GRAVITATION AND RELATIVITY EXPERIMENTS USING ATOMIC CLOCKS

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GRAVITATION AND RELATIVITY EXPERIMENTS USING ATOMIC CLOCKS

R. Vessot

To cite this version:

R. Vessot. GRAVITATION AND RELATIVITY EXPERIMENTS USING ATOMIC CLOCKS.

Journal de Physique Colloques, 1981, 42 (C8), pp.C8-359-C8-372. �10.1051/jphyscol:1981843�. �jpa- 00221739�

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JOURNAL DE PHYSIQUE

CoZZoque C8, supple'ment au n012, Tone 42, de'cenbre 1981 page C8-359

GRAVITATION AND RELATIVITY EXPERIMENTS USING ATOMIC CLOCKS

R.F.C. Vessot

Center for Astrophysics, H m a r d CoZZege Observatory and Smithsonian AstrophysicaZ Observatory, Cambridge, Massachsetts 02138, U. S.A.

Abstract.- Clocks have always played a fundamental role in the development of gravitational and relativity theories. The advent of atomic clocks with stability in the 10-16 domain provides measurement capability for both distance and time measurement at a level significant for the testing of relativistic gravitation. This paper outlines some of the tests now possible with space techniques that have opened the entire solar system to us as a laboratory for physical experiments.

Introduction.- The question of relativity is inherent in metrology since measurement is, by i t s nature, the comparison to a standard by which dimensions a r e related by some physical process.

In the measurement of time we require all clocks to provide a predictable series of events such that, in a narrow localized sense, a one-to-one relationship exists between these events.

To be useful for metrology, we require some means to compare clocks with an accuracy commensurate with the stability and accuracy of the clocks. This requires communications, which a r e usually made by electrical signals and, for long distances, electromagnetic signals.

In determining the accuracy of such measurements, we cannot divorce the clock from its communications system.

When we describe the behavior of space-time according to a given theory of gravitation and relativity, we a r e dealing with a system of metrology whose characteristics a r e governed by a number of factors and assumptions. To date, the most widely accepted theory of gravi- tation and relativity i s the Einstein General Theory of Relativity, which is now about 70 years old. While it is only recently that high precision tests of this theory (say, beyond the 1%

level) have been made, this theory has successfully held its ground and continues to be con- sidered valid.

Criteria for a Valid Theory of Gravitation.- In seeking some orderly way to summarize gravity experiments, i t is appropriate to look at the underlying criteria for a viable theory.

These a r e listed by Thorne and Will (1) a s follows:

1. The theory must be complete - it must be capable of analyzing from first prin- ciples the outcome of every experiment of interest. The theory must incorpo- rate and mesh with a complete set of electromagnetic and quantum mechanical laws which can be used to calculate the detailed behavior of bodies in a gravitational field. (Currently this does not extend to the extremes of quantum gravity.) 2. It must be self-consistent. A theory must predict uniquely the outcome of

every experiment.

3. It must be relativistic. If gravity is "turned ofF' the nongravitational laws of physics become those of special relativity.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1981843

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4. It must have the correct Newtonian limit. In the limit of weak gravity fields and slow motion, we should see convergence to Newtonian physics.

5. It must embody the weak equivalence principle - otherwise known a s the Univer- sality of Free Fall, the experimental fact that all bodies fall in the same way, regardless of their composition.

6. It must embody the Universality of Gravitational Redshift.

In the last decades since the advent of Einstein's General Theory, astronomical observation has benefited greatly from the ongoing development of technology that has led to the dis- covery of many exciting new physical phenomena. During recent years there has been a resurgence of astrophysical research to try to understand these phenomena. These studies have refocused our attention on the validity of the Einstein Theory of Gravitation and Relativ- ity and have led to a number of competing theories, which, in turn, have led us to continue thinking of experiments to confirm o r deny the validity of these theories. We can classify most of these experimental tests in terms of the contradiction and inconsistencies they seek to errpose a s follows (2):

1. Tests to look for variations in the conventional vconstants," for example, the constancy and isotropy of the velocity of light and the time dependence of the gravitational constant.

2. Tests to look for variations in the physics of the flat space-time of Lorentz inertial frames, which include studies of the second-order Doppler effect, length contraction, and mass variation.

3. Tests to confirm that gravitation is described by a metric theory in which a four- dimensional Riemannian geometry describes space-time such that everywhere, locally, the laws of special relativity apply.

4. Tests to evaluate the validity of metric theories proposed a s alternatives to the General Theory. To assess these alternatives, theorists have devised a score- keeping system, which, in essence, is a theory of theories called the Param- eterized-Post-Newtonian ( P P N ) metric theory (3). This provides a valuable means to test theories by clearly establishing their observable experimental consequences.

5. Tests from the anticipated detection of gravitational waves. The recent dis- coveries of superdense matter from gravitational collapse and the strong probability of the existence of black holes have kindled a high level of interest in the search for gravitational radiation, which, when discovered, will open a totally new method of astronomical observation. Determining the characteristics of this radiation, i. e., its velocity of propagation and polarization quali- ties, will provide further critical tests of general relativity.

In the first criterion we generally accept the constancy and isotropy (in the purely local sense) of the velocity of light, c, and a r e thus led t o the notion that time and distance a r e related.

We can therefore use measurements of time-interval to represent distance. This, of course, i s a scheme that has long been used by astronomers in their representation of interstellar distances by light ears. However, with the advent of atomic clocks, whose stability is now well below the lO-I5 level for intervals between 20 min and L hr, and highly stable lasers, the definition of distance in terms of time has become more acceptable as a practical reality.

The measurement of angle, o r angular differences, is an important aspect of astronomy.

To date, the most sensitive resolution of angular separations is done using Very Long Base- line Interferometry (VLBI) techniques with radio astronomy antennas separated by intercon- tinental distances. At present, this method of angle measurement depends on separate atomic clocks to measure the time of arrival of noise fluctuations of a signal from a common source a s shown in Fig. 1. The limitation of accuracy, now at the arcsecond level, i s chiefly due to the troposphere's variable refractive index.

Plans a r e now being made at NASA for operating a radio telescope from an orbiting space station. Several important advantages will result since the limitations of tropo and ionos- pheric refraction are practically eliminated and the baseline can be vastly extended. By choosing different orbital periods and inclinations, the brightness distribution of the sources

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can be mapped in two dimensions to permit very high resolution of extremely distant objects.

To date, we have only scratched the surface of the VLBI technique, and already there a r e highly puzzling observations of movements of bright blobs a t velocities apparently greater than light. This form of astronomy will surely lead to new questions and, it is hoped, some new answers to gravity and relativity theories.

VERY LONG BASELINE INTERFEROMETRY

LOCAL TIME AND MICROWAVE LOCAL TIME AND MICROWAVE

FREQ. STANDARD FREQ. STANDARD

I

A@ = & CORRELATION INTEGRATION

INTERFERENCE

Fig. 1. Schematic description of Very Long Baseline Interferometry.

The theme of this paper is to show that atomic clocks have a very high level of involve- ment in these tests; we can foresee many future applications, especially for experiments in space. The following discussions will outline applications of clocks that have been, o r could be, made in the future and relate these to the categories of tests listed above.

With the dawning of the space age, we a r e now able to consider the entire solar system a s a laboratory in which to work; and we can use the planets and even the sun a s parts of our experimental apparatus. Atomic clocks and long-range microwave and laser communication systems a r e the other essential components of our laboratory equipment.

Solar System Tests of General Relativity.- To set the stage for these experiments it i s useful to look at the way space and time a r e altered by gravitation according to the general theory, and the manifestations of this theory that can be measured.

One of the earliest parameterizations of the general theory was done by Eddington (4).

Later work by Robertson (5) and Schiff (6) described the solar system with a spherical non- rotating sun and treated the planets as idealized test bodies. This metric has the form

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with a*= 1, where r = (x2 + y2 + z2) is the radial distance, M = G M , ~ C ~ and will be used in the following discussions a s the "mass" of the sun.

This simple metric shows the behavior of the line element in space-time, ds, and includes terms in its temporal part accounting for gravitational redshift, 2M/r, and the second-order redshift governed by the term P, which describes the nonlinearity in the superposition law for gr~vity. The use of the parameter a* to describe the validity of the redshift at first order in c- is redundant; if a* were other than exactly unity there would be a conflict with the idea of the metric itself and we would have a contradiction. In tests of planetary motion or particle motion any such departure from unity would be included in the definition of mass M. However, in tests where the behavior of electromagnetic signals i s observed (such a s light bending and time delay from ray paths going near the sun), part of the observed deflection o r delay is due to the temporal 2M/r term and part is due to the spatial 2y M/r term where y is the amount of space curvature from unit rest mass. Even though we may eventually have to face a logical inconsistency, I believe we can benefit by keeping a* in the notation to help us see what is happening in the experimental results.

This metric provides a framework to test experimentally the warping of time and space using the sun a s a massive test body. The three early tests prescribed by Einstein, namely the advance of the perihelion of the orbit of the planet mercury, the deflection of starlight by the sun, and the gravitational redshift, a r e examples of this type of experiment.

The behavior of a body falling in a solar orbit is affected by the mass distribution in the sun, which is expected to be somewhat bulged outward owing to the centrifugal effects of the sun's rotation. The gravitational potential is expected to have a quadrupole moment J2 and, possibly, moments of high order. There i s some question as to whether there may be a time dependence of these quantities.

The behavior of a body falling near the sun in an eccentric orbit is governed both by a relativistic advance of the perihelion of the orbit and by the mass distribution of the sun, which was not included in the metric shown in equation 1. The combination of the two effects is to advance the perihelion an amount 641 during each orbit as shown below:

Here R g is the mean solar radius, a is the semimajor axis, e is the eccentricity of the orbit, M is the mass of the sun, and J2 is the quadrupole moment of the solar gravitational potential.

Measurements of the quantity (2 +2y - P)/3, the perihelion parameter, have been made by radar observations of mercury and the inner planets by Shapiro and his colleagues (7) who report a value of 1.003 + 0.005 assuming the J2 contribution to be negligible.

The predicted deflection of light grazing the sun, 68, is given by

where M is the mass of the sun and 8 is the angle between the earth-sun line and the incoming direction of the light. For a grazing ray, d = R g = 1 solar radius and 8 = 0.

Under these conditions the prediction is dB = (a* + y)/2 X 1.75 arcsec

.

For metric theories (a* +y)/2 = 1.

Tests of light bending have been made by using long baseline and VLBI techniques observ- ing microwave noise signals from quasi-stellar radio sources passing near the sun.

The latest results for this quantity are given by Sramek (8) who puts (a* + y)/2 = 1.007 0.009. According to Formalont and Sramek (9, lo), this technique is currently limited by uncertainties and irregularities in the tropospheric refractive index. While it is likely that a factor of 2, or so, can be gained by modeling the lens-like behavior of the troposphere

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lying over the radio telescopes, the future improvements a r e more likely to occur using VLBI techniques with spaceborne radio telescopes.

In 1964, I. I. Shapiro (11) proposed another test involving the round-trip time delay of radio or radar signals passing very close to the sun. This I1fourth" test of relativity predicts that the time is given by

where d is the distance of closest approach of the ray in solar radii, and r is the distance of the planet o r satellite, in astronomical units.

The latest results a r e truly impressive. Reasenberg and Shapiro (12) give (a* + y)/2 = 1.000 i 0.001 a s a result of using a 24-parameter model of the earth and mars motion and position. They have made over 100 least-squares solutions with several strategies to search for hidden biases. Their data a r e from the Viking Lander on mars, a space system that continues to operate and provide information. From further data, and better understanding of the propagation through the interplanetary plasma, Shapiro and Reasenberg express optimism that the final uncertainty could be at the 2 X 10-4 level. This would be just about the present limit of the accuracy of a* made in the space-borne rocket experiment and would bring the uncertainty in the equivalence principle into the conclusion for the time-delay tests.

By combining the lunar laser results cited earlier with the light deflection and retarda- tion results, and treating these a s independent data sets, Shapiro, Counselman, and King (7) obtain the following values for the parameters P and y excluding the other PPN parameters, that is, assuming general relativity is correct: P = 1.003 0.005 and y = 1.008 i 0.008, with a correlation 0.6.

The role of atomic clocks is very strong in all of the above measurements, however, the limitations to accuracy a r e not from the clock. The use of a space-borne clock system in VLBI deflection experiments and in the time-delay measurements will substantially improve these data by reducing near-earth propagation disturbances.

Some Technical Aspects of Relativistic Measurements in Space.- The application of clocks to tests of relativistic mavitation r e m i r e s a high level of technolodcal smhistication. The effects we seek to measure are very small. -we have seen that the benchg of starlight at the edge of the solar disc is 1.75 arcsec, and the time delay of signals passing near the sun from transponders, or radar reflecting bodies lying at the other side of the sun does not exceed 250 psec. The maximum value of the earth's gravitational redshift is 6.9 X 10-lo; even near the surface of the sun it is only at the 10-6 level. Measurement of these phenomena at accu-

racy levels of a few parts per million is a real challenge.

The clock can play two roles in these measurements. First, and obviously, it keeps time and, under the assumption of constant and isotropic light propagation, we can interpret time intervals as distance intetmals. Second, it represents a time scale in a particular region of space-time and gravitational potential that can be compared with time' scales from other similar clocks in different regions of space time and gravitation. The atomic clock thus plays the roles of proper timekeeper and yardstick of the llgedanken'l or thought experiments discussed in the early tests of gravitation and relativity.

However, to obtain correct distance and range-rate data, we must be careful to account for the medium through which the signals propagate, and to obtain a valid comparison of time and frequency between widely separated clocks, we must separate very precisely the effects contributing to the relativistically different time scales from the effects of signal propagation.

A successful method for removing propagation effects from frequency comparisons made between a space and earth system was used in the 1976 rocket-probe hydrogen maser experiment (13). Figure 2 shows how this system is configured. It is a continuous wave system that was adapted from the National Aeronautics and Space Administration Unified S Band (USB) tracking and data retrieval system with three separate microwave links operating simultaneously at different frequencies.

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r---

I SPACECWFT SYSTEM

1

I

FLORIDA

W P P L E R TRACKING DATA

Fig. 2. Doppler-cancellation system used in the 1976 Redshift Experiment (13).

The one-way link at fo = 2203.08 MHz compares the space maser and earth maser at mixer MI. The frequency is derived from the hydrogen maser output frequency, fh = 1420,405,751 Hz, by multiplication by the ratio 76/49 = P/Q. The output of mixer MI con- tains the relativistic frequency difference between the clocks (here assumed to be identical) plus the number of cycles per second gained or lost in the transmission path. A separate two-way link measure the constantly varying number of cycles of phase in the path. Here the uplink operates at 21 17.70 MHz = fh x R/S, where R/S = 82/55. The transpo&der multiplies the received frequency by M/N = 240/221 and transmits a signal back to earth where it is received and compared with the uplink signal at the mixer M2. The beat signal from the mixer is divided by two and normalized to the space clock downlink frequency by the ratio (S/R) X (N/M) X (P/Q), so as to represent one-half the phase in the two-way path. In mixer M3 it is subtracted from the one-way phase and relativity signal from mixer M1. Path-depen- dent phase shifts a r e thus cancelled in the output signal and the remaining signals represent relativistic and gravitational effects. The figure also shows the way Doppler data are obtained for tracking the space probe using the three-way mode of operation.

Since the system operates at three separate frequencies, time-varying frequency dispersive refraction effects from the earth's ionosphere will cause severe distortions in the output.

The first-order dispersive effects from the ionosphere can be cancelled (14) by choosing the frequency ratios according to the relationship

Using the above cited ratios; we found that the cancellation of the combined ionosphere and tropospheric and path distance effects was at a level below 1 part in 10-14 for averaging intervals of 1000 sec. This limit was set by the clocks and not by the system (15).

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We can extend this cancellation concept by making the system symmetrical through the addition of a fourth microwave link. Fig. 3 shows how this would be done.

- - -

EARTH STATION

Fig. 3. Concept of a four-link time-correlated Doppler system.

This system provides six sets of data relating to the conditions between the space and ground system. Signal loop "An gives a two-way Doppler signal at the earth, E2(t). Link A gives one-way Doppler and relativity data at the spacecraft, Sl(t). Signal loop I1B" gives two- way Doppler data at the spacecraft, S2(t) and link B give one-way Doppler and relativity data at the earth, El(t). Doppler-cancelled data at the earth a r e given by Eo(t) as in Fig. 2;

Doppler-cancelled data at the spacecraft are given by So(t).

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The figure shows a link labeled XS1, which parallels a link labeled X. This link is a means for obtaining the columnar electron density in the propagation data by comparing the phase of simultaneously transmitted signals at S and X bands.

Use of the Four-Link System in Tests of Relativistic Gravitation.- A number of criteria for relativistic theories and a classification of tests were described in the introduction and we will show how data from the four-link system can be used to make some of these tests in three types of space missions.

1. Near-earth eccentric orbit mission

The 1976 rocket probe mission using masers obtained data a s shown by the So(t) output of Fig. 2. According to general relativity, the predicted behavior of this signal is given by

Here +s - +e is the Newtonian potential difference between the spacecraft and earth station, Ts

and ee a r e the velocities of the earth and space stations joined by vector Tse. The quantity

a a, is the acceleration of the earth station owing to the earth's rotation; all quantities a r e referenced to a geocentric inertial frame.

The first term in equation 4 is the gravitational "redshift, I' which, in the present case, i s really a blueshift since the potential difference effect leads to a positive frequency shift.

The second term is the familiar second-order Doppler shift of special relativity, which is always negative. Here we must be a bit careful since the prescription for such a shift has always been discussed in terms of velocity differences between two inertial (unaccelerated) frames. In this situation, we have substantial gravitational acceleration and the attendant curvature of space-time. The last term results from the fact that during the light time rs$c, there is a change in the component of velocity of the earth station in the direction of propagation between probe and earth, which produces an additional Doppler shift. This term is sensitive to our choice of an inertial frame whereas the other are purely relative to each other.

During the vertically launched mission, the output frequency was thus expected to start negative, go through a zero beat, then go positive a s the velocity difference diminished and the gravitational term became more significant. As the probe approached apogee, the shift would reach a maximum and, as it fell, we would see a zero beat and a reversal to negative frequencies. The agreement of the measured data was within 70 X of the total effect predicted in equation 4 (13).

There a r e various ways that this result can be interpreted. For example, if we affirm the correctness of the second term giving the second-order Doppler effect and assume that the third term correctly accounts for a Doppler shift resulting from the change of velocity of the earth station during the light time, we can ascribe all the e r r o r to the equivalence principle and confirm it to approximately 140 X 10-6. (Since the redshift and second-order Doppler terms are very nearly the same in magnitude, the fractional e r r o r in the total effect, now half as large, is doubled.) Alternatively, if we place all the e r r o r in the second-order Doppler effect and assume the equivalence principle and the earth station term a r e correct, we have confirmation that the second-order frequency shift is corrected within 140 X This conclusion is valid over space-time intervals that have considerable curvature.

Yet another interpretation of this data is possible if we ascribe all the e r r o r to a possible anisotropy of the velocity of light during the experiment. Since this experiment involved a substantial change of velocity and depended on the cancellation of the Doppler effect in the one- way path, by taking an average of the two-way Doppler cycles and subtracting them from the one-way cycles, a residual Doppler signature would be present in the data if the velocity of light in the downlink and uplink signals was different. Under these assumptions, a limit of

~ c / c I ^<³^X10-9 can be set for the isotropy of the velocity of light (16).

If the system shown in Fig. 3 were used in a repeat of this mission, with a highly eccentric orbit a s originally proposed (17), we could separate the effects of gravitational potential from those of the second-order Doppler shift since the system provides two sets of Doppler- cancelled data.

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In order to time correlate these two data sets, either by addition, so as to eliminate the gravi- tional term, or by subtraction to eliminate the second-order Doppler term, we must face up to the question of relating their time scales by adopting a coordinate time using a relativistic theory

This illustrates the nature of these tests and shows how we a r e forced to look at the overall results in judging their internal self-consistency. We must be very careful how we

ascribe the discrepancies, realizing that if any one part of the theory breaks down, other parts a r e also affected.

We can search for characteristic signatures of various possible discrepancies in the theory by examining the residuals we obtain when we compare prediction and measurement.

For example, if we look for a first-order Doppler-like signature in Af/f 1, ^and^its^mirror

image counterpart in Af/f Is we can establish limits on the extent of anisotropy in the velocity of light. If this signature recurs consistently from orbit to orbit and shows some sense of direction in space, we will have some explaining to do. Signatures in the residuals that resemble the gravitational potential, where the data are combined (subtracted) to eliminate the second-order Doppler will also lead to questions. Biases in the data could also be intro- duced through the last term, where we could see some effects of an inappropriately chosen inertial frame, and they, too, will show a characteristic signature.

An analysis of the potential accuracy of this experiment using an eccentric, 24-hr earth orbit has been made (18) using information from the 1976 test. The combined sensitivity of the test including random and known possible systematic e r r o r s is expected to be at the 4 X level in the confirmation of the relationship of the Af/f with A+/c2 and would be about 35 times more sensitive than the 1976 test. This test looks at the validity of metric theories as a class and tests the meshing of gravitation and relativistic phenomena. [Criteria 3 and 4 and test categories 2 and 3.1

2. The close approach solar probe mission, "starprobe"

For several years studies have been in progress on a solar probe mission where a freely falling (and therefore, drag-compensated) spacecraft would fall within 4 solar radii from the sun's center (19). This mission, as currently conceived, would be launched toward the planet jupiter and use the gravitation of that planet to alter course s o a s to fly directly toward the sun in a highly eccentric polar orbit. The scenario is shown in Fig. 4. After 3-1/2 to 5 years, depending on the available propulsion energy, the probe will encounter the sun and will pass from one side of the semi-latus vectum of its orbit to the other in fewer than 14 hr. During its time of close approach the probe will operate in such a way that the radiation and particle pressure from the sun i s negated by a carefully controlled drag-compensation system.

PLANE OF

Fig. 4. Geometry of solar probe experiment.

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The principal gravitational objective of this mission is to determine the shape of the solar gravitational field and, hence, its mass distribution. A determination of the sun's quadrupole moment, J2 at the level of accuracy 1 X would give solar and stellar physicists crucial data for understanding the interior of stars. This information would come from the behavior of a freely falling body that would be tracked by a station on earth. Here, of course, is an obvious role for the clock and this simple two-way and three-way tracking mode is the ori- ginal basis of the experiment. There are, however, very good reasons to have a clock aboard the spacecraft. The transponder tracking requires a relatively unperturbed uplink signal so that a phase-coherent signal can be generated for transmission back to earth. Because of the ionization in the solar corona, this phase coherence is likely to be interrupted and lapses would result in the tracking data during the critical time when the probe is briefly near the sun. One-way data from an on-board clock would obviate the need for any uplink phase lock and the signal could be more easily reconstructed, since transmissions, at least, would always be coherent.

By including the clock and four-link system aboard the solar probe, substantially more data would be available during the brief solar encounter to look for higher order gravitational multipoles. Furthermore, there is a reasonably good possibility of measuring the angular momentum of the sun through the "frame dragging1' effect that was predicted from the Einstein Theory by Lense and Thirring in 1918. Assuming that the theory is correct, the angular momentum data s o obtained would be immensely valuable - and how else could this be measured than through its gravitational signature?

An important outcome of having an on-board clock comes from the possibility of obtain- ing Doppler-cancelled data as in equations 5 and 6. In this test the effects we expect would be very large compared to the terrestrial situation,and, to make si ificant use of the clockls stability, the expansion of the relativistic prediction to order c- will be required since the 2?

expressions in equations 5 and 6 a r e only valid to order c-2. These expressions contain data relating to the second-order behavior of the redshift, which lead to a direct measurement of the parameter, p in the field equations describing the bending of space-time by the presence of a massive body. Made at sufficiently high precision, such a measurement could provide a means for discriminating between the Einstein theory and other metric theories as discussed in test category 4.

3. Detection of gravitational waves in deep space probe

Our present capability to devise laboratory experiments to test gravitation theory is limited by the masses available in our solar system. For experiments that seek to extend the range of validity of the theory we must look for naturally occurring astrophysical phenomena involving super dense matter and enormously higher masses. We are thus forced to change our posture to that of observer, rather than cause-and-effect experimenter, and face the problem of unravelling from the data the characteristics of the generating phenomena and the manifestations of the theory we a r e testing. Gravitational radiation appears to be the key to understanding gravitation under these more extreme conditions and pointing the way to post- Einstein theories of relativity. An assessment of the possible astrophysical sources of radiation, the magnitude of the signals, and the manner in which they a r e generated, has been made in a recent book, Sources of Gravitational Radiation, edited by L. L. Smarr (20).

Among the possible gravitational signals, there are very low frequency, approximately 10-3 Hz, pulsed sources thought to result from the collapse of supermassive black holes of 106 to 107 solar masses that a r e now associated with the early formation of galaxies. The level of these signals, assumed to originate at distances associated with the time of formation of galaxies, is estimated to be at the 10-15 to 10-14 level in the deformation of the space- time metric. Since these waves are assumed to travel with the velocity of light, enormous distances a r e required for us to perceive them.

Deep space probes, such a s the solar probe during its cruise to jupiter, offer a means to span this distance, and atomic clocks can be used to detect elongations and contractions of space-time between the stations that could be as large as one-half a millimeter in a period of 1000 sec (21). Studies are under way to see how the four-link system can be used to detect these pulses in the presence of systematic disturbances imposed by equipment and propagation and the thermally produced random noise that is inevitable in clocks and electronics systems.

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Under conditions where the separation between stations is large compared with the dura- tion of the expected pulses, the behavior of the various earth and space station Doppler signals can be described in terms of a light-time diagram as shown in Fig. 5. Here, contrary t o convention, coordinate time goes to the right and the signal paths are shown criss-crossing the diagram. The output Sl(t), S2(t), E l(t), E2(t) a r e shown at their appropriate positions.

Coordinate-time plots of these four functions can be used to show the effects of the various processes. For example, a momentary phase advance in the earth station oscillator is shown in Fig. 6. Here we see a definite pattern of disturbances in the four-time series of data.

Fig. 7 shows the effect of a momentary disturbance of the space-probe antenna. Again, we see a definite pattern of amplitude and phase in the four data sets. The effect of momentary blobs of ionization crossing the space-time diagram is shown in Fig. 8, which illustrates a method for cross-fixing the blobs in space-time. This figure also shows how one-way data can be obtained redundantly by real-time subtraction of one-way data from two-way data.

EARTH STATION POSITIONS COOROl NATE

d TIME t OSCILLATOR (OR CLOCK1

TRANSPONDER E2(t I

Fig. 5. Space-time diagram of Doppler signals.

SPACECRAFT

''%I I-WAY I

Fig. 6. Effect of a momentary offset in the phase of the earth station oscillator.

SPACECRAFT

'4~2 ^2-WAY ^{- N O}

I

EARTH '+EZ 2-WAY

SIGNATURE -

I 1

t = to t ; t + % 2R

0 C t = t ₀+ A _C

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SPACECRAFT

"sl I-WAY SPACECRAFT A's2 2-WAY A+,, EARTH

I - WAY +. ^f

A = Z a L \ "

X

WHERE A IS WAVELENGl MICROWAVE SIGNAL

Fig. 7. Effect of spacecraft buffeting by fluctuations in solar wind or solar radiation pressure.

Signatures for burst arriving at t = to.

I. USE REOUNOANT OATA TO REMOVE UNCORRELATED NOISE 2,CORRELATE ) AND t FLUCTUATIONS TO DETERMINE Ro-Rb

POSITION OF PROPAGATION ANOMALY IN R, t PLANE.

Fig. 8. Illustration of correlation technique to remove effect of phase fluctuations in propagation.

The effect of a gravitational pulse traversing the earth-probe system at 60 degrees is shown in Fig. 9. There a r e 10 signatures of the pulse in the four data sets. Of these, four are the result of direct interaction, the remainder a r e duplicates and echoes of the pulses through the transponders. The magnitude, sign (ie + or -), and time separation between the pulses a r e governed by the parameter, 8 , which is the angle between the signal path and the gravitational-wave propagation.

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A TRADITIONAL GRAWTY WAVE AFTER THORNE, WAHLOUIST, ESTABROOK,

BRAGINSKY (1975-76)

Fig. 9. Illustration of gravity-wave signature for a four-link correlated system 0 = 60".

At present, we estimate that the largest, continuous noise process in the system would result from propagation through the earth's troposphere and ionosphere. By time correlation of the incoming and outgoing signals of the earth station, this noise can be very effectively eliminated with only a relatively small increase resulting from the superposition of random processes that are in the 10-15 level in df/f. Considerable effort has been under way at the Harvard-Smithsonian Center for Astrophysics by Tsvi Piran and others to simulate these processes and assess the sensitivity of this system for detecting gravitational waves. With present technology we estimate the overall noise background for a probe going a s far as jupiter i s at the 5 X 10-15 level for 1000-sec averaging time. This is in the range of pulse amplitudes predicted by astrophysicists and the results a r e encouraging.

The eventual detection of gravitational waves by this, or any other technique, would be a highly significant event in astronomy. Needless to say, this is a high risk-high benefit situation and the eventual implementation of various types of experiments must be carefully evaluated.

Conclusion.- While this paper is far from being a complete assessment of the use of clocks in gravitation and relativity experiments, it is clear to the writer that the use of clocks in spacecraft will provide highly valuable data in future deep space missions. A number of proposed space scenarios for obtaining such data is now being explored with the expectation that, at some time in the evolution of space exploration, new opportunities will arise for making gravitation and relativity experiments with atomic clocks.

Acknowledgments.- This research was supported in part by grant NSG 7176 from the National Aeronautics and Space Administration and by the Smithsonian Institution Secretary's Fluid Research Fund.

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