FRAME- -DRAGGI NG DRAGGI NG FRAME (GRAVI TOMAGNETI SM) (GRAVI - PowerPoint PPT Presentation

FRAME- -DRAGGI NG DRAGGI NG FRAME (GRAVI TOMAGNETI SM) (GRAVI TOMAGNETI SM) AND I TS MEASUREMENT AND I TS MEASUREMENT I NTRODUCTI ON I NTRODUCTI ON Frame- -Dragging Dragging and and Gravitomagnetism Gravitomagnetism Frame EXPERI MENTS EXPERI MENTS � 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- -2006 measurements of the 2006 measurements of the � The 2004 � Lense- -Thirring Thirring effect using the effect using the Lense GRACE Earth’ ’s gravity models s gravity models GRACE Earth Ι gnazio Ciufolini (Univ. Lecce): Firenze 30-9-2006

DRAGGI NG OF OF I NERTI AL I NERTI AL FRAMES FRAMES DRAGGI NG ( FRAME FRAME- -DRAGGI NG DRAGGI NG as Einstein named it in 1913) as Einstein named it in 1913) ( � The local inertial frames The local inertial frames � are dragged by mass- - are dragged by mass ε u energy currents: ε α u α energy currents: αβ = αβ = χ T G αβ = χ T αβ = G α u β + p χ [( [( ε ε + p) = χ αβ ] u α u β g αβ + p) u + p g ] = � It plays a key role in high It plays a key role in high � Thirring 1918 Braginsky, Caves and Thorne 1977 energy astrophysics energy astrophysics Thorne 1986 Mashhoon 1993, 2001 (Kerr metric) (Kerr metric) Jantsen et al. 1992-97, 2001 I.C. 1994-2001

SOME EXPERIMENTAL ATTEMPTS TO SOME EXPERIMENTAL ATTEMPTS TO MEASURE FRAME- -DRAGGING AND DRAGGING AND MEASURE FRAME GRAVITOMAGNETISM GRAVITOMAGNETISM 1896: Benedict and Immanuel FRIEDLANDER 1896: Benedict and Immanuel FRIEDLANDER (torsion balance near a heavy flying- -wheel) wheel) (torsion balance near a heavy flying 1904: August FOPPL (Earth- -rotation effect on a gyroscope) rotation effect on a gyroscope) 1904: August FOPPL (Earth 1916: DE SITTER (shift of perihelion of Mercury due to Sun rotat 1916: DE SITTER (shift of perihelion of Mercury due to Sun rotation) ion) 1918: LENSE AND THIRRING (perturbations of the Moons of solar 1918: LENSE AND THIRRING (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: Van Patten- -Everitt Everitt 1976: Van Patten (two non- -passive counter passive counter- -rotating satellites in polar orbit) rotating satellites in polar orbit) (two non 1960: Schiff- -Fairbank Fairbank- -Everitt Everitt (Earth orbiting gyroscopes) (Earth orbiting gyroscopes) 1960: Schiff 1986: I.C.: USE THE NODES OF TWO LAGEOS SATELLITES USE THE NODES OF TWO LAGEOS SATELLITES 1986: I.C.: (two supplementary inclination, passive, laser r (two supplementary inclination, passive, laser ranged anged satellites) satellites) 1988 : Nordtvedt Nordtvedt ( (Astrophysical Astrophysical evidence evidence from from periastron periastron 1988 : rate of rate of binary binary pulsar) pulsar) 1995- -2006: I.C. 2006: I.C. et et al. ( al. (measurements measurements using using LAGEOS and LAGEOS LAGEOS and LAGEOS- -II) II) 1995 1998: Some astrophysical astrophysical evidence evidence from from accretion accretion disks disks of black of black 1998: Some holes and and neutron neutron stars stars holes

GRAVITY PROBE B

I.C.-Phys.Rev.Lett., 1986: Use the NODES of two LAGEOS satellites. A. ZICHICHI: IL TEMPO, JUNE 1985

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

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

Satellite Laser Ranging Ranging Satellite Laser

l=3, m=1

CONCEPT OF THE LAGEOS III / LARES EXPERIMENT

LARES 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 II: 1992 II: 1992 Lageos 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 GRAVITY MODEL 96 GRAVITY MODEL EGM

EGM96 Model and its its uncertainties uncertainties EGM96 Model and value Uncer- - Uncer- - Uncer- - Even Even value Uncer Uncer Uncer zonals tainty tainty tainty on on zonals tainty tainty tainty on node II II on node l m in l m in node I I node value value W LT W LT 1 W 2 W 20 20 - -0.484165 0.484165 0.36x10- 0.36x10 -10 10 1 2 LT LT 37 x 37 x 10 10- -03 03 W LT W L T 1.5 W 0.5 W 40 0.1 x 10- -09 09 40 0.1 x 10 1.5 0.5 LT L T 0.5398738 0.5398738 6 x 10- 6 x 10 -06 06 W L T W L T 0.6 W 0.9 W 60 -0.149957 0.149957 0.15x10- -09 09 60 - 0.15x10 0.6 0.9 L T L T 99 x x 10 10- -06 06 99 0.07 W W L T 0.32 W W L T 80 0.4967116 0.23x10- -09 09 80 0.4967116 0.23x10 0.07 0.32 L T L T 7 x 10- 7 x 10 -07 07 W L T W L T 0.06 W 0.11 W 10,0 10,0 0.5262224 0.5262224 0.06 0.11 0.31x10- -09 09 L T L T 07 0.31x10 9 x 10- -07 9 x 10

d C d C : d , d 3 main main unknowns unknowns: C 20 C 40 and LT LT 3 20 , 40 and Needed 3 3 observables observables Needed dW I ,dW dW II 2: dW , we only only have have 2: we I II ( orbital ( orbital angular angular momentum momentum vector vector) )

EGM96 Model and its its uncertainties uncertainties EGM96 Model and Even value Uncer- - Uncer- - Uncer- - Uncer- - Even value Uncer Uncer Uncer Uncer zonals tainty tainty tainty on on tainty on on zonals tainty tainty tainty tainty on node II II on node l m in Perigee II II l m in Perigee node I I node value value -10 10 0.36x10 - 1 W W LT 2 W W LT w LT w 20 -0.484165 0.484165 0.8 20 - 0.36x10 1 2 0.8 LT LT LT -03 03 10 - 37 x x 10 37 -09 09 0.1 x 10 - W LT W L T w L 1.5 W 0.5 W 2.1 w 40 40 0.1 x 10 1.5 0.5 2.1 LT L T L T T 0.5398738 0.5398738 -06 06 6 x 10 - 6 x 10 -09 09 0.15x10 - W L T W L T w L 0.6 W 0.9 W 0.31 w 60 60 - -0.149957 0.149957 0.15x10 0.6 0.9 0.31 L T L T L T T -06 06 10 - 99 99 x x 10 -09 09 0.23x10 - W L T W L T w L 0.07 W 0.32 W 0.78 w 80 0.4967116 80 0.4967116 0.23x10 0.07 0.32 0.78 L T L T L T T -07 07 7 x 10 - 7 x 10 W L T W L T w L 0.06 W 0.11 W 0.34 w 10,0 10,0 0.5262224 0.5262224 0.06 0.11 0.34 0.31x10 - -09 09 0.31x10 L T L T L T T 9 x 10 - -07 07 9 x 10

d C d C : d , d 3 main main unknowns unknowns: C 20 C 40 and LT LT 3 20 , 40 and Needed 3 3 observables observables: : Needed dW I ,dW dW II 2: dW I , ) plus plus 2: ( orbital ( orbital angular angular momentum momentum vector vector) II dw II 1: dw 1: (Runge Runge- -Lenz Lenz vector vector) ) ( II dW I d C d C d C + m m (31 mas/ dW x d x d x d = K 2 C 20 + K K 4 C 40 + K K 2n C 2n,0 (31 mas/yr yr) ) I = K 2 x 20 + 4 x 40 + 2n x 2n,0 + dW II d C d C d C + m m (31.5 mas/ dW x d x d x d = K K’ ’ 2 C 20 + K K’ ’ 4 C 40 + K K’ ’ 2n C 2n,0 (31.5 mas/yr yr) ) II = 2 x 20 + 4 x 40 + 2n x 2n,0 + dw II d C d C d C - m m (57 mas/ dw x d x d x d = K K’’ ’’ 2 C 20 + K K’’ ’’ 4 C 40 + K K’’ ’’ 2n C 2n,0 (57 mas/yr yr) ) II = 2 x 20 + 4 x 40 + 2n x 2n,0 - m = dW dW I dW II + c dw II : m = 1 dW II + 2 dw II : + c 1 c 2 I + c (m = = 1 1 40 (m in GR) in GR) d C d C on d and d not dependent dependent on C 20 C 40 not 20 and ≥ C60 = 13% TOTAL ERROR FROM EVEN ZONALS ≥ C60 = 13% Lense Lense- -Thirring Thirring TOTAL ERROR FROM EVEN ZONALS I.C., PRL 1986; I.C., IJMP-A 1989; I.C., NC-A 1996.

e II = 0.04 I.C., NC A, 1996

Nuovo Cimento A 1996 IC

I.C., et al. 1996-1997 (I.C. 1996). (Class.Q.Grav. ...) Gravity model JGM-3 Obs. period 3.1 years I.C., Pavlis et al. 1998 (Science) Result: m @ 1.1 I.C. 2000 (Class.Q.Grav.) Gravity model EGM-96 Obs. period 4 years Result: m @ 1.1

2002 Use of GRACE to test Lense-Thirring at a few percent level: J. Ries et al. 2003 (1999),E. Pavlis 2002 (2000) [see also Nordtvedt-99]

-2 MODEL 2 MODEL EIGEN- EIGEN

EIGEN-GRACE-S (GFZ 2004)

EIGEN- -GRACE02S Model and GRACE02S Model and EIGEN Uncertainties Uncertainties Even Value Uncertainty Uncertainty Uncertainty Uncertainty zonals on node I on on perigee II · 10 -6 lm node II 1.59 W L T 2.86 W L T 1.17 w LT 20 0.53 · 10 -10 -484.16519788 0.058 W LT 0.02 W L T 0.082 w L T 0.39 · 10 -11 40 0.53999294 0.0076 W L T 0.012 W L T 0.0041 w L T 0.20 · 10 -11 60 -.14993038 0.00045 W L T 0.0021 W L T 0.0051 w L T 0.15 · 10 -11 80 0.04948789 0.00042 W L T 0.00074 W L T 0.0023 w L T 0.21 · 10 -11 10,0 0.05332122