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HW3_SOLUTIONS

# HW3_SOLUTIONS - 1 Assume that the Sun's current...

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1) Assume that the Sun’s current luminosity (3.86 x 10 26 W) has remained constant over the last 4.5 billion years. Also, the current mass of the sun is 1.99 x10 30 kg. a) Estimate how many kilograms of hydrogen the Sun has consumed over the past 4.6 billion years. b) Estimate the amount of mass that the Sun has lost as a result. c) What percentage of original mass has the sun lost over its lifetime? d) In fact, the Sun’s luminosity when it first formed was only about 70% of its present value. With this in mind, explain whether your answers above are an overestimate or an underestimate. 1a) We first need to estimate the amount of energy given off by the sun over its lifetime. We first convert billions of years into seconds to get 4.5 billion years ~1.42x10 17 sec (4.6 billion years ~ 1.45x10 17 sec) t * 10 x 3.86 t 26 = = = L E t E L Over 4.5 billion years, the sun gives off 5.48x10 43 J; over 4.6 billion years, the sun gives off 5.60x10 43 J. We know from class that 26.731 MeV of energy is given off when 4 hydrogen atoms combine into one helium atom. This energy (which is equivalent to 4.2x10 -12 J) can be used to determine how much hydrogen has been converted to helium: Over 4.5 billion years or 4.6 billion years, respectively: kg x m kg x J x H J x kg x m kg x J x m J x H H H 28 4 27 12 43 28 4 27 12 4 43 10 9 . 8 ) 10 67 . 1 ( * 4 * 10 2 . 4 4 * 10 6 . 5 10 3 . 9 ) 10 67 . 1 ( * 4 * 10 2 . 4 * 10 48 . 5 = = - - - - b) This question should have likely been asked before part a, but we can use the equation E=mc 2 to determine the mass lost by the sun over 4.5 or 4.6 billion years, respectively: kg x s m x J x c E m kg x s m x J x c E m 26 2 8 43 2 26 2 8 43 2 10 2 . 6 ) / 10 3 ( 10 60 . 5 10 1 . 6 ) / 10 3 ( 10 48 . 5 = = = = = = Many students solved Part B first and got the change of mass.

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HW3_SOLUTIONS - 1 Assume that the Sun's current...

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