FRAME- -DRAGGING DRAGGING FRAME (GRAVITOMAGNETISM GRAVITOMAGNETISM) ) ( AND ITS MEASUREMENT AND ITS MEASUREMENT INTRODUCTION INTRODUCTION Frame- -Dragging Dragging and and Gravitomagnetism Gravitomagnetism Frame EXPERIMENTS EXPERIMENTS � Past, present and future experimental efforts Past, present and future experimental efforts � to measure frame- -dragging dragging to measure frame Measurements using satellite laser ranging � Measurements using satellite laser ranging � The 2004 2004- -2006 2006 measurements of the measurements of the � The � Lense- -Thirring Thirring effect using the effect using the Lense GRACE Earth’ GRACE Earth ’s gravity models s gravity models Ι gnazio Ciufolini (Univ. Lecce): München 12-7-2006
DRAGGING OF OF INERTIAL INERTIAL FRAMES FRAMES DRAGGING FRAME- -DRAGGING DRAGGING as Einstein named it in ( FRAME 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: : ε ε u u α energy currents α G G αβ = = χ χ T T αβ = = αβ αβ = χ χ [( [( ε ε + +p p) ) u u α u β + p p g g αβ ] = α u β + αβ ] � It plays a key role in high It plays a key role in high � Einstein 1913 Thirring 1918 energy astrophysics energy astrophysics Braginsky, Caves and Thorne 1977 (Kerr metric Kerr metric) ) Thorne 1986 ( Jantsen et al. 1992-97, 2001 I.C. 1994-2001
INVARIANT CHARACTERIZATION of INVARIANT CHARACTERIZATION of GRAVITOMAGNETISM GRAVITOMAGNETISM Gravitomagnetism defined without approximations by the defined without approximations by the Gravitomagnetism Riemann tensor in a local Fermi frame. . Riemann tensor in a local Fermi frame Matte- -1953 1953 Matte By explicit spacetime spacetime invariants built with the Riemann tensor invariants built with the Riemann tensor: : By explicit I. .C C. . 1994 1994 I I. I .C C. . and and Wheeler Wheeler 1995 1995: : for the the Kerr metric Kerr metric: : for e q r r r ½ e R s s r R a a b m n = = 1536 1536 J M cos J M cos q ( (r r 5 5 r - - r r 3 3 r + + 3 r r r ) ½ R r R b m n -6 - 6 -5 - 5 16 -4 - 4 ) 3/ /16 a b s r m n a b s r m n In weak- -field and slow field and slow- -motion motion: : In weak º q *R R · · R R º 288 288 ( (J M J M)/ )/r r 7 cos cos q + + · · · · · · * 7 J = = a a M M = = angular momentum angular momentum J
Tartaglia, Mashhoon et al. Clock effect
Spin-Time-Delay and Gravitational Lensing
TIME- -DELAY DUE TO SPIN DELAY DUE TO SPIN TIME • In weak-field and slow-motion, the gravitomagnetic time-delay of a null ray between P 1 and P 2 is: P 2 ∆ T GM = ∫ h 0i dx i P 1 Around a spinning body : Lense-Thirring 1918, Kerr 1963 Inside a spinning shell: Thirring 1918, Bass-Pirani 1955, Brill-Cohen 1966, Pfister
SPIN- -TIME TIME- -DELAY DELAY SPIN Around a spinning body with angular momentum J, r 1 and r 2 are the position vectors of P 1 and P 2 Effect of a rotating central mass on light propagation: Kostyukovich and Mitjanock 1979 Dymnikova 1982, 1986 Datta and Kapoor 1985 Klioner 1991 Goicoehea et al. 1992 I.C. and Ricci 2002a (Class. Q. Grav.) Kopeikin and Mashhoon 2002 ... ... 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.) Inside a spinning shell rotating with radius R 0 , mass M and angular velocity w
Inside a spinning spinning mass mass: : Inside a ∆ T = ! int h 0i dx i May be as large as a few days for a rotating galaxy and a rotating cluster and years for a supercluster of galaxies
int ∆ T = ! int h 0i dx i May be as large as a few days for a cluster of galaxies and years for a supercluster of galaxies
Prospects to observe Spin- -Time Time- - Prospects to observe Spin Delay Delay In systems systems of the of the type type of the of the Gravitational Gravitational In Lens B B0218 0218+ +357 357 – – Biggs et al Lens Biggs et al. . 1998 1998- -2000 2000 The separation angle between the two images is The separation angle between the two images is 335 milliarcsec milliarcsec. . 335 The observed relative time delay is about he observed relative time delay is about 10.5 10.5 T days. . days The present measurement uncertainty in the The present measurement uncertainty in the relative time delay for B0218+357 relative time delay for B 0218+357 is about is about 0.4 0.4 days days If other other time time- -delays delays can can be modeled accurately be modeled accurately If enough and and if if the the spin spin- -time time- -delay delay, , especially especially of of enough the external rotating external rotating mass, e mass, e. .g g. . the the external external the rotating cluster or or supercluster supercluster of of galaxies galaxies, , is is rotating cluster large enough, of the , of the order order of of days days or or years years, , then then large enough we might observe the we might observe the spin spin- -time time- -delay delay ? ?
SOME EXPERIMENTAL ATTEMPTS TO SOME EXPERIMENTAL ATTEMPTS TO MEASURE FRAME- -DRAGGING AND DRAGGING AND MEASURE FRAME 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: : August FOPPL August FOPPL ( (Earth Earth- -rotation effect on a gyroscope rotation effect on a gyroscope) ) 1904 1916: : DE SITTER DE SITTER ( (shift of perihelion of Mercury due to Sun rotation shift of perihelion of Mercury due to Sun rotation) ) 1916 1918: : LENSE AND THIRRING LENSE AND THIRRING ( (perturbations of the Moons of solar perturbations of the Moons of solar 1918 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: : Van Patten Van Patten- -Everitt Everitt 1976 ( (two non two non- -passive counter passive counter- -rotating satellites in polar orbit rotating satellites in polar orbit) ) 1960: : Schiff Schiff- -Fairbank Fairbank- -Everitt Everitt ( (Earth orbiting gyroscopes Earth orbiting gyroscopes) ) 1960 1986: : I I. .C C.: .: USE THE NODES OF TWO LAGEOS SATELLITES USE THE NODES OF TWO LAGEOS SATELLITES 1986 ( (two supplementary inclination, passive, laser ranged two supplementary inclination, passive, laser ranged satellites) satellites ) 1988 : : Nordtvedt Nordtvedt ( (Astrophysical evidence from periastron Astrophysical evidence from periastron 1988 rate of rate of binary binary pulsar pulsar) ) 1995- -2006 2006: : I I. .C C. . et et al al. ( . (measurements using measurements using LAGEOS and LAGEOS LAGEOS and LAGEOS- -II II) ) 1995 1998: : Some Some astrophysical evidence from accretion disks astrophysical evidence from accretion disks of black of black 1998 holes holes and and neutron stars neutron stars
GRAVITY PROBE B
I.C.-Phys.Rev.Lett., 1986: Use the NODES of two LAGEOS satellites. A. ZICHICHI: IL TEMPO, JUNE 1985
John’s office, Univ. Texas at Austin, nearly 20 years ago
Satellite Laser Ranging Ranging Satellite Laser
IC, PRL 1986: Use of the nodes of two laser-ranged satellites to measure the Lense-Thirring effect
CONCEPT OF THE LAGEOS III / LARES EXPERIMENT
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
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.
IC IJMPA 1989: Analysis of the orbital perturbations affecting the nodes of LAGEOS-type satellites (1) Use two LAGEOS satellites with supplementary inclinations OR:
Use n satellites of LAGEOS-type to measure the first n-1 even zonal harmonics: J 2 , J 4 , … and the Lense-Thirring effect
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 ??
EGM- -96 96 GRAVITY MODEL GRAVITY MODEL EGM
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