What Wattage!

The sun, with all those planets revolving around it and dependent upon it, can still

ripen a bunch of grapes as if it had nothing else in the universe to do.

Galileo1

How is it possible to know anything about the stars? They are so far away. To date, no one has ever visited a star. Fortunately, they travel across the abyss to us. The light that they emit brings immense amounts of information about their nature. In addition, one has been conveniently placed nearby. The sun is closer to earth than any of the large outer planets. Let’s begin to decode the messages carried by starlight.

Note: The technique used to calculate the wattage of the sun is adapted from a Project STAR, Harvard-Smithsonian Center for Astrophysics, workshop. This method provides a very impressive approximate solution.

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All of us are familiar with the association of a light bulb and its wattage. The wattage of a bulb is the amount of energy that flows from this source each moment the light is on. Wattage is a measurement of the luminosity of the light bulb. Brightness is a more subjective measurement of the appearance of a source of light. A 100-watt light bulb will always be a 100-watt energy source whether it is near or far. That is the amount of energy it is capable of producing. However, a 100-watt light bulb can vary in brightness due to several things. Your distance from the light bulb and the quality of the medium (think fog) between you and the source are some of the considerations that can affect your judgment about the look or brightness of the light bulb.

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Imagine a large darken sports arena filled to capacity. Then, someone at center court strikes a match. In an instant, the message that the match was struck is communicated to every corner of the large arena. Your detector, your eye, receives only a tiny fraction of the energy that flooded the entire complex. Yet, the fraction of energy that entered your eye contains the entire message of the event that transpired at center court. Everyone there knows of the event.

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Pretend that your seat at the arena is twice as far away from center court as that of a friend who is seated directly across from you. Suppose at intermission you were to compare notes about the luminosity and brightness of the center court spectacle. What qualitatively would be exchanged between you and your friend?

You agree that if a proper measurement of luminosity were made that both you and your partner would be in agreement to its value. On brightness though there is a difference.

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Click on window: Inverse Square Law IVideo~ 3 minutesNote: A few seconds might be needed for the video to load.

Click on window: Inverse Square Law IIVideo~ 5 minutesNote: A few seconds might be needed for the video to load.

http://www.youtube.com/watch?v=iHf9NKeXUUI&feature=related http://www.youtube.com/watch?v=JW3tT0L2gpc

Since your friend sat closer to the event than you, their eye gathered more energy than yours did. As the light expanded to fill the entire volume of the arena your location relative to the match influences the amount of energy that is available for you to collect. Light, like a rubber band stretched thin to the breaking point, weakens in amount that can be gathered as distance is extended.

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Quantitatively, light behaves in a very regular mathematical way. It is an inverse relationship. As distance increases, the amount of light received becomes less. Precisely, it is inversely proportional to the squared value of the distance.

Intensity = 1/d2

Unit Distances ______________1_____2_____3_____4__________ Energy Collected 1 ¼ 1/9 1/16

Since you were two units away from the event at center court and your friend was only one unit distance away, your eye only collected one-fourth as much light as they saw. For you the experience was view to be a fainter one.

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When Albert Einstein was in residence at the Institute For Advanced Studies at Princeton, a guest asked to be shown Einstein’s laboratory. The great man smiled, held up his fountain pen, and pointed at his head. Lets visit our lab and pursue some advanced studies.

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This mind experiment can easily be tried at home. The detector, photometer, describe can be two blocks of “clear” paraffin wax rubber banned together.

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Suppose a 100-watt light bulb illuminates one side of the wax photometer at a measured unit distance as shown.

Unit distance

photometer

Maintaining the need to keep both sides of the paraffin wax, photometer, equally bright, at one, two and three unit distances away, how many 100-watt bulbs will be required at the new lengths?

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At one unit distance only one 100-watt bulb is needed to keep the paraffin brightness level balanced.

one 100-watt bulb will only provide ¼ the amount of energy to illuminate the photometer. The sides of the wax detector will not appear to be balanced in their brightness. Four bulbs each contributing ¼ the energy at the two-unit distance will be required to keep the sides of the wax balanced. At three unit distances nine bulbs are required.

So, just how luminous (wattage) is our neighborhood star?

At two units distance,

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7 Centimeters Unit distance Photometer 1 Unit-7cm 2 Units-14cm Experimentally obtained 1 Bulb Needed 4 Bulbs Needed Outside on sunny day Using a 100 watt bulb

15 x 10e12cm.(earth-sun distance) Divided by 7cm. for each unit Equals-2.14e12 units

Therefore: The number of bulbs needed at the earth sun distance:

(2.14 x 10e12) (2.14 x 10e12) =4.6 x 10e24 bulbs

(4.6 x 10e24 bulbs) x 100 watts/bulb = 4.6 x 10e26 watts/second

This is an ENORMOUS amount of energy each second of time…for the current history of our planet…

Solar Luminosity- 4 X 1024 (100 watt light bulbs)/sec

•Combustion-”Burning” results when a fuel combines with oxygen. Solar surface temperature is too hot to allow molecule formation. Calculated rate of combustion would only last about 2000 years.

•Gravitational infall- If many meteors are hitting the sun, we also would be a major target. If the mass of the sun were to increase significantly our orbit around it would not be stable.

•Contraction-Any given quantity of matter compressed to a higher density gets hotter-penny on a railroad track. Calculated age of the sun would be about 40 million years.

4 X 1026 watts/sec

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http://gizmodo.com/5698143/watch-focused-sunlight-melt-steel-rock-and-anything-else

A measure of sentient maturity!

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Origin and Equilibrium of the Sun

• Gravitational Collapse

• Increase in Kinetic Energy of Atoms

• Increase in internal Pressure

• Energy Generation by Nuclear Fusion

• Equilibrium – balance of gravity by fusion maintained outward pressure

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In the stars like the sun, when the star shrinks the core pressure and temperature increase and that increases the pressure, resisting the shrinkage. When the star swells, the core pressure and temperature drop and reduce the pressure, and gravity makes the star stop swelling. (animation by G. Rieke)

If the sun produced energy more rapidly in its core, it would be hotter. Then the pressure would increase and the core would expand. The larger, lower density core would have fewer proton-proton collisions, reducing the rate of reactions, and causing the production of energy to decrease. Thus, the energy output is self-regulating.

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Sir Arthur Stanley Eddington (28 December 1882 – 22 November 1944) British astrophysics

I ask you to look both ways. For the road to knowledge of the stars leads through the atom, and important knowledge of the atom has been reached through the stars.

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http://primaxstudio.com/stuff/scale_of_universe/Note: Important to view this web site

Atoms• Atoms are the building blocks of ordinary matter.

They have a size of about 1 angstrom.• The ‘states’ of an atom are discrete.

– You can sort of think of this as a mini planetary system in which only certain ‘orbits’ are allowed.

• The energy levels of the atom are quantized.• Quantized does not mean large! Rather, it

means discrete. For instance, our monetary system is ‘quantized’.

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Size of an electron: is to the size of a human being what the latter is to the size of the Milky Way Galaxy

Mass of an electron: is to the mass of a mosquito what the mass of the mosquito is to the mass of the sun.

If you could scale the center of an atom, the nucleus, up to four inches, the surrounding electron cloud would extend to four miles away and essentially all the breach between would be marvelously empty. Source: The Hidden Face of God

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Atom-smallest unit of an element

Particle Charge Mass

Proton +1 1.0076 a.m.u.~1Neutron 0 1.0089 a.m.u.~1Electrons -1 0.0055 a.m.u.~0

2He atomic number (protons)

4He mass (protons + neutrons)

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Atoms consist of nuclei made of protons and neutrons, and electrons around them. Hydrogen (1 proton) and helium (2 protons) are the simplest; there are atoms with up to about 100 protons, giving 100 elements (figure by G. Rieke).

The electrons in an atom are held by the electric force, which is proportional to 1/r2 just like gravity. This force attracts positive and negative electric charges, but repels like charges - two positives or two negatives. The protons in the nucleus of the atom are held together by the "strong force", which is clearly much stronger than the electric one but works only over very small distances.

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• The number of protons in an atom’s nucleus is the atomic number for that particular element

• The same element may have different numbers of neutrons in its nucleus

• These slightly different kinds of the same elements are called isotopes

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If even more energy is supplied to an electron, it can escape from the atom leaving the positively charged nucleus. Because the electron is no longer transitioning between two specific energy states, the atom can absorb a range of energies in this situation. Electrons over a range of energies can be captured by the positive nucleus, emitting photons over a range of energies

Although it is convenient to draw protons, neutrons, and electrons as little dots, quantum mechanics tells us that they cannot be located accurately and are in fact more like fuzzy little fog clouds. We cannot predict precisely what they will do, leading to a scientific confrontation with the philosophy of determinism: science shows that there is fundamental uncertainty in what will happen in the future (Figure from The Essential Cosmic Perspective by Bennett et al.)

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Nothing exists except atoms and empty space…all else is opinion…Democritus-460-370 B.C.

At the atomic level, then, the solid material objects of classical physics dissolve into patterns of probabilities, and these patterns do not represent probabilities of things, but rather probabilities of interconnections. Quantum theory focuses us to see the universe not as a collection of physical objects, but rather as a complicated web of relationships between the various parts of a unified whole.. Fritjof Capra 27

Electrostatic Repulsion in Nucleus (Coulomb Barrier)

• As two nuclei approach each other the energy required to move closer increases due to the repulsion of like electrical charges

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Energy = Mass X The Speed of Light SquaredJoules Kilograms Meters Squared per Second Squared

Four hydrogen nuclei Fusion One helium nucleus + energy

+ energyFusion

High Temperature High Pressure

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The pressure p of the star, considered as an ideal gas of N atoms of mass mA, is

p·V = N·k·T( k = Boltzmann constant, T = abs. Temperature)

With ρ = N·mA / V we get the ratio p / ρ = k·T / mA

To be stable the following equation must be valid: G·M / R = k·T / mA

For the temperature T we get

T = G·mA·M / (k R)

T = 2.3·107 K = 23,000,000 K

G = 6.7·10-11 N m2 / kg2 mA = 1.7·10-27 kg M = 2·1030 kg k = 1.4·10-23 J / K R = 7·108 m

constant of gravitation mass of hydrogen atom mass of the Sun Boltzmann constant radius of the Sun

The core temperature of the Sun

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Click on window: FusionVideo~ 5 minutes

Note: A few seconds might be needed for the video to load.

http://www.youtube.com/watch?v=Ee--KkyR7CU&feature=relmfu

32http://www.youtube.com/watch?v=Czbh_sdqX84&feature=related

Click on window: FusionVideo~ 1 minute

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Note: Our discussion and diagrams about the proton-proton fusion chain reaction are at the first approximation level-nuclear scientsist would have a more detailed description of this process ...under high temperature and pressure at the core of a star-protons which naturally repel each other come into contact (fuse). This first step creates a neutrino. This immediately escapes the core and flies out into space and with a small probability hits a detector on earth. SIGNIFICANT because theorist predict this and our experiments detect them. So we feel confident that our thinking is correct. All the other by-products of this first step take very long to emerge from deep within the core so this is instant gratification that we are thinking correctly about matters secluded deep within the sun. At this step the one proton give up its positive charge and becomes a neutron-a positron is released. This proton neutron combo find another proton (fusion again)...two protons are called helium...as these various steps happen energy is release..."heat" causes expansion so this counterbalances gravity and its wish to collapse the star.

34http://www.nsf.gov/news/mmg/mmg_disp.cfm?med_id=70726

Neutrinos

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Nuclear Fusion in the Sun

• Proton-Proton Chain – Step 1 1H + 1H = 2H + e+ + neutrino– Step 2 2H + 1H = 3He + photon– Step 3 3He + 3He = 4He + 1H + 1H + photon– Net 4(1H ) = 4He + 2e+ + 2 neutrinos + – 2 photons

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Chemical reactions are different than nuclear reactions. In chemistry, mass is conserved as a reaction proceeds. If you burn a newspaper by adding oxygen you get ashes and a gas which as far as can be measured, together weighs as much as much as the newspaper and the oxygen used to burn it. Compounds and elements on one side of the reaction (reactants) recombine and form new compounds and elements on the other side (products). It is the bonds between electrons in the outer shell of these atoms that break and reform in chemical reactions. Energy is absorbed or given off in a chemical reaction depending on which set of molecules is more stable-reactants or products. In nuclear reactions, mass is never conserved. Instead, mass-energy must balance on both sides of the equation.

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Energy and PowerEnergy is the capacity to do work (1 Joule = 107ergs)Work=Force through distance (Same units as energy)1 Joule accelerates 2 Kg from 0 to 1 meter/second Power is the rate at which energy is generated or expended(Ergs/second) or (1 Watt=1Joule/second)  The Sun Uses up 4.4x109 Kg of HydrogenProduces a kinetic energy of 4x1026Joules/secondA Power of 4x1033 Ergs/secondBut will only use up~2% of its mass…

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4 hydrogen nuclei = 6.693 X 10-27kg1 helium nucleus = 6.645 X 10-27kgMass difference = 0.048 X 10-27kg

E = mc2

= (0.048 X 10-27 kg) (3 x 108 m/sec)2

= 0.43 X 10-11 Joules

Sun needs 1038 reactions/second just to stay hot enough to resist gravitation collapse

4 1H 2He + 2e+ (positrons) + 2 neutrinos + Energy

Fusion

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Energy from the Sun• Nuclear chain reaction (hydrogen forming helium)

• Releases radiation (gamma rays)

• The gamma ray loses energy as it bounces around inside the Sun

• It is finally released at the photosphere, primarily as visible light

Image at http://solarscience.msfc.nasa.gov/interior.shtml 40

The process…

•Observation…•Tentative thoughts…•“Ladder of logic”…

Destination…The Theory

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Hiroshima Peace Memorial, a remnant of the city at ground zero of its nuclear bombardment

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Nuclear Reactions

• Fission – release of energy when heavy nuclei break up (generally Atomic # >= 84)

• Fusion – release of energy when lighter nuclei fuse to form a more stable nuclei

• Energy released is equal to E= Δmc2

(where Δ m is the mass loss in the reaction)

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Homestake Mine-Lead South Dakota

MINOS, or Main Injector Neutrino Oscillation Search

Soudan Mine in northern Minnesota

Kamioka Observatory, which is run by the University of Tokyo's Institute for Cosmic Ray Research (ICRR) and known for its Super-Kamiokande neutrino detector.

Sudbury Neutrino Observatory

AMANDA, the Antarctic Muon and Neutrino Detector Array

"A particle that reacted with nothing could never be detected. It would be fiction. The neutrino is just barely a fact." -- Leon Lederman, Physicist, Educator, Nobel laureate.

The only thing that we can detect that comes directly from the center of the Sun are neutrinos. These small particles are so non-reactive that over 99.9% of them go right through the earth without touching (affecting) anything. The small fraction that we do detect gives us information on the nuclear processes in the center of the sun.

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http://www.youtube.com/watch?v=lAAmAbJvvJg

Click on window: NeutrinoVideo~ 1 minute

"We now have high confidence that the discrepancy is not caused by problems with the models of the Sun but by changes in the neutrinos themselves as they travel from the core of the Sun to the earth," says Dr. Art McDonald, SNO (Sudbury Neutrino Observatory) Project Director and Professor of Physics at Queen's University in Kingston, Ontario. "Earlier measurements had been unable to provide definitive results showing that this transformation from solar electron neutrinos to other types occurs. The new results from SNO, combined with previous work, now reveal this transformation clearly, and show that the total number of electron neutrinos produced in the Sun are just as predicted by detailed solar models."

June 18, 200145

(Mass X (fraction of mass that can = (mass that can Of core) be turned into energy) turn into energy)

Life span = mass that can turn into energy Mass loss each year

Life span = 1.4 X 1030

1.4 X 1020 1 X 10 10 years 10,000,000,000 years

E = mc2

Using the equation, shows that the sun converts about 5 billion kg (or about 5 billion metric tons) of itself into energy every second! One might think at this rate the sun would not last long…

Mass of sun = 200,000,000,000,000,000,000,000,000,000,000 kg

Mass conversion rate - 5,000,000,000 kg/second

= 199,999,999,999,999,999,999,995,000,000,000 kg46

Main Ideas1. Neither the burning theory nor the shrinking theory can

explain the fact that the sun has been shining at its presentrate for several billion years.

2. Mass is a special form of energy. 3. The nucleus of a hydrogen atom has one proton; the

nucleus of a helium atom has two protons and two neutrons.4. Hydrogen may be transformed into helium by the

proton-proton reaction.5. In this reaction, a certain amount of mass is changed into

radiant energy. Mass changes form-does not vanish!6. Hydrogen fusion reactions take place in the core of the sun,

where the temperature is many millions of degrees and the number density is quite high.

7. With the proton-proton reaction as its energy source, scientists estimate that the sun can shine at its present ratefor a total of about ten billion years.

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Main Ideas1. Guided by physical laws, astronomers calculate the conditions

that must exist inside the sun. Then they build a mathematicalmodel consistent with the sun’s mass, size, luminosity, andchemical composition.

2. The model indicates that the sun is gaseous/plasma throughout; that thepressure at every point is proportional to the temperature anddensity of atoms at that point; and that the temperature, pressure, and density increase continuously from the surface to the center.

3. The rate at which energy is produced inside the sun exactly equalsthe rate at which it is pouring outward from the sun’s surface.

4. Radiant energy travels in very small packets call photons. 48

Stars have two purposes, they give energy in the form of light, and they produce the heavy elements that we are made of…Astrophysists Robert

Wagoner

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You are a child of the Milky Way…The night is your mother…Chet Raymo

Universe Composition Hydrogen 90%

Helium 9%Oxygen CarbonNitrogen

Living Cell Composition

Hydrogen 99%OxygenCarbonNitrogen

Sodium .7%PotassiumCalciumMagnesiumSulfurPhosphorousChlorine

Iodine .3%IronCopperZincManganese

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Composition of Earth’s crust… You are not made of the soil…

The SunOur Nearest Star

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