Astro 210 Exam 2 Front Page

# Astro 210 Exam 2 Front Page - kg R ⊙ = 7 × 10 8 m R...

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Astronomy 210 Spring 2011 HOUR EXAM 2 1. DO NOT OPEN THIS EXAM UNTIL INSTRUCTED TO DO SO. 2. Write you name and all answers in your test booklet. Turn in everything: your booklet, and the questions. 3. Show all of your work in the test booklet, and indicate clearly your Fnal answer! A correct Fnal answer may not receive credit if no work is shown. 4. Budget your time! Don’t get stalled on any one question. 5. ±or your reference there are formulas below. Many of these constants and formulas you will not need for this exam! Possibly Useful Formulae Astronomical Unit: 1AU = 1 . 5 × 10 11 m. gravitational constant : G = 6 . 7 × 10 11 m 3 kg 1 s 2 speed of light: c = 3 . 0 × 10 8 m s 1 Stefan-Boltzmann constant: σ = 5 . 7 × 10 8 W m 2 K 4 Planck’s constant: h = 6 . 6 × 10 34 J s = 4 . 1 × 10 15 eV s electron Volt: 1 eV = 1 . 6 × 10 19 J Boltzmann constant: k = 1 . 4 × 10 23 J K 1 mass of the proton: m p = 1 . 7 × 10 27 kg M = 2 . 0 × 10 30 kg M Earth = 6 . 0 × 10 24 kg M Jupiter = 1 . 9 × 10 27
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Unformatted text preview: kg R ⊙ = 7 . × 10 8 m R Earth = 6 . 4 × 10 6 m R Jupiter = 7 . × 10 7 m L ⊙ = 3 . 8 × 10 26 Watt T ⊙ = 5800 K age of Sun ≃ 4 . 6 × 10 9 yr v F = mva v L = mv r × v p V circ = 2 πr/P = ωr a c = V 2 /r v F = Gm 1 m 2 /r 2 ˆ r PE = − Gm 1 m 2 /r V 2 circ = GM/r a 3 AU = P 2 yr a 3 = GMP 2 / 4 π 2 λf = c E γ = hf = hc/λ θ dif = 1 . 22 λ/D λ max T = 2 . 9 × 10 − 3 m K F = dE/dt A F = σT 4 L = 4 πR 2 F T = [(1 − A ) / (2 or 4)] 1 / 4 ( R ⊙ /d ) 1 / 2 T ⊙ = (332 or 279 K)[(1 − A ) /d 2 ] 1 / 4 V 2 esc = 2 GM/R V 2 rms = 3 kT/μ V esc ≥ 6 V rms to retain gas F tide = 2 GMmR/d 3 R Roche = 2 . 4( M/m ) 1 / 3 r m = 2 . 4( ρ M /ρ m ) 1 / 3 R M n = n e − λt t 1 / 2 = ln 2 /λ NOTE: the above symbols may have di²erent meanings in di²erent equations!...
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