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------------------------------------ 2542 - SUN - our closest star?
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- This light is generated in the center of the Sun where hydrogen is fused into helium. It is amazing that it takes 170,000 years for that light generated at the center to reach the surface , starting it’s journey to us, in just eight minutes later it is a suntan on the beach.
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------------------------------ distance = rate * time
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----------------------------- 1.496 * 10^11 meters = 2/998 * 10^8 m / sec * time
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----------------------------- 500 sec = time
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----------------------------- 8.3 minutes = time
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- The reason is, the center of the Sun is so dense due the gravitational pressure that the photons of light ricochet like billiard balls off all the other particles before they can make their way to the surface. It takes 170,000 years to make it through this atomic maze.
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- A main-sequence star is one that fuses hydrogen into helium at its core. Our Sun is half way in its lifetime as a main-sequence star, 4,500,000,000 years out of 10,000,000,000 years burning hydrogen. When the hydrogen burns out the stars die and become White Dwarfs, Neutron Stars, or Black Holes depending on the mass they begin with. Our Sun will become a White Dwarf.
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- Stars vary in mass from 8% that of the Sun to 150 times that of our Sun. Objects less than 8% the mass our Sun never begin hydrogen fusion and are technically not stars. However, they can emit energy due to graviational pressure alone and can be seen in the infrared spectrum but not in the light spectrum. These too-little-to-be stars are called Brown Dwarfs. The most massive stars are 15,000% larger than our Sun. Eta Carinae is an example of a supermassive star.
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- The more massive the star, the higher the gravitational pressure, the hotter the temperature, the more dense the core, and the brighter the star. Brightness is called luminosity and there is a relationship defined between luminosity and the mass of a main-sequence star.
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------------ Luminosity of Star / Luminosity of Sun = ( Mass of Star / Mass of Sun )^ 3.5
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- Eta Carinae in the year 1841 was the second brightest object in the night sky. That was when it went supernova. This massive binary star survived and still holds 140 solar mass.
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-------------------------- Luminosity / Luminosity of the Sun = ( 140 / 1 ) ^ 3.5.
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- Luminosity is 32,500,000 times the Luminosity of the Sun, but it is 8000 light-years away. It is expected to go supernova again in 100,000,000 years, because each star is so massive.
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- However, the more massive and brighter the star the shorter its lifetime as a main-sequence star. High mass stars burn up their hydrogen faster and die younger. There is an inverse relationship between mass and main-sequence lifetime.
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----------- Lifetime of Star / Lifetime of Sun = ( Mass of Star / Mass of Sun )^ -2.5
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- Our Sun will live for 10,000,000,000 years. But, if were 10 times bigger it would only be a main-sequence star for 30,000,000 years and if it were 0.1 times the mass of our Sun it’s lifetime would be 3,160,000,000,000 years.
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- The energy of our Sun over it’s entire live time can be calculated as:
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----------------------------- Energy = luminosity * lifetime:
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----------------------------- E = L * time
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----------------------------- E = 3.9 * 10^26 watts * 10^10 years
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----------------------------- L = 3.9 * 10^26 watts = luminosity of the Sun
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----------------------------- Watt = joule per second
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----------------------------- Year = 3.17 * 10^7 seconds
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----------------------------- E = 3.8 * 10^36 * 3.17 * 10^7 joule
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------------ E = 12 * 10^43 joules = the total energy released over our Sun’s lifetime.
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- Could all this energy be created by gravitational pressure or is there some other energy source in the Sun?
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- The energy created by gravitational collapse is proportional to the mass squared and inversely proportional to the radius:
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----------------------------- E = G * M ^2 / radius
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--------------- E = 6.67 * 10^-11 m^3/kg/sec^2 * ( 1.99*10^30 kg )^2 / 6.96 * 10^8 m
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----------------------------- G = gravitational constant
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----------------------------- Mass of the Sun = 1.99*10^30 kg
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----------------------------- Radius of the Sun = 6.96 * 10^8 m
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----------------------------- E = 3.8 * 10^ 41 kg * m^2 / sec^2 = 3.8 * 10^41 joules = the energy with gravitational collapse only
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------------------------ Joule = work = force * distance = mass * acceleration * distance
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----------------------------- Joule = kg * m^2 / sec^2
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- Therefore, gravity alone is 1000 times too little to be the only energy source for the Sun. There must be another source of energy. There is and it occurs at the core of the Sun where the gravitational pressure has created temperatures of 15,000,000 degrees Kelvin.
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- At those temperatures, and corresponding pressures, hydrogen atoms fuse into helium, almost. Almost, because the mass of the helium atom is a little bit less than the four hydrogen atoms combined and that little bit extra gets converted into energy according to E = m* c^2.
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----------------------------- The mass of four hydrogen atoms = 6.693 * 10 ^-27 kg
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----------------------------- The mass of one helium atom = 6.645 * 10 ^-27 kg
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------------------------ The extra mass that is converted into energy = 0.048 * 10^-27 kg
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- This mass is a small fraction, only 0.7% of the starting mass but it is enough to create enormous energy. See footnote (2) for more details on this nuclear reaction.
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----------------------------- E = m * c^2
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----------------------------- E = 0.048 * 10^-27 kg * 8.99 * 10 ^16 m^2/sec^2
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----------------------------- E = 4.3 * 10 ^-12 joules.
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- OK, that does not look like much energy, 4.3 * 10 ^-12 joules. But, there are 10 ^34 hydrogen atoms, or protons, interacting every second in the core of the Sun. So, this adds up fast.
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- 4.3 * 10^ 22 joules per second of energy from the burning of hydrogen. Recognize that burning is a misnomer but none the less used to describe these thermonuclear reactions.
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- The total luminosity, or energy emitted from the Sun, is 4 * 10^26 joules per second. This total energy emitted at the surface is a combination of nuclear fusion energy and gravitational energy.
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- Our Sun burns 600,000,000 tons of hydrogen every second. 4,000,000 tons of hydrogen is converted into energy every second. The surface of our Earth receives the equivalent of 4.5 pounds of this converted energy every second.
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- Larger stars have additional energy sources including helium burning, carbon burning, and iron burning to create their enormous energies.
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- The Sun is powered by gamma rays. This all starts when the gravitational pressure forces two hydrogen nuclei together so close the strong force takes over and the nuclei combine. Hydrogen nuclei are protons. So, two protons fuse, overcoming the electromagnetic force of like polarities repelling each other, the strong fuses the protons together in a proton-proton chain reaction.
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- The fusion creates one proton and one neutron plus the decay products of one positron and one neutrino. The positron and an electron annihilate each other to produce a gamma ray. The combined proton and neutron are the nucleus of deuterium.
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- Next the proton and the deuterium combine to form an isotope of helium, Helium-3. Another gamma ray is released. Then the two helium-3 isotopes combine to form Helium-4 with two protons and two neutrons. The two extra protons are released to start the next chain reaction and another gamma ray is released.
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- It is these gamma rays that power the Sun. The gamma rays take 170,000 years to reach the Sun’s surface. They are colliding and interacting with millions of particles along the way. They weaken and loose energy transforming themselves into longer wavelength electromagnetic radiation, X-rays, untraviolet rays, visible light, and infrared light.
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- This transformed radiation is what eventually radiates from the surface of the Sun and what we receive here on Earth.
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- December 14, 2019 2542 22
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--------------------- Sunday, December 15, 2019 --------------------
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