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Homework 5 Solutions

# 2x109 kgs x 1 msun2x1030 kg x x 107 syr 66x1014 msunyr

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Unformatted text preview: What is the mass loss rate of the Sun due to fusion in M¤/yr at the current luminosity? How long would it take for the Sun to shrink to zero mass? Mass lost/yr = mass/energy x energy/yr = L/c2 = (3.8x1026 J/s)/(3x108 m/s)2 = 4.2x109 kg/s x (1 Msun/2x1030 kg) x (π x 107 s/yr) = 6.6x10 ­14 Msun/yr (d) [5 pts] Is the mass loss rate due to the solar wind larger or smaller than the mass loss rate due to fusion? From p. 374 in the book, the Solar wind mass loss rate is 3x10 ­14 Msun/yr, which is smaller but of comparable magnitude (e) [5 pts] The Main Sequence lifetime of the Sun is 1010 yr. What fraction of hydrogen is converted into helium, and what percentage of mass is lost by the Sun over this period from fusion and solar wind? Based on answer to b above, 10% of the Sun’s hydrogen in burned in 1010 yr. Over that period, 6.6x10 ­4 Msun of fusion mass is lost and 3x10 ­4 Msun of solar wind mass is lost (assuming the latter is constant) (2) [80 pts] Numerically solving the Lane ­Emden equation. (a) [50 pts] Employing a numerical integrator (see below), compute and compare the density profiles for polytropes n = 1.5 (degenerate/fully convective star) and n = 3 (star in radiative equilibrium). In both cases, plot the ratio of the density to the c...
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