# Gravitation Research Using Atomic Clocks in Space

### By Dr. R. F. C. Vessot

Smithsonian Astrophysical Observatory

Principal Investigator, Gravity Probe A

Written in 1976.

Atomic clocks with a stability of one part in a hundred million million (10^{14}) have been developed and adapted for space. With recent advances in space technology, we can now expand our laboratory to span the entire solar system and use massive bodies and large distances to measure directly the changes caused by gravitation on time and dimensions. Communication by phase-coherent microwave systems is now possible over enormous distances, and we can realistically consider performing the "gedanken" or thought experiments described in the literature on gravity and relativity.

Traditionally, relativity has been described in terms of systems moving with respect to one another, each containing rods and clocks. Pulsed-light signals connect the systems observationally and provide the basis for comparisons. To make experimental measurements, we can, in fact, use rods and clocks. However, the rod lengths are related to the clocks by the velocity of light, and we can describe distances in terms of wavelengths of the clock frequency if we postulate that the velocity of light is constant in space-time. Thus, we can design relativity experiments that require clocks only.

Most theories of relativity describe space and time by four-dimensional geometry - the three dimensions of space as we perceive them - and time. The presence of accelerations, and in particular acceleration due to gravity, affects the shape of the geometrical lattice work, or coordinate frames used to describe physical phenomena. These frames are said to be warped by the presence of massive bodies and the warping affects both the spatial and the temporal dimensions.

GP-A, an experiment using an atomic clock aboard a space vehicle, will determine directly the effect of gravitation on time by comparing the rate of the rocket-borne clock with another on Earth. Our new "laboratory" has extended into space and may well be the forerunner of other direct measurements of relativistic and gravitational effects probing even as far as the Sun itself.

Our objective is to test the validity of our geometrical picture of relativity. In particular, we will test the principle of equivalence, the cornerstone of Einstein's General Theory of Relativity. First enunciated in 1907, this principle asserts that there is no way of distinguishing locally between the field effects of gravity and those generated by an oppositely applied acceleration. It is a logical extension of the observed proportionality between gravitational and inertial mass that has been tested by Newton, by Eötvös, and more recently by both Dicke and Braginskii to an accuracy of one part in 10^{12}.

A further and more crucial test of the equivalence principle is to see if light waves are also affected equally by gravity and mechanical acceleration. In the latter, light waves traversing our laboratory in the direction of its mechanical acceleration will be received at a slower rate than they were transmitted. This results from the finite transit time between the transmitter and the receiver; the receiver (still connected to the transmitter) will have gained velocity, and the arriving wave crests will encounter the receiver at a slower rather. This shift in the received frequency of the waves is, of course, the familiar Doppler effect. We could describe the "red shift" of our mechanically accelerated laboratory as the Doppler effect due to the velocity gained by the receiver during the transit time of the signals. Our goal is to see if the signals will behave the same way when our laboratory is on the Earth's surface and experiences the pull of gravity.

To date, the best test has been performed by R. V. Pound and his co-workers at Harvard. [The principle was demonstrated over a vertical drop of 75 feet in an elevator shaft.] They have shown, using gamma rays from iron (Fe^{57}), that the equivalence principle is valid within one per cent (1 x 10^{-2}) for a vertical distance of 75 feet at the Earth's surface. The forthcoming test in space will extend the distance to 6,200 miles and could be as accurate as 50 parts per million (5 x 10^{-5}). Furthermore, the test will be performed continuously as a function of altitude and will establish the behavior of the shift over distances comparable to the Earth's diameter.

We plan to use a clock in a spacecraft and compare it by microwave signals to a clock on the ground. To overcome possible errors due to slow drifts in the clock rates, the clock should be moved into space and back to Earth in a reasonably short time. We must obtain as large a span of gravitational potential as possible, consistent with acquiring a sufficient number of measurements at high and low altitudes and making the best use of the clocks' stabilities. This suggests a space probe that attains a very great altitude and falls back to Earth. Since measurements near the Earth are as important as those far from it, and because in such a trajectory the velocity near the Earth is very high, not much time is available near Earth for making measurements. This puts a high premium on clocks (or oscillators) that can deliver high stability over short time intervals. A further requirement is that the precision of the measurements must also be maintained over the entire experiment so that frequency measurements at both high and low altitudes can be compared.

We have chosen the atomic hydrogen-MASER oscillator as an embodiment of a "proper" clock since it is stable to better than one part in 10^{14} over 100-second intervals and up to periods extending to many hours. The total predicted red shift due to the Earth is about seven parts in 10^{10}. If we take our clock to infinity, this enables us, in principle, to measure the effect with an accuracy of 14 parts per million. By going to a distance of about two Earth radii from Earth's center, we obtain a test only slightly inferior - and definitely more feasible.

The test will consist of a simple, one-shot, up-down experiment in which we can overcome about 90% of the Earth's gravitation and still have reasonable time to perform the experiment.

But what of communications problems? Surely, if we wish to see frequency changes as small as one part in 10^{14} in a rapidly moving oscillator, we must learn to cope with very large Doppler shifts in the frequency of the oscillator signals. Furthermore, the rapid motion of the clock causes a kinematic (or second-order Doppler) frequency shift, described by Einstein's Special Theory of Relativity. (This effect has been well tested by other experiments.) It is here that our space technology in microwave communications comes to bear. To account for the second-order shift at any given time, we will use data available to us from our knowledge of the probe's trajectory and obtain the velocity of the probe at all times.

Far more serious is the problem of removing from the clock signal the first-order Doppler shift - about three parts in 10^{5} - in order to see the six-part-in-10^{10} shift with reasonable accuracy. In addition to the Doppler shifts due to the probe's motion, there are also frequency shifts due to the changes in the electrical path through the Earth's atmosphere and ionosphere. We must account for the total shifts on a real time, point-by-point basis during the flight of the probe.

Fortunately, all these shifts of the probe signal can be directly measured by using a second signal transmitted from the Earth and received and retransmitted by the probe back to Earth. The frequency of this re-transmitted signal received at the Earth is compared with the frequency of the original signal from the Earth. The frequency difference is twice the one-way Doppler shift associated with the probe clock signal as received on Earth.

This correction signal (divided by two) is combined with the signal received from the probe so as to eliminate the propagation effects, and we are left with a signal whose frequency contains the information we seek.

At low altitudes, where the probe moves rapidly, the frequency of the probe clock will appear to be retarded by about two cycles per second due to the second-order Doppler effect. As the probe gains altitude and slows down, this effect diminishes and will be offset by the gravitational shift, which makes the probe block appear to run faster, eventually reaching one cycle per second at apogee.

It will certainly be surprising if these shifts are not as predicted by Einstein's general theory. No doubt, our first question will be "How well did the experiment really work?" However, we expect the experiment will indeed confirm the postulates of relativity.