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Albert Einstein's theory of general relativity predicts that rotating bodies drag spacetime around themselves in a phenomenon referred to as frame-dragging. The rotational frame-dragging effect was first derived from the theory of general relativity in 1918 by the Austrian physicists Joseph Lense and Hans Thirring, and is also known as 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. More generally, the subject of field effects caused by moving matter is known as gravitomagnetism.

Frame dragging effects

Rotational frame-dragging (Lense-Thirring effect) appears in the general principle of relativity and similar theories in the vicinity of rotating massive objects. Under the Lense-Thirring effect, the frame of reference in which a clock ticks the fastest is one which is rotating around the object as viewed by a distant observer. This also means that light traveling in the direction of rotation of the object will move around the object faster than light moving against the rotation as seen by a distant observer. It is now the best-known effect, partly thanks to the Gravity Probe B experiment.

Accelerational frame dragging is the similarly inevitable result of the general principle of relativity, applied to acceleration. Although it arguably has equal theoretical legitimacy to the "rotational" effect, the difficulty of obtaining an experimental verification of the effect means that it receives much less discussion and is often omitted from articles on frame-dragging (but see Einstein, 1921).

Mathematical treatment of frame-dragging

Experimental tests of frame-dragging

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 O and the argument of pericenter ? 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 ~30 milliarcseconds per year (ms/yr or ms yr - 1). Such tiny precessions would totally be swamped by the much larger classical precessions induced by the even zonal harmonic coefficients 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 (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. 1996; 1997; 1998).

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 Pavlis (2002) and Ries et al. (2003b). In Ciufolini and Pavlis (2004) a test was performed with the 2nd generation GRACE-only EIGEN-GRACE02S Earth gravity model over a time span of 11 years (Ciufolini and Pavlis 2004). The total error budget was at a level of 10%.

A number of recent and very detailed papers have fully confirmed the 10% error budget of the measurement published by Ciufolini and Pavlis in 2004, see, e.g., Ciufolini and Pavlis 2005, Lucchesi 2005, and Ciufolini, Pavlis and Peron 2006.

The measurement of the Lense-Thirring effect by Ciufolini and Pavlis in 2004 is based on the innovative ideas published since 1984 by Ciufolini who proposed the use of the nodes of two laser ranged satellites of LAGEOS-type to measure the Lense-Thirring effect. Indeed, the key idea of using the nodes of two laser ranged satellites of LAGEOS-type to measure the Lense-Thirring effect was first published in Ciufolini 1984 and Ciufolini 1986 and later studied in Ciufolini 1989 and Tapley, Ciufolini et al. 1989. The use of the combination of the nodes only of a number of laser ranged satellites of LAGEOS-type was first published in Ciufolini 1989, p. 3102, see also Ciufolini and Wheeler 1995, p. 336, where is written "... A solution would be to orbit several high-altitude, laser-ranged satellites, similar to LAGEOS, to measure J2,J4,J6, etc, and one satellite to measure ....". The use of the nodes of LAGEOS and LAGEOS 2, together with the explicit expression of the LAGEOS satellites nodal equations, was first proposed in Ciufolini 1996; the explicit expression of this combination of the nodes only of the LAGEOS satellites, that is however a trivial step on the basis of the explicit equations given in Ciufolini 1996, was presented by Ciufolini at the 2002 I-SIGRAV school and published in its proceedings, see Ciufolini 2002: precisely this observable was used by Ciufolini and Pavlis in 2004 for their accurate measurement of the frame-dragging effect on the LAGEOS satellites nodes, see Ciufolini and Pavlis 2004. For a study of the determination of the Lense-Thirring effect using laser-ranged satellites see also Peterson 1997. The use of the GRACE-derived gravitational models, when available, to measure the Lense-Thirring effect with accuracy of a few percent was, since many years, a well known possibility to all the researchers in this field and was presented during the SIGRAV 2000 conference by Pavlis, Pavlis 2002, and published in its proceedings, and was published by Ries et al. in the proceedings of the 1998 William Fairbank conference and of the 2003 13th Int. Laser Ranging Workshop, Ries et al. 2003a and 2003b, where Ries et al. concluded that, in the measurement of the Lense-Thirring effect using the GRACE gravity models and the LAGEOS and LAGEOS 2 satellites: "a more current error assessment is probably at the few percent level ...".

Incidentally, two problems of the GP-B mission have been pointed out in NATURE, Vol. 444, 21/28 December 2006. Even though these problems might be, in part, taken care of by the GP-B data analysis, no other team would probably be able to clearly understand the corrections necessary in the data analysis to take care of these problems and thus probably no other group would be able to repeat the data analyis with the understanding of what is beeing done.

Incidentally, a recent analysis of Iorio has been shown to be wrong by at least a factor ten thousand (see: Sindoni et al 2007, http://xxx.lanl.gov/abs/gr-qc/0701141) because he did not consider basic SYSTEMATIC ERRORS; so there is no hope to measure the Lense-Thirring effect using the Mars Global Surveyor, indeed the associated systematic errors are at least 40 times larger than the Lense-Thirring effect to be measured.

WE HOPE THAT ANOTHER CONTRIBUTOR WILL NOT CONTINUE TO CANCEL AND CHANGE THE CONTENT AND MEANING OF WHAT WAS *ALREADY* PREVIOUSLY WRITTEN UP TO HERE!

See also

• Kerr metric
• Gravitomagnetism
• Mach's principle
• Broad Iron K line

References

1. Thirring, H. Über die Wirkung rotierender ferner Massen in der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19, 33 (1918).
2. Thirring, H. Berichtigung zu meiner Arbeit: "Über die Wirkung rotierender Massen in der Einsteinschen Gravitationstheorie". Physikalische Zeitschrift 22, 29 (1921).
3. Lense, J. and Thirring, H. Über den Einfluss der Eigenrotation der Zentralkörper auf die Bewegung der Planeten und Monde nach der Einsteinschen Gravitationstheorie. Physikalische Zeitschrift 19 156-63 (1918)
4. Einstein, A The Meaning of Relativity (contains transcripts of his 1921 Princeton lectures).

External links

• NASA RELEASE: 04-351 As The World Turns, It Drags Space And Time
• New Scientist press release of the MGS test by Iorio in the gravitational field of Mars
• Paper by Giampiero Sindoni, Claudio Paris and Paolo Ialongo about the misunderstandings of Iorio claims
• Paper by G. Felici about the misunderstandings of Iorio claims
• Paper by Kris Krogh about the misunderstandings of Iorio claims
• Paper by Ignazio Ciufolini and Erricos Pavlis about the misunderstandings of Iorio claims
• Frame Dragging
• Duke University press release: General Relativistic Frame Dragging
• MSNBC report on X-ray observations
• Ciufolini et al. LAGEOS paper 1997 - 25% error
• Ciufolini update Sep 2002 - 20% error
• Press release regarding LAGEOS study
• Preprint by Ries et al.
• Ciufolini and Pavlis Nature new article on 2004 re-analysis of the LAGEOS data
• Iorio New Astronomy general paper with full references
• Iorio J. of Geodesy paper on the impact of the secular variations of the even zonal harmonics of the geopotential
• Iorio Planetary Space Science paper
• The Naked Singularity

An early version of this article was adapted from public domain material from http://science.msfc.nasa.gov/newhome/headlines/ast06nov97_1.htm

• Effects of gravitation
• Frames of reference