CHAPTER 4
Does Gravity Do the Twist?
Gravity Probe-B, the Relativity Gyroscope Experiment, may go down in the history of physics as one of the most difficult, most costly and longest physics experiments ever performed. From conception to completion it took almost half a century and cost $750 million, while the actual data taking took only sixteen months. The experiment was the brainchild of three naked men basking in the noonday California sun in the closing weeks of 1959. The three were all professors at Stanford University in Palo Alto. One of them was the eminent theoretical physicist Leonard I. Schiff, well known for his pioneering work in quantum theory and nuclear physics. In the late 1950s, however, he had become interested in gravitation theory. The second professor was William M. Fairbank, an authority on low-temperature physics and superconductivity, who had just arrived at Stanford in September of 1959, lured there from Duke University in North Carolina. The third was Robert H. Cannon, also a recent acquisition by Stanford, an expert in aeronautics and astronautics from MIT.
But before we learn how these naked professors came to formulate this experiment, let us first answer the question, what does a gyroscope have to do with relativity? When we think of a gyroscope we imagine something like a spinning flywheel. If the flywheel spins rapidly enough, its axis of rotation always points in the same direction, no matter how we rotate the platform or laboratory in which it sits, as long as the gyroscope is mounted on the platform using gimbals that allow it to turn freely with minimum friction. In other words, the axis of the gyro always points in a fixed direction relative to inertial space or to the distant stars. The difficulty you have in turning a rapidly spinning bicycle wheel is an everyday example of this gyroscopic effect. This, of course, is the basic principle behind the use of gyroscopes in navigation of ships, airplanes, missiles and spacecraft (GPS has now taken over many aspects of such navigation, of course). When attached more rigidly to a platform, this gyroscopic action is what keeps personal transporters like Segways or hoverboards from toppling over. However, according to general relativity, a gyroscope moving through curved spacetime near a massive body such as the Earth will not necessarily point toward a fixed direction; instead, its axis of spin will change slightly, or precess. Two distinct general relativistic effects can cause such a precession.
The first of these is called the “geodetic effect,” and is a consequence of curved spacetime. Our everyday experience with gyroscopes tells us that as a gyroscope moves through space, its spin axis should maintain the same direction, a direction parallel to its previous direction. However, in curved spacetime, parallel in the local sense does not necessarily mean parallel in the global sense, and so upon completing a closed path, the gyroscope axis can actually end up pointing in a different direction than the one it started with.
A simple way to see how this can happen is to imagine a two-dimensional world, much like that of the nineteenth-century book Flatland by E. A. Abbott, but here confined to the surface of a sphere. Because the inhabitants of this “Sphereland” are only two-dimensional, they can’t really construct the right kind of gyroscopes; as an alternative, they can take a little pointer and slide it about on their sphere in a way that keeps it always parallel to its previous direction, veering neither to the right nor to the left (up and down are not options in Sphereland). The pointer’s tip then plays a role analogous to the spin axis of our gyroscope. To demonstrate what can happen, the Spherelanders consider the following closed route (see Figure 4.1): from a point at zero degrees longitude on the equator, move east along the equator to 90 degrees longitude, then go due north to the North Pole, make a 90 degree turn, and go due south back to the starting point on the equator. Suppose the Spherelanders start the pointer out parallel to the equator, pointing east. When they reach the first turn the pointer will still point east, and when they head north the pointer will now be perpendicular to the path. At the North Pole they make a 90 degree left turn, but now the pointer’s direction is to their rear, which is to the north as they head south. When they reach the equator once again, the pointer, which has been kept parallel to itself all the way, now points north, whereas it started out pointing east. This change in direction of the pointer is what we would call precession in the case of a gyroscope. The curvature of the two-dimensional surface of Sphereland accounts for this precession, and we understand it without much difficulty. The difference between this example and the geodetic effect on a moving gyroscope is that it is the curvature of spacetime and not just the curvature of space that is important.
Figure 4.1 Precession in Sphereland. A pointer is carried parallel to itself from 0 degrees longitude to 90 degrees longitude. The path then turns north, but the pointer continues to point east, and maintains that direction up to the North Pole. A right-angle turn of the path leaves the pointer pointing to the rear. The pointer continues to point to the rear (north) back to the starting point. The result is a precession of the direction of the pointer from an easterly direction to a northerly direction.
The geodetic effect has been known since the early days of general relativity. The first to calculate the effect was Willem de Sitter, the Dutch theorist who had played a pivotal role in bringing general relativity to the attention of Eddington and the British physics community. In a paper published in the Monthly Notices of the Royal Astronomical Society less than a year after Einstein’s November 1915 papers on general relativity, de Sitter showed that relativistic effects would cause the axis perpendicular to the orbital plane of the Earth–Moon system to precess at a rate of about 0.02 arcseconds per year. De Sitter was not thinking in terms of gyroscopes; instead, he had in mind how the combined relativistic gravitational fields of the Earth and Sun would perturb the Earth–Moon orbit. However, Eddington and others soon pointed out that the Earth–Moon system is really a kind of gyroscope, with the axis perpendicular to the orbital plane playing the role of the gyroscope’s rotation axis, so the de Sitter effect was effectively a precession of the Earth–Moon gyroscope. But if this is the case, then the Earth, as it spins about its own rotation axis, is also a gyroscope, so in fact both the Earth and the Earth–Moon system should precess in the same way. At the time, measuring such a small effect was hopeless. Only in recent years has a technique called “lunar laser ranging” (see Chapter 5 for a discussion) given such precise information about the Earth–Moon orbit that the de Sitter effect could be measured, to around half a percent.
Instead of the Earth–Moon system, consider a more down-to-Earth situation: a laboratory-size gyroscope orbiting the Earth with its axis lying in the orbital plane, say pointing vertically (see the gyroscope labeled “start” in Figure 4.2). Without general relativity, the gyroscope would maintain its direction relative to distant stars as it orbits the Earth, and so after a complete orbit it would again be pointing in the same vertical direction. But general relativity predicts that as the orbit carries the gyroscope around through the Earth’s curved spacetime, the gyroscope will experience a precession within the orbital plane at a rate of a little over a thousandth of an arcsecond per orbit. The direction of the precession is in the same sense as the motion of the gyroscope around its path, counterclockwise if looking down on the orbit from above (see Figure 4.2). Since the period of revolution of a low Earth orbit is about 1.5 hours, the net precession in one year will be around 6 arcseconds. This is the geodetic effect.
Figure 4.2 Geodetic precession of a gyroscope in near-Earth orbit. After one orbit, the direction of the gyroscope axis has rotated relative to its initial direction in the same sense (counterclockwise) as that of the orbit. The net effect over one year (5,000 orbits) is 6 arcseconds.
The other important relativistic effect on a gyroscope is known as the dragging of inertial frames, one of the most interesting and unusual of the predictions of general relativity (see Figure 4.3). The origin of this effect is the rotation of the body in whose gravitational field the gyroscope resides. According to general relativity, a rotating body attempts to “drag” the spacetime surrounding it into rotation. The simplest way to get a picture of the consequences of this dragging is to use a fluid analogy.
Figure 4.3 Left: Swimmer and air mattresses in a pool with a whirlpool. All are tethered to the bottom of the pool so that they don’t move around the pool. The air mattress at the edge of the whirlpool rotates in a clockwise direction because water closer to the center moves faster, while the air mattress at the center rotates counterclockwise with the water. A vertical swimmer treading water does not rotate. Right: Dragging of inertial frames. Stationary gyroscopes near a rotating Earth can precess because of dragging of spacetime by rotation of the Earth. If the axis lies perpendicular to the rotation axis of the Earth, the precession will be opposite to the Earth’s rotation for a gyroscope at the equator, and with the Earth’s rotation for a gyroscope at the pole. If the axis is parallel to the Earth’s rotation axis then there is no precession. For other locations and other orientations of the gyroscope axis, the precession will be between these extremes.
Consider a large and deep swimming pool with a very large drain in its center. Water flows down this drain, producing a whirlpool at the surface of the kind we commonly see in bathtubs. To keep the level of the pool constant, let us assume that the water lost down the drain is continuously being replaced through inlets at the sides of the pool. Imagine now three Stanford professors floating in the pool. Professor Schiff is floating on an air mattress between the whirlpool and the edge of the pool, with his feet closest to the drain. Professor Fairbank is floating on a similar air mattress but is straddling the whirlpool, well above the drain of the deep pool. Professor Cannon is treading water. For simplicity’s sake, let us also assume that each professor is anchored to the bottom of the pool by a tether attached to his waist. This is to prevent them from circling the drain, which would complicate the effect we are looking for. With this arrangement, the behavior of these professors is very similar to that of three gyroscopes in a spacetime being dragged by a rotating body. As with all the analogies for relativistic effects that we have used in this book, one must be careful not to push the analogy too far. Gyroscopes in spacetime are not the same as air mattresses in water, but if the analogy helps us remember the qualitative effects, it is a useful one.
First consider Professor Schiff. Because the water closer to the whirlpool moves around more quickly than the water farther away, the foot of his air mattress is dragged more quickly than the head, and so while the whirlpool rotates, say, counterclockwise as seen from above, Schiff’s air mattress rotates or precesses in a clockwise direction. This is precisely the behavior of the axis of a gyroscope on the equatorial plane in a dragged spacetime, with its axis pointing outward (Figure 4.3). Contrast this behavior with that of Professor Fairbank, whose air mattress straddles the whirlpool. The head and foot of his mattress are also pulled by the water, but because they are on opposite sides of the whirlpool the mattress is pulled in the same sense as the whirlpool, in other words counterclockwise. This is just what happens to a gyroscope on the rotation axis of the dragged spacetime, with its own axis perpendicular to the rotation axis. Finally, we see that Professor Cannon, who is treading water, doesn’t do much of anything. The direction of his body remains vertical, no matter where he goes in the pool. The same is true for a gyroscope whose axis is parallel to the rotation axis of the central body; the dragging of spacetime has no effect on it.
Of course, there is another key difference between the air mattress precession and the gyroscope precession due to the dragging of inertial frames: size. The predicted precession for a gyroscope on the equator of the Earth is only one-tenth of an arcsecond per year. Unlike the geodetic precession, the dragging of inertial frames does not depend on whether or not the gyroscope is moving through spacetime (the air mattresses precessed even though they were stationary in the pool), and so there is little difference in this case between the precession of a gyroscope on the Earth and that of a gyroscope in orbit. For a low Earth orbit it is between 0.1 and 0.05 arcseconds per year, depending on the tilt of the orbit relative to the Earth’s equatorial plane and on the initial direction of the gyroscope axis relative to the Earth’s rotation axis.
What makes this effect so interesting and important is that while the other effects that we have described in this book, including geodetic precession, have to do with such concepts as gravitational fields, curved spacetime, and nonlinear gravity, this effect tells us something about the inertial properties of spacetime. If you ask yourself “Am I rotating?” and you wish an answer with more accuracy than you can get simply by seeing if you are getting dizzy, you usually turn to a gyroscope, for the axis of a gyroscope is assumed to be non-rotating relative to inertial space. If you were to build a laboratory whose walls were constructed to be lined up with the axes of three gyroscopes arranged to be perpendicular to each other, you would conclude that your laboratory was truly inertial (and if the laboratory were in free fall, that would be even better). However, if your laboratory happened to be situated outside a rotating body, the gyroscopes would rotate relative to the distant stars because of the dragging effect just described. Therefore, your laboratory can be non-rotating relative to gyroscopes, yet still rotate relative to the stars. Relativists make a careful distinction between a laboratory that is locally non-rotating, that is tied to gyroscopes, and one that might rotate relative to distant stars. In this way, general relativity rejects the idea of absolute rotation or absolute non-rotation, just as special relativity rejected the idea of an absolute state of rest.
To understand this more clearly, contrast it with Newtonian theory. True, Newtonian theory proposed that all inertial frames are equivalent, regardless of their state of motion, but it still had to allow an absolute concept when it came to rotation. A simple example, known as Newton’s bucket, will illustrate this idea (see Figure 4.4). Fill a bucket with water, place it on a turntable, and start the turntable spinning. As the bucket starts to spin, the water doesn’t do much of anything at first, but eventually the friction between the water and the walls of the bucket causes the water to spin along with the bucket. As a consequence of this, the surface of the water becomes concave and the water begins to climb up the sides of the bucket; a depression forms in the center. Quite naturally, we attribute this behavior to centrifugal forces pushing the water away from the rotation axis. When the turntable is stopped, eventually the water slows down and returns to its initial state with a flat surface.
Figure 4.4 Newton’s bucket. Left: The bucket is not rotating and the surface of the water is flat. Right: The bucket is rotating and the surface of the water is concave. Would the surface be concave if the bucket were “not rotating” and the universe rotated around it?
As mundane and commonplace as this simple observation is, it has led to some of the most intriguing and vexing philosophical questions. Newton himself wrestled with them. One question is, how does the water know that it is rotating and should have a concave surface instead of a flat one? If we truly abhor the concept of absolute space, as relativity in either its Newtonian or Einsteinian forms teaches us, we cannot answer that the water knows that it is rotating relative to absolute, non-rotating space. With respect to what then? The best we can do is to answer that somehow the water knows that it is rotating relative to the distant stars and galaxies. As reasonable as this sounds, it does beg two questions. Suppose we performed this bucket experiment in an otherwise completely empty universe. With nothing to which to refer its state of motion, would the water know what to do as the turntable spun? Would its surface become concave or stay flat? That is the first question, to which there is no satisfactory answer based on physics. Up to a point, of course, this question is irrelevant, because we don’t live in an empty universe anyway.
The second question is somewhat more meaningful: Suppose we leave the bucket at rest, and let the entire universe rotate around it with the same rotation rate as the bucket had in the previous experiment, but in the opposite sense. Would the water become concave as before? If only the rotation of the bucket relative to the distant matter in the universe is important, then the two experiments should give the same concave shape for the water’s surface. In other words, it should not matter whether we say that the universe is non-rotating and the bucket is rotating, or that the bucket is non-rotating and the universe is rotating. Only the rotation of one relative to the other is relevant.
Unfortunately, Newtonian gravity predicted that the rotating universe would have no effect on the bucket, and therefore you had to invoke an absolute space to understand rotation. But in general relativity, the dragging of inertial frames provides the way out of this absolutism. As early as 1923, Eddington suggested as much in his beautiful textbook on general relativity. However, it wasn’t until the mid 1960s that theorists could show that the dragging effect provides a good accounting of how rotation is indeed relative. The demonstration consisted of a simple model calculation of the following situation: Imagine a spherical shell of matter, like a balloon, that is rotating about some axis (for the purposes of this discussion we can ignore the flattening of the balloon caused by centrifugal forces). At the center of the shell is a gyroscope with its spin axis perpendicular to the axis of rotation of the balloon. According to Newtonian gravitation, the interior of the balloon is absolutely free of gravitational fields. The gyroscope feels no force whatsoever. To a first approximation, the same is true in general relativity, except for the dragging of inertial frames effect, which produces forces in the interior of a rotating shell just as it would in the exterior. The effect of these forces is to cause the gyroscope to precess in the same direction as the rotation of the shell, but as you might imagine from our previous discussion, for a shell of planetary dimensions, say of the radius of a typical planet and containing the mass of a typical planet, the rate of precession is very small, much smaller than the rate of rotation of the shell.
But now imagine increasing the mass of the shell and increasing its radius (keeping its rate of rotation the same), and consider the limit in which the mass tends toward the mass of the visible universe and the radius tends toward the radius of the visible universe. The remarkable result is that as you increase these values, the rate of precession of the gyroscope in the center grows and, in the limit, tends toward the rate of rotation of the shell. In other words, inside a rotating universe the axes of gyroscopes rotate in step with the rotation of the universe; their axes are tied to the directions of distant bodies in that universe. Therefore, a laboratory tied to the gyroscopes, which we would define to be non-rotating, would indeed be non-rotating relative to the distant galaxies. Imagine now that we placed a bucket inside the shell instead of a gyroscope, and imagine that we kept the bucket fixed, or non-rotating, with the shell rotating around it. As you expand the size of the rotating shell, residual frame dragging forces would cause the water to climb the sides of the bucket. Therefore, an observer in this scenario would see exactly the same physical phenomenon as would an observer looking at a rotating bucket inside a non-rotating universe. The existence of the dragging of inertial frames then guarantees that rotation must be defined relative to distant matter, not relative to some absolute space. This is what makes the detection of this effect so vital.
In addition to resolving this conceptual problem, the relativistic frame dragging effect has important astrophysical implications beyond the solar system. Astronomers have found that some of the incredible outpouring of energy from quasars is directed along narrow jets of matter that stream at nearly the speed of light in opposite directions from a compact central region. The leading model for this phenomenon involves a vast disk of hot gas spiraling inward around a spinning supermassive black hole (we will return to these beasts, including the one in our own Milky Way, in Chapter 6). The combination of the magnetic fields generated by the charged particles in the gas and the extreme dragging of spacetime in the vicinity of the black hole generates strong electric fields that can accelerate particles away from the black hole along its spin axis. The particles can reach speeds close to that of light, and upon interacting with the twisted magnetic field lines they can emit radio waves and other forms of electromagnetic radiation. These radio jets can be seen extending millions of light years away from the central quasar. Rotating black holes represent extreme examples of the effect of the dragging of inertial frames, and so it would be very desirable to verify that this effect exists.
All well and good. But still, the effects on gyroscopes on and near the Earth are horribly small. What would possess anyone to actually try to measure them? It is here that the three Stanford professors return to the story.
At Stanford University in the 1950s, back before the days of coeducational athletic facilities, the Encina gymnasium and its walled-in, open-air swimming pool was restricted to males only (the women’s gym was on the other side of the campus). As such, it was customary for users to swim in the nude. Schiff had a virtually unshakable routine of going to the Encina pool every day at noon, swimming 400 yards, and eating a bag lunch afterwards while sunbathing. Even though he was chairman of the physics department, he would try his best to schedule meetings and appointments so as not to conflict with his noon swim. Fairbank knew about Schiff’s daily routine, and when he bumped into Cannon on campus one day in late 1959 and they began to talk about gyroscopes, Fairbank suggested that they go see Schiff at the swimming pool.
Each of these men had had gyroscopes on his mind for a while. Schiff had been thinking about gyroscopes ever since he opened his December 1959 issue of the professional physicists’ magazine Physics Today and saw the advertisement on page 29. There, hovering in an artist’s conception of interstellar space, was a perfect sphere girdled by a coil of electrical wires, captioned “The Cryogenic Gyro.” The advertisement announced the development at the Jet Propulsion Laboratory in Pasadena of a super new gyroscope consisting of a superconducting sphere supported by a magnetic field (from the coils), all designed to operate at 4 degrees above absolute zero. Schiff had taken a strong interest in tests of general relativity lately, and so he asked himself whether such a device could detect interesting relativistic effects. During the first two weeks of December he carried out the calculations, finding both the well-known geodetic effect, as well as the dragging of inertial frames effect. The latter discovery was entirely new, at least as applied to gyroscopes. Back in 1918, two German theorists, Josef Lense and Hans Thirring, had shown that the rotation of a central body such as the Sun would produce frame dragging effects on planetary orbits that were unfortunately utterly unmeasurable at the time, but no one had apparently looked at the effect of the rotation of a central body on gyroscopes.
Fairbank’s field was low-temperature physics, the properties of liquid helium, and the phenomenon of superconductivity, the disappearance of electrical resistance in many materials at low temperatures. He had also been thinking about the potential for a superconducting gyroscope that could be built in the new laboratory that he was setting up at Stanford, and he and Schiff had begun to talk about how these relativistic effects could be detected. Fairbank suggested measuring the precessions using gyroscopes in a laboratory on the equator, but this did not look promising. The reason was gravity. The best gyroscopes of the day had as their main element a spinning sphere, just as in the JPL advertisement. But the sphere had to be supported against the force of gravity, and the standard method of doing this was by electric fields or by air jets. Unfortunately, the forces required to offset gravity were so large that they introduced spurious forces or torques on the spinning ball that gave its spin axis a precession thousands of times larger than the relativistic effect being sought after, though easily small enough to permit accurate navigation and other commercial uses. This problem would effectively go away if the gyroscope were in orbit, where the gravitational forces are zero to high accuracy, and essentially no support is required. But remember, this was only two years after the Soviet Union’s launch of Sputnik, the first orbiting satellite, and Schiff and Fairbank could not imagine realistically being able to do this.
This was where Cannon came in. Cannon knew gyroscopes. He had helped develop gyroscopes used to navigate nuclear submarines under the Arctic icecap. He also knew aeronautics, and he was active in the fledgling space race that Sputnik had started. Before coming to Stanford from MIT, Cannon had already begun to consider the improvements in spacecraft performance that would come with orbiting gyroscopes.
Finally, the three were together (in their birthday suits) at the Stanford pool. When Schiff and Fairbank told Cannon about the proposed experiment, Cannon’s first response was astonishment. To pull it off, they would need a gyroscope a million times better than anything that existed at that time. His next response was: Forget about doing it on Earth, put it into space! An orbiting laboratory is not at all farfetched, and in fact NASA was already laying plans for an orbiting astronomical observatory. Furthermore, Cannon knew the right people at NASA whom they could contact. With that, a five-decade adventure had begun. Only Cannon would live to witness the end of the story.
It is one of those strange twists of scientific history that, almost simultaneously with Schiff, Fairbank and Cannon, someone else was thinking about gyroscopes and relativity. Completely independently of the Stanford group, George E. Pugh at the US Pentagon was doing the same calculations. Pugh worked for a section of the Pentagon known as the Weapons Systems Evaluation Group, and for him, toying with gyroscopes was a perfectly reasonable activity because gyroscopes have obvious military applications in the guidance of aircraft and missiles. In a remarkable memorandum dated 12 November 1959, Pugh outlined the nature of the two relativistic effects, although he had the frame dragging effect wrong by a factor of two, and described the requirements for detecting them using an orbiting satellite. Some of Pugh’s ideas, such as a technique for compensating for the atmospheric drag felt by the satellite, ultimately became important ingredients in the Stanford experiment. It is highly unlikely, however, that the Pentagon actually incorporated relativistic gyroscope effects into its military guidance systems. Pugh’s classified work could not be published in the open scientific literature, and so Schiff was initially given credit for the idea of a gyroscope test. Only later was Pugh’s work declassified and recognized for equal credit.
In January 1961, Fairbank and Schiff kicked off the experiment officially with a proposal to NASA for an orbiting gyroscope experiment. Fairbank also recruited a young low-temperature physicist named C. W. Francis Everitt to join the Stanford project. Born in England in 1934, Everitt had received a Ph.D. from Imperial College in London in 1959, followed by a post-doctoral stint at the University of Pennsylvania, working on liquid helium. In late 1963, NASA began funding the initial research and development work at Stanford to identify the new technologies that would be needed to make such a difficult measurement possible. In 1971, NASA selected its Marshall Space Flight Center in Huntsville Alabama as program manager, both for the Stanford experiment and for the rocket redshift experiment that was being developed by Robert Vessot at Harvard. NASA headquarters designated Vessot’s experiment as Gravity Probe-A, planned for a 1976 launch, to be followed soon thereafter by the gyroscope experiment, designated Gravity Probe-B or GP-B. While the redshift experiment went off as planned (see Chapter 2), things turned out rather differently for GP-B. It is not known if serious plans were ever made for a Gravity Probe-C, Gravity Probe-D, and so on.
Stanford’s modest research and development effort lasted until about 1981, when Everitt became Principal Investigator of the project, and soon it moved toward the mission design phase. At that time, plans called for a preliminary flight on board the Space Shuttle to test key technologies to be used in GP-B, followed by a launch of the full spacecraft from the Shuttle a few years later. Unfortunately the 1986 Space Shuttle Challenger catastrophe forced a cancelation of the technology test, and a complete redesign of the spacecraft for a launch from a Delta rocket.
The goal of the experiment was to measure both the geodetic effect and the frame dragging effect to an accuracy of better than a milliarcsecond per year. Because the smaller frame dragging effect is only about 40 milliarcseconds per year for the orbit being planned (a polar orbit at an altitude of about 642 kilometers), this meant that a one or two percent measurement of this effect would be possible. The task of building an orbiting gyroscope laboratory that could measure such tiny effects put the Stanford scientists at or beyond the frontiers of experimental physics and precision fabrication techniques, presenting them with apparently insuperable problems. Miraculously, they managed to overcome each one.
A brief description of the experiment will illustrate the things that had to be done. The gyroscopes (for redundancy, there were four) were spherical rotors of fused silica, about 4 centimeters in diameter, housed in a chamber (see Figure 4.5). The rotors had to be uniform in density and perfectly spherical in shape to better than one part in a million. This is like imagining an Earth where the tallest mountain and deepest valley reach 1 meter! The reason for this requirement is that gravitational forces from the Earth and Moon and from the spacecraft itself would interact with any mass irregularities in the rotor and cause spurious precessions. Similar effects caused by gravitational forces from the Sun and Moon acting on the Earth’s equatorial bulge make the Earth’s rotation axis precess with a period of about 26,000 years, causing the North Star to appear to wander from true north. Overcoming the problems of making a perfect sphere and then testing how spherical it is to the above precision required the invention of completely new fabrication and testing procedures.
Figure 4.5 GP-B rotor and its enclosing chamber. In space, the rotor is levitated inside the spherical chamber. Six electrodes spaced around the wall of the chamber sense if the rotor gets too close and send signals to the spacecraft to nudge it in the proper direction. The “pick-up loop” is a superconducting wire embedded in the wall to measure any changes in direction of the magnetic field of the rotor caused by precession of its spin. The “spin-up channel” lets helium gas from the surrounding dewar of liquid helium flow past the rotor, spinning it up to around 4,000 revolutions per minute, after which the gas is vented to space. Credit: NASA and Stanford University.
The main reason for going into space was to avoid having to support the gyroscopes against the force of gravity, because those support forces can generate spurious precessions. Unfortunately, while the gyroscopes move in complete free fall inside the spacecraft, the spacecraft itself is being pushed around by the residual atmosphere of the Earth, by the solar wind and by periodic attitude control forces required to orient the spacecraft. How do you avoid having the gyroscopes collide with the walls of the spherical chambers inside which they are spinning? The answer is a technique called “drag-free control.” Six circular electrodes are installed in the walls of the spherical chambers in which the rotors reside, so that if a rotor gets too close to an electrode a signal is sent to thrusters that nudge the spacecraft a little bit to keep the separation at a pre-selected value. This was a delicate and critical technology, because the average gap between each rotor and the wall of its spherical chamber was about one-thirtieth of a millimeter. We will return to drag-free control in Chapter 9, when we discuss LISA, the planned gravitational wave detector in space.
If a rotor is perfectly spherical, how do you determine the direction of its spin? You can’t just attach a stick to the rotor at one of the poles, because the stray gravitational forces acting on the mass of the stick would cause enormous precessions that would swamp the relativity effects. The solution was to coat each rotor with a thin, perfectly uniform layer of the element niobium. When the ball is spinning at low temperatures, near absolute zero, the niobium becomes a superconductor, its electrical resistance vanishes, and it develops a magnetic field whose north and south poles are exactly aligned with the rotation axis of the rotor. A tiny superconducting wire, called a “pick-up loop,” is embedded in the wall of the chamber that houses the rotor. If the axis of the rotor changes direction, the change in the magnetic field induces currents in the pick-up loop that are measured by very precise devices known as superconducting quantum interference devices, or SQUIDs, also operating at near absolute zero. This required new techniques for working near absolute zero using liquid helium, and adapting those techniques to a space environment. The spacecraft itself contained a very special “thermos bottle” or dewar to hold the 2,400 liters (over 600 gallons) of liquid helium and to maintain it at 1.8 degrees above absolute zero.
If the balls are perfectly spherical, how were they to be set spinning? The solution to this problem was to incorporate into the wall of the chamber that housed each rotor a small “spin-up channel” that forces helium gas past the sphere, using friction to get it spinning. The helium gas came from natural “boil off” from the liquid helium used to cool the apparatus (no thermos can keep liquid helium cold enough to not boil some of it). At the start of the space flight the four rotors were spun up to around four thousand revolutions per minute, after which venting holes in the housing chamber allowed the helium gas to escape to the vacuum of space.
As we described previously, the gyroscopes precess relative to the distant stars, so a very accurate telescope had to be designed and built into the spacecraft package to determine a reference direction accurate to the milliarcsecond level per year. The spacecraft was controlled so that the telescope always pointed toward a selected star, called IM Pegasi. This star lies at a distance of about 300 light years from Earth, about 17 degrees north of the equator. In addition to being optically bright and relatively isolated in the sky, it was also bright in the radio band. This was important because, being in the environment of the Milky Way, it moves, and thus its own motion relative to truly distant objects, i.e. the quasars, needed to be measured to the required precision using VLBI (see Chapter 3).
While simple to state in words, each of these problems was a major multi-year research and fabrication project, and integrating all the components into a functioning spacecraft was a major challenge. The cancelation of the Shuttle test mission in 1986 and the spacecraft redesign resulted in delays and cost overruns for the GP-B program. Similar delays and budget problems with the Hubble Space Telescope, combined with the discovery of its flawed main mirror following its launch in 1990, caused considerable anxiety at NASA about budgets, and worries among astronomers and space scientists about funding for their own projects. One result was rising criticism of the GP-B program and calls for its cancelation. In fact, on more than one occasion NASA and the Office of Management and Budget, the fiscal oversight arm of the US Administration, would set the GP-B budget to zero for the subsequent fiscal year, effectively canceling the project, only to find that members of Congress would restore the budget following judicious lobbying by Francis Everitt and other supporters of GP-B.
In 1992, Daniel Goldin was appointed NASA Administrator by President George H. W. Bush, and he was determined to end the bickering over GP-B. He asked the National Academy of Sciences to conduct a thorough review of the project, promising to abide by their recommendation, whether it be thumbs up or thumbs down.1 In addition to investigating the technical challenges that remained to be overcome and estimating the remaining cost of the mission, the panel debated whether the scientific return of the mission was worth it. This debate was not trivial.
When GP-B was first conceived in the early 1960s, tests of general relativity were few and far between, and most were of limited precision. But by 1994 there had been enormous progress in experimental gravity in the solar system and in binary pulsars, as we have described in this book. Some panel members argued that the many experiments had so constrained the theoretical possibilities in favor of general relativity that GP-B would not give any improvement or new information. The counter-argument was that all the prior experiments involved phenomena entirely different from the precession of a gyroscope, and therefore that GP-B was testing something potentially new. Another issue was that, if GP-B were to give a result in disagreement with general relativity, it would very likely not be believed, and given the high cost of the experiment, the probability of repeating it was extremely small. In the end, while the panel was not unanimous, a majority did recommend going ahead with GP-B, and Goldin committed NASA to the project. NASA then engaged the aerospace company Lockheed Martin in Palo Alto to build, integrate and test the spacecraft in collaboration with Stanford and Marshall Space Flight Center.
The satellite finally was launched on 20 April 2004, and injected into an almost perfectly circular polar orbit at an altitude of 642 kilometers above the Earth’s surface, precisely as planned. Almost every aspect of the spacecraft, its subsystems and the science instrumentation performed extremely well, some far better than expected. The plan of the mission was to begin with a three-month period of testing, calibration and fine-tuning. This would be followed by 12 months of science data taking, and a final month of additional calibrations. Early on in the science phase, the data showed clearly the larger geodetic precession of all four gyroscopes, giving initial hope that all would go well. That hope was soon dashed when a nasty source of error reared its head. Each rotor appeared to be experiencing strange precessions of its spin axis, with no apparent pattern or commonality among them. As the sixteen-month mission period drew to a close in the fall of 2005, there was serious concern that the experiment would fail to detect the tiny frame dragging precession, the main goal of the mission.
What ensued during the data analysis phase following the mission was worthy of a detective novel. The critical clue came from the calibration tests carried out at the end of the mission. The four rotors had been set spinning with their spin axes initially parallel to the axis of the telescope directed to the guide star. The spacecraft also rolled slowly about this axis about once every 78 seconds. For one of the post-science tests, they deliberately forced the spacecraft to point away from the guide star by as much as 7 degrees. This was such an extreme maneuver that you would never try it at the start of the mission, because if anything went wrong the game would be over. After the data has been taken and safely stored away, it is worth the risk. As it happened, the rotors experienced unexpectedly large precessions of their spins during the maneuver, but there was a very specific pattern to the effects. Unraveling this pattern helped the GP-B team to determine that the extra precessions were being caused by interactions between random patches of electric potential fixed to the niobium surface of each rotor, and similar patches on the inner surface of its spherical chamber. Such patches were known to occur on superconducting niobium films, but pre-flight tests of the rotors had shown that the patches would be too weak to cause a problem. For some unknown reason, the rotors in the spacecraft developed stronger patches. This insight allowed the researchers to build a mathematical model for the “patch effects” and thereby to subtract the anomalous precessions from the data on each rotor. When this was done, all four rotors showed the same precession behavior, clearly revealing both the larger geodetic effect and the smaller frame dragging effect. The original goal of GP-B was to measure the frame dragging precession to about 1 percent, but the problems discovered over the course of the mission dashed the initial optimism that this was possible. Everitt and his team had to pay the price of the increase in measurement uncertainty that came from using a complex model to remove the anomalous precessions. The experiment uncertainty quoted in the final result was roughly 20 percent for the frame dragging effect, but the result agreed with general relativity.
This data analysis effort took five years. When the long-awaited results were finally announced at a NASA press conference on 4 May 2011, the feeling of many could be summed up by the opening line of the song by the great blues singer Etta James: “At laaaassst, my love has come along …” The half-century adventure started by three naked professors was over.
The story of Gravity Probe-B has all the ingredients of a case study in science politics, raising many thorny questions about how science, especially “big” science, is carried out. How do we balance the value of a scientific return against the cost of a project? What is the best way to make critical decisions, particularly concerning cancelation of projects? How do we weigh the value of different kinds of science, say fundamental physics versus astronomical discovery, in setting priorities or deciding among competing proposals or competing scientific constituencies?
For GP-B, these kinds of questions became even more relevant in 1986, when a young post-doctoral researcher at the University of Texas named Ignazio Ciufolini suggested a way to measure the frame dragging effect almost as accurately as the stated goal for GP-B, and at a tiny fraction of the cost. He pointed out that general relativity predicts that the tilted orbital plane of a body revolving around a rotating object such as the Earth will rotate by a small amount, in the same direction as the rotation, as a result of frame dragging. One consequence is that the point where the orbit crosses the equatorial plane of the Earth will rotate (see Figure 4.6). This was one of the effects that Lense and Thirring had pointed out in 1918. But in 1976 geophysicists had launched an Earth-orbiting satellite called LAGEOS, and Ciufolini realized that precision tracking of such satellites could potentially detect this frame dragging effect.
Figure 4.6 Frame dragging and LAGEOS. The rotation of the Earth causes the plane of an inclined LAGEOS orbit to rotate at about 30 milliarcsecond per year in the same sense as the rotation of the Earth (short arrow). The variations in the Newtonian gravity of the Earth caused by its flattening and by the uneven distribution of mass also cause the planes to rotate. The amount of rotation is as large as 126 degrees per year, but the direction depends on the inclination angle of the orbit. For LAGEOS I (solid arrow) and II (dashed arrow), the effects are in the opposite direction. Inset: The LAGEOS I satellite, showing the corner reflectors embedded on the surface. Credit: NASA
LAGEOS is an acronym for Laser Geodynamics Satellite, and it is about as simple a satellite as one could possibly imagine. It is a massive spherical ball of solid brass covered in aluminum weighing about 400 kilograms. The surface is studded with 426 fused silica glass mirrors, called retroreflectors, each in the shape of one corner of the interior of a cube (see Figure 4.6). A light ray that approaches any one of the “corner-cube” mirrors will bounce off one face then off an opposite face and then return in exactly the same direction from which it came. By sending pulsed laser beams from Earth and measuring the round-trip travel time of the pulses, researchers can measure the distance between the laser and the satellite with sub-millimeter precision. This technique is called “laser ranging” and was developed during the late 1960s for precise ranging to the Moon (see page 102). The satellite orbits at an altitude of 5,990 kilometers (or 12,200 kilometers from the center of the Earth) on a nearly perfect circle. Because it is so massive and simple (for example, it has no large solar panels), the residual atmosphere at that altitude has almost no effect on it. It even contains a plaque designed by astronomer Carl Sagan providing information about the present Earth for future humanity (if any still exist) when the satellite reenters the atmosphere and falls to Earth in 8.4 million years! Because its orbit is so pure, geophysicists could use laser ranging to it to measure the shape of the Earth, and to study continental drift and other dynamics of the Earth’s crust.
But Ciufolini immediately recognized a difficulty. The Earth is not perfectly spherical, but instead is slightly flattened at the poles and bulges a bit at the equator, a result of its rotation. The deviation is only one part in two thousand, but it modifies the Newtonian gravitational field of the Earth in such a manner that those deviations cause the plane of LAGEOS to rotate in the same direction as the relativistic frame dragging effect. Ciufolini calculated that the relativistic effect would be about 30 milliarcseconds per year. However, the effect due to the Earth’s bulge is huge, 126 degrees per year, almost fifteen million times larger. There was no way to measure this tiny effect on top of such a large effect, and although the value of the Earth’s flattening had been measured to reasonable accuracy, it wasn’t good enough.
Nevertheless, Ciufolini had an idea to get around this problem. If there were a second LAGEOS satellite orbiting at the same altitude and in an equally circular orbit, but with its inclination relative to the equator chosen so that the two inclinations added up to 180 degrees, then the calculations showed that the Newtonian rotation of that orbit would be exactly the same as for the existing LAGEOS, but in the opposite sense. The relativistic rotation would be exactly the same size and in the same direction for both orbits; this effect does not depend on the tilt angle. Thus, one could measure the rate of rotation of the planes of each orbit and simply add them together. The Newtonian part would cancel exactly, leaving twice the relativistic part. Injecting a satellite into just the right orbit would be challenging, but doable. Ironically, Ciufolini’s proposal was a variation of a 1976 idea by none other than Francis Everitt and his colleague Richard van Patten; their proposal was for two satellites in polar orbits about 600 kilometers above the Earth, moving in opposite directions. In this configuration the Newtonian effect is much, much smaller, making it easier to cancel and reveal the frame dragging precession. It never attracted much attention, and Everitt and van Patten returned their attention to Gravity Probe-B. Even though their proposal was published just six weeks before the launch of LAGEOS I, they were apparently unaware of what the geophysicists were working on. Science is rife with missed opportunities caused by the compartmentalization of different fields. It would be ten years before Ciufolini would hit upon LAGEOS as a tool for measuring frame dragging.
At the time of Ciufolini’s proposal, the geophysics community was planning to launch a second LAGEOS satellite in order to advance their studies of the Earth. Ciufolini and many relativists campaigned vigorously to have LAGEOS II launched with the special inclination angle of 70.16 degrees (LAGEOS I was at 109.84 degrees) needed to measure frame dragging, but other considerations prevailed in the end. LAGEOS II was launched in 1992 with an inclination of 52.64 degrees, mainly to optimize coverage by the world’s network of laser tracking stations, which was important for geophysics and geodynamics research.
This was a major disappointment, but Ciufolini, now based in Italy, and his colleagues tried to make the best of it. Because the cancelation effect was not ideal, the errors in measuring the frame dragging rotation would be larger than they had hoped, but between 1997 and 2000 they reported having measured the 30 milliarcsecond effect to between 20 and 30 percent precision, although some critics argued that their error estimate was optimistic.
The turning point came with a space project known as GRACE. This joint mission between NASA and the German Space Agency, whose official name was Gravity Recovery and Climate Experiment, was launched in 2002 and ended in late 2017. GRACE consisted of a pair of satellites (dubbed Tom and Jerry) flying in close formation (200 kilometers apart) on polar orbits 500 kilometers above the Earth. Each satellite carried a satellite-to-satellite radar link to measure the distance between them very precisely, and a GPS receiver to track the orbit of each satellite separately. As the pair pass over a region with excess mass, such as a mountain, the gravitational attraction of the mass pulls the satellites toward each other, while if they pass over a region with a deficit of mass, such as a valley or depression, the satellites are pulled apart (see Figure 4.7). As the satellites passed repeatedly over different parts of the Earth they were able to map out its gravitational field in fine detail and with unprecedented accuracy. Furthermore, over the fifteen years of the mission, GRACE was able to measure time variations in the gravity field of the Earth. For example, it could measure the gravity variation caused by seasonal changes in the amount of water in the Amazon and Ganges river basins, and the changes in gravity caused by mass loss in the ice sheets of Greenland and Antarctica. These measurements have obvious implications for water management and climate change. It could also monitor the rise of the North American and European land masses as they continue to “rebound” from the loss of the ice that had weighed them down during the last ice age.
Figure 4.7 Measuring variations in Earth’s gravity using GRACE. Top: As the two satellites pass over a mountain, its gravitational attraction pulls them toward each other. Bottom: As they pass over a large depression, the absence of mass causes them to separate a bit.
With the dramatic improvements in accuracy for Earth’s gravity field provided by GRACE, Ciufolini and his colleagues could now remove the Newtonian effects and uncover the tiny frame dragging effect more precisely. In 2010 and 2011, as GP-B was in the final phase of data analysis, Ciufolini and colleagues reported a result from LAGEOS in agreement with general relativity to about 10 percent, about a factor of two better than the final GP-B result.
Meanwhile, Ciufolini had succeeded in convincing the Italian Space Agency to go for a third laser-ranged satellite, called LARES (Laser Relativity Satellite), to be launched with an inclination of 69.5 degrees, very close to the required angle relative to LAGEOS I. However, the agency informed Ciufolini that, in order to reduce cost, it would not provide a launch vehicle powerful enough to achieve the same distance from the Earth as that of the two LAGEOS satellites, again preventing perfect cancelation of the Newtonian effect, which varies as the inverse cube of the radius of the orbit. Still, the advantage of having the proper inclination was enough to convince the LARES team to accept the launcher offered. LARES was launched on 13 February 2012, and in 2016, combining data from all three satellites with improved Earth data from GRACE, the LARES team reported a test of frame dragging at the 5 percent level.
The main difficulty in all of these precession experiments is that near Earth, gravity is just too weak! It would be wonderful to measure how gyroscopes precess near a black hole or a neutron star. The magnitude of the relativistic precession effects might be so large that one could see the precession “by eye.” But this, of course, is completely impractical. The nearest black hole observed, V616 Monocerotis, is 3,000 light years away, and the nearest neutron star, Calvera, is between 250 and 1,000 light years away, so sending a gyroscope experiment there (maybe called “GP-X”) is hopeless. But rotating neutron stars themselves can act as gyroscopes as effectively as can spheres of fused silica. And many neutron stars also act as “pulsars,” emitting a beam of radio waves that we can detect, and some are in orbit around other stellar bodies. In fact, these celestial lighthouses have taken testing general relativity into a whole new realm, as we will see in the next chapter.