Dragging on

By Daniel Holz | April 15, 2007 4:33 pm

The annual April meeting of the American Physical Society is currently underway. This meeting brings together thousands of physicists, from all branches except condensed matter. The condensed matter types have their own meeting (in March), which dwarfs ours. For the next few days, there will be a flurry of press releases originating in Jacksonville, Florida. Although I have been missing the action down south, there is one press release which was conspicuous in its absence. A measurement of frame dragging was not announced by the Gravity Probe B satellite (affectionately known as GP-B), as originally planned. Instead, NASA issued an Interim Report summarizing the state of the data analysis thus far. The press release is here.

GP-B is probably the oldest space experiment alive. The mission was first proposed in 1959, and funding began in 1964 (Francis Everitt, the Principal Investigator, has been involved from the very beginning). The science goal is eminently worthwhile: to measure the Lense-Thirring precession (also known as frame dragging) due to the Earth’s rotation. In general relativity a rotating mass will drag space along with it, leading to effects which would be completely absent in Newtonian gravity. For example, a gyroscope in polar orbit about the Earth will show an extra precession due to the Earth’s one-revolution-per-day spin. One of the problems with general relativity is that gravity is much too weak. Every time we come up with some cool effect (gravitational waves, frame dragging, time dilation), it turns out that it’s almost impossible to see the effect. Frame dragging is no exception. If we were near a rapidly rotating black hole, frame dragging would jump out at us: a gyroscope would wobble all over the place. But the Earth’s frame dragging, for an object in orbit 650 km up, adds up to a miniscule 39 milli-arcseconds per year (mas/yr). For some sense of how small this is, consider your average visible, bright star. For generations we’ve considered the stars to be fixed on the sky. As we now know, this isn’t entirely accurate, and the stars do indeed move. The record-holder is Barnard’s star, which moves by 10,000 mas/yr. Typical stars have proper motions closer to 100 mas/yr. In comparison to the effects of frame-dragging, the “fixed” stars are moving all over the place, which emphasizes the difficulty of measurement. GP-B monitors the orientation of the spin axis relative to a particular star (IM Pegasi). This star was specifically chosen because it is bright in both optical and radio, allowing its motion (against a background, fixed frame of distant quasars) to be exquisitely well-measured using radio telescopes (through Very Long Baseline Interferometry, incorporating data from the VLA). (If you’re wondering about GP-A, it was launched in 1976. It carried an atomic clock, and directly measured the time dilation due to the gravitational redshift, confirming relativity at the 0.01% level.)

If the only precession came from frame-dragging, the experiment might be somewhat more straightforward. The problem is that there are other physical effects which cause precession, and which completely overwhelm the signal of interest. The Earth is not a perfect sphere; it is squashed, being 43 km fatter around the equator than around the poles. This provides a convenient handle upon which gravitational tidal forces of the Moon and Sun pull, leading to a precession of 50,000 mas/year. There is also geodetic precession, which is a general-relativistic effect due to the curvature of spacetime about the Earth (and which would be present even if the Earth were not rotating). Geodetic precession is also comparatively large (6,600 mas/year), and is by now well established. It will need to be understood to an unprecedented degree before a measurement of frame-dragging is possible. The two main science goals of GP-B are the precision determination of both geodetic precession and frame dragging. Yesterday they announced a measurement of the former to 1%. A pretty picture from the GP-B website summarizes:
gp-b precession diagram

One major development in the intervening 40 years since GP-B was initially funded has been the use of the LAGEOS satellite system to independently measure frame dragging. These satellites were designed to be orbiting “test particles”, to enable geodynamic measurements of the Earth. They are nicely round and reasonably uniform, completely passive, and each is covered with 426 cube-corner retroreflectors. A retroreflector is just a box with mirrors on the inside walls, and one wall missing: a light ray coming in through the missing wall is bounced back in the direction it came from. (Commonly found in reflectors along highways, or reflecting tape in clothing/bags/shoes.) Apollo astronauts left some large retro-reflectors on the moon. One can shoot laser pulses at these, detect the returning photons, and precisely measure the position of the Moon (to better than a cm!). These lunar-ranging experiments turn out to be an important constraint on alternative theories of gravity. Similarly, the positions of the LAGEOS satellites can be precisely monitored, and the orbital evolution of two of the satellites can be used to accurately measure the precession. In this case, rather than using the spin of the satellite (or a gyroscope within it) as a reference, one uses the orbital plane of the satellite motion. [In the interest of full disclosure, it should be mentioned that my first refereed paper was an analysis of the effect of the Earth’s gravitational and magnetic field on the spin of the LAGEOS satellites. There are a number of important systematics which depend crucially on understanding this spin.] To use the LAGEOS satellites to measure frame dragging, the full gravitational field of the Earth needs to be accounted for (in particular, the mass multipoles due to the non-sphericitiy of the Earth). As it happens, the GRACE and CHAMP experiments have recently provided unprecedented maps of the Earth’s field. Incorporating these results into an analysis of the orbits of LAGEOS, a measurement of the Earth’s frame dragging was accomplished by Ciufolini and collaborators, at the level of ~10%. (Due to subtleties in the analysis there is some debate as to the ultimate precision of the measurement; but a confirmation of frame dragging is generally agreed upon.)

When GP-B was first proposed, measuring frame dragging seemed like a great idea. However, as the decades went by and GP-B was still far from launch, and as the price for the mission broke the $0.5 x 109 barrier, enthusiasm for the experiment started to wane. In addition, general relativity has been tested in many independent ways at this point, and LAGEOS has confirmed that frame dragging is consistent with general relativity at the ~10% level. This is not to say that it’s not worth precisely measuring frame dragging; it’s just perhaps not the first thing on our list of worries. A number of review panels have been convened over the decades to evaluate the mission’s fate, and each time the mission has squeaked by. A study of the politics behind this mission would be quite interesting. My principal worry about GP-B is that there are essentially two possible results: either GP-B confirms general relativity (in which case everyone says great, and continues to do what they were doing), or GP-B claims a result inconsistent with relativity (in which case everybody questions the result). This is an extremely difficult experiment, and there are many ways for things to go wrong. And, for better or worse, nothing like GP-B will be done again in the near future, and so it will be highly non-trivial to independently test its results.

After many difficult years, the GP-B satellite was finally launched on April 20, 2004. The satellite is an amazing feat of engineering. This is truly a precision science experiment, but one that is being flown in the harsh environment of space rather than being lovingly tended to in a lab in the basement. The gyroscopes are superconducting spheres; the most perfectly engineered spheres ever produced (equivalent to a spherical Earth with no mountain (or valley) higher (or deeper) than 2.4 meters). The spins of the four independent gyroscopes, cooled to 1.8 Kelvin, were monitored for over a year. Although the satellite is still in orbit, at this point the liquid helium which cooled the gyroscopes has boiled away (by design), and the satellite is no longer taking precision data. At this point it remains to analyze the data sent from the satellite, and announce whether or not general relativity is correct.

Originally, yesterday was going to be the big press release circus where NASA announced the results of the mission. But the analysis has run into a number of snags. Even though the gyroscopes are very close to perfect spheres, tiny imperfections cause electrostatic patches on the surface of the spheres (and housing). This breaks the spherical symmetry, and causes a polhode motion. Although this effect was anticipated, it was thought that it would remain constant through the life of the mission. This has not turned out to be the case, and the time variation needs to be understood and accounted for in the analysis. In addition, the surface electrostatic patches interact with the rest of the spacecraft, causing miniscule torques (which vary with the relative alignment of the entire spacecraft about the axis of rotation). Until these effects are well under control, a definitive measurement of frame dragging is impossible. Yesterday’s announcement was that the geodetic precession has been measured to better than 1%, and agrees with the predictions. Although this is indeed an important measurement, it is not what everyone has been waiting for.

After over four decades, it is not unreasonable for the GP-B team to ask for a little extra time to check and double-check their results. It is to their credit that they are being deliberate and meticulous in their analysis. The final results are to be announced this coming December, hopefully leading to yet another important observational test of general relativity. And a conclusion to one of the most technically ambitious experiments ever launched into space.

  • http://blogs.discovermagazine.com/cosmicvariance/daniel daniel

    I just noticed that Jennifer has a very nice post on exactly the same subject, where she goes into more detail on the problems with the GP-B data analysis. She benefits from actually having been present at Francis Everitt’s plenary talk.

  • http://blogs.discovermagazine.com/cosmicvariance/joanne/ JoAnne

    Daniel, thanks for posting this!

  • Mr Odin


  • Pingback: Sunday late night sciency links! « Entertaining Research()

  • DIS

    The patches do not cause the polhode motion. The polhode motion would be there as long as the sphere is not perfect and the spin axis does not lie along one of the principal axii of inertia. This is a purely mechanical effect and has nothing to do with the electrical patches. The patches do play a role in providing a dissipation mechanism and making the polhode period be time dependent as you mentioned.

  • DIS

    Also for people who might prefer a earthly rather than stellar analogy a milliarc second would be the angle subtended by a human hair seen from a mile away. The effect to be measured is equivalent to accurately measuring the angle subtended by 39 human hairs a mile away!

  • http://countiblis.blogspot.com Count Iblis

    If this effect could be measured to a very high degree of precision, then one could measure how fast the Earth’s inner core is spinning see here :)

  • http://tyrannogenius.blogspot.com Neil B.

    Part of the precession effect is from “Thomas precession” – a SRT effect. I have never been satisfied with the various accounts of how angular momentum is conserved by the system including the spinning gyro, the AM vector of which shifts around (that goes for the GRT part of it too.) Consider also the curved space problem: transport the AM vector 1/4 circle in perp. direction along a hyperspace, then forward 1/4 circle, then back to starting point and it looks like “free” change of AM direction.

  • http://blogs.discovermagazine.com/cosmicvariance/daniel daniel

    DIS, thanks for the clarification! The electrical patches don’t cause the polhode motion, they just cause it to change with time because of dissipation. What’s perhaps most amazing to me is that the GP-B team is in the process of modeling this effect (we’re talking about describing a complex distribution of pinned quanta of magnetic flux, and their interactions with the various sensors and housings).

  • DIS

    High. Modeling the pinned quanta is certainly a herculean task. It’s is not impossible as the gyros were monitored almost continuously and, here the changing polhode might actually help as it causes the orientation of the gyros to change with respect to the measuring squid and thus giving more thorough sampling of the fluxon distribution. Actually there are two approaches to mapping the quanta, one is trying to model allthe single vortex sources and their effect, almost impossible, or modeling the magnetic field measured by the squid, that is modeling the magnetic field multipole distribution and its time evolution. The second is exceedingly difficult but given the amount of data has a shot of succeeding. We’ll see…

  • George Musser

    If we were near a rapidly rotating black hole, frame dragging would jump out at us: a gyroscope would wobble all over the place.

    Would frame-dragging have any other obvious effects on intrepid BH-skirting astronauts? Would they feel dizzy, would the precession of particles in their bodies produce radiation, etc.?


  • HDG

    GPB seems to be in the position of modeling their system until they get the result that they expect, and now they’ve asked for yet more time and money to do so. They aren’t doing a blind analysis, I don’t believe. Feel free to correct me if I’m wrong.

    If they published a result that disagreed with theory, everyone would think that they didn’t analyse their data (which they’ve had for a year now, and had years to prepare for before that) properly. So how can this be scientifically useful? Their results either agree with theory, in which case they are uninteresting because they’ve essentially massaged their data to get that result, or they’ve wasted a billion dollars getting a result that no one believes. I can launch an experiment which will fail in the same manner for half the price, and take only half the time :)

    And it doesn’t look likely that they’ll get down to the design goal of measuring frame-dragging with 1e-4 precision either. They’re struggling to get 1%.


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