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OCR for page 38
6
Programs After 1995
BASELINE PROGRAM
LAGOS: Baser Gravitational Wave Obeenatione m Space
Important opportunities for valuable new types of scientific
observations in space exist in the area of gravitational wave astron-
omy. GrouncI-based programs for observing gravitational radiation
are being pursued actively in a number of countries, as described
in Chapter 3. Given proper support, the prospects appear good
for detecting signals that give information about several kinds of
sources within the next 5 or 6 years. However, the frequency range
that can be covered relatively easily in ground-based observations
is only from roughly 100 Hz to 10 kHz. With major efforts at ~so-
lating the antennas from ground noise and avoiding t~rne-varying
gravity gradient effects, high sensitivity can be achieved down to
10 Hz or possibly somewhat below. For frequencies of 3 Hz and
below, antennas In space seem essential to achieve sufficiently high
sensitivity.
The types of low-frequency gravitational wave signals that are
likely to be observable fall into several classes. The only one that
is certain to be observed is radiation from various kinds of binary
star systems. Sources of this kind include normal main sequence
38
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39
binary stars, contact binaries, cataclysmic variables, neutron star
binaries, and close white dwarf binaries. The radiation level ex-
pected for the last type is not well known because of uncertainties
in the initial distribution of masses and separations. For each type
of binary the number of sources in our galaxy Is very large, so
that even several years of observations would leave many sources
contributing in each frequency resolution bin with similar signal
strengths. Only a relatively small number of unusually nearby
sources would give signals higher enough than the continuum level
to be individually distinguishable. Thus the observations would
be limited by confusion, since types of antennas suggested so far
have rather poor angular resolution.
A very important class of signals that could be present, but
about which the theoretical predictions are highly uncertain, is
pulses of gravitational radiation resulting from the formation or
collisions of very massive (102 to 105 MC)) or supermassive (>105M<3)
black holes. If stars with masses greater than a few hundred Ma
form at any time, they are expected to evolve quite rapidly and
may well collapse to form black holes. The efficiency of gravita-
tional racliation emission during collapse for some levels of initial
rotation has been estimated to be roughly 0.1 percent. However,
whether stars with such high masses ever form is a major question.
Although a Population II] of massive stars is often suggested to
have formed early In the history of the galaxies and to have pro-
duced the initial heavy element abundance, there is no evidence
for current formation of stars more massive than perhaps 150A,,
even in regions of rapid star formation. Whether conditions were
favorable for the formation of much more massive stars in early
galactic times is not known.
Another possible scenario for the formation of very massive
or supermassive black holes involves pregalactic density inhomo-
geneities. The probable scale for such inhomogeneities is roughly
105 to 106 M<3. However, it is not clear whether objects in this mass
range that initially were very dilute would fragment, form normal
stars, or collapse. Lignite on the density of black holes with masses
of 102 to 107M<' in galaxies currently are about 1 percent of the
closure density. The absence of many such objects in the cores of
normal galaxies is not an argument against their existence, since
the time for them to spiral into the center due to viscous drag is
very long.
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40
The other frequently mentioned possible source for the emis-
sion of strong gravitational wave pulses with frequencies below 1
Hz is collisions between very massive or supermassive black holes.
If two such objects approach each other with substantial angular
momentum, calculations indicate that the efficiency for gravita-
tional wave emission is likely to be fairly high. Whether such
collisions are likely to occur even as frequently as a few tunes
per galaxy lifetime ~ not clear. However, the chances for such
collisions might be substantial if rotating supermassive objects ex-
isted in pregalactic or early galactic times. Then bifurcation could
occur because of the bar instability, followed by collapse of each
mass, and a spiraling into a finli collision. If as much as 10-4
of the mass of the galaxies was put into very massive or super-
massive black hole binaries with relatively close separations, the
chance of detecting them by their gravitational radiation seems
good. Such evidence Knight include fairly strong periodic signals
with a drift toward higher frequencies as the black hole binaries
spiral in toward each other.
As ~ emphasized above, the probability of being able to oW
serve pulses of gravitational radiation due to the formation or in-
teraction of very massive or supermassive black holes ~ not known
at present. If observable, the shapes of such pulses might well be
able to give new information about gravitational interactions at
distances of the order of the Schwarzachild radius, where general
relativity has nearer been tested before. The absence of such pulses
would make it seem unlikely that large numbers of high-mass black
holes played a substantial role in the pregalactic or early galactic
history of the universe. More exotic sources of Iow-frequency grav-
itational radiation such as phase transitions in the early universe
also have been suggested. Despite our current limited knowledge
concerning sources of low-frequency gravitational waves, it appears
important scientifically to carry out a reconnaissance mission in
space at an early date to search for gravitational waves over as
broad a frequency range as possible in the region below 1 Hz.
The basic approach for laser gravitational wave observations in
space is the measurement of changes in the distances between three
separate spacecraft with extremely high accuracy. For the baseline
case that has been studied over the last few years, the three
spacecraft are placed in similar one-year-period nearly circular
orbits around the Sun with separations of about 106 km. The
central spacecraft is in the plane of the ecliptic and has very
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41
,~
-
at"
\
106km ~
E ND SPACECRAfT
/'
/
In ~~ 106km
~1
L ~
CENTRaL
SPACECRaFT
FIGURE 6.1 Laser heterodyne gravitational wave antenna. SOURCE:
Courtesy of University of Colorado.
small eccentricity. The other two "remote" spacecraft have almost
equal eccentricities of e = 0.003 and inclinations of ~ e, but
different longitudes for their nodes and perihelia. By choosing
the differences in node and perihelion correctly, the two remote
spacecraft always wall be very close to 90 degrees apart, as seen
from the central spacecraft. For these orbits, the distances from
the central spacecraft to the two remote spacecraft can be kept
equal to about one part in 103.
With this geometry, a beam-splitter and two end murrors can
be mounted in free-floating test masses inside the three space-
craft to form a Michelson interferometer. As shown in Figure 6.1,
a continuous wave (cw) laser beam is sent to the beam-splitter
in the central spacecraft, and then the two resulting beams are
transmitted through a pair of 5~cm-diameter telescopes to the
two remote spacecraft. There the beams are received by sunilar
telescopes and sent to the end rn~rrors. The return beams are
generated by similar lasers in the two remote spacecraft, which
are phase-Iocked to the received beam. At the central spacecraft,
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42
the phases of the beats between the return beams and the central
laser are measured as a function of time.
The antenna ~ sensitive to gravitational waves, since one arm
of the interferometer will increase in length and the other will
decrease for favorable directions of propagation and polarization
of the waves. For 100 mW of transmitted laser power, the expected
shot noise limit for the detectable gravitational wave amplitude ~
10-2°/~. It appears likely that this sensitivity can be achieved
for gravitational wave frequencies ranging from 0.1 Hz to about
10-4 Hz. For a 104-s integration time, the gravitational wave
sensitivity would be 10-22. Useful but lower sensitivity would
be achievable over the rest of the frequency range from 3 Hz to
10-6 Hz. Thus, a 106-km LAGOS antenna would have extremely
high sensitivity for detecting and observing astronomical sources
of gravitational waves with periods of roughly 0.3 s to 10 days.
The sensitivity of the antenna for short pubes of gravitational
radiation is shown in Figure 6.2, along with the expected noise
level due to random variations in the power from binaries in our
galaxy. Separate curves for the noise level are shown with the close
white dwarf binaries (CWDBs) included or excluded, since the
amplitude of their contribution is quite uncertain. Also shown are
the signal strengths expected for short gravitational wave pulses
if very massive or supermassive stars collapse to form black holes
at red shifts of z = 2.5 or z = 30. It is assumed that the efficiency
is 0.1 percent, the Hubble constant is 55 km/s/Mpc, and the
expansion parameter q(0) = 1/2. The interferometer sensitivity
will be degraded from the curve shown by a factor In(T/r), where
T is the time between pulses near that frequency, and ~ us the pulse
length. If frequent pulses are generated at z = 30, it is clear from
the figure that they would be observable for initial masses greater
than about 104 A(,, provided that the efficiency is 0.1 percent and
the noise from CWDBs is somewhat lower than estimated. For z
= 2.5, the initial masses would have to be greater than about 3 x
104 MA
Laser stability requirements for LAGOS are not as severe as
might be expected at first. Although each arm of the ~nterferome-
ter changes its length at a rate of up to about 20 cm/s due to the
solar attraction and planetary perturbations, there are no solar
system sources of disturbing gravitational forces with periods in
the range of 1 s to 10 days that would not be known accurately
from their effects at longer periods. Thus, apparent changes in
OCR for page 43
43
—15
-16 1—
-17
-18
-
~n
' -19
o
-20
-21
-22 _
-23
Pulse Nolse Limit Due to Galactic Blnarles
\
'_~\
Close White
— Owart Blnarles
excluded
Massive Black Hole Formation
E (efflclency) = 0.1%, qO (acceleration parameter) = 0.5
Z=2.5 7
\ Z=30
\ ~
~10 Me /
\ ~310 Mo
\ ~ ~ W ~
it....
~~ -
\~. 1704M~
'~ 3 103Me
\` Laser Interferometer Pulse Sensitivity
<106km, 100 mW
, 1 1 1 1 1 1 1
-6 -5 -4 -3 -2 -1 0
LOG FREQUENCY (Hz)
FIGURE 6.2 Strain amplitude for gravitational wave pulses. SOURCE:
Courtesy of University of Colorado.
the length of one arm in the period range of interest can be used
to correct for changes in the laser frequency. The difference in
length of the two arms, after this correction, ~ much less sensitive
to laser frequency variations. Preliminary studies indicate that a
laser stability of 1 x 10-~3 from 1- to As period, and less stability
below and above this range, would be sufficient to achieve the full
gravitational wave sensitivity. It appears that the desired stability
can be achieved with laser-diode-pumped Nd:YAG lasers, which
are being investigated for other space applications requiring high
efficiency, long lifetime, and high reliability.
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44
The possibility of locating the LAGOS antenna in geosyn-
chronous orbit instead of in solar orbit also should be considered.
For 90 degree separations between the three spacecraft, the in-
terferometer arm length is reduced to 60,000 km. The sensitivity
of the antenna would be unproved at frequencies above 0.1 Hz
and made worse at frequencies below 3 x 10-4 Hz because of the
shorter arm length. However, changes in thermal gradients inside
the spacecraft probably would generate large spurious signals at
a number of harmonics of 1 cycle/day. The effect of orbit pertur-
bations due to harmonics in the Earth's gravity field would have
to be considered, and tune variations in the mass distribution of
the Earth might cause appreciable perturbations. Whether there
would be substantial savings in propulsion requirements by placing
the antenna in geosynchronous orbit has yet to be investigated.
A third possibility is to reduce the spacecraft separation to
about 300 km, and to reflect the light from the remote spacecraft
directly back to the central spacecraft instead of using phase-Iocked
lasers. For this separation, many bounces of the light back and
forth in each arm could be used with the Fabry-Perot type of inter-
ferometer. This approach would then be analogous to that being
used in ground-based laser gravitational wave experiments, except
for having a much lower frequency range. The main disadvantage
is that any perturbations of the test masses on which the rn~rrors
are mounted will cause proportionately larger fractional changes in
the interferometer arm lengths than for the larger spacecraft sep-
arations. This is expected to be a problem mainly for frequencies
below about 2 x 10-3 Hz. However, much unproved sensitivity
can be achieved from higher frequencies. For 100 bounces in each
arm, about 100 times higher sensitivity can be expected if the
short node limut can be achieved. Such a multipass antenna might
be desirable if it is decided to focus attention on frequencies above
roughly 2 x 10-3 Hz. This antenna could be located either in solar
orbit or in geosynchronous orbit.
POINTS: Smut Astrometric Interferometer m Space
The proposed instrument ~ designed to measure relative an-
gular positions of stars to microarcsecond accuracy and would be
able to detertn~ne the bending of starlight by the Sun to the second
order in the gravitational field strength. The first-order deflection
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45
is 1.7 arcsec at the solar limb and varies inversely with the dim
tance from the limb. The second-order term is expected to be 11
microarcsec, falling inversely as the square of the distance. The
astrometric precision would find application in many branches of
astronomy, particularly in a search for planetary systems by mea-
suring the motions of the star about the center of mass of the
planetary system.
The instrument concept is a pair of Michelson interferometers
of 2-m baseline employing 25-cm-diameter telescopes (see Figure
6.3a). The two interferometers are mounted so their optic axes
are approximately 90 degrees apart on the sky (see Figure 6.3b?.
The nominal 90 degree separation angle is chosen to max~nize
the number of stars that can be referenced to a given star in
establishing an astrometric grid on the sky. The relative position
measurement ~ carried out by executing small changes in the
angle between the optic axes. The instrument should be capable
of cleterm~ning the relative position of a tenth magnitude star to
an accuracy of 5 microarcsec in an integration time of 10 An. The
technical challenge of the instrument Is to maintain dimensional
stability, especially the angle between the optic axes, against the
inevitable thermal drifts and changing gravity gradients over the
integration time. Absolute stability is not required, nor possible.
The consistent solution of multiply measured angular differences
in the astrometric grid can be used to correct for long-term drifts
in the instrument. An internal metrology system using frequency-
stabil~zed lasers and fiducial surfaces would be used to determine
the optical delay in the interferometers and the angle between the
optic axes.
In its present conceptual design the interferometer would take
up about one-third of a Shuttle bay. Useful scientific information
could be gained by observing from the Shuttle; however, the longer
exposure and more stable pointing provided on a platform or free
flyer could be used to advantage by this instrument.
Mercury Relativity Satellite
Major improvements in solar system tests of general relativity
would be made possible by accurate tracking of a small relativity
satellite in a nearly circular orbit around Mercury. One of the
primary benefits would be an improvement by 2 to 3 orders of
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46
\\~?
~V:
~(
~~/:
\
-
1,,,, I I I ~ I 1
0.0 0.5 1.0
meters
FIGURE 6.3a POINTS: Optical stellar interferometer. SOURCE: Courtesy
of Robert D. Reasenberg.
magnitude in our knowledge of whether the gravitational interac-
tion constant G is changing with time. Mach's principle suggests
that local inertial properties can be influenced by distant matter
in the universe. If so, it could be expected that the effective value
of G would decrease as the universe expands. This would cause
a quadratic variation with time in the angular position of each
planet in its orbit.
OCR for page 47
47
GO
A?
FROM RIGHT
TELESCOPE
i,
FROM LEFT
TELESCOPE
\
i)
FIGURE 6.3b POINTS: Optical design utilizing double-plate beamsplitter.
SOURCE: Courtesy of Robert D. Reasenberg.
Tracking of a relativity satellite also would peanut improve-
ments in tests of two other relativistic effects. One is the precession
of perihelion for Mercury. This effect is an important test of the
extent to which gravitational interaction energy ~ itself a source
of curvature in space-time, as measured by the PPN parameter
,8. The other test would be an improved measurement of the rela-
tivistic time delay for electromagnetic signals traveling along paths
near the Sun. The extra time delay depends on the PPN parameter
7, which also determines the deflection of star light or radio waves
by the Sun. In addition to these effects, the tracking data would
peanut an independent measurement of the solar quadrupole mo-
ment 32, which depends on the internal rotation rate of the Sun.
And finally, the data would permit a very accurate determination
of the gravity field of Mercury up to roughly degree and order 10.
This is of great interest to planetary scientists.
For relativity tests, it is necessary to know the spacecraft orbit
well enough that the distance from the Earth to the center of mass
of Mercury can be determined accurately. For a satellite in a
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48
circular polar orbit at 250~km altitude, dual-frequency Doppler
tracking with 5 x 10-~5 accuracy can determine the gravity field
well enough that the Earth-satellite distance can be converted
reliably to the desired Earth-Mercury distance. Phase modulation
of the signals at frequencies of up to 50 MHz also is needed in
order to measure the range to the satellite with 3-cm accuracy.
The resulting overall Earth-Mercury distance uncertainty would
be approximately 10 cm. Tracking data are needed for about 3
periods per week of ~ h each over a minion lifetime of 2 to 8 years.
The expected ma" requirement for a suitable relativity satellite
using low-power X-band and K-band tracking is 50 kg.
Recently, a new class of ballistic trajectories has been d~scov-
ered that would permit sending substantial scientific payloads to
Mercury. The trajectories involve swingbys of both Venus and
Mercury in order to reduce the final approach velocity. A par-
ticularly favorable launch opportunity exists in 1994. The long
flight time involved would delay the arrival at Mercury until the
year 1998. However, the payload would be large enough that it
appears feasible to include a number of separate spacecraft, to be
placed in separate orbits. These could include the following: a
main spacecraft In a low circular orbit for planetary surface stud-
ies; the small relativity satellite; a particles and fields satellite in
an elliptical orbit; and possibly one or two small landers. The task
group recommends the inclusion of a smai} relativity satellite on
such a mission, or on any other mission that could put the satellite
in a suitable orbit around Mercury.
It also is possible to test relativity by using tracking signals
from a lander on the surface of Mercury, provided that accurate
tw~frequency tracking data and long active mission duration can
be obtained. This would have the advantage of eliminating the
need for determining the gravity field of Mercury. However, the
eEects of systematic data loss because of the Today rotation period
have not yet been investigated. Tradeoffs between the lander
approach and a small relativity satellite should be considered if it
is possible to include a lander on a Mercury mission.
For a 2-year nominal mission lifetime with the small relativity
satellite, the expected accuracy for testing the possible change in
the gravitational constant is 1 x 1o-~3 per year. The accuracy
for the precession of perihelion and for 32 are 1 x 10-4 and 3 x
10-8, respectively. For an 8-year extended mission lifetime, the
corresponding accuracies would be 1 x 10-~4, 3 x 10-5, and 1
OCR for page 49
49
x 10-8 per year. The expected accuracy for 7 from the time
delay would be 3 x 10-5, with only a weals dependence on the
mission duration. The present uncertainties are approximately 1
x 10- per year for the rate of change of G. 5 x 10-3 for the
precession rate, 4 x 10-8 for 32, and 2 x 10-3 for 7. However,
the small quoted present uncertainty for 32 is from splittings of
the roughly 5-m~n period normal modes of oscillation of the Sun,
and an independent direct determination of ]2 is desirable. At the
level of 1 x 1o-~4 per year for possible changes in G. the effect
of the comparable rate of mass loss for the Sun by the solar wind
would need to be considered.
STARP ROBE: Second-Order Gravitational Red Shift
Experiment
The experunent proposed is to incorporate a hydrogen maser
clock on the mission being planned to explore the plasma around
the Sun to make the first measurement of the gravitational red
shift to second order in the gravitational field strength (see Figure
6.4~. The experiment would provide a direct measure of the PEN
parameter ,B without assumptions concerning values for the other
PEN parameters and would have a weak dependence on a solar
quadrupole moment. At its closest approach to the Sun the clock
will be at 4 solar radii. At this position the first-order gravitational
red shift is 5 x 10-7, while the second-order term is 3 x 10-~3.
The hydrogen maser flown on Gravity Probe A in 1976, which
performed a gravitational red shift experiment in the field of the
Earth to one part in 104, had a long-term stability of 2 x 10-~5 in
an averaging period of about 3 h. The clocks have been unproved
since then, exhibiting a stability better than ~ x 10-~5 in an
averaging time of one day. A hydrogen maser appropriate to the
my - ion has an estimated mass of 35 kg and would consume led
than 30 W. The intrinsic stability of the clock ~ better than needed
to perform a 10 percent measurement of the second-order red shift
in the tune during closest approach to the Sun, about 10 hours.
The requirements on spacecraft tracking are not severe; the range
error at closest approach should be less than 100 m. However, the
effects of the large spatial and temporal variations in the plasma
around the Sun must be consiclered both in the ranging and on the
measurements thernseIves. The angular position of the spacecraft
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Representative terms from entire chapter:
frequency range
50
r OPTICAL Buff LES ~
/ COINlIAMl~ATION BARRIER
/
Nail
PRIMARY SHIELD me
SECONDARY SHIELD
/
~ - Rut
:~ AN{ENNA
. ~\/~ PLASMA AND
~
51
satellite after 1995. At present, it ~ planned to recover GPB, and
it would require minunum refurbishment for the experunent. GPB
is optimized so that the center of mass stays constant as the liquid
helium boils away. It contains a complete guidance and "zeroing"
system. An experiment performed aboard GPB to an accuracy of
one part in 10~8 would be an unprovement of 106 over the best
existing experiments.
X-ray Large Array/Fast-tan;ng E~peranents and
Correlation with Gravitational Radiation
The program to develop a large array of proportional counters
begun on the Shuttle before 1995 will come to fruition on the Space
Station. The scientific importance of fast x-ray tinning experunents
and their relation to gravitational physics has been discussed in
Chapter 5. The fur-scale concept is described here.
An array of 512 proportional counters, each 2000 cm2, for a
total effective area of greater than 100 m2, would be attached to
the Space Station (see Figure 6.5~. Mechanical collimators would
provide a I-degree-square field of view. The x-ray large array could
utilize the Space Station for assembly, operation, and maintenance
and would need to handle a data base volume of up to 10~4 bits,
and data rates of up to 108 bpe. The planned range of energy
sensitivity is from 0.25 keV to 50 keV.
ENHANCED PROGRAM
Easer Gravitational Wave Observatory
After an initial reconnaissance mission to observe the gen-
eral nature of astronomical sources of gravitational radiation, an
observatory in space capable of much more detailed studies will
probably be needed. Whether such a laser gravitational wave oh
servatory should be planned during the period 1995 to 2015 clearly
will depend on the results obtained from the reconnaissance mid
sign. The task group wid discus here the type of observatory that
should be considered if substantial evidence is found for pubed or
periodic signab associated with black holes or for other types of
sources of major scientific importance.
The main experimental requirements for the observatory are
likely to be in two areas. One is that there be multiple antennas for
52
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53
determining the location of pubed sources, for polarization stud-
ies, and for coincidence observations. Quite accurate information
on the locations of periodic sources can be obtained with a single
antenna by observing when the sources pa" through the sharp
nulls in the antenna pattern. However, this cannot be done for
pulses, unless they arrive frequently and from only a few sources.
It generally will be necessary to have observations of the different
amplitudes, shapes, and arrival times for signal pubes at different
antennas in order to determine source location and polarizations.
Whether or not there is any large-scale structure in the source
locations is import ant to investigate. Coincidence measurements
with multiple antennas also can substantially increase the sensitiv-
ity and reliability of observations made of pulses of gravitational
radiation. Three antennas would be sufficient to obtain a large
amount of additional information. Separating them by a distance
of many gravitational wavelengths is quite feasible if the antennas
are placed in solar orbit. One possibility would be to use sepa-
rations of about 108 km in order to achieve the highest angular
resolution possible.
The other foreseeable requirement would be to maximize the
sensitivity in the frequency region that appears most important
based on the observations from the reconnaissance mission. For
example, if pulses are seen in the frequency region above 10-3
Hz but not at lower frequencies, then the use of roughly 300 km
multipass antennas of the Fabry-Perot type probably would be
desirable. Also, the achievement of additional power output and
improved performance by efficient lasers with long lifetimes for
space applications is highly likely by the year 2000. With 1 W of
transrn~tted power, 100 passes per arm, and an integration time
of 106 a, a sensitivity as high as 3 x 10-26 would be possible for
periodic signals In the frequency range of roughly 10-2 Hz to 3
Hz. The corresponding pulse sensitivity would be 3 x lo-24 to 5 x
10-23 over the above frequency range. Such high sensitivity would
greatly enhance the opportunities for detailed studies of gravita-
tional wave pulse shapes, as well as for Recoveries of completely
unexpected phenomena.
Redight of GPB
With improved superconducting quantum interference devices
s4
(SQUIDS) now available and a laser modulation technique devel-
oped by Cabrera to modulate the superconducting pickup loop
around the gyroscope, it appears possible to reduce the gyro read-
out nome to a level of 10-4 see of arc per year. With such a system
a refight of the gyroscope could make absolute measurements of
several star positions in our galaxy at the two ends of the solar
orbit to an accuracy of 10-4 see of arc. This would provide astrom-
etry data on the distance and proper motion of these stars based
on absolute gyroscope measurements rather than on comparison
of several stars. To make such measurements a 36~degree gyro
readout could be developed to an accuracy of 10-4 see of arc. This
would have unportant applications to other astronomical instru-
ments In space.
It is possible that the Gravity Probe B data will be suffi-
ciently interesting to make a second flight, possibly in a nonpolar
orbit, very worthwhile. Thus, the capability to bring back Gravity
Probe B for refurbishment or to refill with helium in space seems
desirable.
