- 1720 - How do we know the age of the Sun? How fast is it “ burning” hydrogen? What does how fast it spinning have to do with this?
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----------------- 1720 - How do we know the age of the Sun?
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- That lucky ol’ Sun got nothing to do but roam around heaven all day. Like me, stars too slow down as they get older
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- Can we measure the ages of stars by measuring their spin rates?
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- A star’s age tells us the likelihood if the star’s solar system will support life. Our Sun is 4.6 billion years old out of a 10 billion year lifetime. So it is just right for Earth’s to have a habitable environment.
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- A star’s spin rate steadily slows down over time. Larger, heavier stars tend to spin faster. So, given these variables we would really like to discover the math that relates mass to spin to age.
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- We measure spin rates by detecting a sunspot and timing how fast it moves across the surface of the rotating star. Our Sun’s spin rate is 26 days, a weighted average. The equator of the Sun rotates in 25 days. Near the poles its rotation is 30 days. 26 days is the weighted average for a mass of 2 * 10^30 kilograms. Remember the Sun is a rotating ball of gas.
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- If the star is too far away astronomers can measure a brightness decrease when the sunspot appears then a brightness increase when the sunspot rotates out of view. The Sun’s surface is 5,800 Kelvin, but a sunspot is cooler, 4,000 Kelvin.
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- The dim rate is typically less than 1% the star’s brightness, so, this is a very difficult measurement to make. The Kepler space telescope can do this. ( See Review # 1717 to learn about Kepler).
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- The mass of the Sun is 300,000 times the mass of Earth. Its radius is 696,000 kilometers , or, 109 times the radius of Earth. The Sun’s composition is 70% hydrogen, 28% helium and 2% the heavier elements. The surface temperature is 5,800 Kelvin, but the photosphere above the surface, the gas, is 6,000 Kelvin. Why it is hotter is an on going mystery. The temperature of the Sun’s core is 15,000,000 Kelvin.
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- The luminosity of the Sun is 3.8 *10^26 watts. If we could capture and store it for one second it would meet the Earth’s total energy needs for the next 500,000 years. Only 3,000 watts per square meter of the Sun’s energy reaches Earth’s surface. All the rest goes into space and some other civilizations sees it as a twinkling star.
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- Star’s shine because they are fusion machines, mostly fusing hydrogen into helium. 2 hydrogen ( protons) nuclei are slightly heavier the one helium nuclei ( 2 protons). The 0.7% difference gets converted into energy according to E = mc^2.
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- One kilogram of hydrogen fuses to 993 kilograms of helium. 7 kilograms gets converted into energy, sunshine.
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- So, how do we know the Sun’s age or how long it will live?
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- Back to the fusion and the 0.7% that is converted to energy and the photons leaving the Sun to make it shine. When 4 hydrogen nuclei (protons) fuse into a helium nuclei we can calculate the mass loss:
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----------------------- Hydrogen nuclei = 1.6726*10^-27 kilograms
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----------------------- 4 Hydrogen nuclei = 6.6904*10^-27 kilograms
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------------------------ Helium nuclei = 6.6465*10^-27 kilograms
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-------------------- Therefore the mass loss = 0.0439*10^-27 kilograms
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--------------------- E = mc^3
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--------------------- Energy = 0.0439*10^-27 kilograms * (3*10^8 meters / second)^2
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---------------------- Energy = 3.95*10^-12 Joules
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- Only 10% of the Sun’s mass will be involved in fusion. When the Sun gets to 90% of its current mass its gravity will not be great enough to continue the fusion at its core.
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--------------------- Sun’s Luminosity = 3.8*10^26 watts = 3.8 *10^26 kg * m^2 / sec^2
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--------------------- Mass equivalent to that energy = E / c^2 = 3.8 *10^26 kg * m^2 / sec^2 / ( 3*10^8 m/sec)^2 = 4.2*10^9 kilograms / second
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------------------ 4,200,000,000 kilograms / second is equivalent to the mass of 10 oil tankers each second, or , 600 oil tanker mass each minute. Starting out with 600*10^9 kilograms of hydrogen and 4.2*10^9 kilograms is converted into energy, that is 0.7%. 10^38 individual hydrogen / helium nuclei fusion reactions are occurring each second.
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-------------------- Sun’s mass = 2*10^30 kilograms
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--------------------- 10% = 2*10^29 kilograms.
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-------------------- One gram of hydrogen into helium releases 6 * 10^11 joules.
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------------------- The Sun is “burning” 600*10^9 kilograms of hydrogen every second
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--------------------- There are 3.16 *10^7 seconds in a year.
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-------------------- 600*10^9 kg/sec * 3.16*10^7 sec /year = 1.9*10^15 kg / year
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--------------------- 2*10^29 kilograms / 1.9*10^15 kg/year = 10 billion years.
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- The lifetime of the Sun with fusion at the same rate is 10 billion years, before fusion stops and it turns into a Red Dwarf Star and then a Planetary Nebula. Stay tuned we only have 5 billion more years to wait to see if this is how it turns out.
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RSVP, with comments, suggestions, corrections. Index of reviews available ---
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