Wave Energy

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Waves without a Medium

The waves we considered in the preceding chapter consist of regular, periodic disturbances that carry energy farther and farther away from its source. Exactly the same can be said of electromagnetic waves, the carriers of radiant energy. Electromagnetic waves (hereafter EM waves) differ profoundly from other kinds of waves, however, in that they need no material medium—they can carry energy through a vacuum. Seismic waves obviously need a medium; they are disturbances that form in and travel through the solid earth and the liquid iron of the earth's outer core. Sound waves are disturbances that form in and travel through many materials, including gases, liquids, and solids; that they cannot travel through empty space is not immediately obvious to the uninitiated, but most people remember from their school days how the sound of a ringing alarm clock enclosed in an airtight jar fades to silence when the air in the jar is pumped out.

EM waves, by contrast, can travel through empty space. They are regular, periodic disturbances in electric and magnetic fields in space. Admittedly, most EM waves can also travel through some material substances, with the substance acting as no more than a penetrable barrier. But when you look at the stars on a clear, dark night in the country, it is apparent that light travels best, and farthest, through interstellar space— empty but for sparse interstellar dust.

Before attempting to answer the question, What are EM waves? it's necessary to realize that EM waves are not the only possible representation, or model, of what radiant energy (including light) "really" is. EM waves are the so-called classical model. Modern particle physicists prefer to regard radiant energy as a stream of particles of zero mass, known as photons, about which more below.

The existence of different models does not mean, however, that one of them must be wrong. On the contrary, both are simultaneously right and wrong. They are right in the sense that both provide useful mental images of how radiant energy works. The EM-wave model is the most widely known and is almost entirely adequate for comprehending radiant energy on a "large," or "human," scale; the one case in which it is not—the photoelectric effect—is described in a later section. The photon model (in other words, the quantum theory model: a photon is a quantum of light) is needed for comprehending the subject on a subatomic scale. Both models are right in the sense that they provide adequate explanations of the phenomena they set out to explain. Both models could be called wrong in the sense that they certainly provide an incomplete picture. Scientific discoveries will undoubtedly continue for as long as our species, or at any rate our current civilization, persists and for as long as scientists can afford to experiment and observe. It is naive to suppose that there will be no new, unimagined phenomena to detect and no new problems to tackle. When the need arises, ingenious new models will be devised, or new mental images will be envisaged, to explain the new knowledge temporarily. Science will always be incomplete. There is no reason to believe that humans as a species have the capacity to understand everything there is to understand or that our thoughts provide anything more profound than mental images.

That said, we return to EM waves—what they are, how they are generated, and how their energy is dissipated.

The Nature of Electromagnetic Waves

As we saw in chapter 16, a magnetic field appears spontaneously in the neighborhood of an electric current; and a current flows spontaneously in a conduc-



Figure 18.1. Electromagnetic waves. The solid arrows In the vertical plane show the varying strength and direction of the electric field; the dashed arrows in the horizontal plane show the varying strength and direction of the magnetic field. (For each field, the longer the arrow, the stronger the field.) The waves are moving from left to right.

Figure 18.1. Electromagnetic waves. The solid arrows In the vertical plane show the varying strength and direction of the electric field; the dashed arrows in the horizontal plane show the varying strength and direction of the magnetic field. (For each field, the longer the arrow, the stronger the field.) The waves are moving from left to right.

tor moving through a magnetic field. Recall, too, that a current consists of moving electric charges, and moving charges create moving electric fields. Putting these facts together, we realize that moving electric fields create magnetic fields and vice versa: moving magnetic fields create electric fields. The processes are symmetrical. And because the two kinds of fields are absolutely dependent on each other, they can be thought of jointly as the two components of a single electromagnetic field.

Electromagnetic waves are moving "disturbances" in an electromagnetic field, caused when moving electrons accelerate or decelerate. Consider what would happen if you caused an electric field to oscillate or, what comes to the same thing, vibrate. Bear in mind that an electric field has both a direction (see fig. 16.3) and a magnitude or strength, and the same goes for a magnetic field. An oscillating field is one whose strength grows from zero to a maximum pointing in one direction, say to the right, then dwindles to zero again, then grows to the same maximum pointing to the left, then dwindles to zero again, then ... And so on. It never stops accelerating, either to the left or to the right. Now imagine that an electric field starts to oscillate; its coupled magnetic field is forced to oscillate too. The magnetic field's strength grows and dwindles in time with the electric field's, but at right angles to it. The result is a train of EM waves, represented pictorially in figure 18.1.

The figure shows waves, but they are conceptual waves, not physical ones: there are no actual ripples on a surface. The wavy lines simply join the tips of successive arrows drawn to show the instantaneous direction and strength of the coupled electric and magnetic fields. The figure can be interpreted in two ways: either as an instant snapshot of a constantly changing pattern or as a record of the way the field strengths change with passing time at a fixed location. (Recall that the same is true of waves in a material medium; see chapter 17.)

Now for the energy transported by the waves. It is customarily measured as power, in watts, so to calculate the number of joules transported in a given time interval one must multiply the wattage by the number of seconds. The power at any instant is proportional to the magnitude of the electric field (E) multiplied by the magnitude of the magnetic field (B) at the same instant.1 Instantaneous power varies rapidly, from zero to a maximum and back again; practical measuring instruments (and human eyes in the case of light waves) automatically average the instantaneous power over thousands of "instants" to give a measurement of power in the ordinary sense, that is, sustained power.

Electromagnetic waves bear energy through empty space at the enormous speed of 300,000 kilometers per second, or in scientific notation, 3 x 108 m s-1. This is one of the most famous numbers in all science; it is universally represented by the letter c, always in lowercase and always italicized. This is the c of Einstein's famous equation E = mc2. It never varies, because it is determined by the electrical and magnetic characteristics of space, which are unchanging. No material particle, however small, can go as fast as or faster than c; only EM waves can attain this greatest of all possible speeds, and then only in a true vacuum. They travel at somewhat lesser speeds in a material medium; for instance, at about 2.3 x 108 m s-1 in water and 2 x 108 m s-1 in glass.

The mathematical equations relating the speed, c, to the intrinsic characteristics of space were discovered in 1864 by the Scottish physicist James Clark Maxwell (1831-79), and it was he who first computed the numerical value of c. He immediately realized that it was the same as the speed of light, which had been accurately measured not long before. The precise equality of these two speeds led Maxwell to realize that light and all other forms of radiant energy consist of EM waves. Like the discoveries of his predecessor Newton in the seventeenth century and his successor Einstein in the twentieth, Maxwell's discovery advanced human knowledge of the physical world enormously. It was the most important achievement of nineteenth-century physical science.

How Radiant Energy Is Generated

Every source of radiant energy, or equivalently, every generator of EM waves whether natural or artificial, must cause electrical charges to accelerate. It hap pens, or is made to happen, in various ways: sometimes the electrons accelerate sporadically, sometimes they oscillate. Although all EM waves are alike in consisting of disturbances in the electromagnetic field, they are not all alike in their wavelengths (or conversely, their frequencies). In discussing the different kinds of waves, they can be labeled by either their wavelengths or their frequencies, and here we use wavelengths. It's simple to convert from one to the other, using the formula wavelength X frequency = c.

The range of wavelengths to consider is huge, from about one-trillionth of a millimeter to over 5,000 kilometers; theoretically there is no upper limit. Besides differing in wavelength, EM waves also differ in the energy they contain: the shorter the wavelength the greater the energy.

This statement seems surprising at first. It appears to contradict the assertion that the power of EM radiation depends on the intensities of the electromagnetic fields, that is, on the amplitudes of the "waves" in figure 18.1. When EM waves are produced artificially, why can't their energy be increased at will simply by increasing the energy input? On a human scale, this can easily be done. But the statement that shorter wavelengths carry more energy than longer ones refers to the minute, indivisible quanta of which radiant energy consists.

A quantum of radiant energy (a photon) is a single "grain" of energy in the same way that an atom is a single grain of matter, except that it has zero mass. In spite of this, a photon does have energy. Einstein, in 1905, hypothesized that the energy, E, of a single photon in a vacuum depends on the wavelength, L, of the radiating waves thus:2

For a given wavelength, no smaller unit of radiant energy can exist. The constant h is called Planck's constant, after the German physicist Max Planck (1858-1947), who discovered it in another context. Numerically, h is mind-bogglingly small; it is 6.63 X 10-34 joule-seconds; h is as central to modern quantum physics as c is to relativity theory.

Let's compare the energies of some different kinds of photons. They are easily calculated once you know the wavelengths of the radiation concerned. The energies are best measured in electronvolts (eV) rather than joules (J), because they are so small (recall, from chapter 10, that 1 eV = 1.6 X 10-19 J). Some examples, in round numbers:

A photon of hard X rays of wavelength L = 10-11 m has energy of 100,000 eV.

A photon of red light of wavelength L = 7.5 x 10-7 m has energy of 1.7 eV.

A photon of broadcast radio waves with L = 100 m has energy of 0.00000001 eV, and so on.

The energies are given here in "ordinary" numbers (rather than in scientific notation) to emphasize their enormous range. Although the energy in a single photon is always tiny, a photon of "hard" (meaning short) X rays is about ten trillion (1013) times as energetic as a photon from a radio station's transmitter.

Not surprisingly, EM waves of widely different wavelengths are generated by different processes, in nature as well as in artificial settings—laboratories, factories, houses, and the like. The most energetic radiation is y-radiation (y is the Greek letter gamma), which is emitted when certain radioactive nuclei undergo y-decay; the decaying nuclei lose energy while their masses remain unchanged. There is no conversion of mass into energy in y-decay, as there is in a-decay (described in chapter 13); the energy comes from an "excited" atomic nucleus—one with surplus energy—as it returns to its unexcited, ground state. The wavelength of the rays is comparable (in ballpark terms) to the diameter of a nucleus, about 10-15 m. Gamma rays are emitted, along with damaging subatomic particles, by nuclear weapons, faulty nuclear power plants, and radioactive material stored as nuclear fuel; the dangers they pose are known to everybody. Gamma rays also come, in absolutely harmless amounts, from the sun and a variety of other astronomical sources, some immensely distant. They are also emitted harmlessly by naturally occurring radioactive elements such as uranium and thorium, which are present at very low concentrations in the rocks, particularly in granite; all emit y-radiation in negligible amounts.

Below y-rays in terms of photon energy, and with longer wavelengths, come X rays; their wavelengths are in the neighborhood of 10-10 m. They are produced artificially, by bombarding a metal "target" with a stream of fast-moving electrons. On hitting the target, the electrons are brought to an abrupt stop. They are sharply decelerated, or "braked." The kinetic energy lost by the electrons becomes the energy of EM waves, which are emitted by the target; X rays are a form of this so-called braking radiation.3

Longer wavelengths are produced when the electrons inside atoms move. As we saw in chapter 13, most of an atom's volume consists of the empty space surrounding its nucleus, and all this space is available to its electrons. The di ameter of the space depends on the element an atom belongs to: 10-10 m is a representative figure. An electron in this space can occupy any of several distinct energy levels, and if it "jumps" from a higher level to a lower, it emits an amount of radiant energy equal to the "height" of the jump (the difference between the two energy levels). The jump is known as an electronic transition.4

The EM waves emitted when electrons perform such transitions belong to several familiar wave bands: in order of decreasing photon energy they are ultraviolet rays and visible light, with wavelengths ranging from about 10-8 m up to nearly 10-6 m (or 1 |im), and also some longer (infrared) waves. The electrons are first boosted from lower to higher energy levels by energy from an outside source, and then they reemit the energy by dropping back down again.

Ultraviolet light is artificially produced by causing an electric current to flow through a gas, such as hydrogen or mercury vapor, in a sealed tube: the flowing electrons cause electronic transitions in the atoms of the gas. The same process is used to produce some kinds of visible light, for example, outdoors in neon tubes and indoors in fluorescent lights.

Incandescence, the emission of light by objects that are red-hot or white-hot, is the source of most visible light; not surprisingly, light produced in this way is always accompanied by radiant heat. Electronic transitions produce all of the light and some of the heat. Most of the heat is generated by a different process, however, as we see below.

Almost all the natural light on earth comes from the surface of the sun, heated to incandescence by the nuclear reactions in its interior. Indeed, light is emitted by any object heated to a high enough temperature, whether it be the sun, or a glowing ember left after a fire, or the filament of an incandescent lightbulb; the filament heats up because of collisions between the flowing electrons of the current and the particles of the conductor.

Visible light consists of EM waves in the range 0.4 x 10-6 m (violet) to 0.7 x 10-6 m (red), as we saw in figure 11.1. Longer waves, because they are invisible, are labeled "infrared," but the contrast between visible waves and infrared ones is more in the sensations they produce than in the way they are generated. With light waves, the different wavelengths are seen as different colors; with infrared the only sensation is warmth, whatever the wavelength. It is only an accident of human evolution that our skins don't perceive something analogous to colors corresponding to different infrared wavelengths. It would be fascinating if short wave and long wave infrared felt as different from each other as the colors blue and orange look.

Infrared radiation by itself is emitted by heated objects not hot enough to glow. Some of the radiation comes from electronic transitions, but most comes from the "shaking" that electrons undergo as passengers on molecules in constant movement.5 Many molecules vibrate and rotate, and all participate in the constant random motion that constitutes thermal energy. Indeed, thermal (infrared) radiation is emitted all the time, by every object whose temperature is above absolute zero. Recall that in chapter 4 we considered the heat budget of the whole earth and the way the ground reradiates heat from the sun (see fig. 4.1). Similar heat exchanges are always happening on a smaller scale, everywhere; for instance, all the surfaces in a room—floor, ceiling, walls, furniture, people's skins—are constantly radiating, absorbing, and reradiating infrared radiation.

We now come to a narrow waveband centered on a wavelength of about 1 mm. It isn't usually listed as a labeled band, and the waves aren't (except incidentally) generated artificially to serve a useful purpose. They are the EM waves of the cosmic background radiation that is believed to permeate all space and to be the surviving energy of the Big Bang, now thinly spread through the enormously expanded (and still expanding) universe.6

Artificially generated radiation with wavelengths from 1 mm to 30 cm (bracketing the cosmic background radiation) is called microwave radiation. It is used in radar and for microwave cooking.

To conclude this list of wave bands, let's consider some of the longest waves assigned to a labeled band—radio waves. They range in length from about 10 cm to 100 km; wherever there's a radio or television transmitter, they are artificially generated all day long and sent forth over the "airwaves." The heart of any transmitter is an electric oscillator, a circuit so designed that the current in it constantly oscillates at a chosen frequency. The magnetic field around the current-carrying wire automatically oscillates in unison. The oscillating magnetic field creates its own oscillating electric field, which augments the oscillating magnetic field, which augments the oscillating electric field, which . . . And so on. In a word, EM waves are generated. The two oscillating fields can be said to "feed off each other."7

Very long radio waves are transmitted coincidentally wherever alternating currents flow. Ordinary domestic alternating current (AC) alternates—oscil-lates—at a frequency of sixty cycles per second, or 60 hertz. The resultant EM waves are 5,000 km long and have a photon energy about one-ten trillionth that of red light. Theoretically, there is no upper limit to the wavelength of an EM wave. If you wave a garment with static cling back and forth, then some very, very long EM waves (of immeasurably small energy) will be emitted.

Strong radio waves are produced in the natural, outdoor world by lightning flashes; the sudden flow of electrons from one part of a thundercloud to another, or from the cloud base to the ground (see fig. 16.4), sends out powerful pulses of radio waves, heard as loud crackling if you turn a radio on during an electrical storm. Lightning is the only appreciable source of natural radio waves on earth, but extraterrestrial radio sources, including "radio stars," are known to be numerous.

It's worth reemphasizing that all the wavelengths we have considered are present in solar radiation, although not in equal proportions; the biggest proportion of solar energy comes as visible light and "near" ultraviolet light. It is not surprising that human eyes have evolved to be sensitive to a wave band that almost coincides with the strongest segment of the solar spectrum (see fig. 11.1), but why isn't the coincidence total? It is a mystery why we cannot see near ultraviolet radiation, which is as strong a component of sunlight as visible red light; bees can see it.

How Radiant Energy Is Dissipated

The moment EM waves are generated, they start traveling away from their source at 300,000 km per second, bearing energy. Where do they go, and what becomes of the energy?

The most energetic of them, y-rays and X rays, carry so much energy that it takes relatively few photons to cause injury and death to living things (including people) exposed to them. Their energy is transferred directly to molecules of living tissue, causing injurious chemical changes including burns. The photons of these "hazardous" radiations are energetic enough to dislodge electrons from atoms.8 Even waves as long as light waves can shift the electrons in metals, causing a current to flow; comparatively little energy is needed for this, because the electrons in metals "roam" free and unattached (see chapter 16). The phenomenon is known as the photoelectric effect; it is the power source for solar-powered pocket calculators, photographers' light meters, burglar alarm systems, automatic door openers, and the like.

The photoelectric effect doesn't seem especially noteworthy on first acquaintance, but investigation of the details led to a profound scientific ad-vance—the realization that EM waves must consist of "grains" of energy (photons), as we saw above. This discovery, not the theory of general relativity, earned Einstein his Nobel Prize.

Two characteristics of the photoelectric effect underlay the discovery. First, for a current to flow in an irradiated metal, the wavelength of the radiation must be shorter than a certain threshold length that depends on the metal; for example, if it is a pellet of the metal sodium, the radiation must be blue-green or bluer; if it is a copper wire, then only ultraviolet will suffice. Second, provided the wavelength is short enough to cause a current at all, then increasing the intensity of the light increases the current.

These two facts imply that radiation must consist of discrete photons, each a separate package of energy. Experiments show that to cause any current at all to flow in sodium, each photon must carry at least 2.3 eV of energy; the corresponding threshold energy for copper is 4.7 eV. No matter how numerous the photons (no matter how intense the light), if the photons are individually too weak nothing happens: you can't break a window by pelting it with feathers, no matter how numerous the feathers. But if the individual photons are energetic enough, (if their wavelengths are short enough), then the more of them there are—the more intense the radiation—the greater the photoelectric current.

To sum up, when high-energy EM waves strike any matter, or when waves with lower energy strike "susceptible" metals, they dislodge electrons; the energy of each photon of radiation is converted to the kinetic energy of an electron.

Waves of ultraviolet and visible light, though less energetic than y-rays and X rays, are powerful enough to rearrange the internal structures of atoms and molecules by breaking chemical bonds; that is, they bring about photochemical reactions.

Some examples: The ultraviolet rays in sunlight cause chemical changes in human skin cells. The results can be anything from gratifying (a good tan) to unpleasant (painful sunburn) to life threatening (some skin cancers). The bark of trees can also be severely injured by sunburn.9

When bright sunlight shines on city air polluted with nitrogen dioxide, the ultraviolet component of the light energizes a photochemical reaction, producing smog.10

Whenever you take a photo, a photochemical reaction changes every molecule at the surface of the exposed film emulsion.

But these are trivial examples of photochemical reactions. The single most important chemical reaction of any kind, from the point of view of (nearly) all life on earth, is photosynthesis, described in chapter 11. Directly or indirectly, it creates virtually all living matter. Looked at from another angle, it is one of the processes in which electromagnetic energy from the sun is consumed: it is transformed into biochemical energy.

Electromagnetic waves are also consumed, in less spectacular fashion, whenever their energy is transformed into heat directly, by speeding up the random motions of atoms and molecules. The waves are said to be absorbed. Absorption is what happens to most infrared radiation. It goes on everywhere, whenever an object is warmed by the sun, by a fire, or by radiation from anything warmer than itself.

The energy of radio waves emitted by transmitters is used, for the most part, in forcing oscillating electric currents of matching frequency to flow in receiving antennas (and incidentally, in anything else that conducts electricity). The energy that began as the kinetic energy of electrons in a transmitting antenna ends up as the kinetic energy of electrons in a distant receiver, having crossed the gap between transmitter and receiver as energy-bearing waves.

Electromagnetic waves are not automatically absorbed by whatever they strike. This is obviously true of light waves, as anybody can see by looking through clean, clear, colorless glass: it is as though the glass weren't there. In other words, glass is transparent. Other materials—sheet metal, for instance—are opaque; they absorb all the light that falls on them, letting none pass through.

This raises a problem: Why are some materials transparent and others opaque? The answer is a highly technical part of solid-state quantum physics; here it is possible to say only that it depends on the behavior of the electrons in the material, behavior that also affects its electrical conductivity. To generalize, metals are opaque because they are conductors; insulators are transparent because they are insulators.11 For example, glass and clear plastics are simultaneously transparent and good insulators. But what about such seemingly opaque insulating material as china and nonclear plastics? In fact, these materials aren't truly opaque, in the sense that they absorb light. Rather, light shining on them is scattered by a myriad of structural irregularities in the material (more on scattering below).

Different materials are transparent to different wavelengths of radiation. For example, bone is opaque to X rays, but flesh is transparent to them. Flesh is opaque to infrared rays, however; if it were transparent to them, they could have no warming effect. Most glass is transparent to sunlight but opaque to ultraviolet; good sunglasses protect eyesight by blocking ultraviolet rays. Gases can be opaque too. As everybody knows these days, ozone is opaque to ultraviolet radiation; the thinning of the ozone layer high in the atmosphere because of air pollution is permitting energetic ultraviolet rays to reach ground level, where they damage living organisms including humans. As is equally well known, carbon dioxide is opaque to infrared radiation. This is thought to be the principal cause of global warming: a growing proportion of the earth's annual heat income from sunlight is prevented from being reradi-ated skyward by ever-increasing concentrations in the atmosphere of gases opaque to infrared rays—the "greenhouse gases."

The solar energy budget was described in broad outline in chapter 4, and it was noted that, apart from the sunlight reflected by clouds, most of the rest is absorbed and reradiated. A much smaller fraction, too small to be shown in figure 4.1, remains to be accounted for; it too is reflected, but not by clouds. It is scattered. Light is scattered by everything it strikes. Here we consider scattering in the atmosphere; scattered sunlight from the atmosphere is as important for life, especially plants, as direct sunlight. It reaches the ground regardless of whether the sky is clear or cloudy. When it's cloudy, although much of the sunlight is reflected back to space by the tops of the clouds and some is absorbed by cloud droplets, scattering still goes on above, within, and below the clouds. Scattering causes negligible reduction in the energy of the affected light; rather, it spreads the light out over the whole sky.

Scattering is the reflection of light by a vast number of tiny reflectors separated by comparatively wide gaps. Alternatively, one can define reflection as a form of scattering: it is the "scattering of light by a large number of [closely spaced] scattering centers."12 This amounts to saying that scattering and reflection are two forms of a single phenomenon. In some scattering, however, the tiny reflectors, or "scatterers," are no bigger than the wavelength of the light reflected, and instead of sending the radiation back toward its source, they deflect it in all directions. Some of it is even sent onward in its original direction because the energy of the light is absorbed by the scatterer and then immediately reemitted.

The way reemission happens depends on the sizes of the scatterers; the smallest of them are individual molecules of the air's oxygen and nitrogen, with diameters less than one-thousandth of the wavelengths of light.13 Slightly larger are tight clumps of air molecules, airborne bacterial spores, minute salt crystals evaporated from ocean spray, particles of fly ash from forest fires and industry, and the like. With particles of this size, the blue component of sunlight is deflected much more strongly than the red; hence the blue skies of a sunny day. When the particles are larger and the air is hazy with dust or misty with minute water droplets, most of the light is sent onward as white light, away from the source, producing a white glare in all directions, brightest toward the sun. When the particles are much wider than a wavelength— as large as falling raindrops, for instance—much of the sun's energy is reflected back into space without deflection: less light reaches the ground, and the cloudy sky becomes noticeably dark.

As for solar energy, the point to observe is that little of it is returned skyward on a clear day and scarcely more on hazy or misty days. Rather, it is scattered and spread around. Some reaches the ground from all directions, while that coming in a straight line from the sun itself is correspondingly reduced. Life on the surface, especially at low elevations, has adapted accordingly: "shade plants" obtain enough indirect light energy to photosynthesize; at the same time, desert life is able to survive the direct light.

Finally, what becomes of all the solar energy that bypasses the planets? The earth intercepts less than one-billionth of the radiation flowing out from the sun in all directions. The EM waves travel away into space, almost unhindered, becoming attenuated as they spread out. They inevitably lose a tiny amount of energy whenever they encounter a "body" of any kind, but this becomes apparent only when the body is a comet not too far from the sun. Then it is possible to see how radiation pressure imparts some solar energy to the cloud of minute ice crystals and fine dust that forms the comet's tail. The pressure is proportional to the number of joules of energy per cubic meter of space.14 The wave-borne electromagnetic energy is converted to kinetic energy of the particles, causing them to stream away from the comet's head on the side away the sun. Both the big comets of the 1990s, Hayakutake in 1996 and Hale-Bopp in 1997, demonstrated the phenomenon splendidly. Comets' tails give us our only chance to observe what is probably the weakest manifestation of solar energy at work. Radiation pressure produces no discernible effect on earth.

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