Click for next page ( 25


The National Academies | 500 Fifth St. N.W. | Washington, D.C. 20001
Copyright © National Academy of Sciences. All rights reserved.
Terms of Use and Privacy Statement



Below are the first 10 and last 10 pages of uncorrected machine-read text (when available) of this chapter, followed by the top 30 algorithmically extracted key phrases from the chapter as a whole.
Intended to provide our own search engines and external engines with highly rich, chapter-representative searchable text on the opening pages of each chapter. Because it is UNCORRECTED material, please consider the following text as a useful but insufficient proxy for the authoritative book pages.

Do not use for reproduction, copying, pasting, or reading; exclusively for search engines.

OCR for page 24
Experimental Tests of General Relativity: Opportunities TESTS FOR "MAGNETIC" GRAVITATIONAL EFFECTS At present there is no experimental evidence arguing for or against the existence of the gravitomagnetic effects predicted by general relativity. This fundamental part of the theory remains untested. The reason is simple; predicted effects, such as the dragging of inertial frames by rotating massive bodies, are exceedingly small near solar- system bodies (though they can be enormous and astrophysically crucial near a rotating black hole). The precision solar-system experi- ments described above probe space-curvature effects and the gravitoelectric field, but the predicted effects due to rotation of the Sun and Earth are too small to be detectable in experiments performed to date. Relativity Gyroscope Experiment An experiment has been devised to search specifically for the frame dragging effect. NASA's Relativity Gyroscope Experiment (Gravity Probe B. see Figure 3.1) will use test gyroscopes in orbit to look for frame dragging by the rotating Earth. A test gyroscope defines the orientation of the local inertial frame, and the experiment looks for a precession of this frame with respect to the fixed stars. The main difficulty is to reduce external torques on the gyroscope to an excep- 24

OCR for page 24
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: OPPORTUNITIES 25 ULTRAL OW MAGNETIC - f IELD r SUPERCONDUCTING SHIELD ~~ / ''~ GYROSCOPES ( 2 of ~ ) l ~ DRAGfREE PROOF IdASS ~- SUPERFLUID HEL I US TANK . ESCOPE FIGURE 3.1 The Relativity Gyroscope Experiment is our best hope of testing the unexplored magnetic-like effects in general relativity. In polar orbit, the telescope will be accurately pointed to a reference star, and the precession rates of the precision gyro- scopes will be monitored to an accuracy of a few milliarcseconds/year. tionally low level; otherwise they would induce mechanical precession, which masks the tiny precession due to frame dragging. The most interesting precessional effect predicted by general rela- tivity goes by several names: motional, frame-dragging, Lense- Thirring, and gravitomagnetic among others. As a consequence of coupling between the gyroscope spin and the rotating Earth, the effect is analogous to the spin-spin coupling that gives rise to atomic hyper- fine spectra. For an orbital altitude of about 600 km above the Earth, the maximum frame-dragging precession is 0.044 arcsec/year; thus, the design goal for the experiment is a precision of 0.001 arcsec/year. General relativity also predicts a geodetic precession of 6.9 arcsec/ year, which is split between two physical effects. There is a spin-orbit precession where the gyroscope spin couples to the gravitomagnetic field induced in the gyroscope's rest frame by its motion through the Earth's gravitoelectric field. This amounts to 2.3 arcsec/year. The remaining 4.6 arcsec/year arises from the gyroscope's motion through the curved space near the Earth. Neither the frame dragging nor the geodetic precession has been directly observed in any past experiment. Gravity Probe B is planned around four identical gyroscopes and a

OCR for page 24
26 GRA VITA TION reference telescope, all fabricated from fused quartz and kept at a temperature of 1.6 K. Each gyroscope will consist of a quartz sphere almost 4 cm in diameter, coated with a superconducting niobium film and suspended electrostatically. The initial spin rate of nearly 200 revolutions per second is expected to decay by less than 0.1 percent during the course of a year because of the very low (10-~ Torr) pressure maintained within the vessel. To reduce external torques from the suspension and from gravity gradients, each gyroscope rotor has to be round to better than 1 part in 106 and homogeneous to within a few parts in 107. The orientation sensor uses the sphere's London moment and low-noise superconducting quantum interference device (SQUID) magnetometers to read the spin-vector alignment with the necessary precision and without exerting significant sensing torques on the gyroscope. Superconducting lead bags are used to reduce residual do magnetic fields to below 10-7 gauss. The spacecraft uses a drag-free proof mass to reduce nongravitational accelerations on the gyroscopes to about 10-7 cm/s2. To modulate the precession signal, and to average out some unwanted torques, the spacecraft is slowly rolled. The telescope views a bright reference star (probably Rigel) along the roll axis; the proper motion of this star will be determined from separate observations. Clearly, this is an exceedingly difficult experiment, many times more sophisticated than any yet attempted in space. Some of the critical technology is new and therefore of higher risk than is usually consid- ered prudent for space experiments. Yet, the experiment has withstood intensive technical reviews, which found that a successful experiment is possible, if done with care. Scientific reviews have always been enthusiastic because the science is compelling, and the experiment is unique. NASA's current plan is to develop the experiment in two stages. Stage 1 will consist of building the flight Dewar and instrument, including all four gyroscopes, and performing an engineering test in the relatively low-g environment of the Shuttle spacecraft. In stage 2 the refurbished instrument will be flown in a free-flying spacecraft to obtain the ultralow-g environment required for the experiment. This approach is designed to minimize the risk associated with the experiment's advanced technology. Black-Hole Jets It is possible that astronomers may now be seeing a very dramatic gravitomagnetic effect. A few quasars and strong radio galaxies exhibit

OCR for page 24
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: OPPORTUNITIES 27 long jets of gas and associated magnetic field emanating from their nuclei. Some jets are surprisingly straight, requiring good alignment of the source for ~ 107 years. Others show corkscrew patterns, suggesting precession with periods of104 years; and others are more compli- cated. A plausible current theory is that the sources of these jets are rotating supermassive black holes, M107 solar masses, in the nuclei of some galaxies: the gyroscopic action comes from the hole's rotation- induced gravitomagnetic field, and the corkscrew jets may result from geodetic precession of the hole's spin as it orbits around another massive body. How might a black hole generate a collimated, energetic jet? One exotic but physically plausible mechanism relies on the dipole-shaped gravitomagnetic field of a rotating black hole. That field, derived from the interaction of the hole's horizon and the magnetic field deposited on the hole by a surrounding accretion disk, drives charged particles away from the hole's poles in ultrarelativistic beams. The energy ultimately comes from the black hole's rotation. Figure 9.2 in Chapter 9 depicts this model. Unfortunately, the complexity of such a system, and the poor prospects for getting detailed data, make it unlikely that observations of jets will ever constitute a quantitative test of gravitomagnetism in general relativity. RANGING TO THE MOON AND INNER PLANETS For the coming decade, range measurements to the Moon and inner planets will continue to provide important tests of general relativity. Ranges are currently being measured with the exquisite accuracy of 1 part in 10~ in some cases, and as we see in Table 2.1, the scientific payoff has been outstanding. But we can do even better by pushing the measurements to the technically feasible limits and by scheduling observations for best scientific advantage. Before discussing specific possibilities we should point out two important characteristics of solar-system range measurements. 1. The whole is much greater than the sum of its parts. At the levels probed, the solar system is a complex network of gravitational inter- actions, modeled by an elaborate ephemeris. Each experiment couples to this network with its own unique matrix, and often the interrelations of different experiments are important but by no means apparent. Furthermore, many effects (such as Mercury's perihelion precession) are cumulative with time, so measurements made over the long term are especially sensitive. For these reasons analysis of the total avail- able data set can enhance the reliability and accuracy of any single test

OCR for page 24
28 GRAVITATION of a theory of gravitation, and data obtained during one space mission might be of only moderate value in themselves but, when combined with data taken in another, might be of great interest. 2. Measurements of the dynamics of the solar system, made with modern instrumentation, will be an extremely valuable legacy to leave to future generations of scientists, who will combine their data with those obtained in the present era and reap more sensitive tests of the fundamental theories of gravitation. The history of gravitation physics provides a shining example of the importance of such legacies. The observational work of Tycho Brahe, its use by Kepler, and the work of many generations of observational astronomers enabled Leverrier in the mid-nineteenth century to detect the anomalous advance in the perihelion of Mercury's orbit, later to become general relativity's first successful test. Radar Ranging Radar ranges to Mercury currently provide our best measurements of the perihelion precession predicted by general relativity. The uncertainty in the determination of the total perihelion advance de- creases as the -3/2 power of the time interval spanned by the data, so a long-term program is important. Given the current infrequency of planetary spacecraft missions (see below), it is particularly important to maintain and improve our radar capability. Sustained high-accuracy measurements of the echo delay of radar signals between the Earth and the inner planets are being accomplished at present with the NASA-supported radar facilities at the Arecibo Observatory and at the Goldstone Tracking Station. The main limita- tion on the utility of such data for tests of relativistic gravitational effects has not been measurement accuracy but rather measurement sparsity and the unknown topography of the target planets. Increasing the frequency of measurements and exploiting techniques to map planet topography can substantially improve the radar-ranging contri- butions to this field. Ranging to Planetary Landers and Orbiters Range measurements from the Earth to the Viking Landers on Mars have been particularly valuable in testing gravitation theories. Ranges were measured with uncertainties as low as 3 to 5 m near opposition, the highest fractional accuracy achieved so far in solar-system mea-

OCR for page 24
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: OPPORTUNITIES 29 surements. However, the Viking Landers are no longer in operation, and there are no specific plans at present for future U.S. landers on any of the planets. The most likely location for a future lander would be Mars, and the possibility of ranging to such a lander with an overall measurement accuracy approaching 1 cm should be pursued actively. The striking scientific success of the Viking Lander tracking measure- ments provides a strong justification for obtaining range measurements to future landers and for increasing the accuracy as much as possible. In view of the infrequent opportunities that are likely to arise for ranging to planetary landers, it is important to utilize improved techniques for ranging to orbiters to obtain high-accuracy planetary distance measurements. This is particularly desirable for Mercury for several reasons. One is the greatly increased accuracy with which the precession of Mercury's perihelion could be obtained. Several years of high-accuracy radio-tracking data would give an independent measure- ment of the solar quadrupole moment, allowing separation of the relativistic precession and the precession due to the solar quadrupole. A Mercury orbiter also offers good prospects for lowering the present upper limit on GIG of 10-'~ per year by several orders of magnitude. This is partly because of improvements in measurement accuracy and partly because asteroid perturbations are smaller for Mercury and the Earth than for Mars. The main limitation on obtaining interplanetary distances by ranging to planetary orbiters comes from uncertainty in the spacecraft orbit with respect to the planet's center of mass. This uncertainty, in turn, stems in large part from a lack of knowledge of the planet's gravita- tional field. For this reason, the use of a relativity subsatellite in a fairly high-altitude orbit, with a small eccentricity, is most favorable. Track- ing of such a satellite simultaneously at two radio-frequency bands, say the X band and the K band, should allow removal of virtually all uncertainties in distance measurements, and in radial velocity mea- surements, due to interplanetary plasma. The first major opportunity to utilize a planetary orbiter will be through the Mars Observer Mission. Such an opportunity, of interest in its own right, would also enable the refinement of the techniques proposed for use with Mercury orbiters. Determination of the gravity field could be accomplished via use of a dual-frequency tracking system similar to the system incorporated in the Galileo spacecraft. Inclusion of an accurate ranging system would allow the Mars Ob- server itself to be utilized to improve on the spectacular results for testing general relativity obtained from the Viking Landers on Mars.

OCR for page 24
30 GRAVITATION ~3- '~ ::: p FIGURE 3.2 The array of corner reflectors placed on the Moon by Apollo 14 astronauts (note footprints). The bubble level and gnomon, used for pointing the array toward the Earth, can be seen. Laser range measurements are routinely made to three widely separated arrays. No degradation of their optical reflectivity has been observed. Lunar Laser Ranging Laser range measurements to optical corner reflectors on the Moon (see Figure 3.2) have been made for over a decade with an uncertainty of about 10 cm from 20 minutes of observation. Recently, additional sites in Hawaii and Australia have joined the McDonald Observatory in Texas and the Grasse Observatory in France in making regular range measurements. The accuracy from the new stations and, after improve- ments, from the older stations is expected to be a few cm. We expect that the equivalence principle test (does gravitational binding energy

OCR for page 24
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: OPPORTUNITIES 31 have inertial mass?) will be improved tenfold over the current accu- racy. EThis test already provides our best accuracy for measuring the parameterized-post-Newtonian (PPN) parameter 'S.] Geodetic preces- sion of the lunar orbit (with the Earth-Moon system playing the role of a gyroscope in orbit around the Sun) might also be determined to about 10 percent of the predicted effect. This accuracy, however, is far lower than is expected from the Relativity Gyroscope Experiment (GP-B) discussed earlier. Additionally, these laser-ranging data should allow an accurate measurement of a possible change in the gravitational constant, because the Earth-Moon tidal acceleration is being measured independently by LAGEOS ranging experiments. Laser observations are also useful for a variety of applications in geophysics and selenophysics such as the determination of Earth rotation and notation, the lunar mass distribution, and the excitation of free libration of the Moon. Finally, we emphasize the important interrelationship between plan- etary and lunar-ranging measurements. The combination of the equiv- alence principle test from lunar ranging with information on the planetary mean motions, perihelion precession, and time delay from planetary ranging strengthens our present ability to set a limit on the solar quadrupole moment and to determine other important solar- system parameters such as GMSUn. Also, the planetary observations aid the analysis of lunar-ranging data. Thus, the contribution of any given set of measurements must be judged not in isolation but in regard to its effect on deductions from the ensemble of measurements, past as well as future. It is for this reason that each feasible opportunity for ranging to the Moon and planets should be seized. MEASUREMENT OF SECOND-ORDER SOLAR-SYSTEM EFFECTS All past measurements of nonlinearity in the superposition of grav- itational potentials (PPN parameter p) have involved the dynamical motions of test bodies such as Mercury, whose perihelion precession rate agrees with that predicted by general relativity. A high-precision clock experiment would probe ~ in a different physical context and would check whether, at a nonlinear level, gravitation can be repre- sented by a metric theory. It has been proposed to put a hydrogen- maser clock aboard a solar probe spacecraft, called STARPROBE, which would travel in an eccentric, near-Sun orbit. Such a mission would provide a superb gravitational redshift experiment as well as making the first clock measurement of p. The change in gravitational

OCR for page 24
32 GRA VITA TION potential is 103 larger than that experienced by the rocketborne hydrogen maser, which holds the record for gravitational redshift tests, 1 part in 104. To measure ~ with 10 percent accuracy requires a clock stability of 1 part in 10~5, or better, for averaging times of 102 to 106 seconds. Comparable performance has been achieved in the laboratory for averaging times up to 104 seconds. Development of a spaceborne experiment requires careful environmental control to accommodate extreme solar heating. During its several-year cruise to the Sun, a solar probe with an ultrastable oscillator on board would offer an unprece- dented opportunity to search for long-period gravitational waves, as discussed later in the section on Pulsar Timing and Millisecond Pulsars. Another space project has been proposed to test general relativity to unprecedented levels of accuracy three orders of magnitude more sensitive than present solar-system tests. The idea is to measure solar deflection of starlight with sufficient accuracy to detect the second- order contribution of the gravitational potential, a deflection of 10.9 ~arcsec at the solar limb. The instrument envisioned is an articulated pair of stellar interferometers with their viewing axes approximately 90 apart. The instrument (called POINTS, an acronym for Precision Optical INTerferometry in Space) would have two pairs of mirrors of 1-m diameter and an interferometer separation of 10 m; statistical accuracy after 5 min of integration on 10th-magnitude stars is under 1 ~arcsec. The challenging problem of achieving absolute accuracy appears to be solvable by means of internal laser-beam metrology. Figure 3.3 shows a smaller version of the interferometer that could fit fully assembled with a supporting spacecraft into the Shuttle bay. This instrument would have 25-cm mirrors separated by 2 m. For a pair of 10th-magnitude stars, it would measure the separation with a statistical uncertainty of 5 ~arcsec after a 15-min observation. Although possibly falling short of the accuracy needed for a second-order test, this interferometer would allow at least a 2-order-of-magnitude improve- ment to be made in the accuracy of the solar light-deDection experi- ment. Such an experiment could be conducted from the bay of the Shuttle and provide an estimate of the PPN parameter ~ ten times better than did the Viking Lander mission using the time-delay test. POINTS also has obvious applications in precision astrometry. Parallax and proper motion studies could be extended to all visible parts of the galaxy, contributing to our understanding of the cosmic distance scale and galactic dynamics. Statistical studies of the abun- dance of planetary systems should be possible. Although the decision to develop a space-based astrometric instru- ment must be based on the predictable scientific results of such a

OCR for page 24
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: OPPORTUNITIES 33 - - l , . := Go ~ An' /~ ~ _ _ Phi - ,,,,,,,,,,, ~ ~ 0.0 0.5 4.0 meter - FIGURE 3.3 An artist's rendition of a small optical interferometric satellite to be used for precision astrometry. It consists of two U-shaped interferometers joined by a bearing that permits the angle between the principal axes of the interferometers to vary by a few degrees around its nominal value of 90. Each telescope has a 25-cm-diameter mirror and is separated by 2 m from its companion. NASA's Multimission Modular Spacecraft is shown mounted under the instrument. mission, the most important results may be the serendipitous discov- eries that seem to follow when a new instrument provides a large set of observations that are orders of magnitude more accurate than previ- ously available. Further studies of such an optical interferometer are required now to prepare for an eventual space mission. GRAVITATIONAL QUADRUPOLE MOMENT OF THE SUN A solar quadrupole moment causes the perihelion of Mercury's orbit to process, and uncertainty in the magnitude of this effect has been a long-standing problem for the relativistic interpretation of the mea-

OCR for page 24
34 GRA VITA TION sured precession. A large quadrupole moment could be caused by rapid rotation of the solar interior; however, a uniformly rotating Sun has a small quadrupole and negligible effect on Mercury's perihelion at the present level of measurement accuracy. Despite considerable effort, neither solar-system tracking experiments nor ground-based optical oblateness experiments have convincingly measured or ruled out a solar quadrupole elect. The recent discovery of high-Q solar oscillations with periods near 5 min has introduced a new method of indirectly determining the solar gravitational quadrupole moment. These modes of oscillation have radial extent going deep into the Sun, so rotational splitting of the mode-frequency structure is being used to probe the rotation rate of the solar interior. Knowing the radial dependence of rotation, the solar model can be used to calculate the gravitational quadrupole moment. Early results of this method indicate a value close to that for uniform rotation of the Sun, with small quoted uncertainty. Work is under way on better observations, which will include spatial resolution, and on more detailed models relating mode structure and the solar interior. We have already noted (see section on Ranging to Planetary Landers and Orbiters) that accurate radio tracking of a satellite orbiting Mer- cury would give a much more accurate measurement of the perihelion precession, as well as a direct measurement of the solar quadrupole moment. The direct measurement would not only support a more accu- rate perihelion measurement, but would also be an important check on our understanding of the solar interior and of solar oscillations. SYSTEMS OF COMPACT STARS Multiple systems of neutron stars and/or black holes present new opportunities for research in gravitational physics. The ideal of study- ing a system of pointlike objects of large mass with negligible non- gravitational interactions was just a dream before the discovery and close study of the binary pulsar system PSR 1913 + 16. This is a 16-Hz pulsar in an 8-h orbit around an unseen companion. Pulse timing data of high precision allow unprecedented scrutiny of many orbit parame- ters, including four relativistic effects periastron precession rate, gravitational redshift, transverse Doppler shift, and orbital decay due to gravitational radiation. As our first evidence for the existence of gravitational radiation, we will highlight this system in Chapter 5 (in the section on Sources of Gravitational WavesRecent Developments). Here we are concerned with the potential of such systems as astro- physical laboratories for testing other predictions of general relativity.

OCR for page 24
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: OPPORTUNITIES 35 The binary pulsar is an almost ideal gravitational laboratory. Large orbital eccentricity (0.617127 + 0.000003), small orbital size (a sin i = 2.34185 + 0.00012 light seconds), and large masses (each mass = 1.41 + 0.03 MSun) lead to relatively large gravitational effects. The periastron precession rate is found to be 4.2263 + 0.0003 degrees/year compared with 43 arcsec/century for Mercury. Why is this measure- ment of periastron precession to 2 parts in 104 not listed in Table 2.1 instead of Mercury's precession (5 parts in 103~? The reason is that pulsar timing data do not independently give the masses of the pulsar and companion, and these are needed to calculate the size of the relativistic precession. Instead the measured precession rate is used to find the masses (including the first high-precision mass measurement for any neutron star), assuming that general relativity is correct. The model and data are all self-consistent and strongly suggest that we are observing a clean gravitational system with relativistic periastron precession and gravitational radiation. Nevertheless, the possibility remains that the companion might be a helium star or white dwarf. Calculations indicate that these objects could conceivably have a mass quadrupole moment large enough to cause the observed periastron precession and/or tidal dissipation sufficient to cause the observed orbit decay. Thus' the agreement of the measurements with the predictions of general relativity could be fortuitous. The binary pulsar is a breakthrough in gravitation physics. By exhibiting large gravitational effects, such systems offer exciting op- portunities for testing general relativity. Suppose, for example, that the companion in PSR 1913 + 16 had turned out to be a pulsar; neutron stars are sufficiently pointlike that no ambiguity would remain in interpreting the measurements. One can imagine other systems similar to this one where pure gravitational interaction could be shown with certainty to dominate the dynamics. Systematic searches for compact star systems and detailed measurements of their properties should be vigorously pursued whenever possible.