ARTIFICIAL SATELLITES AND THEIR associated hardware have opened new horizons for the amateur scientist. Scores of amateurs are already participating in the Moonwatch and Moonbeam programs sponsored by the U. S. National Committee of the International Geophysical Year. These formal activities marshal the services of advanced amateurs to man elaborate stations which make observations of immediate scientific value. But the amateur does not need elaborate equipment to keep track of a satellite's path, or even to predict with fair accuracy how long a satellite will stay on orbit. Anyone can do it. Those most interested will doubtless acquire at least a low-power telescope or a pair of binoculars. Others will be able to settle for a pair of pocket mirrors, a sheet of glass and some adhesive tape The amateur who prefers to make observations with a minimum of equipment can get into business with nothing more than three wooden slats and a stop watch.

These techniques require that the observer be outdoors, often before sunrise. For the comfort-loving amateur there is another means of keeping track of satellites, at least so long as they transmit radio signals'. Many ordinary radio receivers have built-in converters which enable them to pick up the short waves broadcast by satellites. Even those receivers without converters are easy to adapt to short-wave reception. Converter units, available from dealers in "ham" radio supplies, are priced at about $50. Those amateurs who prefer to build their own converters will find complete instructions in The Radio Amateur's Handbook. Parts for a two-tube converter cost about $15.

Ralph H. Lovberg and Louis C. Burkhardt, physicists at the Los Alamos Scientific Laboratory, have suggested a way in which the amateur can determine the height of a satellite as it passes overhead. Their method is based on the Doppler shift, the apparent decrease of pitch noted when a source of sound, such as a train whistle, rushes past the observer. Radio-equipped satellites are in effect whistling objects. Their radio transmitters radiate signals at predetermined frequencies. In the case of the first two satellites the frequencies were approximately 20 and 40 megacycles per second. To measure the distance between the observer and a satellite, the signal from the satellite is tuned in on a radio receiver and mixed with a signal generated by a local oscillator of somewhat higher or lower frequency. The difference frequency is then amplified, fed into a loudspeaker and converted into sound. For example, when a signal of 40 megacycles is mixed with a locally generated signal of 39.997 megacycles, the amplified difference frequency of 3,000 cycles will produce a whistling sound pitched about two octaves above middle C. The period during which the pitch changes may last more than five minutes. The distance of the satellite is determined by measuring the pitch of the sound at brief intervals during this period, and noting the time at which each tone is identified. The frequency of the sound at each interval can be estimated by comparing it with the notes of a piano or, preferably, by following the whistle down the scale with an accurately calibrated audio-frequency oscillator. Whenever the signal and comparison tone (piano or oscillator) coincide (are in zero beat), the corresponding time should be recorded as read from the second hand of a watch or clock.

"In the case of our measurements of the first satellite," write Lovberg and Burkhardt, "we used a conventional Hallicrafter SX-28 receiver at 40 megacycles. The local beat-oscillator was left off and a surplus BC-221 frequency meter was coupled loosely (by means o a twist of insulated wire) to the antenna lead. The signal generator is set at approximately 3,000 cycles below the satellite frequency when the 'little traveler' is first detected. This results in an audible tone in the receiver output. The tone is now fed into a loudspeaker together with the output of an audio oscillator. In a typical run one sets the audio oscillator to a tone lower than that of the satellite, say 2,500 cycles per second, and waits for the satellite tone to drop to the same value. The zero beat between the two tones is first heard as a fluttering sound which diminishes in frequency to a slow swelling and fading of the 2,500-cycle note. At the instant the tone becomes steady, one records the time as well as the frequency (2,500 cycles in this instance) and quickly shifts the audio-frequency oscillator to, say, 2,400 cycles, and waits again for the matching of the tones.

"The resulting table of frequencies and times is then plotted as a curve like the one shown on page 102. This indicates the passage of the first satellite over Los Alamos, N. M., on October 18. Next we draw a line tangent to the curve at its steepest point. The slope of the tangent line represents the number of cycles per second that the frequency changes per second and varies in proportion to the distance of the satellite. If we call this slope m, then the distance of the closest approach of the satellite is given by the simple formula d = fv²/cm. Here f equals the frequency of the satellite's transmitter (40 megacycles), v equals the velocity of the satellite in miles per second (about 4.9 miles), c is the speed of light in miles per second. The velocity v will vary somewhat from the 4.9-miles-per-second value, depending on such factors as the eccentricity of the satellite's orbit. The amateur may obtain fairly accurate velocity figures from agencies such as the Smithsonian Astrophysical Observatory. These figures are sometimes reported in the daily press."

It was by this method that Lovberg and Burkhardt learned that the first satellite was coming over Los Alamos at a height of about 170 miles at night and 260 miles during the day. The figures are in good agreement with those released by the Smithsonian Observatory.

An optical means of getting the same result is suggested by Walter Chestnut, a physicist at Brookhaven National Laboratory:

"If an object is in a stable, circular orbit around the earth, one may say that the gravitational force of the earth pulls the object with a force which equals its centrifugal force. The relation may be expressed in mathematical terms in such a way that the object's altitude may be determined by a simple measurement of the number of degrees traversed by the satellite in one second as the object passes overhead. This angular velocity may be measured by timing the transit of the satellite as it passes stars, the positions of which are known. If the amateur does not have a star chart, the angle can be easily measured by a fixed astrolabe, a triangle of wooden slats nailed together and supported as shown in the accompanying illustration [at right]. The astrolabe forms an angle of 10 degrees. The nails serve as sights; they should be painted white so that they will be clearly visible in poor illumination. The construction of the instrument should be as light as possible, because it must be swung into position quickly when a satellite is spotted. The two outer nails should be placed in line with the satellite's path and held steady. The number of seconds are then counted from the time the object appears to touch the first nail until it reaches the second one. The corresponding altitude in miles can then be read from the accompanying table [see below].

"Readers may calculate their own table for astrolabes of other angles by the equation:

In this equation d₁ equals the altitude of the satellite in miles; t is the time of transit in seconds for an angle of a degrees. For an astrolabe of 15 degrees and a transit time of 60 seconds the altitude would be

or 1,128 X .8474(956) miles. The same calculation is carried out for each value of time desired in the table.

"Both the table and the equation assume that the satellite is observed within 15 degrees of the zenith. If the satellite is more than 15 degrees from the zenith, multiply the distance given in the table by the cosine of the angle between the orbit and the zenith. The equation and table also assume that the orbit is a circle. Most orbits, however, will be ellipses. But if one knows the maximum and minimum heights of the satellite, the table (and equation) can be corrected for ellipticity by the equation:

In this equation d₁ is the altitude obtained from the table (or the first equation). C is the distance (in miles) to be added to d₁ if C is positive, or to be subtracted from d₁ if C is negative. The average of the maximum and minimum altitudes of the satellite is represented by d_e. In the case of Sputnik I the maximum and minimum altitudes were respectively 570 and 170 miles; d_e accordingly equals 370 miles.

"By following these instructions carefully the amateur can determine the altitude of a satellite with an accuracy of about 20 miles for every 1,000 miles of its height. The limits of error will doubtless be determined more by the accuracy of the observer's measurements than by errors of the method.

"We have observed the rocket of Sputnik I on two occasions. The first time we merely wanted to find out if it was really there. On the second look the astrolabe was propped against a convenient tree. As the rocket traveled from one sighting nail of the astrolabe to the other, a transit time of 11.6 seconds was recorded. Unfortunately the tree swayed a little in the stiff morning breeze; this doubtless introduced an error of a few miles. The altitude for an 11.6-second transit, as it is read from the table, is 314 miles.

What about methods of measuring changes in the time it takes a satellite to make a trip around the world? As a satellite encounters atoms and molecules of the rarefied air at altitudes above 100 miles, it gradually loses speed. Paradoxically it appears to gain speed, because as it slows down it spirals closer to the earth and takes less time to complete its orbit. When the orbital time of a satellite decreases to about 87 minutes, the satellite will soon be consumed by friction with the lower atmosphere. Thus by timing the passage of a satellite during a few transits, its lifetime can be predicted. If the measurements can be made with good accuracy, two timings are sufficient for an approximate prediction.

A convenient instrument for timing the orbit of a satellite is the dipleidoscope, a device invented about 1860 by an English barrister named J. M. Bloxam. It consists of a pair of mirrors tilted toward each other at an angle of somewhat more than 90 degrees and covered by a sheet of glass as depicted on this page. The three elements may be supported by a pair of end plates, as shown, or simply taped securely. Ideally the mirrors should be front-surface silvered and the cover glass should be silvered so that it reflects 38 per cent of the light striking it and passes the rest. But ordinary back-silvered mirrors ( or even plain glass with a back-coating of black paint) will work, and the cover glass need not be silvered at all.

When the dipleidoscope is held at an angle which reflects light from the satellite into the eye, two images will be seen. One image is reflected by the cover glass, the other by the mirrors As the satellite passes overhead, the two images move toward one another, merge and then pass out of the field of view in opposite directions. The time is recorded at the instant the images merge. The device should be set up in advance of the transit on a firm but easily adjusted support such as the ball-and-socket tripod head popular with photographers. The axis of the dipleidoscope should be adjusted roughly at a right angle to the anticipated path of the satellite. During one transit the instrument is adjusted so that the two images will merge. On the same transit the time is recorded. The instrument is then left undisturbed for a second observation during the next transit. In the case of Sputnik I observations made 24 hours apart would show the approximate apparent gain in time for 15 revolutions.

Most satellite observers will also want a good low-power, wide-field telescope. An inexpensive one of the type used by Moonwatch teams is depicted below. It is designed for table-top use, the front-surfaced mirror being an anti-crick-in-the-neck feature for those who prefer to look down rather than up. The achromatic objective lens and Erfle eyepiece together retail for about $25.

Roger Hayward, who makes the drawings which illustrate this department, is a restless intellect. Between assignments for "The Amateur Scientist" he is an architect, but he still finds time for multifarious activities ranging from the design of optical instruments to the making of decorative mobiles. One of his recent concerns has been to devise experiments which demonstrate the remarkable properties of the human eye. "During the past few days," he writes, "I have been enjoying a brainstorm which might amuse other amateurs. It all started when I came across the description of an ingenious optical trick involving a mirror polished on the flank of a contact lens arranged so-the observer's eye is presented with an image of a dark vertical line which remains fixed on the retina regardless of any eye movement. The general result of the experiment was that the image of the line kept disappearing. The image would be observed with distracting clarity for about a tenth of a second. Then it would disappear, reappearing now and then at irregular intervals. The conclusion was drawn that if any image is presented continuously to the eye without any relative motion with respect to the retina, the mind simply learns to ignore it. Although not specifically mentioned in the article, this sort of thing brings to mind the fact that visual acuity is greater for moving objects than for fixed ones.

"It has also been observed that the human eye is always in motion. An irregular vibratory motion of from 5 to 25 seconds of arc inamplitude and from 10 to 100 cycles per second in frequency seems to be ever present, and appears to be necessary to maintain consciousness of the background scenery. It is also well known that the retina is crisscrossed by a many-layered network of nerves and blood vessels which cast shadows on the light-sensitive cells. Yet we are not conscious of this complex obstruction between the lens and retina. According to physiologists the network which overlies the light-sensitive cells is about a thousandth of an inch thick.

"This is where I come in. It seemed to me that if one could present the eve with a view of a uniform field of light, one without any detail, and arrange matters so that this view is perceived by light which would come alternately through the two sides of the pupil of the eye, then shadows cast by the blood vessels, nerves and so on could be made to fall alternately on different light receivers, and the flickering shadows would be perceived because of their movement. One would in effect see a vibrating silhouette of the obstructing network in his own eye.

"That the mind is capable of ignoring fixed blind spots is well established. A relatively large one, some seven degrees high, is situated about 15 degrees toward the nose from the center of attention This feature marks the area where the nerves and blood vessels enter the eyeball. When both eyes are open, the brain always fills in this blind spot with a continuum identical to the one surrounding it. Even when one eye is closed the brain does the best it can to fill in the missing portion of the scene. Hence the 'blind spot' is really blind only for those images which lie wholly within it. The effect can be observed with the aid of the accompanying drawing [left]. Close the right eye (or mask it with your hand) and with the left eye look directly at the white dot from a distance of about 15 inches. The page should be held so the dot is centered in front of the left eye, the cross being about 2 5/8 inches to the left. Both the dot and the cross will be seen, but attention should be centered on the dot. Now move the page gradually closer. At a distance of about 10 inches the cross will abruptly disappear. The image of the cross has entered the area of the blind spot. Continue moving the page closer. The cross will reappear at a distance of about six or seven inches. If the page is now held at a distance of about eight inches and moved from side to side, the same effect will be observed. By noting the distances at which the test pattern disappears, and taking the focal length of the eye lens into account, it is possible to compute the shape and area of your own blind spot.

"The setup required for perceiving the network of blood vessels and nerves in your own eye involves somewhat more elaborate apparatus, but even so it is simple enough to suit most amateurs. A rotating disk with slots, or merely a disk painted black and white and masked by an aperture [see Figure 8], is focused on the pupil of the eye. In effect the image created by the dark part of the disk alternately covers the two sides of the pupil, while the white portion alternately admits light to each side. Any lens system will serve to focus the image of the source on the pupil, such as a conventional eyepiece or even a pair of pocket magnifiers held together with rubber bands. An eye ring is handy for locating the eye point in space. This can be made from a narrow strip of cardboard as shown in the drawing. The painted disk should be turned at about 10 or 15 revolutions per second. I accomplished this with a hand-cranked pulley only because I did not happen to have a slow-speed motor at hand.

"The image of the network leaves something to be desired in the matter of contrast. Even with the 1Rickering light the obstructions are not too easy to see. The silhouette appears as little more than a texture. A number of details disappear and reappear at irregular intervals and are about as distinct as the small objects which appear and disappear, seemingly out of nowhere, when the gaze is fixed on the sky or a smooth surface without observable detail. Some of these, incidentally, are blood corpuscles.

"One of the jokers is that the picture presented to the consciousness seems to float about in space. If you try to bring any single detail into sharp view the whole pattern drifts because the details move with the eyeball. The fovea, the small area of the retina which provides the most acute vision, appears to be almost devoid of detail. I can see it by masking the rotating disk so that the flicker moves up and down (by fixing the circular diaphragm at the top of the disk instead of at the side). I see a patch about half a degree in diameter in the middle of the field of each eye. It does not appear during horizontal flickering. The patch is elliptical in shape and not as wide as it is high, perhaps two thirds as high as wide. It is covered by about 10 very fine wavy lines and seems to agree well with the published dimensions of the fovea. My center of visual attention is always at the left of the elliptical shape, regardless of which eye I use. One would naively suppose that the eyes would exhibit symmetry instead of this same handedness.

"Each person who makes this experiment will see his own retinal pattern. No other person can see it nor can it be photographed. If the observer wants to show his pattern to someone else he must draw it. This would seem to pose a problem somewhat like that of recording the features of the planet Mars, in which the few persons who can draw are the only ones capable of showing others what they think they see. If enough people make sketches of their own retinas, however, perhaps some conclusions can be drawn about the nature of the nervous network of the retina. At most the experiment might yield information about the structure of the retina. At least it will give the experimenter a view of something no one else can see."

Bibliography

AMATEUR TELESCOPE MAKING-ADVANCED. Edited by Albert G. Ingalls. Scientific American, 1952.

THE DISAPPEARANCE OF STEADILY FIXATED VISUAL TEST OBJECTS. Lorin A. Riggs, Floyd Ratliff, Janet C. Cornsweet and Tom N. Cornsweet in Journal of the Optical Society of America, Vol. 43, No. 6, pages 495-501, June, 1958.

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