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homework5sol - Key for AST3018 HW 5 21 Points Leah Simon 7...

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Key for AST3018 HW 5 21 Points Leah Simon 7 Dec 2009 9.1 (3 pts) a.) For the gravitational potential energy of the Sun, use: E G = 3 GM 2 5 R , (1) Where M is the mass of the Sun, and R is the radius of the Sun. Then we find E G = 2.3 × 10 48 ergs = 2.3 × 10 41 Joules. b.) For the gravitational potential energy of a black hole, with mass M Sun , we must first calculate the radius of the black hole. The effective radius of a black hole is called the Schwarzschild radius: R S = 2 GM c 2 (2) Which gives R S = 3 km. Then using equation (1), we find E G = 5.3 × 10 53 erg = 5.3 × 10 46 Joules. 9.4 (3 pts) Start with the gravitational energy from equation (1): E G = 3 GM 2 5 R (3) We know M = 10M sun and also know that L M 3 . 5 for main sequence stars meaning L = 3160 L sun . Estimate the radius from Appendix E to be 5 R sun Plug into t = E L we find t = 3.63 × 10 12 sec = 1.15 × 10 5 years. 9.6 (2 pts) The amount energy released by the core of the Sun must equal its Luminosity. Therefore we can use Einsteins famous equation E = mc 2 , except in our case 1
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L = mc 2 where m is in units of kg /s. Plugging in L
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