[PPT] - AND ITS MEASUREMENT AND ITS MEASUREMENT INTRODUCTION INTRODUCTION PowerPoint Presentation

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FRAME FRAME-

DRAGGING

DRAGGING ( (GRAVITOMAGNETISM GRAVITOMAGNETISM) ) AND ITS MEASUREMENT AND ITS MEASUREMENT

INTRODUCTION INTRODUCTION

Frame Frame-

Dragging

Dragging and and Gravitomagnetism Gravitomagnetism

EXPERIMENTS EXPERIMENTS

Past, present and future experimental efforts

Past, present and future experimental efforts to measure frame to measure frame-

dragging

dragging

Measurements using satellite laser ranging

Measurements using satellite laser ranging

The

The 2004 2004-

2006

2006 measurements of the measurements of the Lense Lense-

Thirring

Thirring effect using the effect using the GRACE Earth GRACE Earth’ ’s gravity models s gravity models

Ιgnazio Ciufolini (Univ. Lecce): München 12-7-2006

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DRAGGING DRAGGING OF OF INERTIAL INERTIAL FRAMES FRAMES

( (FRAME

FRAME-

DRAGGING

DRAGGING as Einstein named it in

as Einstein named it in 1913 1913) )

The local inertial frames

The local inertial frames are dragged by mass are dragged by mass-

energy currents

energy currents: : ε ε u uα

α

G Gαβ

αβ

= = χ χ T Tαβ

αβ

= = = = χ χ [( [(ε ε + +p p) ) u uα

α u

uβ

β +

+ p p g gαβ

αβ]

]

It plays a key role in high

It plays a key role in high energy astrophysics energy astrophysics ( (Kerr metric Kerr metric) )

Einstein 1913 Thirring 1918 Braginsky, Caves and Thorne 1977 Thorne 1986 Jantsen et al. 1992-97, 2001 I.C. 1994-2001

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INVARIANT CHARACTERIZATION of INVARIANT CHARACTERIZATION of GRAVITOMAGNETISM GRAVITOMAGNETISM

Gravitomagnetism Gravitomagnetism defined without approximations by the defined without approximations by the Riemann tensor in a local Fermi frame Riemann tensor in a local Fermi frame. .

Matte Matte-

1953

1953

By explicit By explicit spacetime spacetime invariants built with the Riemann tensor invariants built with the Riemann tensor: :

I I. .C C. . 1994 1994 I I. .C C. . and and Wheeler Wheeler 1995 1995: :

for for the the Kerr metric Kerr metric: : ½ ½ e e

a b s r a b s r

R Rs

r s r m n m n

R Ra

b m n a b m n

= = 1536 1536 J M cos J M cosq q ( (r r5

5r

r

6

6

r

r3

3r

r

5

5

+ + 3

3/ /16 16

r r r r

4

4)

) In weak In weak-

field and slow

field and slow-

motion

motion: : * *R R · · R R º º 288 288 ( (J M J M)/ )/r r7

7

cos cosq q + + · · · · · · J J = = a aM M = = angular momentum angular momentum

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Tartaglia, Mashhoon et al. Clock effect

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Spin-Time-Delay and Gravitational Lensing

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TIME TIME-

DELAY DUE TO SPIN

DELAY DUE TO SPIN ∆TGM = ∫ h0i dxi

P1

P2

Around a spinning body: Inside a spinning shell:

In weak-field and slow-motion, the gravitomagnetic

time-delay of a null ray between P1 and P2 is: Thirring 1918, Bass-Pirani 1955, Brill-Cohen 1966, Pfister Lense-Thirring 1918, Kerr 1963

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SPIN SPIN-

TIME

TIME-

DELAY

DELAY

Around a spinning body with angular momentum J, r1 and r2 are the position vectors of P1 and P2 Inside a spinning shell rotating with radius R0, mass M and angular velocity w

Effect of a rotating central mass

n light propagation:

Kostyukovich and Mitjanock 1979 Dymnikova 1982, 1986 Datta and Kapoor 1985 Klioner 1991 Goicoehea et al. 1992 Kopeikin and Mashhoon 2002 ... ...

I.C. and Ricci 2002a (Class. Q. Grav.) I.C. and Ricci 2002b (Class. Q. Grav.) I.C., Kopeikin, Mashhoon and Ricci 2003 (Phys. Lett.A) I.C. And Ricci 2004 (sub. Phys. Rev. Lett.)

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Inside a Inside a spinning spinning mass mass: :

May be as large as a few days for a rotating galaxy and a rotating cluster and years for a supercluster of galaxies

∆T = ! h0i dxi

int

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May be as large as a few days for a cluster of galaxies and years for a supercluster of galaxies

∆T = ! h0i dxi

int int

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Prospects to observe Spin Prospects to observe Spin-

Time

Time-

Delay

Delay

In In systems systems of the

f the type

type of the

f the Gravitational

Gravitational Lens Lens B B0218 0218+ +357 357 – – Biggs et al

Biggs et al. . 1998 1998-

2000

2000

The separation angle between the two images is The separation angle between the two images is 335 335 milliarcsec milliarcsec. . T The observed relative time delay is about he observed relative time delay is about 10.5 10.5 days days. . The present measurement uncertainty in the The present measurement uncertainty in the relative time delay for B relative time delay for B0218+357 0218+357 is about is about 0.4 0.4 days days If If other

ther time

time-

delays

delays can can be modeled accurately be modeled accurately enough enough and and if if the the spin spin-

time

time-

delay

delay, , especially especially of

f

the the external rotating external rotating mass, e mass, e. .g g. . the the external external rotating cluster rotating cluster or

r supercluster

supercluster of

f galaxies

galaxies, , is is large enough large enough, of the , of the order

rder of
f days

days or

r years

years, , then then we might observe we might observe the the spin spin-

time

time-

delay

delay ? ?

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SOME EXPERIMENTAL ATTEMPTS TO SOME EXPERIMENTAL ATTEMPTS TO MEASURE FRAME MEASURE FRAME-

DRAGGING AND

DRAGGING AND GRAVITOMAGNETISM GRAVITOMAGNETISM

1896 1896: : Benedict and Immanuel FRIEDLANDER Benedict and Immanuel FRIEDLANDER ( (torsion balance near a heavy flying torsion balance near a heavy flying-

wheel

wheel) ) 1904 1904: : August FOPPL August FOPPL ( (Earth Earth-

rotation effect on a gyroscope

rotation effect on a gyroscope) ) 1916 1916: : DE SITTER DE SITTER ( (shift of perihelion of Mercury due to Sun rotation shift of perihelion of Mercury due to Sun rotation) ) 1918 1918: : LENSE AND THIRRING LENSE AND THIRRING ( (perturbations of the Moons of solar perturbations of the Moons of solar system planets by the planet angular momentum system planets by the planet angular momentum) ) 1959 1959: : Yilmaz Yilmaz ( (satellites in polar orbit satellites in polar orbit) ) 1976 1976: : Van Patten Van Patten-

Everitt

Everitt ( (two non two non-

passive counter

passive counter-

rotating satellites in polar orbit

rotating satellites in polar orbit) ) 1960 1960: : Schiff Schiff-

Fairbank

Fairbank-

Everitt

Everitt ( (Earth orbiting gyroscopes Earth orbiting gyroscopes) ) 1986 1986: : I I. .C C.: .: USE THE NODES OF TWO LAGEOS SATELLITES USE THE NODES OF TWO LAGEOS SATELLITES ( (two supplementary inclination, passive, laser ranged two supplementary inclination, passive, laser ranged satellites satellites) ) 1988 1988 : : Nordtvedt Nordtvedt ( (Astrophysical evidence from periastron Astrophysical evidence from periastron rate of rate of binary binary pulsar pulsar) ) 1995 1995-

2006

2006: : I I. .C C. . et et al

al. (

. (measurements using measurements using LAGEOS and LAGEOS LAGEOS and LAGEOS-

II

II) ) 1998 1998: : Some Some astrophysical evidence from accretion disks astrophysical evidence from accretion disks of black

f black

holes holes and and neutron stars neutron stars

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GRAVITY PROBE B

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I.C.-Phys.Rev.Lett., 1986: Use the NODES of two LAGEOS satellites.

A. ZICHICHI:

IL TEMPO, JUNE 1985

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John’s office, Univ. Texas at Austin, nearly 20 years ago

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Satellite Laser Satellite Laser Ranging Ranging

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IC, PRL 1986: Use of the nodes of two laser-ranged satellites to measure the Lense-Thirring effect

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CONCEPT OF THE LAGEOS III / LARES EXPERIMENT

SLIDE 24

MAIN COLLABORATION University of Lecce

I.C.

University of Roma “La Sapienza”

A. Paolozzi

INFN of Italy

S. Dell’Agnello

University of Maryland

E. Pavlis
D. Currie

NASA-Goddard

D. Rubincam

University of Texas at Austin

R. Matzner

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Lageos Lageos II II: : 1992 1992

However, NO LAGEOS satellite with supplementary inclination to LAGEOS has ever been launched. Nevertheless, LAGEOS II was launched in 1992.

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IC IJMPA 1989: Analysis of the orbital perturbations affecting the nodes of LAGEOS-type satellites (1) Use two LAGEOS satellites with supplementary inclinations OR:

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Use n satellites of LAGEOS-type to measure the first n-1 even zonal harmonics: J2, J4, … and the Lense-Thirring effect

SLIDE 28

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IC NCA 1996: use the node of LAGEOS and the node of LAGEOS II to measure the Lense-Thirring effect However, are the two nodes enough to measure the Lense-Thirring effect ??

SLIDE 30

EGM EGM-

96

96 GRAVITY MODEL GRAVITY MODEL

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EGM EGM96 96 Model and Model and its uncertainties its uncertainties

0. .11 11 W W

L T L T

0. .06 06 W W

L T L T

0. .31 31x x10 10-

09

09 0. .5262224 5262224 9 9 x x 10 10-

07

07 10 10, ,0 0. .32 32 W W

L T L T

0. .07 07 W W

L T L T

0. .23 23x x10 10-

09

09 0. .4967116 4967116 7 7 x x 10 10-

07

07 80 80 0. .9 9 W W

L T L T

0. .6 6 W W

L T L T

0. .15 15x x10 10-

09

09

0.149957

0.149957 99 99 x x 10 10-

06

06 60 60

0. .5 5 W W

L T L T

1 1. .5 5 W W

LT LT

0. .1 1 x x 10 10-

09

09 0. .5398738 5398738 6 6 x x 10 10-

06

06 40 40

2 2 W W

LT LT

1 1 W W

LT LT

0. .36 36x x10 10-

10

10

0.484165

0.484165 37 37 x x 10 10-

03

03 20 20 Uncer Uncer-

tainty

tainty

n
n

node node II II Uncer Uncer-

tainty

tainty

n
n

node node I I Uncer Uncer-

tainty

tainty in in value value value value Even Even zonals zonals l m l m

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3 3 main unknowns main unknowns: : d d C C20

20 ,

,d d C C40

40 and

and LT LT Needed Needed 3 3 observables

bservables

we only have we only have 2 2: : d W d W

I I

, , d W d W

I I I I

( (

rbital angular momentum vector
rbital angular momentum vector)

)

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EGM EGM96 96 Model and Model and its uncertainties its uncertainties

0. .34 34 w w

L T L T

0. .11 11 W W

L T L T

0. .06 06 W W

L T L T

0. .31 31x x10 10-

09

09

0. .5262224 5262224 9 9 x x 10 10-

07

07

10 10, ,0 0. .78 78 w w

L T L T

0. .32 32 W W

L T L T

0. .07 07 W W

L T L T

0. .23 23x x10 10-

09

09

0. .4967116 4967116 7 7 x x 10 10-

07

07

80 80 0. .31 31 w w

L T L T

0. .9 9 W W

L T L T

0. .6 6 W W

L T L T

0. .15 15x x10 10-

09

09

0.149957

0.149957 99 99 x x 10 10-

06

06

60 60

2 2. .1 1 w w

L T L T

0. .5 5 W W

L T L T

1 1. .5 5 W W

LT LT

0. .1 1 x x 10 10-

09

09

0. .5398738 5398738 6 6 x x 10 10-

06

06

40 40

0. .8 8 w w

LT LT

2 2 W W

LT LT

1 1 W W

LT LT

0. .36 36x x10 10-

10

10

0.484165

0.484165 37 37 x x 10 10-

03

03

20 20 Uncer Uncer-

tainty

tainty

n
n

Perigee Perigee II II Uncer Uncer-

tainty

tainty

n
n

node node II II Uncer Uncer-

tainty

tainty

n
n

node node I I Uncer Uncer-

tainty

tainty in in value value value value Even Even zonals zonals l m l m

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3 3 main unknowns main unknowns: : d d C C20

20 ,

,d d C C40

40 and

and LT LT Needed Needed 3 3 observables

bservables:

: 2 2: : d W d W

I I

, , d W d W

I I I I

( (

rbital angular momentum vector
rbital angular momentum vector)

)

plus plus 1 1: : d w d w

I I I I

( (Runge Runge-

Lenz vector

m ( (57 57 mas mas/ /yr yr) )

m m = = d W d W

I I +

+ c c1

1

d W d W

I I I I

+ + c c2

2

d w d w

I I I I

: :

not dependent not dependent on

n d

d C C20

20 and

and d d C C40

40 (

(m m ∫ ∫ 1 1 in GR in GR) )

TOTAL ERROR FROM EVEN ZONALS

TOTAL ERROR FROM EVEN ZONALS r r C C60 60 = = 13 13% % Lense Lense-

Thirring

Thirring

I.C., PRL 1986; I.C., IJMP-A 1989; I.C., NC-A 1996.

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eII º

0.04

I.C., NC A, 1996

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I.C., et al. 1996-1997 (I.C. 1996). (Class.Q.Grav. ...) Gravity model JGM-3

Obs. period 3.1 years

Result: m > 1 . 1 I.C., Pavlis et al. 1998 (Science) I.C. 2000 (Class.Q.Grav.) Gravity model EGM-96

Obs. period 4 years

Result: m > 1.1

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E. Pavlis 2000-2002, J. Ries et al. 1998-2003

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EIGEN EIGEN-

2

2 MODEL MODEL

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EIGEN-GRACE-S (GFZ 2004)

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EIGEN EIGEN-

GRACE

GRACE02 02S Model and S Model and Uncertainties Uncertainties

0.0023 w L T 0.00074 W L T 0.00042 W L T 0.21 · 10-11 0.05332122 10,0 0.0051 w L T 0.0021 W L T 0.00045 W

L T

0.15 · 10-11 0.04948789 80 0.0041 w L T 0.012 W L T 0.0076 W L T 0.20 · 10-11

.14993038

60 0.082 w L T 0.02 W L T 0.058 W

LT

0.39 · 10-11 0.53999294 40 1.17 w LT 2.86 W L T 1.59 W

L T

0.53 · 10-10

484.16519788

20 Uncertainty

n perigee II

Uncertainty

n

node II Uncertainty

n node I

Uncertainty Value · 10-6 Even zonals lm

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IC Nuovo Cimento A 1996

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Using Using EIGEN EIGEN-

GRACE

GRACE02 02S S: : 2 2 main unknowns main unknowns: : d d C C20

20 and

and LT LT Needed Needed 2 2 observables

bservables:

: d W d W

I I

, , d W d W

I I I I

( (

rbital angular momentum vector
rbital angular momentum vector)

+ K K* * d W d W

I I I I

: :

not dependent not dependent on

n d

d C C20

20 free from

free from non non-

gravitational errors

gravitational errors on the

n the perigee

perigee

TOTAL ERROR FROM EVEN ZONALS TOTAL ERROR FROM EVEN ZONALS r r C C40 40 = = = = 3 3% % to to 4 4 % % Lense Lense-

Thirring

Thirring

I

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

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Observed value of Lense-Thirring effect = 99%

f the general relativistic
prediction. Residuals after

fitting and removing 6 known frequencies General relativistic Prediction = 48.2 mas/yr Observed value of Lense-Thirring effect using The combination of the LAGEOS nodes. RAW residuals. I.C. & E.Pavlis, Letters to NATURE, 431, 958, 2004.

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Post-fit residuals: fit of linear trend only. Post-fit residuals: fit of linear trend plus 6 known frequencies

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Error Error budget budget

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

GRACE

GRACE02 02S S uncertainties uncertainties): ): 3 3 % % to to 4 4 % % ( (the EIGEN the EIGEN-

GRACE

GRACE02 02S S uncertainties uncertainties include include systematic systematic errors errors) ) Time Time dependent gravitational field error dependent gravitational field error: : @ @ 2 2 % % Non Non-

Gravitational perturbations

Gravitational perturbations: : 2 2 % % to to 3 3% % [ [most most of the

f the modeling errors

modeling errors due due to to the non the non-

gravitational perturbations

gravitational perturbations are on the are on the perigee perigee, in , in particular particular due the due the Yarkowski effect Yarkowski effect on the

n the perigee

perigee, , but with but with in in this combination we only used this combination we only used the the nodes nodes] ] TOTAL

TOTAL: : 5

5 % % to to 10 10 % % (

(RSS RSS) )

Ι.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

non-gravitational errors)

In the error analysis we have summed up the absolute

values of the errors due to each individual even zonal harmonic uncertainty: thus we did not use the correlation (anyhow small) among the even zonal harmonic coefficients

The EIGENGRACE02S model was obtained with the use
f 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

f a polar, circular orbit satellite generated by the even

zonals is orthogonal to the acceleration generated by the Lense-Thirring effect).

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Potentially weak points of the 2004 analysis:

The analysis was performed with the NASA orbital

Estimator GEODYN, but what would happen by Performing it with a different orbital estimator ?

The 2004 analysis was perfomed with EIGENGRACE02S

but what happens if we change the gravity field model (and the corresponding value of the even zonal harmonics) ? Answer:

Let us use the GFZ German orbital estimator EPOS

(independent of GEODYN)

Let us use different gravity field models obtained using

GRACE

SLIDE 50

IC (Univ. Lecce), E. Pavlis (Univ Maryland Baltimore County),

R. Koenig (GFZ Potsdam), H. Neumayer
G. Sindoni and A. Paolozzi (Univ. Roma I),
R. Tauraso (Univ. Roma II),
R. Matzner (Univ. Texas, Austin)

Using GEODYN (NASA) and EPOS (GFZ)

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NEW 2006 ANALYSIS OF THE LAGEOS ORBITS USING THE GFZ ORBITAL ESTIMATOR EPOS OLD 2004 ANALYSIS OF THE LAGEOS ORBITS USING THE NASA ORBITAL ESTIMATOR GEODYN *PRELIMINARY SOLUTION: by subtracting the geodetic precession of the orbital plane of an Earth satellite (not present in the first EPOS analyis).

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Comparison of Lense-Thirring effect measured using different Earth gravity field models

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JEM03

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EIGENGRACE02S

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Some conclusions by John Ries of the Center for Space Research

f the University of Texas at Austin.

Introduction: The principal goal was to attempt to validate the earlier published results using a wider variety of GRACE-based gravity models that are now available. This would provide a more confident error assessment. In addition, some sensitivity tests were conducted regarding the modeling of important related effects, and no important limitations were

bserved. The results show that with the latest generation of GRACE models appear to

support a detection of the Lense-Thirring effect at about the 15 percent level. This relativistic test will continue to improve as the the GRACE-based gravity models incorporate more data and the processing methods improve. Method: The analysis followed the procedure outlined in Ciufolini et al. 1998 (for the node-node- perigee combination) and Ciufolini and Pavlis (2004) for the node-node combination. LAGEOS-1 and LAGEOS-2 satellite laser ranging (SLR) data covering the span of October 1992 through April 2006. Several ‘second-generation’ GRACE-based gravity models were tested. These included GGM02S (Tapley et al., 2005), EIGEN-CG02S (Reigber et al., 2005), EIGEN-CG03C (Förste et al., 2005), EIGEN-GL04C (Förste et al., 2006), an unpublished gravity model (JEM04G) from the Jet Propulsion Laboratory based on 626 days of GRACE data (D. Yuan, personal communication, 2006).

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Results. Several points are clear. The LT estimates from the various models are all consistent with the GR prediction to within about 30% maximum or about 17% 1-sigma. The mean across all the models used here agrees with GR to 1%. If we allow some reduction due to averaging across the various solutions, the error is reduced to approximately 7%. Comparing the case where LT was modeled for GGM02S to the case where it was not modeled, the difference is exactly 1.00, indicating that the method is clearly sensitive to the modeling (or lack of modeling) the LT effect. A similar test was conducted regarding the effect of geodesic precession (de Sitter precession). This effect is roughly 50% of the LT effect, and failure to model it leads to a roughly 50% error in the LT

estimate. We also note that removing the rates for J3, J4 and J6 from the analysis has a

negligible effect, whereas failure to map J4 to a consistent epoch is much more significant (12%). Finally, we note that the scatter in the estimates for C40 and C60 are significantly larger than the error assigned to these coefficients. In the case of C40, all coefficients were mapped to the same epoch, yet the scatter is larger than even the most pessimistic error

estimate. When estimating the expected uncertainty in the LT experiment due to these

harmonics, a more pessimistic error estimate should be used rather than those in the gravity model solutions.

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Put constraints on gravitational

theories with torsion propagating in vacuum.

In addition, it was recently pointed
ut by Ciufolini (Ciufolini et al. 2004)

the possibility of testing with WEBER- SAT some recently proposed theories, based on a BRANE-WORLD model, which can explain the DARK ENERGY problem and the

bservations of accelerating

supernovae (Dvali 2004). However, this possibility will imply the need of a much higher altitude orbit for the LASER satellite and therefore a MUCH more expensive mission.

GOALS OF LARES POSSIBLE PERSPECTIVES

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Conclusions Conclusions

Analyze Analyze LAGEOS and LAGEOS II LAGEOS and LAGEOS II with with additional additional future future gravity models gravity models ( (GRACE GRACE). ). Using Using GEODYN, EPOS and UTOPIA GEODYN, EPOS and UTOPIA Launch Launch the LARES satellite the LARES satellite. .