Ast 207 F2009 Dec-09Ast 207 F2009Weighing the Universe with Supernovae—7 Dec• Final exam– Covers entire course with emphasis on 20thcentury cosmology (Oct 28 to end of term, Hwk 7−10)– One 8.5×11” cheat sheet– Mon, 14th, 3:00-5:00, 1410 BPS (large classroom next door)• Please fill out on-line SOCT http://rateyourclass.msu.edu– Will close when grades are submitted.• Test answers are on angel.• Last class: Review or SOAR Telescope?• Weighing the universe means to find mass density•Why?– What is the universe made of? Is there mass that we cannot see?•How?– Mass in a large sphere surrounding us pulls on a galaxy on the surface– Measure how much the galaxy slows.– Use supernovae to measure the time for the universe to expand.• What we will find: Expansion of universe speeds up!– “Dark energy” is dominant. Dark energy repulse whereas matter and radiation attract.Distant supernovaeRiess et al, 2004, ApJ 607, 665.Ast 207 F2009Cannon Ball• Cannonball is shot out of cannon at speed v.– Kinetic energy is ½ v2.• Gravity pulls on cannonball to slow the motion.– Potential energy is G M /R• Cannonball will escape if shot fast enough so thatKE ≥ PE• Define “Density parameter”Ω = PE / KE = 2 G M / (R v2)1. A cannonball is shot with Ω=0.7. Will the cannonball escape? Same question for Ω=1.1. Do this on your own.A. YYB. YNC. NYD. NNvMRAst 207 F2009 Dec-09Ast 207 F2009Universe & “Density Parameter”• Sphere expands and galaxy moves because universe expands.• Galaxy is moving at speed v.– Kinetic energy is ½ v2.• Gravity pulls on galaxy to slow the motion.– Potential energy is G M /R• Galaxy will escape if moving fast enoughKE ≥ PE• Define “Density parameter”Ω = PE/KE = 2 G M / (R v2)• Use Hubble’s Law v=HRΩ = PE/KE = 2 G M / (R3H2)• Mass/volume is mass density ρ. M=volume ρ = 4/3 π R3ρ.Ω = PE/KE = (8π/3) G ρ / H2.• Does not depend on particular galaxyvMRAst 207 F2009Does universe expand forever?• Density parameterΩ = PE/KE = 8π/3 G ρ / H2.2. If the density parameter Ω=0.7, will the universe expand forever? Do this on your own.A. YB. NvMR1Exam 3• Top 1/10 31/39 (80%)• Top quartile 28/39 (72%)• Median 23/39 (59%)• Bottom quartile 18/39 (46%)20 40 60 80 100Rank5101520253035Exam 3141234910Course grade• Grades are on angel•Includes–Tests– Homework 1-9– Clickers 9/2 – 12/4• Weights adjusted so that weights of tests:hwk:clicker is same as at end of term• Grade curve may change slightly at the end of the term.• Use your grade on angel as guidance. Final exam is 31% of the course grade.857%2.51763%3.02269%3.53176%4.0751%2.0546%1.5840%1.030.0% of classMinGrade2Difficult Problems: (Key idea is underlined.)• 1a. (1 pt.) At the present time, does the value of Hubble’s constant depend on the galaxy in which the observations are made? (2 pts.) Explain your reasoning.– “1/H gives the present age of the universe… If we consider only the present time, 1/H should not change with the galaxy we are observing from.”⎯K Garafoli– We measure the speed v and distance D of another galaxy and findH=v/D. On the other galaxy, the speed and distance of the Milky Way have the same values v and D. Therefore Hubble’s constant isthe same on the other galaxy.– Most incorrect answers addressed different questions.• Does speed depend on distance? Is Hubble’s Law valid on other galaxies?Difficult Problems: (Key idea is underlined.)• 2b. (1 pts.) In the inner part of the galaxy (R<4 kpc), how does the rotational velocity depend on R? (2 pts.) How does the mass enclosed within R depend on R?– The rotational velocity depends linearly on R, v=constant R. v=R (if I leave out the constants)– M(R)=v2R=R3. (Kelper’s 3rdlaw)3Difficult Problems: (Key idea is underlined.)• 3b. (3 pts.) Compute the expansion parameter a of the universe when 0024+1654 emitted the light that we see now.– The key idea is that the wavelength of light expands as the universe. The wavelength of Hβ line expands by the factor 6757/4861=1.39. The universe was smaller by that factor when thelight was emitted. The expansion parameter is 1/1.39= 0.719• 3c. (3 pts.) What was the temperature of the radiation of the Big Bang when 0024+1654 emitted the light that we see now?– The key idea is that the wavelength of light expands as the universe and therefore by Wien’s Law the temperature of the radiation is inversely proportional to the expansion parameter. T=2.7K/a = 2.7/0.719 =
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