21st Century Astronomy
21st Century Astronomy
6th Edition
ISBN: 9780393428063
Author: Kay
Publisher: NORTON
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Chapter 14, Problem 44QP
To determine

The time period up to which sun would emit energy.

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if the nuclear fusion reaction of converting 4 H → He occurs at anefficiency of 0.7%, and that mass is converted into energy accordingto the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2)in years if the Sun (⊙) has a surface luminosity L⊙ = 3.839×1033erg. Assume the Sun’s core (10% of the total mass) is convertedfrom H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 g
The Sun’s luminosity (or power) is 4 x 1026 Watts (=J/s). How many kilograms of hydrogen must be fused every second to maintain this luminosity? (hint: work backwards from the energy per second to the mass released to the amount of hydrogen required, using the results from the previous question.) The Sun’s mass is ~2x1030 kg. If 10% of this is Hydrogen available in the core, how long will the Sun be able to continue fusing hydrogen at this rate? This is considered the Sun's "lifetime". If the Sun is 4.6 billion years old (and assuming it's power output is constant), how many years does it have left?
The Sun is estimated to have about 5.00 billion years left in it’s “normal” (main sequence) lifetime. Assume the average “burn” rate that you computed in question #1, what % of the Sun’s current mass will have been converted at the end of it’s estimated 5.00 billion years of additional life? Actually, the Sun will lose more mass due to the solar wind, CMEs, the neutrio flux etc. the answer to number one was 3.683x10^14
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