1. Total solar eclipses were once used to look for an additional planet orbiting very close to the Sun. Because of the glare of the Sun, such a planet would be invisible at any other time. Astronomers had even proposed a name for is--Vulcan. No such planet was ever seen, and astronomers today agree that none exists.

   In the early 1800s, the German amateur Heinrich Schwabe, using a telescope (with a projected or filtered image) watched the Sun day after day for years, trying to see Vulcan passing in front of the disk of the Sun, when it should be visible as a dark spot (click here for a picture of the planet Mercury in front of the Sun). To distinguish such spots from sunspots, Schwabe carefully noted down all the sunspots he saw. He never found a planet, but after about 17 years, in 1843, he discovered the 11-year cyclical rise and fall in the number of sunspots, which had eluded professional astronomers.

    Most of those planets are as big as Jupiter or bigger, because obviously the heaviest planets shift the center of gravity by the greatest amount (the effect of an Earth-size planet is still too small to be measured). Many of them were detected by Paul Butler (Carnegie Inst.), Geoffrey Marcy (U. Cal Berkeley) and Steve Vogt (U. Cal Santa Cruz), who worked out a sensitive method for such observations.

    The observations do not tell much about how the orbit is oriented in space, but for one recently discovered planet we now know a bit more. It orbits a star catalogued as HD 209458, some 153 light years from Earth, and happens to pass right between us and it. The researchers were hoping to find such a planet, and sure enough, Greg Henry of Tennesse State Univ, using an Arizona telescope, detected on November 7, 1999 a temporary drop in the light intensity by 1.7%. It is a big planet with about 2/3 the mass of Jupiter, and its orbital period is about 3.5 days. Because it orbits very close, and its size is expanded by the heat of its nearby star, it is considerably larger than Jupiter, able to block a measurable amount of starlight.

Teacher's explanation of the heat outflow of the Sun:

That heat moves outwards from the core, towards the Sun's surface, by processes somewhat like the ones by which heat works its way through the atmosphere, from the surface of the Earth to space (section S-1).

No one of course can observe what happens deep inside the Sun, but a theory has been developed about the interior of stars, suggesting heat in the deepest layers travels by radiation. Atoms radiate light and neighboring atoms absorb it, but since the deep layers are compressed with atoms packed close to each other, the process is more like the conduction of heat. As heat moves outwards, the temperature keeps dropping, because net flow of heat can only take place from hot material to colder one.

Closer to the Sun's surface, the theory predicts, heat is carried by convection, as in the Earth's atmosphere--by gas flowing around closed paths. All these layers are still fairly dense, and any light emitted is quickly absorbed again. The photosphere is the final layer. Not enough material remains above it, allowing any light emitted there to spread out into space. It is a relatively thin layer, of the order of 100-200 kilometers

Because most sunlight comes from the photosphere, the much fainter chromosphere and corona are only seen during a total eclipse, when the light of the photosphere is completely blocked by the disk of the Moon.

However, astronomers can also view the Sun through special filters which reject all of the Sun's light except one or another narrow range of color ("spectral line," discussed in a later lesson). In some such colors, the chromosphere or the inner corona shine brightly enough to be seen even without a total eclipse.

• About 5000 kilometers.

• It is less than 1% of the Sun's radius, which is about 700,000 kilometers.

• It is more than 100 times bigger.

• About 50,000° and 1,000,000°.

• Because the only credible source of the heat is the Sun itself. However, heat always flows from a hot temperature to a lower one--never the other way around. The photosphere below these layers is cooler: how then can it heat the chromosphere and corona?

• The light from the corona is characteristic of atoms which have lost quite a few electrons (more about that, in a later lesson). At the density of the corona, this requires collisions between fast atoms, and the speed of the atoms of a gas is directly related to its temperatures.

• The energy must arrive at the corona in a form different from heat--perhaps as sound-like waves, or as a population of fast ions produced by such waves.

• At one time it was proposed that a steady flow of small meteorites was hitting the Sun. However, nothing like them was ever observed passing near Earth.

• A fast flow of ions, streaming out from the Sun in all directions.

• Its energy comes from the heat of the corona. Its top layers are so hot that they manage to escape the Sun's gravity.

  [If the corona were like the Earth's atmosphere, its temperature would gradually drop with height. However, the corona is hot enough to be a plasma, a mixture of free-floating positive ions and negative electrons. Plasmas conduct heat well, and this does not allow the high layers to stay cool.]

• Its velocity is about 400 km/sec, density at the Earth's orbit about 6 ions/cm³ , both these varying widely (at a distance of r astronomical units, the average density becomes 6/r²). Its composition resembles that of the Sun--mostly ionized hydrogen (protons), some helium and a small amount of heavier elements.

A calculation on the board

(This calculation tests ability to use scientific notation when working with very large and very small numbers. The teacher might call up a student to derive it on the board, with the class copying).

The area of a sphere with radius r = 1 AU around the Sun is

Imagine behind every square centimeter a column of solar wind 400 kilometers long, waiting to cross it during the next second! (Teacher could illustrate this with a sketch on the board).

The entire surface of the sphere is therefore crossed each second by the solar wind particles contained in a volume

And with a density of 6 ions/cc, the number of ions is

The total mass lost by the Sun each second is

The Sun therefore loses about a million tons each second. It sounds like a lot but really isn't--one cubic kilometer of the ocean contains about 1000 times more, and the Sun is not much diminished even if this loss continues for many billions of years.

(end of calculation)

• It gets lost in interstellar space. Actually, a boundary is expected, the "heliopause" marking the outer limit of the solar wind domination, from where on the interstellar gas determines the ambient conditions. The space probe "Voyager 2" is going to reach it, but whether it will still be transmitting remains to be seen.

"From Stargazers to Starships" home page and index:
          http://www.phy6.org/stargaze/Sintro.htm

• That magnetic forces in nature rarely involve iron, but are actually forces between electric currents.

• About sunspots and their intense magnetism, with a strength of about 0.15 Tesla (1500 gauss).

• About the 11-year sunspot cycle and its discovery.

• About "solar activity" associated with sunspots and their cycles, e.g. the abrupt brightenings known as solar flares.

• That solar activity is probably associated with the release of magnetic energy, and that such releases can propel fast plasma flows towards Earth, causing there "magnetic storms."

Terms: Sunspot, magnetic field lines, magnetic fields, sunspot cycle, solar activity, solar flare, magnetic storm, magnetic energy

Stories: The discovery of electromagnetism by Oersted and Ampere, the discovery of the sunspot cycle by Heinrich Schwabe and the discovery of solar flares by Richard Carrington.

The teacher is advised to read those stories ahead the class, to be better able to present them to students, including the original articles, here and here. (Students can also be assigned to do so and to make the presentations.)

Starting the lesson:

No area of science draws as much interest as stories of discovery, and of the unusual people who made them. This class has already covered some interesting discoveries. Which of them were associated with the names of... Aristarchus? Erathostenes? Columbus (even if it wasn't a scientific discovery)? Copernicus? Kepler? Newton?

Louis Pasteur was a French biochemist in the 19th century, whose many discoveries included a way of preserving food by heating ("pasteurization") and a procedure for saving the lives of people bitten by animals infected with rabies, which up till then meant almost certain death. Commenting on scientific discoveries, Pasteur said "chance favors the prepared mind". Discoveries often depend on luck--but luck is not enough, the mind must be prepared to exploit its opportunity.

[a student might prepare a poster with that quote, to hang in class]

Today as we discuss magnetism and magnetic phenomena on the Sun, we will discuss three discoveries in which luck had a part--but luck wasn't the only reason. (List on the board--students copy.)

1. The discovery of electromagnetism in 1820 by Hans Christian Oersted, in Denmark, and its explanation by Andre-Marie Ampere, in France.

2. The discovery of the sunspot cycle (1843, widely accepted around 1851) by Heinrich Schwabe in Germany.

3. The discovery of solar flares (1859) by Richard Carrington in England

(possible comment: Each discovery occured in a different country!. Science is truly international.)

The discovery of the connection between electricity and magnetism

What do we know about magnetism of iron magnets?

• Like poles repel, unlike poles attract.
• The magnetic compass tends to point north-south.

[Why is plain iron attracted to a magnet? Because when iron is in the region of influence of a magnet--its "magnetic field"--it becomes temporarily magnetic itself, with the pole closest to a pole of the magnet having opposite polarity, causing it to be attracted.]

What magnetic phenomena do not involve iron, and why are they called "electromagnetic" phenomena?

• The attraction between parallel currents in the same direction, and the repulsion between them if the currents flow in opposite directions.
      The forces between the coils, etc. used in electric machinery all follow from this basic property.

(optional)

The magnetic field which satellites observe in space is often different from what one would expect, based on the fields we observe on the ground.

The reason is that large electric currents often flow through the space surrounding the Earth, and they contribute their own magnetic fields as well. The currents can flow there, because of the presence of free electrons and ions (a "plasma").

What to you think--would such currents tend to spread out to cover as much space as possible, or would they narrow down to string-like filaments? You must give a reason.

[If no one answers:"It has to do with the forces between electric currents."]

• They might tend to narrow down. A current flowing along a wide tube may be viewed as composed of many narrower parallel currents, and we know that parallel currents attract each other.

(This tendency of currents to narrow down has also been observed in laboratory plasmas, where it is named the "pinch effect.")
(end of optional part)

Suppose you had a compass needle able to point in any direction in space, not just horizontally. How would the northward-pointing end of the needle point at

1. The northern magnetic pole
2. The southern magnetic pole
3. Halfway between
4. Elsewhere?

[Note: such needles are available--see end of section S-3, or click here: http://www.cochranes.co.uk/BNRVP30/edu5.htm]

• Straight down at the north magnetic pole, straight up at the southern pole, horizontally northward at the magnetic equator, northward slanting down in the northern hemisphere, northward slanting up in the southern hemisphere.
      (By the way: the early Chinese who discovered the magnetic compass claimed it pointed south.)

How would such a needle point near a straight wire carrying an electric current? (Neglect the Earth's magnetism)

• Perpendicular to the current.

How was the connection between electric currents and magnetic force discovered? (Students tell about it, or else, the teacher.)

What are magnetic field lines? Base your definition on the magnetic needle described above.

• They are imaginary lines giving at each point the direction in which our 3-D needle would point, if placed there.

What are magnetic field lines used for?

• They were originally used to graphically describe magnetic fields. In the rarefied plasmas of space, however, they also guide the flow of particles and currents. This is why arching solar formations above magnetic sunspots sometimes resemble the field lines of bar magnets.

  (The guiding property of field lines also makes possible the trapping around Earth of ions and electrons in the Earth's radiation belts. The motion of these particles stops and reverses before they hit the Earth, because they are also reflected from regions of stronger magnetic field, found closer to Earth.)

What is Andre-Marie Ampere remembered for?

• He explained the observations which baffled Oersted, and in doing so gave the first clear idea of what magnetism was. In his honor the unit of magnetic current is called the "Ampere."

[P.S.: He is also remembered as the man who was invited to dinner with Napoleon and forgot to go!]

The intensity of the Earth's magnetic field at the magnetic equator is about 31,000 nT (nanotesla) or 0.31 gauss. The field intensity goes down with distance r like 1/r³. If the intensity of the interplanetary magnetic field at the Earth's orbit is 5 nT (a typical value), at what distance--in Earth radii--is this matched by the Earth's field? (Needs calculator capable of extracting cube roots.)

• If at a distance of 1 Earth radius the field is 31,000 nT, at distance of r earth radii is is 31,000/r³ . If r is the distance where it drops to 5 nT, we get 31,000/r³ = 5 . Multiply both sides by r³, divide by 5 to get

Then go on to the discovery of sunspots.

When and how were sunspots discovered?

• In 1609, when telescopes were first used in astronomy. Galileo, Fabricius and Scheiner all claim credit and might be independent discoverers.

What did the discoverers see?

• They saw dark spots on the Sun.

How do we know that the Sun rotates around its axis?

• Sunspots were observed to travel across the face of the Sun in a way that suggests they rotated with it.

What is unusual about the Sun's rotation?

• The rotation period depends on latitude: the equator rotates fastest, in about 27 days. Nearer to the pole it can be 2.5 days longer.

Optional: The teacher may draw a table with the observed latitude dependence of the rotation period (in days) and let students graph it:

Question: Why is the period viewed from Earth longer by about 2 days?

• Say we track a sunspot at latitude 20°, which at a certain time faces Earth. After 25.65 days the spot again faces the same direction in space as before--in the direction of the same stars, for instance. However the Earth orbits the Sun, and has by then moved ahead in its orbit. It takes the Sun's rotation 2 more days to reach the position where the sunspot faces Earth again.

(end of optional part)

Here tell the story of Schwabe's discovery of the sunspot cycle.

Why do we think that magnetism plays an important part in solar phenomena?

Some clues:
• From the light of sunspots, it was found that they were intensely magnetic.

• During a total eclipse, the "plumes" of the corona above the poles and the "arches" above sunspot regions suggest the form of magnetic field lines near magnets.

• Eruptions on the Sun are linked to "magnetic storms" on Earth.

What suggests that the 11-year sunspot cycle is a magnetic phenomenon?

• Sunspots are intensely magnetic

• In each sunspot cycle, the magnetic polarity order of the leading and trailing sunspots in sunspot pairs reverses.

• Each sunspot cycle the large-scale polar magnetic field of the Sun reverses.

[Optional: Does the Earth's own magnetic field ever reverse?

Yes, it apparently does, but at very infrequent intervals. That magnetic field is caused by electric currents in the Earth's molten core, and is observed to change slowly from year to year. On rare occasions, however, the dominant pattern of currents seems to reverse direction.

How do we know? We know because the floor of the oceans contains fissures, caused when the sea-bottom is pulled away in opposite directions, away from them. The pulling-apart is caused by forces deep inside the Earth, and a typical speed of those "plates" is about one inch a year. The most famous fissure is the one running down the entire middle of the Atlantic ocean, in a roughly north-south direction but with bends and kinks.

As the seafloor plates are pulled away to both sides, lava comes up from the fissure and solidifies into a black rock called basalt, which become part of those plates. However, basalt is weakly magnetic, and when it solidifes it becomes magnetized in the direction of the magnetic field existing at the time. Thus each part of the seafloor records the Earth's magnetism at the time it emerged from the fissure, just as the tape of a tape recorder records the magnetism of the recording head at the time it passes near it.

In this way, the seafloor has recorded the magnetism of the Earth during the last 10-20 million years. It turns out that the seafloor is not magnetized in a uniform direction! Rather, it is magnetized in long parallel stripes, parallel to the central fissure, and each two neighboring stripes have opposite magnetic polarity. This suggests that between the times those two stripes emerged, the Earth's magnetic field reversed direction. The last time that has happened (assuming a rate of about an inch a year) was about 700,000 years ago.](End of optional section)

"From Stargazers to Starships" home page and index:
          http://www.phy6.org/stargaze/Sintro.htm

• How a glass prism resolves light into its rainbow components, which can be recombined to create white light.

• The difference between spectral colors and the colors perceived by the eye.

• That hot solids (or dense gases) radiate a continuous spectrum, related to their temperature.

• That the colors of a glowing rarefied gas are characteristic of the atoms emitting them, with examples.

• That cold atoms in a gas absorb the same colors as the ones they emit when hot, and that such absorbtion causes dark lines in the Sun's spectrum.

• That light is a wave spreading through space, with a very short wavelength, or the order of a few microns (0.001 millimeter).

Note: at this level, the student is told that the wave nature and wavelength are deduced from the way parts of a beam of light resonate with each other. The question of why these waves are called "electromagnetic" is left for the next lesson.)

Terms: [Refraction of light, dispersion of light], spectrum, spectral color, perceived color, 3-color theory, black body spectrum, spectral lines, diffraction grating, wave, wavelength, absorption spectrum.

Stories: Discovery of helium.

Starting the lesson:

(One way of introducing the subject of color is through the rainbow. Accordingly, unless time is short, the teacher may devote the beginning of the class to the phenomenon of the rainbow. The discussion here also extends into optics--the study of light.)

One striking phenomenon involving color is the rainbow. People generally divide the rainbow into 7 colors. Anyone knows what they are, in the order in which they appear?

(Students may answer--put on board, make sure class copies). Red, orange, yellow, green, blue, indigo, violet

(All of you know "indigo"? It is the name of a dye. What color are blue jeans?

• dark ones are indigo, light ones are blue)

We obtain the same sequence when light passes a prism--red is bent least, violet the most (draw on board). Anyone knows why? (students may answer)

Because (draw on board, students copy) light hitting a flat surface of glass gets bent by an angle. (That is known as refraction--"The beam of light is refracted.")
  However, different colors are bent by different amounts. (That feature is known as the dispersion of light).

When a beam of light hits a glass windowpane (draw on the board) with two parallel sides, the beam is refracted one way as it enters the glass, then the opposite way as it leaves. The net result is that it emerges with the same direction as before. So, inside the glass diffect colors may be separated, but when they emerge again they all move again in the same direction, and no separation remains.

In a prism (refer to drawing already on the board), the entry side and the exit side are inclined, not parallel, and therefore the direction is changed--by a different amount for each color.

            (optional)

      How about rainbows? When do you see rainbows?

• We see rainbows when the Sun is shining on falling rain. Typically, a rain cloud has passed over you and you are now in the sunlight again. (Students may also mention rainbows in sprays from large waterfalls or from garden sprinklers.)

Has anyone noticed where in the sky the rainbow appears?

• Always on the side opposite the Sun. In fact, it is part of a circle whose center is exactly in the opposite direction from the Sun. And the outermost color is always red.

Now, the big question: why the colors?

Let me give you a hint. When a beam of light goes through a windowpane (refer the drawing on the board), not all the light goes through. Some of it, instead of being refracted the second time, is reflected back, as if the back of the glass was a mirror. (add the reflected beam to the drawing on the board, a broken line.)

Given this hint--does anyone know how the colors arise, or can you guess?

Raindrops are tiny spheres (draw on board) and act very much like prisms. The light that is reflected inside is separated into colors, and when it comes out--at a point where the angle of the surface is different, just as it is in a prism--the different colors are separated.

Sometimes you see a second, outer rainbow--fainter, larger, with red now the innermost color. Any guess how it gets produced?

• By light reflected twice inside the raindrop

How did Newton show that white light was a mixture of all colors?

• He used a second prism to bring all the colors together again, and the result was white light, like the one which entered the first prism.

In 1800 William Herschel, the astronomer who discovered the planet Uranus, made the following experiment. He split a beam of sunlight using a prism, and let the spectrum coming out of it--the spread of colors--fall on a table. (Draw on the board, adding details as described below.)

He then placed a thermometer on the place where the spectrum fell, and noted that the temperature rose.

He then moved the thermometer past the red edge of the spectrum, and noted that even there a higher temperature was recorded. What did this mean?

• The heating of the thermometer in the middle of the spectrum meant that light carried heat (or in our terms, carried energy).

• The heating of the thermometer past the edge of the spectrum suggested that light was shining there as well--a new invisible color which the eye could not see, but the prism was able to separate. Today we would call it infra-red ("infra" means "below"--related to "inferior")

So we have now 7 colors in the rainbow, plus perhaps others which we cannot see (but instruments can). Now let us look at a TV screen.

In a TV with a black-and-white picture tube, the screen contains many small dots which glow when a beam of electrons passes them. The beam sweeps over the picture many times each second, and by controlling its strength, each dot it passes over can be made to shine brightly, dimly or not at all. This way a picture is painted on the screen. The newer flat screens have no electron beams, but the glowing dots are directly connected electrically--otherwise it is very similar.

Anyone knows how a color TV gets its color?

• The screen of a color TV has 3 types of dots, each glowing in a different color, each connected separately to a source of electricity. At any time only one color is connected, and only it responds to the beam. Then the next color is switched on, then the third, and then the cycle repeats. The electrons therefore always paint, very quickly, a red picture, a yellow one and a blue one, and the eye sees the three combined.

But then the eye can only see three possible colors! How can we see all colors of the rainbow?

• Our eye's ability to distinguish color is limited. It contains three types of cell, each sensitive to a different range of colors. Any color--of the rainbow or otherwise-- is therefore seen as equal to some combination of the 3 "primary colors. " Color printers, too, need only use inks in three colors.

Does combining yellow and blue produce green?

• To the eye, yes. To the prism spectrograph, no.

Does combining yellow and red produce orange?

• (see preceding answer)

Who discovered the "three color theory"?

• Tell about James Clerk Maxwell.

How did he show that 3 colors were sufficient?

• A combination of the 3 colors produced white.

What is a spectrum?

• A distribution of colors, as obtained (for instance) by a prism.

From now on we only discuss "spectral color" as seen by a prism instrument ("spectrometer").

You are given a closed box with a hole, from which a beam of light emerges. You are given a spectrometer and asked to tell whether the light comes from a filament lightbulb or a fluorescent lamp. How can you tell?

• The light of a glowing filament has a smooth continuous spectrum ("black body spectrum"), most intense at a color which depends on temperature.

• The light of glowing gas, like that in a fluorescent tube, has a "line spectrum" concentrated in "spectral lines" of well-defined colors, characteristic of the gas. If you see them in the spectrometer, the light source in the box is a fluorescent tube; if they are absent, the light comes from a hot filament.

(The fluorescent coating inside the tube absorbs light and re-emits it in a broad continuous spectrum, so even if you see spectral lines, you will also see a continuous spread.)

The star Antares (in the constellation of Scorpio) is reddish, Sirius is white and our Sun is yellow by comparison. How would the surface temperature of the Sun compare to the ones of the two stars?

• The Sun is hotter than Antares, not as hot as Sirius.

When the battery in your flashlight runs down, the light it produces looks more orange than yellow. Why?

• Because the battery cannot supply as much electric current as before, the filament in the lightbulb isn't as hot as it should be.

Why are most flames yellow?

• Heat easily makes sodium atoms emit a distinct yellow "spectral line" (actually two lines, very close in color). Firewood, paper, candle wax and most other combustible materials contain at least traces of table salt (sodium chloride), which colors the flame.

(optional)
The polar aurora or "northern lights" comes from beams of fast electrons from space that slam into the upper atmosphere, at a typical height of 100 km. These electrons are guided by the Earth's magnetic field lines and therefore are generally observed only in an "auroral zone" around the magnetic pole, typically 2500 km from the pole. At locations like Fairbanks, Alaska, aurora is not all that rare. (See here for more about the aurora, and here about the auroral zone.)

Light is emitted when those electrons collide with atoms, a bit like the way light is emitted when a beam of fast electrons inside a TV picture tube hits the screen. Different spectral lines are observed, but the brightest and most common one is a green line at 5.577 micron. A red line at 6.300 micron is also sometimes emitted.

These emissions used to puzzle scientists, because they failed to match spectra in the laboratory. Did the upper atmosphere contain any new unknown substance?

Around 1925, the answer was found--both colors came from oxygen. When an oxygen atom was activated ("excited") by a collision in a certain way, it took about half a second before it emitted light, an unusually long time. In laboratory experiments, the gas used was so dense that other atoms usually collided with the excited atom and carried away its extra energy. Only high in the atmosphere could the emission process proceed undisturbed.
(end of the optional section)

A spectrometer can use a prism to separate light into its other components. Do any other ways exist?

• Yes, for instance the so-called diffraction grating. (Teacher may explain what it is and perhaps demonstrate.)

The grating acts like many closely spaced slits: the light hitting between the slits is scattered irregularly, and only what hits the slits goes through. If light acts as a wave, one can show mathematically that each slit acts as a new source of the wave.

(By the way--the "slits" are really the ridges between the grooves of the grating, which transmit light like a windowpane, not the grooves themselves)

Suppose light arrives at the grating from a direction perpendicular to it. Waves have peaks and valleys, and when the arriving wave-front is at a peak, all slits also start their "local waves" with a peak.

Suppose we continue in the same direction 1, 2, 3... wavelengths. The wave from each slit will then also have a peak at those locations. These peaks would be in the same distances if the wave passed intact through the grating, as if it wasn't there, suggesting that much of the wave goes straight through, with no modification.

But wait! If each slit is the source of a wave spreading in all directions, what about the part spreading in slanted directions?

Consider the part spreading at an angle q to the original direction of light. The wave front of a wave moving in that direction would be along the drawn slanted line. However, the distances of the points on that line from the various slits--each a separate "light source"--are all different! If at the slits the wave has a peak, at the wavefront, different parts of it are in different parts of the cycle. They are at a peak if the distance to a slit is an exact multiple Nl of the wavelength (N is some whole number), at a peak in the opposite direction if the distance is (N+0.5) l, and in other parts of the cycle for other distances. The sum total--say 2000 slits, 2000 different distances--is close to zero, so we get very little light scattered in the direction of q. (That cancellation of peaks is called "destructive interference between the waves.")

Except... if the angle q is such that the distances of the wave-front from two neighboring slits differ by exactly one wavelength l. In that case, the distances from the next slits in line are 2l, 3l... and so forth, and the waves continue propagating "in step." That is "constructive interference" between the waves, and in those directions, you will see a fairly bright beam of light.

Note that the angle q at which the light undergoes constructive interference depends on the wavelength l, that is, on the spectral color of the light. Each color is therefore bent by a different angle--just as it is in a prism. Because most of the beam goes straight through, the light may not be as bright as in a prism, but the separation of neighboring colors may be muchmore sensitive.

The important thing to note is that such behavior is only expected from a wave. This therefore suggests that light is a wave, even though (at this stage of the discussion--like scientists for most of the 19th century) nothing tells us what exactly forms its peaks and valleys.

In fact, the above formula allows the light's wavelength to be calculated. For example: you observe the yellow line of sodium with a grating having 1000 lines per centimeter, and find that light is brightest at an angle q=36°. What is the wavelength l?

In fact, methods based on interference have measured wavelengths with such accuracy, that the international meter--originally defined by two scratches on a bar, kept in a vault in Paris--was at one time redefined in terms of the wavelength os a certain emission.

Another interference effect are the colors seen when a thin layer of kerosene floats on a puddle of water--layers with a thickness of the order of a wavelength of light. Some light is reflected from the top of the kerosene layer, some from its bottom (which is the top of the water), and the two reflected waves interfere with each other. For some colors the interference is destructive, for others, constructive, leading to a shimmering of colors.

(end of optional section)

What does the spectrum of sunlight tell about the Sun?

• The continuous spectrum? ... It tells that the temperature of the photosphere is about 5780° Kelvin.

• The bright lines in the spectrum?... They tell us about the composition of the photosphere--mostly hydrogen, some helium, a bit of oxygen, carbon and heavier stuff (some lines, carefully recorded and analyzed, can also tell of the presence and strength of the local magnetic field).

• The dark lines of the spectrum?.... They identify cooler material in the higher levels of the photosphere.

• The spectrum of the corona, for instance, the presence of iron that has lost 13 electrons? ... It tells us the corona is very hot, and provides an estimate of its temperature.

• How was helium discovered? (The teacher can tell more about the discovery. The helium line was in the yellow part of the spectrum, and at first some astronomers credited it to sodium--but it had a different wavelength, and they gradually recognized that in no way could sodium produce it.)

"From Stargazers to Starships" home page and index:
          http://www.phy6.org/stargaze/Sintro.htm

• About the many types of electromagnetic waves, and about observing the Sun using different members of that family.

• Qualitatively, about the concept of an electromagnetic (EM) wave, as a linked oscillation of magnetic fields and electric currents, spreading through space.

• How James Clerk Maxwell proposed a slight modification of the equations of electricity, under which electromagnetic (EM) waves could exist, and how he identified light as such a wave, after which Heinrich Hertz created radio-frequency EM waves in his lab.

• That although light spreads like a wave, it only gives up its energy in well-defined amounts, known as photons.

• That the shorter the wavelength, the bigger the photon energy. Thus hot regions of the Sun, whose atoms move faster and therefore have more energy, are likely to emit shorter wavelengths.

• That light is also emitted in photons. When an individual atom emits light, it usually changes from some "excited state" of higher energy to one with lower energy. The energy (and hence, color) of the emitted photon is very precisely determined by the difference between those levels.

  Terms: wave, electromagnetic wave, wavelength, wave velocity, frequency, photon, Planck's constant, (atomic) energy level, excited atom, solar prominences.

  Stories: The discovery of electromagnetic waves. This lesson plan also includes (optional) the story of whistlers and a brief comment on laser action.

The lesson may be started with a discussion of waves.

• --Ripples forming on the surface of water, after a stone is thrown in. (Strictly speaking, those are surface waves, almost 2-dimensional.)

• --Ocean waves. That also includes tides and tsunamis, a Japanese word for waves generated in the ocean by earthquakes (widely misnamed "tidal waves").

• Sound waves, in air, water and solid materials.
      "Ultrasound" is sound too high-pitched for the human ear to hear (though dogs can hear some of its range).
      "Infrasound" are sound-like waves too low in frequency for the ear--for instance, the shaking of the ground when a heavy truck or train passes nearby.

• Earthquakes propagate as waves in the solid earth.

• Waves on a string such as on a guitar string, or a "slinky" toy, or a rope whose end is waved (and even a flag waving in the wind). These can be viewed as one-dimensional waves, spreading along a given direction only.

• (Someone may name shock waves. Shocks are propagating disturbances and carry energy, but the equation they satisfy is not the wave equation, and they lose energy as they spread, so that scientists usually omit the "wave" designation. We never claimed our working definition was perfect!)

• Infra red (IR) waves (also known as infra red light).
  
• Ultra violet (UV) waves or UV light (also "extreme ultra violet").
  
• Radio Waves.( AM, FM, TV are all ways in which radio waves are used to carry signals, not different kinds of waves.)
  
• Microwaves
  
• X-rays
  
• Gamma rays

(But not cosmic rays--these are particles. So are electrons and ions.
  Unless raised by a student, the following is better skipped, to save time and potential confusion. Strictly speaking, any moving particles are also associated with so-called "matter waves." Such waves, describing the particle's "wave function" in quantum mechanics, are of a different kind, giving the probability of the particle being observed at various locations.)

(If someone mentions Alfven waves or "whistlers" these are among known types of plasma waves, many of which are electromagnetic waves modified by the presence of plasma, for instance, in space around Earth.)

(If someone mentions "standing waves," these are waves of any kind confined between boundaries and therefore not traveling outside them. For instance, a wave on a guitar string, confined to the section between the bridge and the fret.)

• Amplitude, the height of the crests, a measure of how strong it is; e.g. loudness of sound.

• Wavelength l (Greek "lambda") the distance between two crests.

• Wave velocity v, the velocity with which crests advance in space. The "velocity of light" at which electromagnetic waves spread in vacuum is usually denoted by the letter c.

• Frequency f or n (Greek "nu"), the number of crests passing a fixed point each second

The length v of the wave passing in one second through a given point in space contains many up-and-down swings, each of length l. Their total number in that second is.... (a student may try complete on the board, or else, teacher continues)

(length of wave train)
(length of one wave)
                    = v/l
So....   f = v/l

      --In principle, a big difference:

• A ray propagates along a single line only.
• A wave fills all of space,

(Teacher explains) For many years it was believed that light consisted of rays. Then, however, scientists discovered interference--when two or more rays from the same source overlapped, they could reinforce or weaken each other--depending whether their crests overlapped (reinforced) or crest matched dip (=crest in opposite direction), in which case they were weakened.

The diffraction grating is an example. It was then realized that light was a wave, but with a very small wavelength. Beams of light are well defined on distance scales much larger than a wavelength, but they "fuzz out" when one tries to define their boundaries within a wavelength or less.

(This should be familiar from section S-3 "The Magnetic Sun").
    A magnetic field is the region in which magnetic forces can be observed--forces on an iron magnet or on an electric current.

Iron magnets and electric currents are also the sources of magnetic fields.

  Similarly, friction among dry garments creates an electric field, which makes them cling to each other. In a laser printer or a xerox-type copier, a roller is electrified and finely powdered carbon sticks to it; later, under the influence of light, electric charge is removed preferentially, leaving it (and the carbon sticking to it) only where it contributes to the printed picture.

All these electric fields persist, because the comb, fabric, roller and surrounding air are all insultating materials, which do not allow electric charges to move freely. On the other hand, an electric field in a metal wire that conducts electricity (=allows charges to move) will move charges and will create an electric current. That is how home electricity works.

Because such currents expend energy, electric fields in a conductor quickly die out, unless they are maintained by an electric battery or generator, which provide a steady input of energy.

Now the big question: can electric currents ever drive electric currents in a vacuum or in an insulator--currents that creat magnetic fields? Usually--no. However... (students answer, teacher supplements)

James Clerk Maxwell in 1861 found that if one added to the basic equations of electricity (now known as "Maxwell's equations") a certain term that permitted such a current, those equations had, as one solution, a wave which advanced in vacuum at the speed of light.

The additional term was only significant if the electric field changed very rapidly. When the electric field stayed steady, the extra term was absent. Maxwell showed that such a wave had properties actually observed in light, and proposed that the added term was indeed necessary, and that light was an electromagnetic (EM) wave.

Light is usually produced by heat, or by glowing gases. If Maxwell was right, however, it should be possible to produce EM waves by purely electrical means. Can it be done?

•   Yes, and that is how radio waves are produced--for instance, by a current bouncing back and forth, very rapidly, in a conductor we call antenna. Heinrich Hertz in Germany did something like this in 1886.

• EM waves in air travel nearly a million times faster than sound waves
• EM waves are carried by rapidly varying magnetic and electric fields. Sound waves in air are carried by rapidly varying pressure changes.
• EM waves are transmitted through electrical insulators but are stopped by conductors. Sound propagation through a material depends on its elastic properties, not on electrical ones.

[Do not raise the following point unless some student does. In electromagnetic waves, the disturbances--the electric and magnetic forces which mark the waves--are transverse to the direction in which the wave travels--see animated figure from section (S-5). The shaking is directed sideways--like a wave on a rope. Sound waves in air are longitudinal, with the oscillating pressure force along the direction in which the wave spreads. However, sound-like waves in solids--e.g. earthquake waves--may also be transverse.]

--They are of glass, but with a metal mesh in them. The glass allows one to see the cooking food, but the microwaves are reflected back by the mesh and cannot escape.

Whistlers can be picked up by long wire antennas. They were occasionally heard along the end of the 19th century, on long-distant telephone lines, sounding like long whistles dropping in pitch. In World War I (1914-8) they were heard on telephone lines employed by the armies in the field, and in 1919 the German scientist Heinrich Barkhausen proposed they were coming from outside Earth.

In 1953 Owen Story showed that they were broadcast from lightning strokes. Lightning emits a wide range of radio frequencies, as first shown in 1895 by Aleksandr Stepanovich Popov in Russia--indeed, its crackling is easily picked up by ordinary radios during thunderstorms. Storey showed that whistlers often started from lightning in the opposite hemisphere, near the other end of the observer's magnetic field line, whose attached plasma guided them. Whistlers have since then provided unique information about the density of ions and electrons in space around Earth.
(end of optional section)

• Absorption of energy always occurs in well-defined chunks of energy, known as photons.

Its frequency n (nu)--or in other, equivalent terms, its wavelength l (lambda), or for light, its color (all three statements are equivalent). When the frequency gets higher, the wavelength shorter or the color moves from red towards violet, the energy of each photon also gets larger.

Photons of blue light have more energy then those of red, which in turn have more than those of infra-red, and all these are less energetic than photons of ultra-violet. The energies of X-rays are even larger, and gamma-ray photons have energies larger still.

where h stands for a measurable quantity, a constant of nature, called "Planck's constant" because it was discovered by Max Planck in Germany in 1900. Today the chief scientific institution in Germany is the "Max Planck Institute."

• The red photons do not have enough energy to knock out electrons, whereas the blue photons do, because each of them has a higher energy. Note that it is the quality of the light that makes the difference, not the quantity. An intense red beam will not trigger the tube, but a faint blue one will!

• Same reason as before. The red photons had too little energy to affect the light-sensitive material on the film.

• They do because each of their atoms emits light independently, and can do so only after it is elevated (by collision or by absorbing light) to one of its higher energy levels. These levels (different for each atom) are well defined, and so is the final "ground level" of each type of atom in its usual (unexcited) state.

  When the atom changes from its high level to a lower one (or to its ground level), the amount of energy given to the resulting photon is always fixed, equal to the difference between the energy levels. Therefore the emitted color is also fixed.

• Because the speed of atoms in a hot gas, and therefore their kinetic energy, increases with temperature. Atoms in the photosphere and chromosphere move too slowly for their collisions to provide enough energy to create an X-ray photon--for instance, by exciting one of the high energy levels of an atom (or ion).

"From Stargazers to Starships" home page: ....stargaze/Sintro.htm
Lesson plan home page and index:             ....stargaze/Lintro.htm

The student will learn

• About the observation of "coronal holes," by x-rays, also about related fast streams and moderate magnetic storms that recur at 27 day intervals

• About "coronal mass ejections" (CMEs), their effect near Earth and their monitoring from space.

• About high-energy ions and electrons accelerated by solar activity, probably from magnetic energy, and the hazard they pose to spacefarers.

• About NASA's "great observatories," expanding the coverage of the electromagnetic spectrum by astronomers.

Terms: Coronal holes, coronal mass ejections, magnetic storms, solar wind streams, interplanetary magnetic field

Stories, additions and features: A graphic excercise in which the expected shape of interplanetary magnetic field lines is obtained;   The "Chandra" X-ray observatory

Starting the lesson

Today we will talk largely about X-rays and the Sun. In the "Superman" comic books, Superman not only flies through the air and leaps over tall buildings, but also has the power of "X-ray vision" that allows him to see through walls.

X-rays can indeed penetrate walls, but even with X-ray vision, Superman would never see what is behind them--for at least two good reasons. Any guess?

1. X-rays are not too well reflected from objects the way light is--they usually go through until they are absorbed.
2. You only see objects around you when they are illuminated by sunlight or by lamps. In normal surroundings there are no X-rays. Unless he used an X-ray flashlight, Superman's X-ray vision would work no better than your own vision in total darkness.

Suppose you wanted to build an X-ray telescope. How can you focus X-rays? It turns out that they can be reflected if they hit at a very shallow angle--just as a flat stone will bounce off water if it hits at a shallow angle, but will surely go through and sink if dropped vertically.

The "Chandra" orbiting X-ray telescope, launched from the Space Shuttle on July 23, 1999, focuses X-rays in this way. Imagine you cut off the tread of a tire, to produce a ring with a curved cross section (drawing). The "Chandra" telescope has metal focusing surfaces shaped like the inside of this ring, and by shallow reflections they bring X-rays to a focus.

What part of the Sun do X-rays and related wavelengths see best?

•   The Solar Corona

•   Because the corona is very hot, about a million degrees centigrade. In a hot gas ions and electrons bounce around with greater speed, and when they collide, more energy is released. The photons they produce are also likely to have more energy--that is, rather than visible light, they may be in the region of X-rays or EUV.

•   Dark areas of the corona, seen in EUV or X-rays. The first extensive observation of such "holes" was done from space station "Skylab" in 1973.

What is the connection between coronal holes and the solar wind?

•   The solar wind coming from coronal holes seems to move faster.

Any reason suggested?

•   Coronal holes probably occur in regions where the magnetic field does not greatly impede the flow of plasma.

(teacher may supplement)

Strong magnetic field lines can guide the motion of plasma--it moves easily along them, not so easily from one field line to its neighbor.

Weak magnetic fields, on the other hand, get instead pushed around by the plasma, which modifies their structure. (We'll come to that later.)

Sunspots are sources of strong magnetism. Usually, they come in pairs of opposite polarity--one is like the northward pointing end of a magnet, the other like the southward pointing end--and magnetic field lines seem to connect them, forming arches above the solar surface. Ions and electrons guided along such arches by their strong magnetic fields find it hard to escape.

In between sunspot groups, field lines stick out like blades of grass after a rain, and plasma can ride along them outwards.

So--where do you think sunspots are found--in coronal holes or outside them?

•   Outside them.

Over the poles, eclipse photographs show "plumes" sticking out (sketch on the board). Does this suggest "coronal holes" avoid the poles, or not?

•   They don't avoid the poles, on the contrary--each polar region seems to be a near-permanent "coronal hole." The space probe "Ulysses" passing over them observed fast solar wind streaming out of them, similar to the way it streams from coronal holes.

Spacecraft in the solar wind observe there a weak magnetic field. What is the origin of that field?

•   The field comes out from the Sun, and is dragged out by the solar wind. (Here, if time allows, the class may learn more about the interplanetary magnetic field and draw its configuration. That project is described here.)

What are "Coronal Mass Ejections" (CMEs)?

•   CMEs are big bubbles of plasma, threaded by field lines of the Sun, which get blown away by releases of magnetic energy.

Why are space researchers interested in CMEs?

1. The can cause magnetic storms if they reach Earth.
2. They are big and energetic, but we are still not sure how they are propelled.
3. Some move much faster than the solar wind and pile up shock fronts at their boundaries. Such shocks may generate high energy particles and might play an important role in magnetic storms

Note: an interesting shock-produced event occured on 24 March 1991. A student might read up on it and briefly tell the class about it. See http://www.phy6.org/Education/wbirthrb.html.

(Teacher explains) The main feature of a magnetic storm is that it greatly increases the amount of fast ions and electrons trapped in the Earth's magnetic field, typically at distances 2 to 8 Earth radii (R_E). All one notes on the ground is a small change in the magnetic intensity--a drop of 1% at the equator is already a big storm--but at synchronous orbit (6.6 R_E), so many fast ions and electrons are added that on a few occasions (in big storms) communication satellites have sustained damage.

The additional particles originate on the nightside of the Earth, in the long "magnetic tail" formed there. The same procedure also accelerates electrons along magnetic field that come down in the "auroral zone, " about 2500 km from the magnetic poles. When these electrons hit atoms of the upper atmosphere, around an altitude of 100 km., they produce light--the "northern lights" or "polar aurora. "

In the "auroral zone," aurora is no rarity: but during big magnetic storms, the added trapped plasma modifies the Earth's magnetic field in such a way that aurora forms on field lines closer to the equator. Therefore on such occasions people in the middle of Europe and the US also sometimes see auroras.

How can we be warned that an interplanetary shock is approaching?
(teacher supplements the answers of students)

•   Monitoring satellites are stationed at the L1 Lagrangian Point, an equilibrium position between the Earth and the Sun, at about 1% of the Sun's distance. Any ordinary feature in the solar wind arrives at that point about one hour before reaching Earth. Unfortunately, a shock moving at twice the solar wind speed gives only half that lead time.

  --Special spacecraft cameras can actually see CMEs being ejected. If the spacecraft is near Earth and the CME is coming right at us, the detection of CMEs is difficult, because the Sun is on that same line of sight--although it has been done. In the future, however, spacecraft orbiting the Sun in the same orbit as Earth but located far from Earth (the "solar stereo" mission) should observe such CMEs from points far from their line of motion, and get a much better view.

What is "solar activity"?

•   Active solar phenomena associated with sunspots and their cycle, such as flares, CMEs, bursts of radio waves, bursts of X-rays, emission of high-energy particles from the Sun and related features. All these seem to be powered by magnetic energy.

(Teacher explains) When magnetic energy is released on the Sun, many electrons are accelerated (just as auroral electrons arise on Earth). Electrons are lightweight (they only form about 0.05% of the weight of matter to which they belong) and are therefore held much more tightly by magnetic forces. Because magnetic field lines tend to form arches with both ends on the Sun, they guide the electrons accelerated on them back to the Sun's denser atmosphere. When those electrons hit matter, X-rays are produced.

How are medical X-rays produced in a doctor's office?

•   Same way. Inside the X-ray machine is a glass tube empty of air, at one end of which electrons are emitted by a glowing wire. They are accelerated by a high voltage towards a metal target at the other end, and as they hit the target, X-rays are produced.

Do you think the polar aurora produces X-rays? Give your reason.

•   Yes, it does, because here too, fast electrons hit matter--in this case, atoms of the atmosphere.
      (In fact, the "Polar" satellite carries an X-ray camera which takes auroral pictures in X-rays from above. This gives information about the energy of the electrons, which the visible auroral glow itself does not provide.)

Do you think that picture tubes of TVs and and computer monitors produce X-rays? Give your reason.

•   Yes, they do, because again, a beam of electrons is stopped by a screen. These X-rays are all inside the tube, however, and the thick glass does not let them get out. Good reasons exist for not watching too much TV, but X-rays are not among them.

Similar processes take place when electrons are accelerated near the Sun. (The teacher may discuss here the Yohkoh picture of X-rays in a magnetic arch and include some of the material below.) Monitoring satellites, such as the GOES satellites whose main task is weather observation from synchronous orbit, also record solar X-rays. They alert observers to unusual solar activity when the X-ray intensity suddenly rises.

CMEs and shocks are not the only factor in producing magnetic storms. The direction of the interplanetary magnetic field is also important--if it slants southward, arriving plasma is much more likely to produce magnetic storms than when it slants northward. Unfortunately, that direction cannot be sensed remotely. Only when a disturbance passes the L1 point can we tell what its magnetic field might be.

Why would the best time for a manned mission to Mars be the quiet part of the 11-year cycle, when solar activity is rare?

•   Because high energy ions associated with flares and CMEs can be hazardous to the health of astronauts.

(A student who has read Ben Bova's "Mars" may tell about the chapter in which the book tells about astronauts hiding in a "shelter" during a solar outburst.)

What is the idea behind NASA's "Great Observatories" such as "Hubble" and "Chandra"?

•   Each "great observatory" space mission is supposed to open new ranges of the electromagnetic spectrum, with a better resolution than that of earlier observations (i.e. distinguishing smaller and fainter objects). By using the new capabilities to survey the sky, new phenomena may be discovered.

              (S-7A) The Discovery of Atoms and Nuclei
                                    http://www.phy6.org/stargaze/Ls7adisc.htm

"From Stargazers to Starships" home page: ....stargaze/Sintro.htm
Lesson plan home page and index:             ....stargaze/Lintro.htm

The student will learn

• About the "solar constant," the average flow rate of solar energy to Earth.

• That stars contain appreciable gravitational energy, which they can release by shrinking. This is an important source of energy in the early and final stages of the evolution of a Sun-like star.

• That the composition of radioactive elements suggests the Earth is billions of years old. The only credible source that can power the Sun for so long is nuclear energy.

• About the structure of the atomic nucleus, an extremely compact object governed by 3 types of force:
  1. The electric repulsion of its protons, trying to blow it apart.

  2. The "strong nuclear force" which makes neutrons and/or protons stick together, provided they are first brought very close to each other, within the short range of that force.

  3. The "weak nuclear force" which tries to equalize the number of protons and neutrons in the nucleus and can, under suitable conditions, convert one kind to the other. It, too, has a short range.

• About the "curve of binding energy." That is the graph showing how the binding energy of a nucleus depends on its mass ("atomic weight"), telling us that the most stable nucleus is that of iron. Energy can be gained either by combining lighter nuclei ("nuclear fusion") to form nuclei up to iron, or by breaking up heavier ones.

• That the Sun gets its energy by fusion, combining hydrogen nuclei ("protons") to form helium. Because that energy comes from the strong nuclear force, fusion requires nuclei to come very close to each other. That usually happens only when atoms collide with great force. The high temperatures and pressures needed for such collisions appear to exist in the core of the Sun.

• About "controlled nuclear fusion" in which scientists try to release fusion power for commercial use, by magnetically confining and heating ions.

• About the way stars are believed to evolve. First a cloud of gas is pulled together by its own gravity, which supplies energy until nuclear fusion begins at the core of the new star. A long period of "nuclear burning" then follows. This ends when the star runs out of fuel and collapses, rapidly releasing a great amount of gravitational energy.

• About the remnants of such collapses--white dwarfs, neutron stars and black holes.

• About the gravitational collapse of larger stars in the ("type 2") supernova process, creating elements heavier than iron. The energy released by the collapse blows away the outer layers of the star.

• About the Crab Nebula, the remnanat of the 1054 supernova explosion

This is a delicate subject. Most students will accept taught facts without questioning them--for instance, accept that Mt. Everest exists, even if none of them ever saw it. Yet sometimes so much is accepted on faith that the entire structure becomes suspect.

Students need to realize that all the abstract concepts of science--atoms, nuclei, protons and neutrons, none of them visible to us--evolved gradually, that scientists questioned them at every step, and in the end accepted them only because no other interpretation seemed possible.

One is reminded of a story (possibly even true) about a 19th century meeting in which British teachers discussed the math curriculum. The question arose whether to teach Euclid's classical geometry, with its interlocking sequence of theorems and proofs. One teacher rose up and said something like the following: "If a duly accredited teacher tells the student that the sum of the angles in a triangle is 180 degrees, the student should accept it and not be required to prove it as well."

Today we smile at this argument, the very opposite of the scientific approach we try to impart to students. Yet in physics and astronomy, just as much as in mathematics, the student must learn to appreciate the reasons, not just memorize the contents.

If time permits, an additional historical review is provided for this section, linked further below.)

Starting the lesson

Today we discuss energy generation by the Sun, which involves atoms and nuclei. Most high school teachers (and most texts) simply tell students (teacher writes on the blackboard, and students copy):

• Matter is made up of atoms.

• Each atom has at its center a compact positive nucleus, surrounded by a cloud of negatively charged lightweight electrons.

• Nuclei in nature contain from 1 to 92 protons, positive particles which also form the nuclei of hydrogen atoms.

• Nuclei also contain neutrons, particles similar to protons but without any electric charge, in about equal number to that of protons.

No one has ever seen an atom, nucleus, electron, proton or neutron.The fact is, it took well over a century to reach these conclusions. And as in the rest of physics, the existence of these objects was accepted only after the evidence of observations and experiments left us with no alternative.

(Click here for a brief history, S-7A The Discovery of Atoms and Nuclei.)

Questions in Class.

You read that "the solar constant is 1.3 kilowatt/m²." What does this mean?

• That would be the power carried by sunlight falling perpendicular to the surface of the Earth, if the atmosphere did not scatter, absorb or reflect any of it.

• Since only 5% of the solar energy is converted to electricity, the solar cells need to receive 20 times the power they deliver, or

        20 x 3300 = 66,000 watt.

  The power provided by sunlight is 0.5 of the solar constant or about 650 watt/m² Therefore the required area is

        66,000/650 ~ 100 m² or about 1100 ft²

  comparable to the area of the house itself.

• They examine rocks containing long-lived radioactive elements and measure the accumulated percentage of decay products.

• Radioactive dating suggests the oldest rocks are several billions of years old. Perhaps the most reliable estimate is from Moon rocks brought back by Apollo astronauts, which remained relatively undisturbed from the time they were formed. They give about 4.7 billion years.

• It was suggested that the Sun extracted gravitational energy by shrinking. All its mass was gradually falling down, inwards, and heating up from that fall.

• It did not provide enough energy. Even though the Sun has a much stronger gravity than Earth, it was estimated that its shrinkage could provide the Sun's energy for only about 20,000,000 years.

• Nuclear energy.

• Atomic nuclei are made up of two kinds of particle, similar in mass and in the way they react to nuclear forces: protons and neutrons. The proton has a positive electric charge and the neutron is uncharged.

The teacher may supplement: Since protons and neutrons create very similar nuclear forces, they are sometimes given a common name "nucleons. "

Neutrons are slightly heavier, and if free neutrons are produced, they convert spontaneously into (proton + electron) in about 10 minutes (a 3rd particle, a very light "neutrino," is also produced).

• Two protons of course repel each other electrically, both having the same kind of electric charge, a positive one.

• In addition, however, once they get very close to each other, nucleons attract very strongly--and it is this attraction, called the strong nuclear force, that holds them together in a nucleus.

• It tries to equalize the number of protons and neutrons inside the same nucleus.

• It gains energy, that is, energy is released by the process.

On the other hand, to lift the stone from the floor against gravity, separating the two attracting objects, you must... ?

• ... you must invest energy.

• Gain energy, since the neutron is attracted. (Think of a little magnet latching onto a refrigerator door!)

This is more complicated:
• A nucleus is electrically charged, and so is the proton--both positively. So the two repel each other, and energy must be provided to let them approach each other. For instance the proton may be flung at the nucleus with great speed, and some of that speed (and of the associated energy) is lost as the two come closer, because of their mutual repulsion.

• Once the proton is very close to the nucleus, it is attracted by the nuclear force, which releases energy.

• Up to iron, energy is gained by adding a proton to the nucleus. Energy must be invested in overcoming electric repulsion, but the energy gain from the nuclear attraction outweighs that. That is the fusion process, taking place inside the Sun and the source of its energy.

• For heavier nuclei, energy is lost. These atoms contain larger number of protons, their repulsion is stronger, and it outweighs the energy gain from the nuclear force.

• True. In fact, the heaviest atoms (uranium, for instance) do so spontaneously. They shoot out packets of two protons and two neutrons--"alpha particles" which are actually helium nuclei. That is one form of radioactivity.

How do we know? From the light emitted by helium on the Sun, we know that it contains a small percentage of "light helium" whose nuclei have two protons but only one neutron. The light of stars suggests that they, too, contain a little of this variety.

But on Earth, this kind of helium is very rare! Its rarity suggests that almost all of the helium present when the Earth first formed was lost to space. Meanwhile, however, new "ordinary" helium was produced in rocks, in the form of alpha particles from uranium and similar elements. Some of it diffused, over millions of years, into natural gas, and that is where we get most of our helium today.

• The Sun gets its energy from converting hydrogen (the fuel) to helium (the product or "ashes").

• "Nuclear fusion"

Instead, the reaction occurs in stages (outline on the board)

1. First two hydrogen nuclei (protons) combine to form "heavy hydrogen," a proton plus a neutron. In this process, one proton converts into a neutron, and a "positron," the positive counterpart of an electron, is emitted.

   (If a question is asked: isolated neutrons convert into protons, but inside the nucleus, with extra energy available, the conversion can also work the other way around.)

2. Then another proton is added, to create "light helium."

3. Finally a 4th proton is added, to create regular helium. Again a proton converts into a neutron, and another positron is emitted.

Where does the released energy appear? The nuclei emit gamma rays, while the positrons meet with electrons and both are "annihilated," also creating gamma rays. All this gamma radiation is absorbed in matter and heats it up.

Interestingly, the helium nucleus is lighter, it has less mass than the combined mass of the 4 protons that the Sun started with. If m is the difference in mass (the term is "mass defect"), then the energy E released is given by E=mc², Einstein's famous formula.

• Controlled nuclear fusion is the attempt by scientists to extract energy by fusion reaction in the laboratory.

• They use magnetic fields.

If stars get their heat by the fusion of hydrogen to form helium--what happens when all the hydrogen is used up and converted to helium?

(Teacher might explain) For a while the star may gain energy from the fusion of nuclei larger than hydrogen, but that energy source does not last long. When the star is no longer able to generate heat, gravity takes over and heat is released by shrinkage--the process originally proposed for the Sun.

A Sun-sized star has a complicated final evolution, including a "red giant" stage when it "puffs up" with a radius greater than that of the Earth's orbit, relatively cool and rarefied. In the end, what is left probably becomes a "white dwarf," a star in which gravity has crushed all atoms and smeared out their electrons. This is an extremely dense star, no bigger than Earth, but with a mass that is still an appreciable fraction of the mass of the Sun. After energy generation dies out, it becomes a dark dwarf, and it is anybody's guess how many of those are hidden in space, because we have no way of observing them.

• It will probably collapse into a neutron star, as dense as the atomic nucleus. Here electrons are not just smeared out, but they combine with the protons to form neutrons, held together by the enormous gravity.

• Because gravity in all these configurations acts as if mass were concentrated at the center, so that its force increases like 1/r². The smaller the final value of r, the stronger is the force, and the more energy can be released by letting it move matter.

What does the general theory of relativity suggest about the final fate of a star 50 times more massive than the Sun?

• Gravity is then so strong that the object collapses into a "black hole" of extremely small size. We cannot see its true size (or anything else about it) because the intense gravity does not allow any light to escape. However, the mass still exerts a gravitational pull on surrounding objects.

Calculation of Escape Velocities

(Teacher explains)

The escape velocity V from the surface of the Earth, at radial distance r, was calculated in an earlier lesson to satisfy

where g is the acceleration due to gravity. Using SQRT to denote square root

By Newton's theory of gravitation, if m is the mass of the Earth

Here G is the number that measures the strength of the gravitational pull, the one which the delicate experiments by Cavendish and Eötvös determined. Then

and for a star of mass M and radius R

That is the velocity needed for an object to fly off the star to infinity, starting with distance r. But by the conservation of energy, it is also the final velocity of an object coming from far away and hitting the surface. It is therefore a measure of the energy that a star releases by collapsing to radius R.

Let us go through some very approximate calculations, just to get orders of magnitude. We start from a result derived in section #21 of "From Stargazers to Starships," by which a space vehicle launched from the Earth's orbit needs 12.4 km/sec to escape the solar system altogether.

This is above and beyond the 30 km/sec which it already has from the Earth's motion around the Sun, making the total "escape velocity" from a distance 1 AU from the Sun

with M the mass of the Sun and R₁ the Earth-Sun distance, the "astronomical unit" (AU).

1. What is the escape velocity V₂ from the Sun's surface? The radius of the Sun is R₂ = 700,000 km or about 1/200 AU. So

   V₂ = SQRT [2GM/(R₁/200)] =            

       = SQRT[200 x (2GM/R₁)] = SQRT[200] x SQRT[2GM/R₁]

               = 14.1 x 42.4 km/sec = 597.8 km/sec            

   In round numbers this is about 600 km/sec--twice the velocity of NASA's planned "solar probe" which at its closest approach will whiz by the Sun at 300 km/sec, at a distance of 4 solar radii. At 1/10,000 the velocity of light, that would be the fastest man-made object ever made, excluding accelerated atomic particles.

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2. Next, let the Sun shrink to the size of a white dwarf, say from a radius of R₂=700,000 km to R₃=7000 km, comparable to Earth's. What is the escape velocity V₃ now?
   V₃ = SQRT[2GM/(R₂/100)] =

       = SQRT[100 x (2GM/(R₂)] = SQRT[100] x SQRT [2GM/(R₂]

               = 10 x 600 km/sec = 6000 km/sec

   A lot of energy can be released by material collapsing onto a white dwarf. If it were to come from far away, it would hit at 6000 km/sec, hundreds of times faster than any asteroid impact, fully 2% of the speed of light!

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3. Now let us go even further and let the Sun-size star collapse to a neutron star, of radius R₄=7 km, 1000 times smaller. If the escape velocity is now V₄, we get
   V₄ = SQRT[2GM/(R₃/1000)] = SQRT[1000] x SQRT(2GM/R₃)]

               = 31.6 x 6000 km/s = 189,600 km sec

   Say 190,000 km/sec (we neglect relativity here, which would change the result somewhat). That is close to 2/3 the velocity of light! Even a pebble hitting such a star will release a great amount of energy. And it is no wonder that with moderately larger masses, we get into black hole territory.

(End of derivation)

• So much energy is released by the collapse that the outer layers of the star are blown off with tremendous speed.

  And in addition?

• The final collapse creates a brief instant of tremendously rapid nuclear fusion, in which many heavy nuclei are created. All nuclei heavier than iron that are found on Earth are believed to have arisen in this way.

Experiments in large tanks of water or special fluids, buried deep underground (to shield out the effects of "cosmic rays," fast ions from space) can detect occasional neutrinos, usually from the Sun's core. On 24 February 1987, a supernova became visible (mainly from the southern hemisphere) in the Large Magellanic Cloud, a small galaxy attached to ours. Although some 150,000 light years distant, that star became visible to the eye, and was studied extensively since that time (see picture). At the time of collapse, underground experiments in Japan and the US detected a simultaneous flow of more than a dozen neutrinos, simultaneously! This agreed with the theory of supernova collapse and with the brief but very intense spurt of nuclear fusion, creating new elements.