Experiments in Radar Detection of the Moon

V. S. Vavilov

1. On the Possibility of Flight to the Moon

The advances of physics in recent years, and especially during the war years, have brought closer to reality the solution of problems which, ten or twenty years ago, seemed to lie in the realm of science fiction. The development of the technology of rocket flight, especially in connection with the real possibility of using the energy of nuclear reactions, has with new force given rise to the idea of interplanetary travel. In this connection it is interesting to mention the calculations of Himpman and Reichel[^1], who set themselves the task of resolving the question of the possibility of the “simplest” interplanetary flight to the Moon, proceeding from concrete technical data. From their approximate, but sufficiently convincing, computations it follows that, with very large expenditures on experiments and with the use of optimal materials and fuel, it is in principle possible to construct a rocket with chemical fuel (i.e., using the energy of a chemical reaction) which, with a total takeoff weight of 50 t, would deliver to the Moon a payload of the order of 10 kg.

A rocket capable of delivering to the Moon and back a man with a minimum of equipment would have to have a takeoff weight of about \(10^{10}\) kg. It follows from this that, if one has in mind the flight of a man to the Moon, the design of a rocket using chemical energy is evidently impracticable.

But it is not only the small energy of molecular fuel that constitutes an obstacle to the construction of an interplanetary flying projectile.

One may imagine two types of engines using the energy of a nuclear reaction. In the first of them the liberated nuclear energy is used to heat some working substance (analogously to heat engines) and to transform this substance into a gaseous state. The direct cause of the rocket’s motion would be the outflow of gas from a Laval nozzle—just as in ordinary rockets. If one performs an approximate quantitative calculation, taking into account the permissible temperature of the issuing gas, then for a lunar rocket with a useful

with a payload of several hundred kilograms the total weight will be about \(10^7\) kg. As is clear from this, an engine with a working medium gives no decisive advantage over chemical fuel. In another type of nuclear engine, which can be imagined only by invoking a considerable share of fantasy, the products of the nuclear reaction are emitted in the form of a stream of particles concentrated within a sufficiently small solid angle. In this case the ratio of the weight of the nuclear fuel to the weight of the rocket turns out to be very favorable, so that even massive shielding of the crew from radiation appears feasible, thanks to a significant reserve in weight. The chief obstacle in this case consists in the necessity of dissipating the heat released by the rocket engine, since, in order to obtain the same thrust, a nuclear engine must release approximately 1000–2000 times more energy than an engine using chemical fuel. Since in modern rocket designs the dissipation of thermal energy nearly reaches the theoretical limit, it must be considered unlikely that this limit can be exceeded by a factor of 1000 or more, or that the efficiency of such a nuclear engine will be sufficiently high. However, the completely negative conclusion of the authors of the calculations in the latter case is far from being as obvious as for a rocket with chemical fuel, or with nuclear fuel and an intermediate working medium.

In any case, from the point of view of the authors named, if interplanetary flights are possible, their realization will not be a matter for our generation.

2. REFLECTION OF RADIO SIGNALS FROM THE MOON

However, in the hands of experimenters of our day there is a real means of “reaching the Moon.” This is a narrow beam of electromagnetic waves which, under certain conditions, are capable of penetrating through the ionosphere and, after being reflected from a celestial body, returning to Earth. The question of radio radiation incident upon the Earth from surrounding space began to be studied by physicists some 20 years ago. However, the radio-technical means of that time—the use of long waves and the small directivity of antennas due to this—made experiments in the field of extraterrestrial radio communication impossible.

The appearance of sufficiently powerful generators of ultrashort waves and the creation of highly directional antennas made it possible to carry out the first experiments in sending pulsed signals beyond the limits of the ionosphere and receiving signals reflected from the Moon. An experiment of this kind, whose purpose was to determine the distance to the Moon, was proposed by Academicians L. I. Mandelstam and N. D. Papaleksi, who had carried out all the necessary calculations as early as 1943.[^2] Shortly before the publication of N. D. Papaleksi’s article, reports were received[^3] that in the USA, with the aid of modified radar appa-

ratus succeeded in obtaining positive results, i.e., in receiving a pulse of ultrashort radio waves reflected from the Moon. True, despite the excellent equipment and the experimenters’ great capabilities, their results are of value rather as proof of the possibility of the experiment and do not yet provide an exact method for determining the distance to the Moon or for studying its surface. Moreover, the first reports about radio echoes from the Moon, as often happens with work done in the USA, were of an advertising-sensational character and were set forth in a very general, non-detailed form. The article published in 1949,^4 to which we shall return below, serves as a substantial supplement to these first reports.

Simultaneously with the preparation of the experiment in the USA, and quite independently, work was being carried out in Hungary. The results of the Hungarian physicists, also positive, were published in November 1946.^5 Despite the much more modest technical means at their disposal and repeated forced interruptions in the work, the Hungarian researchers, thanks to the ingenious method of cumulation (signal accumulation) developed by Z. Bay, succeeded in obtaining results of the same order of accuracy as the American ones. Bay’s method, which undoubtedly deserves great attention, will be described below.

3. THE APPARATUS AND EXPERIMENT OF DE WITT’S GROUP

As the calculations of De Witt’s group show,^4, ^6 with a transmitter power of 10–100 kW in a pulse, with an effective antenna diameter of 7–10 m and a receiver bandwidth of 50 Hz, in order to obtain sufficient power of the signal reflected back to the Earth it is necessary that the entire surface of the Moon visible from the Earth take part in the reflection. The pulse must have a duration of more than 0.1 sec, i.e., exceed the duration of the pulses usually used in radar practice by approximately \(10^5\) times. The antenna power-gain coefficient must then have a value of about 250. Larger values at a frequency of about 100 MHz would be difficult to realize.

Both in the American and in the Hungarian experiments, the considerable angular width of the beam (about 12° in the experiment in the USA and about 20° among the Hungarian physicists) and the impossibility of a detailed investigation of the form of the reflected pulse accounted for the low accuracy of the results obtained in both cases. However, there can be no doubt that the tendency toward shortening the operating wavelength in radar and new methods of generating radio-microwave pulses of sufficient power will make possible in the very near future more accurate experiments both in determining the distance to celestial bodies and in directly studying their surfaces.

The experimental apparatus of De Witt’s group consisted of a specially modified experimental model of a radar that operated at a frequency of 111.5 MHz. We give (Fig. 1) a simplified

Fig. 1. Simplified block diagram of a radar installation for detecting signals reflected by the Moon.

Labels visible in the diagram:

• Transmitter
• Quartz, 516.20 kc
• Frequency multiplier \((\times 24)\)
• 12.4 Mc
• Keying amplifier
• 12.4 Mc
• Frequency multiplier \((\times 9)\)
• Amplifier
• 111.6 Mc
• Antenna
• Switch from transmit to receive

• Keying pulse

• Keying device and indicator (oscillograph)

• Sweep generator, 3 sec

• Amplifier

• Receiver

• Preliminary high-frequency amplifier
• Amplifier
• Frequency converter, 111.6 Mc
• 1st mixer stage
• Amplifier
• Frequency converter, 32.5 Mc
• 2nd mixer stage
• Amplifier
• Frequency converter, 6.6 Mc
• 3rd mixer stage
• Amplifier
• Frequency converter, [[unclear: frequency value]] Mc
• 4th mixer stage
• Detector
• Amplifier with a 300-cps band
• Quartz, 515.2 kc; heterodyne frequency for obtaining [[unclear: value]]
• Frequency multiplier \((\times 3)\)
• Frequency multiplier \((\times 10)\)
• Frequency multiplier \((\times 5)\)
• Frequency multiplier \((\times 17)\)
• Frequency multiplier \((\times 9)\)
• 79.1 Mc
• 26.6
• [[unclear: frequency value]]
• [[unclear: frequency value]]

block diagram, from which the principle of frequency stabilization is clear, which made it possible to receive signals with a final pass band of 50 cps. As can be seen, the realization of such a narrow band required the use of a very complex circuit. In order that the receiver should always be tuned to the required frequency, one and the same quartz crystal determined the frequency of the transmitter and of all the receiver heterodynes, except for the last stage. By means of a number of mixers, whose heterodynes were stabilized by this quartz, the frequency of the received signal was lowered to 1.55 Mc/s. At the same time the signal was also amplified at all intermediate frequencies. The frequency of the output stage, equal to 180 cps, was obtained with the aid of a heterodyne with a second quartz crystal, whose frequency could be varied within certain limits. The tuning frequency of the receiver had to differ from the transmitter frequency by the amount of the Doppler shift due to the motion of the Moon relative to the installation.

Fig. 2. Oscillogram of the reflection of a radio signal from the Moon. January 22, 1946. Moonrise.

A more detailed description of the receiver may be found in [3]. The power of the transmitter, which at the beginning of the experiments was 3 kW and proved insufficient, was subsequently raised to 15 kW. For this purpose a stage was added consisting of a neutralized power amplifier on two triodes. The antenna consisted of a system of 64 dipoles with an area of about \(13 \times 13\) m and had a power gain of about 250.

According to the authors’ calculations, with the above installation data, the ratio of the power of the received reflected signal to the radiated power of the transmitter should have been about \(10^{-21}\) (attenuation about 200 db). The experiment showed that the calculations were correct as to order of magnitude. The reflection coefficient of the lunar surface was taken in the calculation as equal to 0.17, i.e., the same as for the surface of the Earth (of course, the mean value is meant). Power losses during the passage of the pulse through the atmosphere and due to depolarization of the oscillations upon reflection were not taken into account, but did not exert any substantial influence on the results of the experiment, in view of a certain reserve of receiver sensitivity.

The signal-to-noise ratio for pulses reflected from the Moon in the most favorable cases reached three. In the oscillogram shown (Fig. 2) it is somewhat smaller.

4. METHOD OF CUMULATION (SIGNAL ACCUMULATION)

The apparatus that was at the disposal of the Hungarian physicists did not make it possible to obtain at the receiver output a signal-to-noise ratio exceeding 0.1. To obtain reliable experimental results it was necessary to find a means of increasing this ratio. As such a means, Z. Bay proposed the method of cumulation (accumulation), which, in a somewhat different form, is used in radar.

The essence of the method used in radar is that, when a pulse is repeated sufficiently often, the signal/noise ratio increases owing to the afterglow of the cathode-ray-tube screen, which strengthens the trace of the signal and smooths out the noise pulses arriving in statistical disorder. Since in the experiment being described the pulses followed at intervals of 3 sec., the authors of the experiment considered the use of phosphors impossible. This consideration is quite justified in the case of ordinary phosphors, where electronic excitation gives an afterglow of short duration. However, by using two layers of suitably selected phosphors, the second of which is excited not by the electrons of the tube beam but by the luminescence of the first, it would have been quite possible to obtain an afterglow of the duration required for the experiment. This possibility, which would have made it possible to avoid complicating the apparatus, evidently remained unknown to the authors. Accumulation of charge on capacitors also presented difficulties because of the very high requirements imposed on dielectrics. In view of this, hydrogen coulombmeters were used (an instrument for measuring the quantity of electricity by the amount of electrolytically liberated substance).

The registration of the signal was stepwise, i.e. the coulombmeters were connected at the output of the receiver, after the demodulator, one after another at equal intervals of time by a rotating commutator (Fig. 3). This same commutator, rotated by a synchronous motor, switched on the transmitter for a certain time before the beginning of registration.

Thus the signal reflected from the Moon fell, in accordance with the distance to it, on one of the coulombmeters and successively accumulated a certain volume of hydrogen. The interference, however, expressed in statistical fluctuations of voltage, was averaged out.

With a random distribution of noise, the quadratic error in one coulombmeter after $n$ pulses is proportional to $n$, so that the error itself will be a quantity proportional to $\sqrt{n}$. At the same time, the signal registered by the given coulombmeter, in the case of its repetition with the same amplitude, will increase after $n$ pulses by a factor of $n$. The signal/noise ratio will therefore increase by a factor of $\sqrt{n}$ in comparison with the ratio at the receiver output. Hence it is clear that, with a sufficiently large number of pulses $n$, the signal will considerably exceed the noise level, i.e. will become observable.

Expressed in radio-engineering terms, one may say that the application of the method described is equivalent to narrowing the pass band to the reciprocal of the total time interval during which the recording instrument (coulometer) is switched on. For example, with the number of pulses \(n = 1000\) and the time of one switching-on equal to \(0.06\) sec, we obtain \(1000 \cdot 0.06 = 60\) sec, corresponding to a pass band of \(\frac{1}{60}\) c/s. The signal-to-noise ratio will thereby increase by \(\sqrt{1000}\) times,

Fig. 3. Block diagram of radar installation 3. Bay with cumulative electrolytic signal recording.

which corresponds to a narrowing of the band by \(\sqrt{1000}\) times and is equivalent to increasing the transmitter power by 1000 times.

Coulometers that do not receive the signal give the mean “zero level” during the experiment. Thus, current fluctuations, possible shifts of the operating points of the receiver tubes, and other random changes in the apparatus are averaged out. It may be said that the coulometers not receiving the signal carry out a control experiment.

From the above it is clear that the accumulation method, despite certain difficulties, guaranteed the success of the experiment with considerably less sophisticated apparatus (the transmitter had a power of \(3 \div 4\) kW, the antenna power gain was lower than in the De Witt installation, the receiver pass band was 200 kc/s) and enabled the authors to obtain a positive result. The most unpleasant circumstance in the case of the method described is the necessity for prolonged operation of the installation, which is not always easy to carry out in practice. A second drawback is the stepwise recording, which lowers the accuracy of the experiment.

However, with a narrow passband (which will require coordination of the receiver and transmitter frequencies), Bay’s method makes it possible, without increasing the radiated power, to shorten the pulse duration. This creates the possibility of moving from the initial experiments, which in H. D. Papaleksi’s expression constitute a “sporting interest,” to real radiolocation in interplanetary space and to the determination of distances with great accuracy.

Increasing the directivity of the antenna, in turn, will make it possible to investigate the Moon in sections or, while maintaining a considerable pulse duration, to proceed to experiments on the reflection of signals from more distant celestial bodies.

5. ON THE RESULTS OF THE FIRST EXPERIMENTS

It would be too bold to say at present that, on the basis of radio echoes from the Moon arriving after 2.5–2.6 sec, in accordance with the expected time, distances can be measured with the accuracy with which this is done in astronomy. It should not be forgotten, however, that preparation of the experiments was carried out at the end of the war or in the first postwar months. All the more highly, therefore, should the results of the Hungarian researchers be valued.

In the experiment of de Vitta’s group, it was very inconvenient that the radiation of the transmitting antenna could be directed arbitrarily only in azimuth and lay in the horizontal plane. This limited the time for carrying out the experiment to the rising and setting of the Moon.

The authors note that, as a rule, the results at moonrise were better than at moonset, probably because at moonrise the radiation was reflected from the surface of the sea, which created the effect of additional directivity, weaker in the case of the land surface.

No noticeable correlation was found between the intensity of the reflected signal and the time of day, weather conditions, or the position of the Moon in azimuth.

It was observed that the moment of receiving the first reflection from the Moon differs from its “optical” rising by a time that varies from day to day by several minutes. Very often the radio echo preceded the optical rising of the Moon. The cause is undoubtedly in part the variation of atmospheric refraction and of the transparency of the atmosphere. Another cause may be peculiarities of the antenna directivity pattern. Sometimes, with the apparatus and the antenna directed toward the Moon operating correctly, it was not possible to obtain a reflected signal at all.

One of the interesting effects was strong and rapid variations in the amplitude of the received signals. They occurred so rapidly that they cannot be ascribed to the influence of the antenna directivity pattern. The level of the received signals, following one after another—

in 4 sec, varied from 2 to 20 db. An interval of 4 sec corresponds to a change in the angular altitude of the Moon of approximately \(0.016^\circ\), which is much less than the beam width (\(12^\circ\)). These rapid fluctuations of the signal amplitude should perhaps be attributed to changes in the refraction or absorption of radio waves by the atmosphere. Another probable cause may be the libration of the Moon. At moonrise and moonset it reaches \(3^\circ\) per day. This corresponds to a velocity of the “outer edge” of the Moon of about \(1\ \text{m/sec}\). Thus, in 4 sec one edge of the Moon approaches the observer by 4 m, while the other recedes by the same amount. If, in the given reflected pulse, a significant part of the energy of the reflected signal is contributed by the surface near the edge of the Moon, from the point of view of the terrestrial observer, then libration may quite well account for strong fluctuations in the intensity of reflection. To be sure, this explanation is difficult to reconcile with the conception of the reflecting surface of the Moon as a uniformly rough hemisphere. Attempts to observe variations in signal intensity on those days when the libration of the Moon, both in latitude and in longitude, is minimal have not yet led to definite results.

The oscillographic recording of the reflected pulse, used by de Witt, is convenient for studying the shape of the pulse, from which one could judge the law of reflection. The question of the shape of the reflected pulse and its dependence on the law of reflection and on the duration of the pulse has been treated with exhaustive completeness by N. D. Papaleksi in his article².

However, the American investigators, who used very long pulses—up to 0.5 sec—were in an unfavorable position. A solution of the question may follow as a result of the use of cumulative registration and short pulses. The use of double layers of phosphors with long afterglow would in this case be incomparably more convenient than electrolytic registration according to Bay.

Sources of external noise—local and cosmic—were a major hindrance to the experiments. To suppress nearby interference of high intensity, de Witt’s installation employed a narrow-band (about 1.0 kc, using high-\(Q\) resonators) amplifier cascade at \(111.5\) Mc.

This considerably reduced the influence of interference at frequencies lying outside the passband of the receiver. Interference within the 100 kc band, of course, was not thereby eliminated.

The “noise” of the Sun’s radio emission was observed in the daytime as a significant increase in the level of interference at the receiver output, on which shorter pulses were superposed. At sunrise and sunset it was possible, from the change in the noise level, to distinguish the maxima and minima of the antenna directional pattern. It was usually not possible to obtain reflection of signals from the Moon at a moment when the Sun was separated from it by a small angle.

6. ON THE POSSIBILITY OF A COMMUNICATION LINK USING THE MOON AS A PASSIVE REFLECTOR

One of the aims of studying the Moon as a radar target was to clarify the possibility of stable radio communication between two points on the Earth’s surface along the path Earth—Moon—Earth. However, in view of the obvious considerations given below, the use of such a communication path is limited to special cases and is unlikely to be able to compete with ordinary radio communication.

1) Even in the case of antennas giving very sharply directed radiation, the expenditure of transmitter power will be very large.

2) It is necessary to take into account the possibility of multiple reflection of the signal by the Moon, which, owing to the need to have a sufficiently wide passband for communication, will lead to complication of the apparatus.

3) For antennas of sharply directed radiation it is necessary to carry out continuous movement of the beam, for which complex mechanical devices analogous to astronomical mechanisms are needed.

4) A communication line via the Moon will be able to operate only during periods when the Moon is visible both from the transmitting point and from the receiving point.

5) The very long time of propagation of the signal may be a source of inconvenience.

6) The intensity of the reflected signal, at least in the range of 100 MHz, changes rapidly with time, in all probability for the reasons already indicated above. If the cause of the changes lies in atmospheric refraction, then the use of extremely sharply directed radiation will be made still more difficult.

7) In the case when direct radio emission from the Sun is received simultaneously with the reflected signal, the level of interference is greatly increased. However, that part of the Sun’s radiation which is reflected by the Moon evidently does not serve as a source of noticeable interference.

Thus, although the experiments of 1946 may serve as proof of the possibility of radio communication using the Moon as a passive reflector, the technical realization of such a communication line is rather difficult.

7. ONE-WAY RADIO COMMUNICATION WITH PLANETS

It is of interest to discuss the possibility of one-way communication with the Moon or other planets on sufficiently short radio waves. At a distance \(R\) from the transmitting antenna, the flux of radiation energy falling on a unit area is equal to

\[ S_1=\frac{P_{\mathrm{prd}}G_A}{4\pi R^2}, \tag{1} \]

where \(P_{\mathrm{prd}}\) is the radiation power of the transmitter, \(G_A\) is the power gain of the antenna (in comparison with a nondirectional radiator), and \(R\) is the distance.

If there were on the Moon a receiving antenna with an effective area \(A_{\mathrm{pr}}\), then the power received by it would be expressed as

\[ P_{\mathrm{pr}} = S_1 A_{\mathrm{pr}} . \tag{2} \]

If \(G_{A'}\) is the power gain of the receiving antenna, then

\[ A_{\mathrm{pr}} = \frac{7160\,G_{A'}}{F^2}\;(\mathrm{m}^2), \tag{3} \]

where \(F\) is the frequency in MHz.

The ratio of the power received on the Moon to the transmitter power on the Earth is:

\[ \frac{P_{\mathrm{pr}}}{P_{\mathrm{prd}}} = \frac{571G_{A'}G_A}{R^2F^2}. \tag{4} \]

To evaluate the formulas given, let us consider a nondirectional transmitting antenna \((G_A = 1)\) and a simple receiving antenna with gain \(G_{A'} = 10\) at a frequency of \(100\) MHz. In this case, for \(R = 4.07 \cdot 10^8\) m,

\[ \frac{P_{\mathrm{pr}}}{P_{\mathrm{prd}}} = 3.45 \cdot 10^{-17}, \]

which corresponds to an attenuation of \(164.6\) dB. It is evident from this that an ordinary \(50\)-kW station operating with frequency modulation on a wavelength of \(3\) m would be easily received on the Moon, if there were located there a receiver of no more than ordinary sensitivity and with a passband of about \(200\) MHz.

If antennas of the type used by the de Witt group \((G = 250)\) were placed at both ends of the communication line, the power ratio would be reduced to \(127\) dB. Even at a distance of about \(80{,}000{,}000\) km the signal would be received. Thus, Mars and Venus also sometimes lie within the range of an ordinary modern \(50\)-kW station operating on a wavelength of \(3\) m and having a good directional antenna.

Of course, in the example given not all the factors have been taken into account which so strongly affected the experiments with reflection of signals from the Moon and which may make reception of terrestrial signals on the planets a rather difficult matter.

If it were possible to establish on the Moon even an automatic relay station, the prospects of the communication link considered above would become much more attractive. Unfortunately, as is evident from the material cited in¹, the realization of this is not yet possible in our day.

8. CONCLUSION

Independently of immediate technical applications, further experiments on the reflection of radio waves from “extraterrestrial” objects are undoubtedly of great interest and will continue. It should be pointed out that the experiments described above have for the first time proved quite rigorously

that radio microwaves, at the intensities provided by the transmitters of our time, pass through the ionosphere. Before these experiments were carried out it was known that, beginning at a certain angle to the horizon, the beam of a directional antenna ceases to be reflected. However, it had not been proved whether the waves pass right through the ionosphere or are absorbed in its higher, little-studied layers, although theoretically this question had in the main been resolved. On the other hand, we can judge the radio emission of the Sun reaching the Earth “from the other side” of the ionosphere only by its intensity at the point of reception. It is quite likely that information about the ionosphere will be among the most interesting results of further experiments on the reflection of radio signals from the Moon.

In order to obtain reflections of the signal from the Moon in the future, one should first of all expect the use of pulses shorter than 0.116 sec, i.e., shorter than the time in which the signal travels “along the Moon” and back. It would also be important to have results of experiments over longer periods, to test other wavelengths, and to use narrower beams. Valuable data might possibly be obtained by applying the recently developing method of radiolocation using the Doppler effect to determine the radial velocity of the “target.”

REFERENCES

1. J. Himpran and R. Reichel, Am. J. of Phys. 17, 251 (1949).
2. N. D. Papaleksi, Uspekhi Fizicheskikh Nauk 29, 250 (1946); “Elektrichestvo,” No. 5, 1946, p. 9.
3. J. Mofenson, “Electronics,” April ’946, p. 92.
4. De Witt and Stodola, PIRE 37, 229 (19?9).
5. Z. Bay, Hungarica Acta Physica, 1, 1–22 (Nov. 1946).
6. Norton and Omberg, PIRE 35, 4 (1947).