lilllOJl. l!ll)(

variation of t.he atiollal COllstant, and illterior st !'tIel urc uf t IH' '.10011 I,). Til, "11\'I!-

source Planetary Eplwmeris Program (PEP) is i\ major ill the Harvard-Smithsonian Center for (CIA). It was also used for Olle of Ihc lirsl ttl{

to test the SEP [601 and was recently used 10 tcst for Lorentz violillion LLH dillil A model at the' l of IIanllO\'e]' was also recently used to prud\lCE' liJlIll;-; OJJ

parameters. including t he preferred framE' PI'S parilllJet ('rs , :)7:, now rout illt' op{'j'iII iOIl of .\ PO LLO ill Point llllililllctn kve! Uillil J~

produced 110]](' of t 1](' Jl10cicis is cap"bk, of ilC!lIdliJlg Illi1-liltleter class data to lllaxilllulll,?' Sew drecb aud (IITOr reductiuu t m'(j I ()

be added to the tools t.hat become important at the millimeter level. To Like advililtage' of

the next generation of LLR instruments, these codes will need to be furt.her modified and rigorou" theoretical work will need to be performed to permit tests of new ideas in physics. Substallt i,d effort is also required to address the multitude of effects that will contribute at that level.

Many of these effects will be scientifically interesting in their own right. In . the lunar interior models require significant improvement. There are also additional Earth effects that need further model development, such as the of the lithosphere by the elllel ocean which causes the station to move (and horizontally) with the tides illll] weather. Models of these effects are available that are deerned accurnte to better thilll 0.1 Jlll:l a.nd tested in VLBI :;oftware at CfA but need to lw incorporated illto t 1)(' i!

progralllS. As precision is further improved. lllore sophistiulteci IIl()d(·I~ <11111 rneasurerrwnls will need to be clevJ:iopeci. Other importilllt effect.s for ad\',)lJccd LUi

include solar rncliat ion pressure, t hel'llwl i ng of the refiectors. wlar t ides Oil I he JllO()JI. and solar nJass

7 Next Generation Lunar Laser Ranging

The current lunar retrorefiecturs all lie within 26 latitude of the lunar equatul'. ilnd tIl( most useful ones within :24 longitude of the sub-(·;uth meridian as show II ill

This clustering is sub-optimal. particularlY with respect to the lund!' libnltiolls. III addition. the active LLR ground station,; do not cover a range uf latitudes. further the geometric strength of the observations. Additional observatories could improve t he sit lW t iUll

somewhat, but lVlt. Stromlo in Australia IS the only station capable of to t he :'I [(JOll l1ut situated at similar northern latitudes. Mt. Stromlo has not been active ill ranging to the :\loOYL

The and quality of observations also varies greatly with the and power of I he laser employed. :'Ilost ranging over t he recent past has occurred betweell t hr('(> (:'IlLES. OCA. and Apache Point) and Olle' ]'efi('ctor (A polio l~)). The solM lIoise ill Iii

ot her issues IllH ke to SOllle' refl(,ct ors ollh· aro1l11d t h(, (Jllilr1 ('j'-Jll()(JJI POilll whici: hilS \'('[.\. p.o()(1 ciistriiJ::tiuL ,1l1lUliP. til(' l'dl(,(lurs ,\l'UJ.I.(j

1'; of ill! I \illar wit Ii ot her progrMl1S.

impact 011 the science through LLH, St uciil's of 111(' strun tll'(' dlld (,Olll[lOSit iOll ()f 1/1(' iliiE'lI()1

measureJllents of the lunar librCltiolls, whil<- \('sls of ell requin' till' posilioll of llie Innl,!'

center of mass, In all. six of freedolll d,re required 1.0 consl ram the geollletry oj (1)(' Larll]-'\loon sysrem addition to Earth A stat iOll and reflector is ill:,uflicit'lil \'0 det ermine i'dl six tlw rota 1.ion of the EmtlJ wit h n'sjl('ci

w the '\loon, The additioll of one or Illore reflectors dlld one or mOH' additional rallging 51 III iUII~ ill the Eart.h' s southern would strengt hell the geoll1et ric cO\'crage ill I d i lInCII5(' d 1('

to lunar motion as llluch as i\ rdct or ofl ill the SiHlle level of :U

AP14,

•

AP15

• AP11 ••

Figure 4: Location of the lunar retrorefiector arrays, The three Apollo arrays are labeled AP and the two Luna arrays are labeled LUN, ORI and SHK show the potential location of two additional sites that would aid in strengthening the geometric coverage,

Satellite Laser Ranging (SLR) began in 1961 at 'JASA's Goddard Silln' then it has grown into a global effort. represented (ILRS) The ILRS includes ranging to Earth to tllt, I!lllilr reflectors. and is toward supporting t rall::;pclllcler The current SLR network consists of over ,10 stn(ions worldwidE:, fUllclc-:cl and o]lcrated )'eseilnli

gO\'t'1'll11WnIS, It \'aril:s fur t L\cki IIi.; recei\'ers. t elect r0111('::-=', dud Ll:;('r 1 r;:-lllslnlt 1c1':-;,

The devcloplllE'l1t of .\:\S..-\'s '...;exl CC'IlC'l'I\1illll :-lill('llill' Llser H'I moved sYstem opera! ion from t he of laser (,lIngv low r(>jwI it iOlI )'i1 \(' t U 1'<'!)('I: I I()ll

rate photon detection r:2[ This teclllliqu(' use,; recein' photons more d-ficl('lllh' i\lld because of the return rate. millimizes time (mel (,llaLles closed loop t

The current laser in use (:)00 picosecond pulsewiclth) lilllits ::;ho\ IlleaSUremellt d(,Cl11'(1n' 10

:2 to:i em but because of the high return rate normal data can be redllceclto the millilllE'1er level. As many as 12 '...;GSLH ::;tation~ arc to be built and around t lw \\'()rld

under ,\,ASA's Earth Science Program in (hc' cOllling decade, The of this new network of SLR 5( ilt iOllS a opport t ()

the number of LLR stations, To be lunar the SLR stations would either need to be with higher pO\'\'er lasers or new high cross-section retrorefiectors laser transpoll-

[0

;) ~Worldwide distribution of satellite laser O3t Cl t iOlls~ part :illg III 11](, llUnl

tionaJ Laser Service

del's would need to be put on the !\]oon. of thE' StH infnlslrllClurt' is

C1 very way to increase both the spati,d and temporal LUi COVt'rage at lllillililid cost. lWe! would ensure cOlltim[OllS or LtH dilta t the illCkt111;tC fUlu!E' dS it Ilollic! Illli

OIl ulliqlH' Ll(iliti('~ ilwl illdil';d:;;t! ill\t'SilgdIO)",S cOlltilllling ()I)('nlliull~.

8 Next Generation Lunar Retroreflectors

Remarkably, four of the five lunar retroreflector arrays are still visible and producing uscJul datil after 40 years of exposure to the lunar environment. During that time. the precision of th' nlllg(' measurements was improved each time the ground stations were to the lllost advanced ranging technology at the time. Incredibly. it Ims taken nearly 40 years for the statiollS til catch up with the potential capability of the retroreHector arrays.

The first LLR measurements had it of about 20 cm. Since 1969. sevenll statiolls have successfully to the lunar retroreflectors and have increased the range aCCUPlc\' a fact or

of 10 to the level of it fe\\' centimeters. Poor detection rates have historically lilllited LLH (not e\'ery laser pulse sent to the !\crOOlJ results in ,1 detected return photon). IIU\\,('\"(,r. TIli r('li1-

Ilew APOLLO ,","::item llses I he collect i!r('cl of t Lc co[]jrnated bCc111L ilt llllClgc lllld \Tn~ db< :ell l m'il

such thcH ThollS('l1ld~ of dc({'c1ion;--; (tn' recorded {'-\-('ll 1l1111t

H) i\ sUIt ist iced llllcert "illt \. "I" i\ hOiI! The dOllliwlllt nllldoJl] HllC('rl per

Il

size of the arrays and their orientation cim' to t hE' lunar librations. The p\lI~('

from ,\POLLO will illuminate all ellt ire HlTil\', but olliv Olle (::;OIlH'1 illl(,::; i\ f(,w) of tIl(' ph01()lIS \\'iII be c!e1('ct ed UPOll re1 Urli APO LLO Cillillclt de\(T11llll(' \\'hill im'il of the· a IT in' cOli1 ri i)\" cd illOS 1 "i

so the t ill or the ((lTdY wit]) ]'('S))('C 1 to t L(, Enrt]l SpH'i\d:-- UIl1 111(" \ ')<1' lU:i 'Ii

laser a full-width

ani),' cliuWllSiOll ul (J.C) 111 illlCl d iibnltioll of (i llilllsl,lt I(l

of about 0.1 Ill. or 670 ps ill the roulld-trip tilllt'. As the .\]U()ll Iiimll('s.

the alDount of spreading cha.nges since the array is ,lIso the ground station.

its orientation with respect tu

Fid ucial Returns lor) ps 121n5

ti!li.C off~et ! ns f

Figure 6: data from APOLLO from the Ii! array' on Sowillber 10. 2()07 ill w]wh 6624 photons were collected in a 5000 shot run. The raw time evellts are slim,']) ill the tup plut li the initial predicted round trip time subtracted). The bottom plot shows the dis1ributioll of lilt' on t II' hieh WIWll (:011\'01 ut eel wi tilt he ret mreflector tilt is consist ell! with t!Jt· llWilS\lI('( i n't\lrll~ ShOWll ill tile (,('111ml The i 0\ ('!'plu] ]'('p),('.~('l\1S iile tCllI[Jonli <lilt' ill rhe oriclltation of 11ll' relrurdll'C\or ilt lilt' tilll(' of tlie "!JS('I'\."tiull c:j(j

,\1

:\Iodest in the will not the l'il!lgl' ;)1"(,-

cision as the array tilt will continue to dominate the error rut me. lu new arrays with more cubes of the same size would resuit in no

dimension doubles the random four times as many what doubling the linear army dimension

12

would eliminate any benefit of going with a smaller array. To maintain the advantage that multiple cubes provide in response, but eliminate the issue~

with orientation, one can ~eparate the cubes far enough that their responses do not overlap whell seen the Earth stations. A range separation of about 10 cm between the cubes should be sufficient to distinguish them in the data. Since the (for APOLLO) 5 lllicromdiall laser beam covers a 2 km spot on the mOOll. any reasonable will result in illuminatioll of thl' entire set of reflectors Ht once. The cubes could be coarsely to )J]'()\·id(· ('llUII::.11

information to be acquired by the lower energy Eart h laser stations. ur the illit ial ion flUlll

the ground could be performed with the higher laser (;llergy I telescope lurlilr las(']' Earth stations which will have good ratios.

cube corllers call also hi' made to prm'icle similar ret urll nl1es ilS t l1e Aoollo illTil\S

wii hout significant pulse The responsE' Cmlll il 7Ji Clll cube would l)(, I (i I illJ(',~ Ien!';(T 1 hilll

1 hat of the Apoilo :3.1'1 elll cuiles. fI()w('\Tr. Sllllph' lllil solid (111)(·s ilinCil.~(·S I Ii"i!' \\'el::.11 1

Ihe ratio of tIll' cliallll'tn cubed. !'lll' lldditiulliil size' alsu adds tu IhlTlll,d IIObC df(',h :111<1

decreases the cube's miss the station clue w different from 90 degrees) can cross section.

it very lWITO\\'

aberration. Cilll calise t 1)(, rellll'li .SpOI 10 COlli ('1\

tIlt: dihedral of the euiw

aberration but red uces 1 he etfect in'

Solid cube corner retroreflectors (up to 11 em) have flown on over a hUlldnxlmissiolis. for bOlh satellites and lunar laser ranging. Recent tests of the 10 em cube shown in 7 has cl(-Illlollstulled it meets relevant requirements for the lunar environlllent [11]. Designs for the housing are lOt ill ill

development [22].

7: A 10 em solid cube corner reflector Also showll for comparison is a 3.K Clll Apollo of Currie.

for tile IUllill l'II\:r()I.Il]('Li

model cube (lOnltT II Phul () C,)I

The malll of solid cubes is that the thermal l)('c()]:;e n'n'

challenging because of t he temperature of the cube materiar~ index o[ refract ion. .\ alternative is to use hollovv (open) cube corners. Since hollow cubes arE' reflect in'. t lll'

index of refraction problem goes awm·. also potent iall\' weigh les;,. liil\"(' ~Iwdl('r 1 hcrillill distortions. Clnd do not introduce signitiCi\llt pol,uiziltion efreet". 1 lieretort'. C;11l 1)(, '11;)(11'

without as much ill optical Hollow cubes Ilan' fiowil (Jil d fl"\

lnissiollS, but are not used on satellites for laser because of a Im:k of tesl dill" and some indica t ions of inst Cl bi lit ies at t em peratures. A recellt program il t \1:\ S:\ Cuddil I'd Space Flight Center is looking at Clcl\'c\.llced bonding t I'm SpilCE' optics that hm('

the pot ential for these proiJlellis. Isulatiun from motion and tlH'rrmd changes iln' ,dso for going lwyolld I)W .\pO]]I)

array capabilities. Each refiector should be rigidly grounded to direct Iv sense IUIliIr !Jod\' mut iU11 and be located far enough away from normal human to avoid vibration and cOlllillilill;1tiull (dust) from affecting the cubes. To provide thermal stability, the retrorefiectors could be thermally coupled to the ground below the surface layer. As shown in Fig. 8, measurements from the Apollo 15 and 17 heat fiow probes indicate that the large diurnal temperature fiuctuations are negligibly small at depths below 0.8 meters [31, 27], To take advantage of this one could drill Cl hole about it meter deep and insert a rod with conductivity. low coefficient of thermal to anchor the retrorefiector which would be mounted to the exposed end of the rocL A 111lTIIliii blanket positioned over tilt' lunar surface around Clnd below the retrordleclor would ,il"o r<,d \Ill' the therllJal fluctuations induced from tht;

E 100 o I' f­a.. w o

200

Gradients In Kim

250 252 TEMPERATURE. K

254 256

8: Tempewture fluctuations ill the lUllitr as c\ fUllction of depth fl'Olli ,\pollo I:) IllId 17 nWClsurernents. Hatched are,IS show temperat ure fluel Uil t iOll:;. BC'ic)\\' il bOlll .J() ('Ill

t.here was no obsc,rvil ble telll peril t un' Ii uctlli1 t i011 d \1(' lot he 1 UlIdr 1l'lll jl(']it1 it]"('

:n

9 Laser Transponders

Laser are currently deployed on the IUllar surface as an alternatin' to reTrordiectors

and can be used for that both send and receive have approximately a r2 link VdJIVl"" over direct loss of

ing in only one direction before being regenerated. \Vith the

11

(ll:--:o bt,

{lfC d('\-iCl):-'

. as the is [Jl'llpagilt-and indusion of !e,ser

communications for spaceflight missions. it is logical to include etn optical t hilt uses

the same opto-mechanical infrastructure with minimal impact on the missioll resources. These instruments could be used to support the relativistic and lunar science in addition to communications support to astronauts and/or other scientific instruments. These IUllar instru­ments would also provide a pathfinder for applications on Mars and other bodies where the use of passive retroreflectors is not

Asynchronous Laser Transponders (A[;[) are relat simple devises 111<] I have [loki I! j,d for space The ground eWe! remote stations or an ALT fire tileir l"cot'rs illdl'!)('lld('\I! II (as opposed to etn echo transponder which \\'ork,s !J\' sellding !Juck it I ililingsigllid I\ill, i\ [lXI,<I

delay from the of the base-sIal ion This allows lilt' use of the terminal to operate at their most d-ficient dil<l

po\.emietlly more reliable than other types of laser It docs, 110\\'e\'('1'. n'([uirl' iI "I(j(k on both ends,

Figure 9: An Asynchronous Laser is under developmenl ilt SASA CuddilJ(1 SpiI(1

Center that is compatible with the Sext Generation Satellite Laser Ranging syst t'lll i 1 ~r

Several interplanetarY Im;er I ram,pollcier ~ were perforlllcd ir()111 ! li, :\ASA Goddard Space Flight Cenl(-,r satellite laser nlllgillg fcHilit)' '1'1](,111'81 I)WO-IliI\',:2l X 1U'

utili%ed the Llser All illH'i (']' Uli tl)(, sj)ll(('crallG:.l IIlId ! Ii('s('«()wi (uili'-

way, i-\U x IOu km link) utilized tIlt' .\,Iars OriJil Lts"r Altinwter on tll(' '\'lms Orili\('r Spi\«'C!;1i 1

'\'lore two-wa)' was performed using t bi L Ulla!' 0 I;i l Lise!'

Altimeter (LOLA) on the Lunar Reconnaissance Orbiter (LRO) orbiting the .\,IOUll rlles( have proven the concept of able to point both transceivers, detect t he pilot 0118,

and retrieve useful parameters at low-link margins over distances, An ALT, shown in Fig. 9. is under development at ~ASA Goddard Space Flighl

Center that uses technology derived from the Next Generation Satellite Laser Rangillg (SCSLH) system [19], Other efforts at Goddard and other institutions are th'lt colllbill(, laser ranging and laser communications, The robust link budget combined with the compatibility with l'\GSLR would open up to the possibility of using a large number of

stations. which \\'ould not only increase the scientific potential. but also rcouce the st ation and

10 Outlook

III addit ion 10 the test S 01 interior SI ructure or I he '.jOO]],

costs,

('I' (O]}"I raillt s n',;n!t [rOll I Ilion'

15

10: NASA's Next Generation Satellite Laser Ranging (:'-JGSLR) systelll IS

laser range to the Lunar Reconnaissance Orbiter (LRO) orbiting the moon uscd lu

aid ill 1 he sPe;rch for a solid inllPr core, The second-degree tielal lunar Love 1lI1111iwrs an' d('I(,(I('d

L LH .. ao; well as lheir phase shifts, From past measurements, a fluid core 01 ~ :2()~~ ul the '-loon'::; radius i::; indicated, A lunar tidal dissipC1tioll of Q 30 ha.'; becll rC[lllrt('d cO !:d\'(' ;l

weak dependence on tidal Evidence for the oblateness of the llm,;r lluid-cOl('/suiJt!­mantle boundary may be reflected in a century-scale polar wobble frequencv, The lunar \'(']'t ind and horizontal elastic tidal displacement Love numbers h2 and 12 are known to no better theW

of their valnes, and the lunar dissipation factor Q and the gravitational potential tidal Lon'

number k2 no better than 11 %, These values have been inverted jointly for structure and densitv of the core [29, 28], implying a liquid core and regions of partial melt in the lunar mantle,

Lunar interior studies have arguably suffered the most from the clustering of the Apollo arrays on the central portion of the moon, Placing retroreflectors far from the Apollo armys, at (\ pole

or a limb, would improve the measurernents by up to a factor of 4 at the salllP level of precision as is performed [33]

The advancement of active laser systems also opens up the beyond the \loon, Laser ranging to ]\Iars can be used to measure

delay as '-lars passes behind the Sun relative to the Earth, \Vith 1 em precisioll tiJ(' 1'1''\ parameter ~, em] be measured to abOUt lO-G ten times better than the Cassilli l'l'suit (jCi '1'11('

Principle ion efleCl is abOUt 100 times for Eelrth-\Llrs miJih than for the iUllm orbit. \\'ith 1 e1l1 the ,\ordtn'clt pmCll!l('l 1/

Gill iJ(' measured tu betwecln (j x lO-I, dlld :2 x 10"" for obscn'<ltioll:-i jH'IW('('1l ":iI' ItLd

ten years Combined with the tillle measurements this leads to a IllC'nSlll'l'111c'lIl "I' 1'1) paralileter to the Ic"veL '-lars can also be used in combinH tilln h hillel" 1'21111).1

to get more accurate limits on the time variation of thel const"I]!, The of :\Iars itself is known w meters in plane. but hundreds of llIet e]'s

would get an order of better estimate, for illt Better measurements of Mars' rotational could provide estimat es of the sizl'

of its core ?vIars' elastic tidal Love number is to be less than 10 em, within rC'dcb

16

of laser There is also an unexplained low value of Q, inferred froIll t lIe ~(,c\llm decay ,)i Phubo,,' orbit thaI a cOllstraint to the present tlwrllwl snlte of the :\!cus illlnim 10 L:.~"I

10 Pllot)()s would 80]nl Ihis I ll\'sl ery. LtH remaills OIl(' of tIle be"t tests of in tIl(' weak field and to COllllllll( I,) 1)(

a too] for IllClIlY years to COllW. Four of the five lunar retrurefleclOrs relll:\] \'isihk t(Jd:n dlH!

continue to produce valuable data. Advances in ranging technology has finally reached I he point where the precision of the data is being limited by the physical characteristics of the lunar mrm's The natural next step in LLR is to place new retrorefiectors and/or laser transponders on the :\10011 at sites far from the Apollo arrays that have a high enough return rate to take advantage of the SLR network of ground stations. vVith the retroreflectors and transponder technology :waila ble today. these new instruments could easily support laser ranging and advances in ground statioll technology for another productive 40 years of LLR

11 Acknowledgements

I thank Pete Bender. Ken Nordtvedt, and Tom Murphy for invaluable discussions and COIllllH'llts

on this review. The LUNAR consortium (http://lunaLcolorado.edu). headq\l:\rtercd III tlte l'lli-

or Colorado. is funded t.he :.J ASA Lunar Science lnst itute (via ('()()jJcr<l1 in' 1('1 It

:\:\A(91)B:)OA) to iuvest c concepts for rlst.rophvsical obst'rvutorIl';'; on t.lll' \IU()11

References

Adelberger. K G., Heckel, R R. and Nelson, A. K, "Tests of the Gravitatiollal Law". Annu. Rev. Nucl. PaTL SCi .. 53. 77, (December 2003).

Anderson. J. D .. Gross. M .. Nordtvedt. K L, and Turyshev. S. G .. "The SolM Test of till'

Equivalence Principle". Astmphys. L 459, 365. (1996).

[3] Arnold, David A., Cmss section of the APOLLO LunaT TetmTefiectoT aTTa)jS, (2005).

[4] BaeJ3ler, S., Heckel, R R, Adelberger, K G., Gundlach, J. R. Schmidt. R K, "Improved Test of the Equivalence Principle for Gravitational Lett.. 83(181. 3585. (November 1999).

l' .. and SwansUlL . Phljs. HCl'.

Battat. J. 13. R.. T \V .. Adellwrger. E. C. C ]) \Ic:\li lall. R. ,L \1ichelspn. F L .. :\ordt\'l'dt. K. Orin. A. E .. Stubbs. (' \\ illlli S\\,llIS{)I,

H. E .. "The Poillt LUliar Opend iUI: i .\]>OLLO) Years uf :\Iillillwter-Precisioll \ leIlSUH'Illf'llts of the Eart Ii-:\ IOOll I) iJ IJ .L I fI) II. SO, Pac .. 121 . 29. 20(9)

Balta!. James R R. ChandleI'. John F .. anel Stubbs. Christopher \\' .. "Test for L,lr('lllZ

Violation: Const raints on Stanclard-:\Iodel Extellsion Parameters via LU1lar Laser ReI. Lett .. 99(21). 2[110:). (December 200/). [07lCL070:2\'!:.

'7: Bellder. P. L .. (lurrie. I). C; .. Ponlrlley. S. K" ~\lle~·. C', ().. l)icke. fL H. \\'ilkili:--;Oll. I). r. Eckhardt, D. I-I.. FaIleI'. J. E.. Kaula. W. :\L '\lulhollancL J. D .. Plotkill. II. ll. E, and J. G., "The Lunar Laser Ranging : Accuul1t' ranges llilH'

a large improvement in the lunar orbit and new selenophysical information". SCi(~n(;{.

182(4109),229, (October 1973),

Bertoni. R. less. L, and Tortora. P .. "A test of general Cassini Nl1tILTC. 425. :371. 2(03).

17

using radio links wit h the

o Bntot t i. Brullo. Ciuiolilli.

\lcasurellH'llt of de Sit tel' 106:2, (\larch 19S7).

ra\(' for l\lllar

Bills, Bruce G .. :'-Jeumann. A., Smit.h, David E .. and Zuber. \121ri;1 T. "IlllPJ'()\('t!

estimat.e of tidal dissipation within Mars from MOLA observations of the shadow of PlIobos" J. Geophys. Res .. 110, E07004, (2005).

[11] Currie, Douglas, DellAgnello, Simone. and Monache. Giovanni Delle. "Lunar L21ser Retrorefiector array for the 21st Century", in Ryan, S .. ed., Pmceedings of tlu AdU!LfII:f:d Mau,/ Optical and Space Surveillance Technologies Conference, (2009).

[12] Damour, T., and Polyakov, A. l\L "The string dilaton and least coupling principle". l'v'IU/ Phys. B, 423, 532, (1994),

Damour, 13(J 1

the equivillence principle: 1996).

and how?". Cluss. (ju,(wl. (,'1111,

: 1 ,1' Damour. Thibault. mid :\orclt vedl, l\:elllH't Ii. "TClisor-.scaLlr relaxation t,oward general relat l'hys, 1111'. j) 48(1'1) 313() (Oc\uil('! i~)(j:l)

Darnour. Thibault. and Vokrouhlick, David. Hev. D. 53. 4177. (April 19(6).

DamouL Thibault, and Vokrouhlicky, David. using the lunar orbit", Phys. Rev. D, 53(12), 67'10.

din'cli()l1~

Cedric, DvalL Gia. and Gabadadze. "Accelerated ulliwl'se from

leaking to extra dimensions", Ph!)s. Rev. D, 65(:1), 0440:23, (January 2002).

i18] Deffayet, Cedric, Dvali. Gia, Gabadadze, Gregory, and Vainshtein, Arkady. continuity in graviton mass versus perturbative discontinuity", Ph!)s, Rev. D. 65(4) 044026. (January 2002),

, J .. McGarry, J .. Dabney, P .. and Interplanetary Laser Tnl.11::ipOlldcr" ill 11 ih Jllicl'lw.tIlJIW.l

John ,J .. "

time transfer", J. laser t n\llSpOllclers for

(:200:2).

~kGarrY. Jan F "SLR2000: clUe! 11UtOllOliiOllS Degnan. John J.. and pilotoelect ron satellite 3218{l). 6:3. (1997).

a1 kilohertz nttes", Proc. SPJE /II.!. S'(J(' Op!.

et ,d .. "SII11U~ of till' J\F:\ SII\(,llite;]ll1liil' 1",;(']" J'ilw:;illg Cllill'l"\"l'I/:ill;()I:

1Il 16th Inl.fTnatwllai fAlSI 'I' Ran(jilig Workshop.

Dickey, J, 0., Bender. P. L.. Faller. ,J, E" X X, Ricklefs, R. L.. Hies . .1. G .. SIH']us. p, J" VeilleL c., vVhippie, A. L., Wiant, J, R., Williams, J, G" and Yoder. C. F"LUlWl

Laser Ranging: A Continuing Legacy of the Apollo Program", Science, 265(5171). :182, (July 1994) .

Flasar. F. \IichaeL and Birch, Francis, of Core Formation: A Correction". J. Res" 78(26), 6Hll. (September

18

Follmer. v\' 'I! Yoder. C. F .. YWlIl. D. '\ .. Stiilldi_~l: F. \1. illid Pn'sloll. H .. \·llli('l;m ::)(1'UCI ure and ::)('c\solli"d \I",,;s R"distribUI lOll or \Ims (rum R'Hiio S'c/enee. 278( S3·jcj), 1749. 1 D~)7)

Ga.rcia-Berro, E., bel'll. J. and KH!wshin. Y. A .. "i\strollolllicallllU1S1lJ'E'Il](']J'C' 1111d (,Oil:'; - 11..;

on the of fundamental constant,,", Astl'on. Reu .. 14(:2). 1 U. ("limi] :2007).

Heiken, Grant H., Vaniman, David T .. and French. Bevan '\1.. LUJWT SOl!n;eboOA:: A CSI:I'S

Gllide to the Moon. (Cambridge Press. 1991).

[28] Khan, A., and Mosegaard, K., "Further constraints on the deep lunar interior", Geophys. Res.

Lett" 32, L22203, (2005),

Khan, A, '\ilosegaard, K" Williams, J, G., and Lognonne, P .. "Does the '\loon possess it

molten core? Probing the deep lunar imerior results from LLR and Lunar Prospector" I Ceophys. Res., 109, E09007, (2m)!!).

i:30j Konopliv, Alex S .. Yoder. Chal'l(,,, F .. Standish. E. Ymlll. Del \Villiam L., "A global solution for the \lan; static and seasonal Phobos and Deirnos mas::;es, and \IMs learns, 182(l), 2:),

,t II( I :\LHS ()l'i('lltatioll.

:200() )

::Hi LcHlgseth, Marcu'=1 G" and Keihllll'. ::)t.ephell ,1.. "Ill-situ llleaSUH'lllcnlS of IUliar i)(-,11 11,)\\' ill Proceedings the Sml'tet·Amencan Oil tht: COSrnJ)()II~rrllstrl) Ih, JI{)()n UII,!

Plane/.s, p. :28:) .

. J.. T .. H..Zeliar. Torn'lIc('. \1 .. llorval h, J. C'lmk(. C p,]t\(,!~()lI ])

Cheek, J" Ricklefs, R" \Iallanli1. ,\" '\olL C .. Pearl II Jail , \1.. l(lIc! '\(,Wlldll);, C. ",\CSLJ{ Sharing Eye-safe Kilohertz SLR with Transpollder , ill 16th interno[wlI.o/ Lllst'!

Ranging Wor'kshop, (2008).

[33] rvIerkowitz, Stephen M., Dabney, Philip W" Livas, Jeffrey G, McGarry, Jan F., :'\eumanll. Gregory A., and Zagwodzki, Thomas W" "Laser Ranging for GravitationaL LunaL and Plan­etary Science". Int, J. Mod, Phys. D, 16(12a), 2151. (December 2(07). [arXiv:0712.3539v I].

\liiller. J, :\ordtvedt. K .. Schnelder. '\1.. and Vokl'Ouldick. l).. l)(,\('lliliwil iOll ()~

Relativistic from LLR", in 11th inItT!lu/wTlui WorkshojJ Oil Luser RUIi!jIlUj.' iDl)'Si

'\Iuller. Jurgen, and Biskupek. Lilialle, "Variatiolls of the lo.8er ranging da.ta·' Class. Q'uanL Grav .. 24(17). ·iS33.

':30i \liiller. :'\ordtvedt. Kenlleth, and Vokrouhlick. Davie!, "lmpro\'('d ()llSlntilll Oil lhi

,dphcl 1 PP:'\ p<tr21111eter frolll iUlli\l' Illot lOll" Ph!}s. ReI'. fJ. 54, H.S927. (.\'u\'(>llli)('r j<)()(i).

37 \liillel.

Reiutiut8lu;

T. \\'.. C. \\'" and Swanson, H. E .. in 15th Inl,ernational Laser

ill Las!'!'s. Clock., an.d f)ruq-Fui' ('oil/wi: 1{)1I (;/

vol. 349. p.lS7. (:200K)

E. G .. Battat. J. B.. C. D., '\Iiclwl>iell. E. L. :-illd)l)~

"Absolute Calibration of LLR Rd!('Cl0Y' lk,dlh ::)\dl\h

(2000).

1'. \V.. , E. G .. Battat. J. 13. R.. C. D .. Leblallc, P .. ~Iichelsen. E. L .. :'\ordtvedt. K .. Orin, A. E.. J. D .. Stubbs, C. vv· .. Swansoll, H. E .. and \Villiams, E .. ''The Point Observatory Lunar Operation:

11)

IllstruIllellt ])(~,scriptioJl Hlld First Detectiolls". Pillil. As/roIl .. ')'{JI·. FlU .. 120lX(i3). :20. (.Ltlilldl\· :200X) 07100x'JO

Jr. T \Y .. "Luum H,I (February 20(9).

~Iurphy. Jr.. T. \,\' .. :"iordtvedt. K., and Turyshev. S. G .. "Gravitolllagll('tic lnfhWlI(( ul Gyroscopes and on the Lunar Orbit". Phys. R.ei'. Lett.. 98(7). 071102. (2()(17) /070:202".

:\Iurphy, .If., Thomas W .. Strasburg . .1. D .. Stubbs. C. W .. Adelberger. E. G .. AIlgle . .1 .. Nordtvedt. K., Williams, .1. G .. Dickey, J. 0 .. and Gillespie, B .. ''The Apclclw Poillt Ol.Jscr­vatory Lunar Laser-Ranging Operation (Apollo)", in 12th International Workshop on Laser Ranging, (2000).

:"iesseris, S .. and Perivolaropoulos, L .. "Limits of extended quintessence". Phys. ReI!. LJ. 75 023517. (2007).

~\'ordtveclt K. llxCi. (June 196x).

Relali\'itv with Laser Ranging to the :\[OOll"

:"iorcltveclt. Ken. "Probillg to the secolld posl-:"i('wtOlliclll order ,mel to OIle part ill 10

to the 7th using the spin axis of tile SUll". AsLmpliys. J .. 320. 871. (Sept('lillwr 1(87).

:\'ordtvedt. Ken. "G-clot/G alld ,I cosmological m:celendioll of Rei'. Lett... 65. 95;) 1(90).

·17 Sordtwcl1. Kellllet h. "Eqllivah'llCl' Prillciple for :\Ia~sive Bodie". l. Hel .. 16915). 1014. 196x)

:"iorcltveclt. Kenneth. "Equivalence Prillciple for '\Iassiw Bodie;:;. II. Theun··. 169(5), 1017, (May 1968).

J )III}'.

HI'I.

[49] ;.Jordtvedt, Kenneth, "Lunar laser ranging and laboratory Eotvos-type experiments". Ph!!.). Rev. D. 37(4), 1070, (February 1988).

:"iordtvedt. Kenneth. "The Relativistic Orbit Observables in Lunar Laser Ranging". !WI'Il,.

114(1).51. (1995).

151] :"iordtvedt. Kenlleth. "30 years of lunar laser wllgillg cilld the Cmu .. 16( . AlO1. 199D).

Sordtvedt. Kenneth. "d G \ l1ll'ilS1.Jrement enid the [iOllS" ('Ius.'!. qUllnt. Gml .. 20( 11). L117. 200:3)

:l3! :"iord\vedt .. Jr. Kl'llllC'th. "l'ost-S"wtolliall Cr;\\itatio]]ld Ef!('cts ill LUllill' L1SlT Hl'llglllg niT. f) 7.2317. (;\pril 11)7:1\

':l·1: :"iordtwdt. Jr. Kellneth. and Will. Clifford \1.. "Collsen'dtioll LeIW'; and l'rl'ielTcd FtIIIH's

II. Experillle]]tal Evidellce to Rule Out Prd'crred-Fnlll]C Theories uI J.. 177. 775. ID72).

Pearlmall. \1. R.. Degnan. J . .1 .. and Bm-;worth. J. \1.. "The International Laser Service". Adv~ Res .. 30(2). 135. 20(2).

20

[56] Samain, E., Mangin, J.F., Veillet. c., Torre, J.J\I., Fridelance. P .. Chabaudie. J.E .. D., Glentzlin, M., Van, J. Pham, Furia, M .. Journet, A., and Vigouroux, G .. "J\Iillillletric Lunar Laser Ranging at OCA (Observatoire de la Cte d'Azur)", Astmn. Astmphys. SeT .. 130. 235. (June 1998).

Schlamminger. S .. Choi. K.-Y .. Wagner. T. A .. Gundlach. J. H .. and . E. C. "TI'~l

of the C~lIlg <l H..otnt Torsion B,dall("(;·. I'll/Fl. NIl'. LII/ 1001 I; (H I j 0 I. (2008)

Sereno. J\Iauro. and .Jetzer. Philippe. "Sol,u' alld sldLI!" S\'stClll \('sts of Ill<- I ('Oli-

stant Rev. D. 73(6). 06:3()Ol. C20(6).

Shapiro. Irwin 1.. "Fourth Test of Celleral Relat bel' 19(4).

. Phi/s. Rer. J~etl.. 13(:2()) 7:-<:}. (1)("(1111-

GO Shapiro. Irwin 1.. COllllseilll(ln. C]wrles C . ,md Killg. Robert VV .. "Vl'rific2l1 iOll uf t hi- I'rilillpil of for J\lassive Bodills··. Ph)!). ReI'. Lett. 36(11). 555. lCJ7(i)

Shapiro, Irwin I., and Reasenberg. Robert D. Private COrllmunicatiull.

Shelus, P.J., "MLRS: A Lunar! Artificial Satellite Laser Ranging Facility at the J\lcDollalcl Observatory", IEEE Tmns. Geoscience and Remote Sensing, GE-23(4), 385, (July 1(85).

[63] Smith, David E., Zuber. J'vIaria T., Sun. Xiaoli, ::-l"eumann, Gregory A., Cavanaugh. John F .. McGarry, Jan F .. and Zagwodzki. Thomas VV .. 'Two-Way Laser Lillk over Interplillletnl\ Distance". SCience. 311 .53. (JalluCll'V 20(6).

Soffe!' \lichael. Klioller. J\fiiller. and Biskupck. Liliill]('. "Crmil()lllilgl:« i.~I::

and lunar laser . Pltys. ReT. D. 78(2). (]240:33. :200K)

Turyshev. Slava G .. and \Villiams. J:lllles C .. "Space-Based Tests Of \\'iI1, LdSl1

Ranging". into J. kiod. Pity!!. D. 16(l:2A). 2165. (December [g;r-qcjOEii 10DS\):

S],1\'" C. \\"illi:ll11s . .I:lll]('S C .. SL:w \!ieh:wl. .\llderSllll .loll!: J) .11 1--:('lilll'll: L. ~ordtv('dl. alld .Jr. TlluIllilS \\'. \!urp!t\·. "La.s(']" f{llIlglllg to tile \Iu(J11. \Ims :\lld The .2U{)4 :VASA/JPL vVolksl/ojJ Oil I'1i/r'lcs f'/O{{(/UJij (:2Ull!;

Jean-Philippe. "The fundamental COllstants and their variation: obst'l"vatiuwd illlCll1l('­oretical status". Rev. Mod. Phys .. 75, 403. (2003).

[68] WilL C. M .. Theory and 1993).

in Gravdal;ional Physics, Pre;:;,;.

71

Will, Clifford 1\1., and ::-l"ordtvedt. Jr., Kenneth. "Conservation Laws and Preferred Frallies III

Relativistic . 1. Preferred-Frame Theories and an Extended PP::-l" Fornlil1isllI" Astr'J­

J .. 177. 757.

vVilliams. J. G .. Dicke. R. H .. Bender. P. L.. Alley. C. 0 .. Carter. W. E. Currie. f) (;

Eckhardt. D. H" Faller. J. E .. Kaula. \V. M .. l'Ilulhollancl. J. D .. Plotkin. H. II 1'011111]('\

S. K.. Sinclair. W. S .. Slade. \1. A .. and \Yilkill:iOIi. I). T "~e\\' Test of 1 from LllllCl;- La;;er I'lu/s. Ihc /JIt. :Hi. :)51. (\lill'c!t ID7ti)

Willialils . .J. (; '\e\\"l1i11:. X. X. ;llld I J U. ·H.I'icll i 1 \ pdnHlit'l llll:('{; 1]\!: i:

1<:1:-)(,1' Pllys. HI'I'. j) 53. Ii 7:l0. I .J 1111(" I ()D(j i

21

7:2 \Villia IllS , JamE's C;" Dall' II., Slm'a G" dIlel [{;ddifL J. Todd,'LIIII;':

Lmwr Scil'I1c('" ill Gmilil', .J , I)illilil, .1. \1.. :\1I1L C. dlld !"'drillli!!: \j (,d, fniel'Twtwnu/ IA]'s!'! RIJII(j!luj It·u/j,'//I)/J. Il. I.),). (:2(J():»). Y,l-'ll OlllU():)

\rVilliams, James G" Boggs, Dille IL Yoder. Charles F ' H.iltclifL J. Todd, <lilt! Uick(,\, .Je;!]] U.

"Lunar rotiltional dissipation in solid hodv and molten core". J. (;eophljs, He'., 106(EII' :2793:). (20(H),

\Villiallls, James G" Turvslwv, Slav;) C;" and Dale H" "Progress ill tUllill Llsel

Tests of Helativistic Pilys. Hill. LeU.. 93(26), 261101. (2lH)l),

\rVilliams, .James G., Turyshev. Slava G" and Dale H" "Lunar Las(']' HaIlging 1'(':o1.S

of the Equivalence Principle with the Earth and l\Ioon", Int, I iviod. Phys, D, 18(7), lUD,

(July 2009). [gr-qc/0507083j.

Williams, James G" Turyshev, Slava G" Boggs. Dale H., and Ratcliff, J, Todd, "Lunar laser ranging science: Gravitational physics and lunar interior and , Adv. Res.. 37(1),67, (2006). [gr-qc/0412049].

\rVilliams, James G" Of Gravitational

, S]cIV,1 G ' illid :\1 . .lr. TIIOlllitS \\' "Illlplmllig LUi] ('.SI,

Inl. j A/od. Pilys. 1) 13(:)), :1li7. (2()OI). gr-C[l llllltJ21

Zuber. Maria T" "Seconds of Dat,) Years of . PhotoniCS :16. (\121\

22