Ιgnazio Ciufolini- A heritage of John Archibald Wheeler: the accurate measurement of dragging of...

8/3/2019 gnazio Ciufolini- A heritage of John Archibald Wheeler: the accurate measurement of dragging of inertial frames using the LAGEOS satellites and the forthcoming LARES satellite

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A herita e of John Archibald Wheeler: theA herita e of John Archibald Wheeler: the

accurate measurement of dragging of inertialaccurate measurement of dragging of inertial

frames using the LAGEOS satellites and theframes using the LAGEOS satellites and the

or com ng sa e eor com ng sa e e

e ca on o o n rc a ee er e ca on o o n rc a ee er an r ean r eintroduction on frameintroduction on frame--draggingdragging

a n exper men a e or s o measure ramea n exper men a e or s o measure rame-- ragg ngragg ng

brief description of Lunar Laser Ranging testbrief description of Lunar Laser Ranging test

Satellite laser ranging measurements of theSatellite laser ranging measurements of the

--

LARES (LARES (LAserLAser RElativityRElativity Satellite)Satellite)

gnazio Ciufolini (Univ. Lecce): Virginia 7-7-2008


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the accurate measurement of dragging of inertialthe accurate measurement of dragging of inertial

frames using the LAGEOS satellites andframes using the LAGEOS satellites and

e or com ng sa e ee or com ng sa e e

WHEELER ONE OF THE MASTERS OF PHYSICSWHEELER ONE OF THE MASTERS OF PHYSICS

REINASSANCE OF GENERAL RELATIVITYREINASSANCE OF GENERAL RELATIVITY

If today we are here we also owe this to Johnny, he was theIf today we are here we also owe this to Johnny, he was thesc ent c at er, gran at er an gransc ent c at er, gran at er an gran --gran at er ogran at er o

many of us!many of us!

gnazio Ciufolini (Univ. Salento): Virginia 7.7.2008


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Johns office, Univ. Texas at Austin, nearly 20 years ago


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ASTROPHYSICAL

IS DEDICATED,SINCE 2006TO JOHNNY


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I.C. & E.Pavlis,

,

21 October, 2004.

I.C., E.Pavlis and R.Peron,, New

2006.

I.C., Dragging of Inertial

, ,

September, 2007.

I.C., Lunar Laser Ranging,

Gravitomagnentism by Spin

.

I.C. A. Paolozzi E.PavlisR.Matzner, et al. in General

Relativit and John Archibald

Wheeler(Springer, 2008).


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DRAGGINGDRAGGING OFOF INERTIALINERTIAL FRAMESFRAMES((FRAMEFRAME--DRAGGINGDRAGGINGas Einstein named it inas Einstein named it in

frames are dragged byframes are dragged bymassmass--energy currents:energy currents:

GG = = TT ==

= [(= [( +p)+p) uu uu + p+ p Braginsky, Caves and Thorne 1977Thorne 1986

gg

Jantsen et al. 1992-97, 2001

I.C. 1994-2001

energy astrophysicsenergy astrophysics

(Kerr metric)(Kerr metric)


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GRAVITOMAGNETISM


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GravitomagnetismGravitomagnetism defined withoutdefined without

approximations by the Riemann tensor in aapproximations by the Riemann tensor in alocal Fermi frame.local Fermi frame.

MatteMatte--19531953

By exp c tBy exp c t spacet mespacet me nvar ants u t w t t envar ants u t w t t eRiemann tensor:Riemann tensor:

I.C. 1994I.C. 1994I.C. andI.C. and WheelerWheeler 1995:1995:

oror ee errerr me r cme r c:: eea sa s RR

srsrnn RR

abmnabmn = 1536= 1536 JJ M cosM cosq (q (rr55rr--66 -- rr33rr--55 ++ 3/163/16r r rr--44))

In weakIn weak--field and slowfield and slow--motion:motion:

* =* = 77 J =J = aaMM = angular momentum= angular momentum


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Lunar Laser Ranging has been and is a basic tool for testing

fundamental physics, it has provided:

Very accurate test of the weak equivalence principle

effect)

ccura e measuremen o os ew on anParametrized) parameters

Limits on G-dot

accuracy of about 0.6 percent

, . ., , . ., , . . . . .Williams, J.G., Newhall, X.X., and Dickey, J.O. Phys. Rev(1996).

For a discussion on frame-dragging, Lense-Thirring effect and geodetic precession,

see: OConnell, R.F. A Note on Frame Dragging. Class. Quant. Grav. (2005) and Proc.of Course CLXVIII of the International School of Physics "Enrico Fermi", Varenna, Italy,2007, ed. E. Arimondo, W. Ertmer and W. Schleich, (2008).


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Has Lunar Laser Ranging measured the gravitomagnetic

field by spin (Lense-Thirring effect) or not?.Debate:

Murphy, T.W. Jr., Nordtvedt, K. $\&$ Turyshev, S.G. Gravitomagnetic Influence onGyroscopes and on the Lunar Orbit. Phys. Rev. Lett. 98, 071102--1-4 (2007).

Kopeikin, S.M. Comment on ''The gravitomagnetic influence on gyroscopesAnd on the lunar orbit". Phys. Rev. Lett. 98 229001 (2007).

Murphy, T.W. Jr., Nordtvedt, K. $\&$ Turyshev, S.G. A Reply to theComment by Sergei M. Kopeikin. Phys. Rev. Lett. 98, 229002 (2007).

In:

I.C. Gravitoma netism, Frame-Dra in and Lunar LaserRanging. ArXiv:0704.3338v2 [gr-qc] 10 May 2007; );

I.C.and Pavlis E. Proc. of 15th International LaserRanging Workshop, Camberra, Australia, October 16-20, 2006 and

-. . , ,

It is proven, using two different methods, that LLR measures frameragg ng, n e sense o geo e c precess on, u rame-dragging by spin, in the sense of Lense-Thirring effect. One method

substantially zero on the Moon orbit near the ecliptic plane.


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. .- ys. ev. e ., :

Use the NODES of twoLAGEOS satellites.

A. ZICHICHI:

IL TEMPO, JUNE 1985


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Satellite Laser RangingSatellite Laser Ranging


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l=3, m=1


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IC, PRL 1986:

nodes of two

laser-ranged

measure the

Lense-Thirring

e ec


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CONCEPT OF THE LAGEOS III / LARES EXPERIMENT


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MAIN COLLABORATIONLARESI.C.

University of Lecce and INFNA. Paolozzi

Sa ienza Universit of Roma

and INFN-

E. Pavlis

R. Matzner

University of Texas atAustinD. Rubincam

-


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Lageos II: 1992Lageos II: 1992However, NO LAGEOSsatellite with supplementary

has ever been launched.

Nevertheless, LAGEOS II

.


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Anal sis of the orbital

perturbations affecting

e no es oLAGEOS-t e

satellites

(1) Use two LAGEOS

satellites with

supp emen ary

inclinations

OR:


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Use n satellites of

LAGEOS-type

n-1 even zonal

harmonics: J2, J4, an e ense- rr ng

effect


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EGM96 Model and its uncertaintiesEGM96 Model and its uncertaintiesEvenEven valuevalue UncerUncer UncerUncer-- UncerUncer-- UncerUncer--zonalszonals

--taintytainty

taintytainty taintytainty taintytainty

mm nn node Inode I IIII IIII

----

0.484160.48416. x. x1010 LTLT LTLT .. wwLTLT

3737 xx 1010--0303

4040 0.1 x 100.1 x 10--

0909

1.51.5 WWLTLT 0.50.5 WWL TL T 2.12.1 wwL TL T..

386 x386 x1010--0606

6060 --0.149950.14995

0.15x100.15x10--0909

0.60.6 WWL TL T 0.90.9 WWL TL T 0.310.31 wwL TL T


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= .

I.C., NC A, 1996


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-

J. Ries et al. 2003 (1999),E. Pavlis 2002 (2000)


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- -


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EIGENEIGEN--GRACE02S Model andGRACE02S Model andUncertaintiesUncertainties

zonals

lm 10-6

on node I

on

node II

on perigee II

20 -484.16519788 0.53 10-10 1.59 WL T 2.86 W L T 1.17 w LT

40 0.53999294 0.39 10-11 0.058 WLT 0.02 WL T 0.082 w L T

60 -.14993038 0.20 10-11 0.0076 W 0.012 W 0.0041 w

80 0.04948789 0.15 10-11 0.00045 WL T 0.0021 W L T 0.0051 w L T

10,0 0.05332122 0.21 10-11 0.00042 W L T 0.00074 W L T 0.0023 w L T


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Using EIGENUsing EIGEN--GRACE02S:GRACE02S:2020

dWdWII ,dW,dWIIII ((orbital angular momentum vector)orbital angular momentum vector)

dWdWII = K= K22 xx ddCC2020 ++ KK2n2n xx ddCC2n,02n,0 ++mm (31 mas/yr)(31 mas/yr)

dWdWIIII= K= K22 xx ddCC2020 ++ KK2n2n xx ddCC2n,02n,0 ++mm (31.5 mas/yr)(31.5 mas/yr)

not dependent onnot dependent on ddCC2020--

TOTAL ERROR FROM EVEN ZONALSTOTAL ERROR FROM EVEN ZONALS rr C40 =C40 =

--

I.C. PRL 1986 I.C. IJMP A 1989I.C. PRL 1986 I.C. IJMP A 1989I.C. NC A, 1996;I.C. NC A, 1996; I.C. Proc. I SIGRAV School, Frascati 2002, IOP.I.C. Proc. I SIGRAV School, Frascati 2002, IOP.


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ICuovo C mento A

1996


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Observed value of-

The combination of the

.

Observed value of

Lense-Thirring effect = 99%

prediction. Fit of linear trend

p us nown requenc es

Prediction = 48.2 mas/yr

I.C. & E.Pavlis,

,

431, 958, 2004.


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Static gravitational field (using the EIGENStatic gravitational field (using the EIGEN--GRACE02SGRACE02S

uncertainties):uncertainties):3 % to 4 %3 % to 4 % (the EIGEN(the EIGEN--GRACE02S uncertainties includeGRACE02S uncertainties includesys ema c errors orsys ema c errors or oo ou ng eou ng euncertainty published with EIGENuncertainty published with EIGEN--GRACE02S.GRACE02S.

2 %2 %

--2 %2 % to 3%to 3% [most of the modeling errors due to the non[most of the modeling errors due to the non--ravitational erturbations are on the eri ee inravitational erturbations are on the eri ee in

particular due the Yarkowski effect on the perigee, butparticular due the Yarkowski effect on the perigee, butwith in this combination we only used the nodes]with in this combination we only used the nodes]

error ue o ran om an s oc as c errors an o er errorserror ue o ran om an s oc as c errors an o er errors

a oua ou

.C., E. Pavlis and R. Peron, New Astronomy (2006).

I.C. and E. Pavlis, New Astronomy (2005).


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The 2004 analysis with EIGENGRACE02S:Does not use the perigee (i.e., no problems to assess the

-

In the error anal sis we have summed u the absolute

values of the errors due to each individual even zonalarmon c uncer a n y: us we no use e corre a on

an how small amon the even zonal harmonic coefficients

of GRACE data only and did NOT use any LAGEOS data

The even zonal harmonics obtained from GRACE are

independent of the Lense-Thirring effect (the acceleration

,zonals is orthogonal to the acceleration generated by the

Lense-Thirring effect).


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Potentially weak points of the 2004 analysis: e ana ys s was per orme w t t e or ta

Performing it with a different orbital estimator ?

The 2004 anal sis was erfomed with EIGENGRACE02S

but what happens if we change the gravity field model

an e correspon ng va ue o e even zona armon cs

(independent of GEODYN)

Let us use different gravity field models obtained using

GRACE


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IC (Univ. Lecce), E. Pavlis (Univ Maryland Baltimore County),R. Koenig and Neumayer (GFZ Munich/Potsdam),

. . . ,

R. Matzner (Univ. Texas, Austin)

Using GEODYN (NASA) and EPOS (GFZ)


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NEW 2006-2007 ANALYSIS OF THE

GFZ ORBITAL ESTIMATOREPOS

OLD 2004 ANALYSIS OF THE

LAGEOS ORBITS USING THE*by adding the geodetic

NASA ORBITAL ESTIMATORplane of an Earth satellite

n e or a es ma or.


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Comparison of

Lense-Thirring

usin different

Earth gravity

e mo e s


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LARESLARES

Radius about 18 cmRadius about 18 cm Material Solid sphere of Tungsten alloyMaterial Solid sphere of Tungsten alloy

Eccentricity nearly zeroEccentricity nearly zero Inclination about 70 degreesInclination about 70 degrees

data it will provide a measurement ofdata it will provide a measurement offrameframe--dragging with accuracydragging with accuracy


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LARESLARES

collaboration with Sapienza Universit dicollaboration with Sapienza Universit di, ., . Main contractor Carlo Gavazzi Space.Main contractor Carlo Gavazzi Space. Launched in 2009 using the new EuropeanLaunched in 2009 using the new European

, ,, ,AVIO)AVIO)

es gne y ap enza n vers oma,es gne y ap enza n vers oma,School of Aeros ace En ineerin Prof. AntonioSchool of Aeros ace En ineerin Prof. AntonioPaolozzi)Paolozzi)


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