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Frame-dragging

From Academic Kids

According to Albert Einstein's theory of general relativity, space and time get pulled out of shape near a rotating body in a phenomenon referred to as frame-dragging. The effect was first derived from the theory of general relativity in 1918 by the Austrian physicists Joseph Lense and Hans Thirring. Other names for this effect are gravitomagnetism and the Lense-Thirring effect.

Lense and Thirring predicted that the rotation of an object would alter space and time, dragging a nearby object out of position compared to the predictions of Newtonian physics. This is the frame-dragging effect. The predicted effect is incredibly small—about one part in a few trillion—which means that you have to look at something very massive, or build an instrument that is incredibly sensitive.

Frame-dragging is one of the last predictions of general relativity remaining to be confirmed by experiment. More familiar and already-proven effects of special relativity include the conversion of mass into energy (as seen in atomic bombs and stars) and back, and the Lorentz transformations which make objects near lightspeed seem to grow shorter and heavier from the point of view of an outside observer. Recent measurements of satellites in Earth orbit appear to show frame dragging, and, if confirmed, would represent another successful prediction of General Relativity.

Contents

Attempts to test the existence of frame-dragging

Using recent observations by X-ray astronomy satellites, including NASA's Rossi X-ray Timing Explorer, a team of astronomers announced in 1997 that they had seen evidence of frame-dragging in disks of gas swirling around a black hole. The team included Dr. Wei Cui of the Massachusetts Institute of Technology, and his colleagues, Dr. Nan Zhang, working at NASA's Marshall Space Flight Center, and Dr. Wan Chen of the University of Maryland in College Park.


The gyroscope-based Gravity Probe B experiment aims to detect any frame-dragging effects on the direction of spin of its gyroscopes as it orbits around the Earth. It was successfully launched on April 20, 2004 for an 18 month experiment. If this experiment is successful, it is expected to yield the most accurate measurements yet performed in this field. Indeed, an accuracy of better than 1% is expected.


Another consequence of the gravitomagnetic field of a central rotating body is the so-called Lense-Thirring effect (Lense and Thirring 1918). It consists of small secular precessions of the longitude of the ascending node <math>\Omega<math> and the argument of pericenter <math>\omega<math> of the path of a test mass freely orbiting the spinning main body. For the nodes of the LAGEOS Earth's artificial satellites they amount to <math>\sim 30<math> milliarcseconds per year (mas <math>{\rm yr}^{-1}<math>). Such tiny precessions would totally be swamped by the much larger classical precessions induced by the even zonal harmonic coefficients <math>J_{\ell},\ \ell=2,4,6...<math> of the multipolar expansion of the Newtonian part of the terrestrial gravitational potential. Even the most recent Earth gravity models from the dedicated CHAMP and GRACE missions would not allow to know the even zonal harmonics to a sufficiently high degree of accuracy in order to extract the Lense-Thirring effect from the analysis of the node of only one satellite.

Ciufolini proposed in 1996 to overcome this problem by suitably combining the nodes of LAGEOS and LAGEOS II and the perigee of LAGEOS II in order to cancel out all the static and time-dependent perturbations due to the first two even zonal harmonics <math>J_2,\ J_4<math> (Ciufolini 1996). Various analyses with the pre-CHAMP/GRACE JGM-3 and EGM96 Earth gravity models were performed by Ciufolini et al. over observational time spans of some years (Ciufolini et al. 1997; 1998). The claimed total accuracies were in the range of 20-25% (Ciufolini 2004). However, subsequent analyses by Ries et al. (2003a) and Iorio (2003) showed that such estimates are largely optimistic. Indeed, a more conservative and realistic evaluation of the impact of the uncancelled even zonal harmonics <math>J_6,\ J_8,\ J_{10},...<math>, according to the adopted EGM96 model, yield a systematic error of about 80% at 1-sigma level. Moreover, also the systematic error due to the non-gravitational perturbations mainly affecting the perigee of LAGEOS II was underestimated.

The opportunities offered by the new generation of Earth gravity models from CHAMP and, especially, GRACE allowed to discard the perigee of LAGEOS II, as pointed out by Ries et al. (2003b). In 2003 Iorio put explicitly forth a suitable linear combination of the nodes of LAGEOS and LAGEOS II which cancels out the first even zonal harmonic <math>J_2<math> (Iorio and Morea 2004). Such an observable was used by Ciufolini and Pavlis in a test performed with the 2nd generation GRACE-only EIGEN-GRACE02S Earth gravity model over a time span of 11 years (Ciufolini and Pavlis 2004). The claimed total error budget is 5% at 1-sigma level and 10% at 3-sigma level. However, Iorio (2005a, 2005b) criticized such results because of the neglected impact of the secular variations of the uncancelled even zonal harmonics <math>\dot J_4,\ \dot J_6<math> which would amount to about 13%. This would yield a total error of <math>\sim<math> 20% at 1-sigma level. Moreover, the latest CHAMP/GRACE-based Earth gravity models do not yet allow for a model-independent measurement. Indeed, the systematic error due to the static part of the even zonal harmonics amounts to 4% for EIGEN-GRACE02S, 6% for EIGEN-CG01C and 9% for GGM02S at 1-sigma level.

See also

References

  • Thirring, H. ▄ber die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19, 33 (1918). [On the Effect of Rotating Distant Masses in Einstein's Theory of Gravitation]
  • Thirring, H. Berichtigung zu meiner Arbeit: "▄ber die Wirkung rotierender Massen in der Einsteinschen Gravitationstheorie". Physikalische Zeitschrift 22, 29 (1921). [Correction to my paper "On the Effect of Rotating Distant Masses in Einstein's Theory of Gravitation"]
  • Lense, J. and Thirring, H. ▄ber den Einfluss der Eigenrotation der Zentralk÷rper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19 156-63 (1918) [On the Influence of the Proper Rotation of Central Bodies on the Motions of Planets and Moons According to Einstein's Theory of Gravitation]
  • I. Ciufolini. On a new method to measure the gravitomagnetic field using two orbiting satellites. Il Nuovo Cimento A, 109, 1709-1720, (1996).
  • I. Ciufolini, F. Chieppa, D. Lucchesi, and F. Vespe. Test of

Lense-Thirring orbital shift due to spin. Classical and Quantum Gravity 14, 2701-2726, (1997).

  • I. Ciufolini, E.C. Pavlis, F. Chieppa, E. Fernandes-Vieira,

and J. Perez-Mercader, J. Test of General Relativity and Measurement of the Lense-Thirring Effect with Two Earth Satellites. Science 279, 2100-2103, (1998).

  • I. Ciufolini. Frame Dragging and Lense-Thirring Effect, General Relativity and Gravitation 36, 2257-2270, (2004).
  • J. C. Ries, R. J. Eanes and B. D. Tapley. Lense-Thirring Precession

Determination from Laser Ranging to Artificial Satellites. Nonlinear Gravitodynamics ed. R. Ruffini and C. Sigismondi (World Scientific, Singapore, 2003a) pp. 201-211.

  • L. Iorio. The impact of the static part of the Earth's gravity

field on some tests of General Relativity with Satellite Laser Ranging. Celestial Mechanics and Dynamical Astronomy 86 277-294, (2003).

  • J. C. Ries, R. J. Eanes, B. D. Tapley and G. E. Peterson. Prospects

for an Improved Lense-Thirring Test with SLR and the GRACE Gravity Mission. Proc. 13th Int. Laser Ranging Workshop NASA CP 2003-212248 ed. R. Noomen, S. Klosko, C. Noll and M. Pearlman. (NASA Goddard 2003b). Preprint [[1] (http://cddisa.gsfc.nasa.gov/lw13/lw_proceedings.html#science)]

  • L. Iorio and A. Morea. The impact of the new Earth gravity

models on the measurement of the Lense-Thirring effect. General Relativity and Gravitation 36, 1321-1333, (2004). Preprint [[2] (http://www.arxiv.org/abs/gr-qc/0304011)].

  • I. Ciufolini, E. C. Pavlis. A confirmation of the general relativistic prediction of the LenseľThirring effect. Nature 431, 958 - 960 (21 October 2004); doi:10.1038/nature03007
  • L. Iorio. On the reliability of the so-far performed tests for measuring the LenseľThirring effect with the LAGEOS satellites. New Astronomy in press. (2005a); doi:10.1016/j.newast.2005.01.001 [[3] (http://www.arxiv.org/abs/gr-qc/0411024)]
  • L. Iorio. On the impact of the secular rates of the even zonal

harmonics on the measurement of the Lense-Thirring effect: a quantitative analysis, (2005b). Preprint [[4] (http://www.arxiv.org/abs/gr-qc/0412057v3)].

External links

An early version of this article was adapted from public domain material from http://science.msfc.nasa.gov/newhome/headlines/ast06nov97_1.htm de:Lense-Thirring-Effekt el:Βαρυτομαγνητικό πεδίο

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