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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 25
EXPERIMENTAL TESTS OF GENERAL RELATIVITY: OPPORTUNITIES 25
ULTRAL OW MAGNETIC - f IELD
r SUPERCONDUCTING SHIELD
~~ /
''~
GYROSCOPES
( 2 of ~ )
l ~
DRAG—fREE 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 26
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 27
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 of—104 years; and others are more compli-
cated. A plausible current theory is that the sources of these jets are
rotating supermassive black holes, M—107 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 28
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 29
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 30
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 31
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 32
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 33
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-
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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 Waves—Recent Developments).
Here we are concerned with the potential of such systems as astro-
physical laboratories for testing other predictions of general relativity.
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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.
Representative terms from entire chapter:
range measurements
