The Satellite Goes Into Orbit

The French radome looms over the Brittany countryside

A ground station very similar to the Andover installation has been built by the French National Center of Telecommunications Studies at Pleumeur-Bodou in Brittany. The British General Post Office has established a station at Goonhilly Downs in Cornwall, England, which uses alarge, deep parabolic dish rather than a horn-reflector antenna. Both British and French stations participated in the first Telstar experiments. Satellite communications ground stations also have been set up in Fucino, Italy, and near Rio de Janeiro, Brazil, and others are under construction in West Germany and Japan.

At 4:35 a.m. (Eastern Daylight Time) on July 10, 1962, a Thor-Delta rocket launched Telstar I into its orbit, almost exactly according to plan, from the National Aeronautics and Space Administration’s Cape Canaveral base. On Telstar’s sixth orbit around the earth—at 7:26 p.m.—the first transmission to and from the satellite took place. During this pass telephone calls, television, and photos were transmitted between Andover and Holmdel. Some of these signals were also picked up in Europe. On the next day, a taped television program was sent from France to the United States, and a live program came from England via Telstar. During the next four months, more than 400 transmissions were handled by Telstar—including 50 television demonstrations (both black-and-white and color), the sending of telephone calls and data in both directions, and the relaying of facsimile and telephotos.

In addition, the satellite performed more than 300 valuable technical tests. Almost all of them showed remarkably successful results. Radio transmission was as good as was expected. Telstar’s communications equipment worked exactly as it should, with no damage from the shock and vibration of the launch. Temperatures inside the satellite were kept under good control. The satellite was successfully stabilized—prevented from tumbling over and over—by being spun around its polar axis, with the spin rate gradually decreasing, as predicted, from its rate of 177.7 revolutions per minute just after launch. The solar cells worked almost exactly as expected. Much extremely valuable data about radiation in space was reported. The ground stations accurately traced the fast-moving satellite in almost routine fashion.

But it would be asking too much to have everything perfect. Telstar I unexpectedly met radiation in space estimated to be 100 times more potent than had been predicted. As a result, difficulties arose during November 1962 in some of the transistors in its command circuit—and on pages78to85we tell you what these problems were, how they were discovered, and what steps were taken to overcome them. Some time later thesatellite again failed to respond to commands from the ground, and on February 21, 1963, it went silent.

New gold-domed device on the Telstar II satellite can measure electrons in an energy range from 750 thousand to 2 million electron volts.

On May 7, 1963, the Telstar II satellite was launched into an elliptical orbit almost twice as large as that of Telstar I, ranging from an apogee of 6697 miles to a perigee of 604 miles. The new satellite circles the earth once every 225 minutes. The higher altitude provides Telstar II with longer periods when it is visible at both Andover and ground stations in Europe, and keeps it out of the high-radiation regions of space for a greater part of the time. The satellite itself is much the same as Telstar I, except for a few minor changes that make its weight 175 rather than 170 pounds. Its radiation measuring devices have a greater range of sensitivity, and there are six new measurements to be reported back to earth. Telemetry can now be sent on both the microwave beacon and, as before, on the 136-megacycle beacon. To help prevent the kind of damage that occurred in the transistors of Telstar I’s command decoders, Telstar II uses a different type of transistor, in which the gases have been removed from the cap enclosures that surround the transistor elements. A simplified method of operation for the giant Andover horn antenna is now in operation, with the autotrack alone being used for precise tracking and pointing. Telstar II’s first successful television transmission took place on May 7, and a new series of technical tests, radiation measurements, and experiments in transoceanic communications has begun.

A lot of facts and figures sometimes lead only to confusion, but these pages may help make things clearer. Here you can see—step by step—exactly what happens during a typical pass of the Telstar satellite over the Andover ground station:

{Telstar satellite at work}

1The satellite comes over the horizon.2The command tracker, knowing from computer data the satellite’s approximate location, begins to search for its continuous 136-megacycle beacon. A quad-helix antenna (four long spirals) tracks the satellite to an accuracy of one degree.3When the satellite is located, the command transmitter turns on the satellite’s transistor circuits and telemetry. The ground station then checks on the satellite’s operating condition, as reported by telemetry.4The command transmitter then turns on the satellite’s traveling-wave tube, which starts the transmission of a 4080-megacycle beacon signal.5The precision tracker—an eight-foot parabolic dish (known as a Cassegrainian antenna) mounted on a pylon—locates this beacon and tracks it to within one-fiftieth of a degree.6The horn antenna’s autotrack mechanism, which is pointed by both the precision tracker and data from magnetic tapes, locates the satellite’s beacon signal.7Now the horn antenna locks onto the satellite, with the autotrack continuing to make fine adjustments in pointing the horn.8The equipment is now ready for communications signals to be sent from the two-kilowatt ground transmitter to the satellite.9The satellite receives the signals and converts them down to a frequency of 90 megacycles; they are amplified in transistor circuits and converted up to a new frequency of 4170 megacycles.10The signals are amplified again by the traveling-wave tube—for a total amplification of as much as ten billion times—to get a radiated power of 2¼ watts.11The 4170-megacycle signals are now transmitted in all directions by the satellite’s equatorial antenna.12These signals can be picked up at Andover or at any other ground station equipped with a suitable antenna that is within line of sight of the satellite.13At Andover, the received signals are amplified by means of a solid-state maser and a frequency-modulation-with-feedback circuit.14They can now be relayed via regular land lines to their destination.15Near the end of a pass, the command tracker turns off the communications circuits and telemetry in the satellite.16The satellite drops below the horizon.

1The satellite comes over the horizon.

2The command tracker, knowing from computer data the satellite’s approximate location, begins to search for its continuous 136-megacycle beacon. A quad-helix antenna (four long spirals) tracks the satellite to an accuracy of one degree.

3When the satellite is located, the command transmitter turns on the satellite’s transistor circuits and telemetry. The ground station then checks on the satellite’s operating condition, as reported by telemetry.

4The command transmitter then turns on the satellite’s traveling-wave tube, which starts the transmission of a 4080-megacycle beacon signal.

5The precision tracker—an eight-foot parabolic dish (known as a Cassegrainian antenna) mounted on a pylon—locates this beacon and tracks it to within one-fiftieth of a degree.

6The horn antenna’s autotrack mechanism, which is pointed by both the precision tracker and data from magnetic tapes, locates the satellite’s beacon signal.

7Now the horn antenna locks onto the satellite, with the autotrack continuing to make fine adjustments in pointing the horn.

8The equipment is now ready for communications signals to be sent from the two-kilowatt ground transmitter to the satellite.

9The satellite receives the signals and converts them down to a frequency of 90 megacycles; they are amplified in transistor circuits and converted up to a new frequency of 4170 megacycles.

10The signals are amplified again by the traveling-wave tube—for a total amplification of as much as ten billion times—to get a radiated power of 2¼ watts.

11The 4170-megacycle signals are now transmitted in all directions by the satellite’s equatorial antenna.

12These signals can be picked up at Andover or at any other ground station equipped with a suitable antenna that is within line of sight of the satellite.

13At Andover, the received signals are amplified by means of a solid-state maser and a frequency-modulation-with-feedback circuit.

14They can now be relayed via regular land lines to their destination.

15Near the end of a pass, the command tracker turns off the communications circuits and telemetry in the satellite.

16The satellite drops below the horizon.

We hope the last few pages haven’t given you a wrong impression of satellite communications. It is easy to assume, when we list the orderly, step-by-step progress from purely theoretical ideas to a working satellite such as Telstar, that everything has gone like clockwork. That isn’t the case at all—and in the rest of this book we are going to show you why it isn’t. Many problems had to be solved; many scientific and technological advances had to be made.

We touched on a number of the problems of satellite communications in our detailed account of Project Telstar. Most of them are not confined to that project—they are the sorts of questions that any complex advance in satellite communications will run into. We will list some of the more important ones here. Then, inPart II, we will talk about some general methods of solving scientific and technological problems. All this is a rather roundabout—but necessary—way of leading up to our main interest: the accounts by six Bell Laboratories engineers and scientists of their work to solve some typical problems in satellite communications.

The many complications of satellite communications can be divided into several groups. First of all, there are the problems involved infitting satellite communications into an already established world communications system. There are, next, many problems, both small and large, indesigning the right kind of satellite. There are the problems oflaunching a satellite and getting it into the proper orbit. There are the problems inmaking sure it stays in the right orbit once it gets there. And, finally there are the problems inseeing that it continues to do its job reliably.

In these five categories there are a lot of specific questions that must be answered to plan a working satellite communications system. A list of some of them follows. We haven’t attempted to cover everything, but these should give you some idea of the tasks and questions involved in planning an immense project like this.

Circular Orbit—an orbit whose altitude from the earth remains constant; it makes a circle that has the center of the earth as a center.

Elliptical Orbit—an orbit whose altitude from the earth varies from one extreme to another; it makes an ellipse with the center of the earth as one focus. The orbit’s lowest altitude is called the perigee, its highest altitude is called theapogee.

Equatorial Orbit—an orbit in the plane of the earth’s equator.

Polar Orbit—an orbit in a plane formed by the North and South Poles.

Synchronous Orbit—an orbit whose period is 24 hours, the same as that of the earth revolving on its axis—so that the satellite’s and the earth’s angular velocities are the same. Although there are many possible kinds of synchronous orbits, each must have an average altitude above the earth’s surface of approximately 22,300 statute miles.

Stationary Orbit—an orbit that is circular, equatorial, and synchronous—so that the satellite will appear stationary from any point on the earth.

Inclined Synchronous Orbit—an orbit that is synchronous but not stationary, since it does not follow the plane of the equator. From a point on earth, it will appear to follow a figureeightpattern about a line of constant longitude.

Title image

The questions we listed inPart Icover a very broad area of science and technology. Their answers involve, more than anything else, physics, electrical engineering, and mechanical engineering. Some, however, also require that the men who work on them know chemistry, metallurgy, mathematics, and occasionally even biology, psychology, geography, and economics.

We obviously can’t show you how all the problems inPart Ican be solved. Rather, we have picked six of them as examples. They are not necessarily the most important ones, but they seem to us to be typical of what engineers and scientists working in the satellite communications program actually have to do. These are the six problems we will be talking about at length:

As you can see, we have picked problems that offer a good deal of variety. Some of them have been satisfactorily solved; for others the solutions are not yet complete. Some deal with basic scientific research; others are much more concerned with the engineering applications of technical knowledge. Some were solved by careful, logical thinking; others were solved almost by accident. Some deal with a particular immediate task (in this case, Project Telstar); others are more concerned with general planning for satellite communications.

Despite these many important differences, there is one common thread running through the solving of all the problems we have chosen. The men who have been working on them had to know some basic principles of classical physics—principles that most of them first learned in their high school physics classes. You can’t, for example, calculate a satellite’s orbit without knowing Newton’s Laws of Motion. You can’t make optical measurements on a satellite without knowing the law of reflection of light. You can’t decide what color a satellite should be without knowing the law of heat exchange.

To emphasize the importance of a solid grounding in basic physical principles, we have tried to have our problems touch on most of the generalareas of physics: mechanics, heat, sound, light, electricity and magnetism, electronics, the properties of matter, atomic physics, physics of the solid state. But most of them, of course, are not limited to just one of these—they cross the lines of a number of areas. For instance, the problem of keeping solar cell power plants working in space involves laws of heat, mechanics, and atomic physics, as well as physics of the solid state. And, in studying the perception of time delay, we even branch out into experimental psychology.

When you start to solve a problem in science or engineering you can go about it in several ways. In some cases you have no choice: There may be only one practical method of doing the job. Other times, there may be several ways to attack the problem. You may try one, find it to be unfruitful, and then work on another approach. You will see both these methods of attack in the case histories we present in the next chapter.

Here are some of the techniques of scientific problem solving that we will be discussing:

Franz T. GeylingMechanics Specialist—Head, Analytic and Aerospace Mechanics Department

Before you can do anything with a communications satellite you have to know where it is at every instant of its motion around the earth. In other words, you need to know its orbit quite accurately. When you know this, you can predict when a particular station on the ground will be able to see the satellite and communicate with it. You also can tell when two or more stations can see the satellite simultaneously and communicate with each other. And you can estimate how many satellites will be needed to provide a group of ground stations with enough working time to maintain a communications service. This last, after all, is the ultimate goal of all our efforts in the communications satellite field.

In determining a satellite’s orbit, we find that we must do three things:

In the case of the Echo I satellite (seepage 16), we engaged in the first and third of these activities. We had many chances to follow the satellite with our radars, and we could speculate how its orbit was changing through the months. In the case of the Telstar I satellite, we engaged in all three kinds of activity. We shall take a look at these problems in the sequence in which we came across them, for both the Echo and Telstar satellites.

We collect on the ground most of the information to calculate a satellite’s orbit, using optical instruments or radar equipment. Following a satellite through the sky is calledtracking; in the early days after the first Sputniks, some of this tracking was done with the naked eye or with very simple telescopes by the Moonwatch teams. Many of you may have observed Echo I on a clear night without any kind of instrument.

Figure 1

If we use a telescope, we note the time of the observation and we usually take a photograph of the satellite. We locate the satellite in terms of the two angles shown inFigure 1. One of these is theelevationangle—the number of degrees a telescope must be tilted above the horizon to see the satellite. The second is theazimuthangle—the number of degrees between the plane in which we measure the elevation angle and the north direction. Of course, we can also point a radar antenna at the satellite in the same manner. The radar can receive a signal transmitted by the satellite, or else it can send a signal to the satellite and watch for the reflected waves that eventually return. In the latter case, the satellite must have sufficient surface area to produce an adequate reflected signal. These two kinds of precision tracking were both possible with Echo I. Radar can also do something that optical equipment usually can’t do: measure the distance out to the satellite.

Figure 2

The Echo I satellite was launched into a circular orbit inclined at an angle to the plane of the earth’s equator. InFigure 2this equatorial plane intersects the plane of the satellite orbit along the line OPM. The point O represents the center of the earth, the point M is on the satellite orbit, and the Point P is on the equator. At any instant, the satellite may be located in its orbit by the angle θ, which is measured between the line OM and the line OQ, where the point Q is the satellite’s location. If the satellite moves in a circular orbit, as in this case, the angle θ is proportional to time. That is, we can write θ =nt. We callntheangular speedof the satellite; one way of measuring this is in degrees per second.

Thus, the satellite is whirling at a constant speed about the earth like a stone tied to a string. Let us examine the physics of this situation a little more closelywith the help ofFigure 3. If the satellite is moving with the velocityv, then we know that the centrifugal force acting on it is

mv²r,

wheremis the mass of the satellite andris its distance from the center of the earth. Obviously, no string ties the satellite to the earth, but the force of gravitational attraction between the earth and the satellite has the same effect. Newton’s law of mutual attraction tells us that this force is proportional to the product of the two masses divided by the square of the distance between their centers, or

kmr²,

wherekis a constant that essentially represents the mass of the earth.[1]Newton’s law also tells us that this force will be pointing toward the center of the earth if the earth is spherical. When the satellite is in circular motion, the centrifugal force and the gravitational force must balance each other. Hence we have

kmr²=mv²r

and from this we can solve to find that the velocity of the satellite must be equal to

v=√kr.

In the case of the Echo I satellite, which was designed to have a radial distance ofr= 5000 miles, this velocity amounts to about 4.4 miles per second. The time for one revolution in orbit is obtained with the formula

T=2πrv.

For the Echo satellite this time,T, turns out to be just about two hours.

Figure 3

These basic physical principles of satellite motion can give us many useful answers. They tell us how fast we must move a precision tracker to follow the satellite through the sky, how much time a satellite will spend above the horizon, and how long will be the time from one chance of seeing it to the next. However, in the Echo project we were not merely concerned with planning our experiments from hour to hour; we also needed to know how the satellite would move for weeks and perhaps months in advance. When you study the motion of a satellite over such a length of time, you discover that its circular orbit will not remain the same as it was at launch. This fact had been observed on other satellites and was to be expected also with Echo.

In everything we have said so far it was assumed that the earth was a perfect sphere, which is the way a geographer’s globe presents it to us. In reality, the earth is somewhat flattened, with its diameter from the north pole to the south pole being somewhat shorter than its diameter at the equator. One way of looking at this is to visualize the earth as a sphere with some material added in the equatorial zone, which we may callequatorial bulge. This bulge causes Echo’s orbit tohave a slow “wobble” about the earth’s polar axis, somewhat like that of a spinning top.

Another force that makes the satellite’s orbit shift slightly is the faint pressure caused by the light from the sun. Although this pressure is much too small for us to perceive without the help of very delicate instruments, it is enough to affect a satellite, which has nothing to support it in space and is exposed to solar pressure for a very long time. Since the Echo balloon is a plastic sphere, 100 feet in diameter, that weighs only a little more than 100 pounds, the light rays striking its surface are enough to cause a second “wobble” effect. This wobble centers about the line from the earth to the sun. Light pressure also forces the orbit to go slightly out of round from a perfect circle, and other gradual effects on the satellite’s orbit are caused by the gravitational attraction of the moon and the sun.

All these disturbances are ever-present and act simultaneously, and a satellite’s total response to them is very complicated. Fortunately, however, most of the changes take place at a very slow and uniform rate, and we can predict them fairly accurately.

Figure 4

In Project Telstar we had to calculate the satellite’s orbit from observations made by our precision trackers. This introduced a few problems in addition to the ones we encountered with Project Echo. In the first place, the orbit of the Telstar satellite is a elongated ellipse, as indicated inFigure 4, rather than being almost circular, as in the case of Echo I. We mentioned earlier that a precision tracker can furnish data on a satellite’s elevation angle,E, and azimuth,A(seeFigure 1). It can also give us a reading for ρ, the distance from the tracker to the satellite (Figure 4). If we know the position of the tracker on the earth, we can reduce the quantitiesA,E, and ρ to the angle θ and the distancer(measured from the center of the earth to the satellite). These two quantities locate the satellite in the plane of its orbit, but in order to describe its position completely we must also specify this orbital plane. InFigure 5the orbital plane is shown as a shaded surface, with θ andrbeing the same as before. You will recall that the line OM represents the intersection between this plane and the equatorial plane; we call the angleibetween the two planes theinclinationof the orbit. Finally, we have the angle Ω between the line OM and some line OA to the point A, which we can choose as any convenient spot in the equatorial plane. Now we have specified the orbital plane completely. The point A can be found from day to day by fixing its position relative to a certain star in the sky.

Figure 5

Figures4and5tell us something about the geometry of the satellite’spositionin space, but for the complete story we must also give thetimeat which it can be found there. For this purpose, there are some astronomical laws that relate position on an elliptic orbit to time. Two of these are illustrated inFigure 6; in looking at this figure, you should imagine that you are standing off to one side of the orbital plane to get a good view of the entire orbit. The longest dimension of the ellipse, 2a, is called themajor axis; this dimension is related to the satellite’speriod—the time it takes to go once around the ellipse. More than three hundred years ago the astronomer Johannes Kepler observed that the periodT, of an ellipse is

T= 2π√a³k,

wherekagain was (using Newton’s work) essentially the mass of the earth.

Figure 6

Instead of a complete revolution, we may only be concerned with part of one orbit. Let’s say that this part lies between the two positions P₁ and P₂ that the satellite occupies at the two timest₁ andt₂ (seeFigure 6). Then another of Kepler’s laws says that the ratio between the time differencet₂ -t₁ and the periodTequals the ratio between the sector of the ellipse OP₁P₂ and the area of the entire ellipse.

Now let us see how we can use the quantitiesr, θ,i, and Ω as well as Kepler’s two time laws to determine the motion of the satellite in space. Suppose that we have made observations of the Telstar at two timest₁ andt₂ and that we have measured its distance along lines ρ₁ and ρ₂ inFigure 7. In other words, we know that at these two times the satellite was at the points P₁ and P₂. Since three points determine a plane, we know in this case that P₁, P₂, and O define the satellite orbital plane. Knowing this, we can now calculate the angles θ₁ and θ₂, the distancesr₁ andr₂, and the anglesiand Ω. (The detailed formulas for this are derived from analytic geometry.)

Figure 7

However, we still do not know the length and the width of the particular ellipse the satellite is following and how this orbit is oriented within the orbital plane. Let us imagine again that we canstand off to one side of the orbit and take a good look at it;Figure 8shows us what we would see. There are the two points P₂ and P₁ at which we have observed the satellite. We know the positions of these points relative to each other and in relation to the center of the earth, because we have already calculatedr₂,r₁, θ₂, and θ₁, But any number of ellipses could be made to pass through these two points. Some might be very large, others might be so narrow that they would intersect the earth and thus be impossible. However, only one of these ellipses will satisfy the time difference that we observed between P₁ and P₂. In other words, the shape and period of this particular ellipse must be such that it will cause the satellite to pass through P₁ and P₂ in exactly the time intervalt₂ -t₁. If we work out our time formulas, we will convince ourselves that there is only one such ellipse. When we have found it, we have determined the orbit of the Telstar satellite from the two observed positions and times.

Figure 8

Figure 9

In principle then, we could keep track of the Telstar satellite by making a pair of observations P₁ and P₂, and then predicting ahead a short segment of an orbit that is the ellipse we have computed. After a while we must verify this ellipse with two more observations P₃ and P₄, predict ahead over another segment, and verify again with P₅ and P₆ (seeFigure 9), The reason we have to keep taking new measurements is that the elliptic orbit does not remain the same. As we discussed in connection with Echo I, the orbitalplane will “wobble” about the earth because of the equatorial bulge. We also know that the orbit’s major axis will revolve within the orbital plane. As we have seen before, these effects are small and can be represented by appropriate mathematical formulas. If we calculate them, we will see the connection between one pair of observations and a later one, and eventually we can increase the time interval between successive pairs of observations. There are also mathematical formulas that we can use to predict the position of the satellite for many revolutions in its elliptic orbit.

In order to predict orbits successfully, we must also realize that the measurements we obtain from a precision tracker, such as the anglesAandEand the distance ρ, are always subject to small inaccuracies. Thus it is not really possible to take just two measurements like P₁ and P₂ and determine a satisfactory orbit from them. In reality, our tracker takes many readings, and these are averaged to give adequate information about the orbit. Therefore, the picture we have in mind is not quite likeFigure 7, but rather likeFigure 10. Here the trackers have established a series of points that are somewhat scattered, and by taking averages we can calculate an orbit that passes through them in a smooth fashion.

The trackers we have mentioned so far have given us azimuth and elevation angles and also the distance to the satellite at every instant. Sometimes we must use simpler instruments that do not yield all this information. They might, for instance, only give us the two angles. The mathematics of calculating an orbit from such measurements is somewhat different, but the process is fundamentally the same as we have discussed here.

When you do these calculations for the Telstar satellite from one day to the next—and especially if you have more than one satellite to keep track of—the amount of work will become quite large. Nowadays our calculations are done for us on electronic computers, which both receive information from the tracking instruments automatically through Teletype or DataPhone channels and send back information concerning future positions of the satellite to the ground stations. There are still quite a few problems to be solved, and we are presently working on ways of making all this equipment perform the orbit predictions for the Telstar satellites automatically and efficiently.

Figure 10

Franz T. Geylingwas born in Tientsin, China, and received a B.S. in 1950, an M.S. in 1951, and a Ph.D. in 1954 from Stanford University. He joined Bell Telephone Laboratories in 1954, and has been engaged in celestial mechanics studies of rockets and satellites, as well as stress analysis of submarine cables.

Peter HrycakMechanical Engineer—Member of Staff, Electron Device Laboratory

It is important for a satellite to stay at the proper temperature while it is orbiting in space. The instruments aboard it must continue to operate properly, and one way of insuring this is to keep them from being exposed to extreme heat or cold. We can, of course, regulate a satellite’s temperature somewhat with various kinds of devices, and we can see that one of its ends does not point towards the sun for too long. But in designing the Telstar satellite we also wanted to control temperature in an easier way: by covering the satellite’s external surface with material with the best properties—including the right color—for maintaining its over-all temperature at the right level.

A satellite’s temperature is determined by the balance between the heat that enters the satellite and the heat that leaves it. This means that we must be concerned with how heat is transferred. Heat can be transferred in three ways: byconduction, when two bodies are in direct contact and their molecules collide; byconvection, which utilizes the movement of warm currents in a fluid; and byradiation, in which heat energy travels as electromagnetic waves at the speed of light. With a satellite, we are concerned only with the last of these, since the only way energy can be gained or lost in space is by radiation.

In the transfer of heat by radiation, the surface of the heated body—such as a satellite—is very important. All energy gained must be absorbed at the surface; all energy leaving must be emitted at the surface. So the physical properties of this surface control how energy is absorbed and how it is emitted. The origin of the radiant energy is vitally important; most surfaces, for instance, will behave differently when exposed to solar radiation from the sun’s temperature of 10,000° Fahrenheit than when exposed to radiation from nearby objects at room temperature.

The physical property of a material that controls the way it absorbs radiant energy is called itsabsorptivity, and the property that controls its emission of energy is itsemissivity. For absorptivity we use the symbol α; for emissivity we use the symbol ε.

When radiant energy reaches a surface, only a certain part of it is absorbed; the rest is either reflected, just as light rays are reflected, or else passes right through it. The absorptivity, α, of a substance tells us what percentage of radiant energy it will absorb. A perfect absorber, orblack body, would absorb all the radiant energy that reached it. If such an ideal substance existed (which it doesn’t) we would say it had an α of 1. The actual absorptivities of real substances are indicated by numbers between 0 and 1: The α of black velvet cloth, for example, is about 0.97; that of a polished silver mirror is about 0.08 for solar radiation (absorptivity for most polished metals for room temperature radiation is even lower).

We measure emissivity, ε, in very much the same way. A hypothetical black body would emit all the energy it possibly could and have an ε of 1; the emissivities of real substances are indicated by numbers between 0 and 1. For any given frequency (or color) of light, a substance’s absorptivity and emissivity are equal; however, the total spectrum of frequencies of the energy absorbed is usually different from that of the energy emitted.

The ratio between emissivity and absorptivity, α/ε, is very important, as we shall see later. If this ratio is greater than 1, it means that a substance absorbs heat faster than it emits it, and thus tends to become warmer. If the ratio is less than 1, the reverse is true—the surface emits radiant energy at a faster rate than it absorbs it, and tends to become cooler.

This is one of the fundamental relationships of modern physics:

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