Frame-dragging in the news in 2004

Clifford Will¹ , Washington University, St. Louis cmw-at-howdy.wustl.edu

Frame-dragging made headlines twice during 2004. First, on April 20, came the long-awaited launch of Gravity Probe-B, the joint project of NASA, Stanford University and Lockheed-Martin to measure the dragging of inertial frames (Lense-Thirring effect), using an array of orbiting gyroscopes (see Bill Hamilton's article in MOG, Fall 2004). By the middle of August, the mission had completed the commissioning and calibration phase, and commenced science operations. Now at the mid-point of the 10-month science phase, the spacecraft and instruments are performing as expected [1]. It is too early to know whether the relativistic effects are being measured in the amount predicted by general relativity, because an important calibration of the instrument exploits the effect of the aberration of starlight on the pointing of the on-board telescope toward the guide star (IM Pegasi), and completing this calibration requires the full mission data set. In addition, part of the measured effect includes the motion of the guide star relative to distant inertial frames. This is being measured separately by Irwin Shapiro's group at Harvard/SAO, using very long baseline interferometry (VLBI), and the results of those VLBI measurements will be strictly embargoed until the GPB team has completed its analysis of the gyro data.

Meanwhile, on October 21, Ignazio Ciufolini and Erricos Pavlis made science headlines with a paper in Nature, in which they claimed to have measured frame-dragging to between five and 10 percent [2], using laser ranging to the Earth-orbiting satellites LAGEOS I and II.

This is not the first report of a measurement of frame dragging using the LAGEOS satellites. In 1998 and 2000, Ciufolini and colleagues reported measurements of the relativistic effect with accuracies ranging from 20 to 30 percent [3,4,5]. What makes this newest report different from the rest?

The idea behind the LAGEOS experiment is to measure the precession of the orbital plane caused by the dragging of inertial frames. For the LAGEOS satellites, the precession is about 31 milliarcseconds (mas) per year. The satellites, launched mainly for geophysical purposes, are massive spheres studded with laser retro-reflectors, and as such are not as strongly affected by atmospheric drag and radiation pressure as are complex satellites with solar panels and antennae, and can also be tracked extremely accurately using laser ranging.

Unfortunately, Newtonian gravity makes a whopping $126^{\rm o} \, {\rm yr}^{-1}$ contribution to the precession. This haystack must be subtracted off, in order to find the relativistic needle buried within. The Newtonian precession depends primarily on the so-called even zonal harmonics $J_n$ of the Earth's gravity field, with $J_2$, $J_4$, $J_6 \, \dots$ contributing in ever decreasing amounts. These moments have been measured over the years using a variety of Earth-orbiting satellites, but have never been known accurately enough to permit a simple subtraction of the Newtonian precession.

In their earlier work, Ciufolini et al. tried an alternative method. Noting that the orbit of LAGEOS II had a small eccentricity, they argued that, if one measured the two precessions together with the perigee advance of LAGEOS II, all of which depend on frame dragging and the zonal harmonics, and if one adopted the existing values of the harmonics for $n=6$ and higher, then one could use the three observables to measure the two poorly known $J_2$ and $J_4$, and the unknown relativity parameter. This was the basis of the results presented in Refs. [3,4,5]. Unfortunately, the perigee precession is strongly affected by non-gravitational perturbations, and so it is difficult to assess the errors reliably. A number of experts argued that the 20 to 30 percent errors assigned by Ciufolini et al. were too small by factors as high as five [6,7].

But then along came CHAMP and GRACE. Europe's CHAMP (Challenging Minisatellite Payload) and NASA's GRACE (Gravity Recovery and Climate Experiment) missions, launched in 2000 and 2002, respectively, use precision tracking of spacecraft to measure variations in Earth's gravity on scales as small as several hundred kilometers, with accuracies as much as ten times better than had been obtained previously. GRACE consists of a pair of satellites flying in close formation (200 kilometers apart) in polar orbits. Each satellite has on-board accelerometers to measure non-gravitational perturbations, satellite to satellite K-band radar, to measure variations in the Earth's gravity gradient on short scales, and GPS tracking to measure larger scale variations in Earth's gravity.

With the dramatic improvements in $J_n$ obtained by CHAMP and GRACE, Ciufolini could now treat $J_4$ and above as known (well enough), drop the troublesome perigee advance, and use the two LAGEOS precessions to determine $J_2$ and the relativity parameter. This is what Ciufolini and Pavlis reported in the recent Nature paper [2].

While all this is valid in principle, the big question is the treatment of errors. Iorio [8] has criticized the error analysis on a number of grounds, including (i) adopting one GRACE/CHAMP Earth solution for the analysis, rather than analyzing many solutions for the zonal harmonics and seeing how the relativity parameter varies; (ii) inadequate treatment of correlations among the zonal harmonics in the GRACE/CHAMP solutions; and (iii) inadequate treatment of temporal variations in the low-order harmonics ${\dot J}_4$ and ${\dot J}_6$. Iorio suggests that the $2-\sigma$ errors should be more like 30 percent [9]

With results from GPB not expected until well after the end of the mission in July, and with this lingering discussion of errors in the LAGEOS solutions, we may not have a solid answer about these measurements of frame dragging before the end of the Einstein year.

References:

[1] The website for Gravity Probe B is at www.einstein.stanford.edu, and gives regular updates on the performance of the instruments and spacecraft, as well as information about how the experiment is designed.
[2] I. Ciufolini and E. C. Pavlis, A confirmation of the general relativistic prediction of the Lense-Thirring effect, Nature 431, 958 (2004).
[3] I. Ciufolini, F. Chieppa, D. Lucchesi and F. Vespe, Test of Lense - Thirring orbital shift due to spin, Class. Quantum Gravit. 14, 2701 (1997).
[4] I. Ciufolini, E. C. Pavlis, F. Chieppa, E. Fernandex-Vieira and P. Pérez-Mercader, Test of General Relativity and Measurement of the Lense-Thirring Effect with Two Earth Satellites, Science 279, 2100 (1998).
[5] I. Ciufolini, The 1995-99 measurements of the Lense-Thirring effect using laser-ranged satellites, Class. Quantum Gravit. 17, 2369 (2000).
[6] 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, in Proceedings of the 13th International Workshop on Laser Ranging: Science Session and Full Proceedings CD-ROM, edited by R. Noomen, S. Klosko, C. Noll, and M. Pearlman, NASA/CP-2003-212248 (2003); available online at
http://cddisa.gsfc.nasa.gov/lw13/lw_proceedings.html#science.
[7] L. Iorio, Some comments on the recent results about the measurement of the Lense-Thirring effect in the gravitational field of the Earth with the LAGEOS and LAGEOS II satellites, preprint gr-qc/0411084.
[8] L. Iorio, Some comments about a recent paper on the measurement of the general relativistic Lense-Thirring effect in the gravitational field of the Earth with the laser-ranged LAGEOS and LAGEOS II satellites, preprint gr-qc/0410110.
[9] Similar comments were made by Ries et al. [6] in reference to the 1998 analysis of [4]