exam1-05-sol

exam1-05-sol - main sequence stars. However, stars of about...

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Astro 346, Spring Semester 2005 Intermediate exam, solutions Problem 1: The lifetime of the sun N = 0 . 7 5 M ± m p ' 4 · 10 57 δE = N 4 δmc 2 ' 5 · 10 52 erg L M 4 L = 625 L ± τ = 0 . 1 δE L ' 2 · 10 15 sec ' 6 · 10 7 years In the red-giant phase I use twice the amount of fuel (hydrogen) and radiate at 16 the rate compared with the main-sequence phase. The lifetime must therefore be a factor of 8 shorter. τ RG ' 2 . 6 · 10 14 sec ' 9 · 10 6 years Red giants have a luminosity a factor of 30 higher, but live a factor of 15 shorter. In a steady state the relative contributions to the total luminosity of a galaxy scale as the the relative contributions to the total radiated energy, so red giants contribute twice as much as
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Unformatted text preview: main sequence stars. However, stars of about one solar mass or less havent had time to turn into red giants, so a steady state is not established and we these stars presently only contribute radiation in the main-sequence phase. Problem 2: The rotational energy of pulsars Angular momentum conservation: n ' R 2 R 2 n ' 4 10 10 The period P n = 2 / n ' 1 . 6 10-10 -1 E = 1 2 I 2 = 1 2 P E n ' 4 10 10 E The energy comes from the gravitational potential energy....
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