Reminders Website http starsarestellar blogspot com Lectures 1 18 are available for download as study aids Reading You should have Chapters 1 16 and 18 read Read Chapters 19 by tomorrow Homework The homework 5 is due Wednesday July 1st Final Exam This Thursday Bring a SCAN TRON 882 form Chances to review Discussion Mon and Tue 1 2 and Wed 9 10 Wednesday s class will be open for questions Final Exam The final is Thursday July 2nd in class Don t be late The test will cover Chapters 1 16 and 18 19 with a STRONG EMPHASIS on Chapters 9 16 18 and 19 It will consist of 50 questions and you will have until 12 o clock to complete it The test is true false and multiple choice Make sure you have a SCAN TRON 882 form and a 2 pencil I will NOT have these available in class Bring your student ID The test is closed book closed notes and no calculators There will be a sheet of equations available A practice final is available Take the practice test for 1 5 hours and see how you do EXTRA CREDIT Get 1 extra percentage point for each mistake you find on the practice test The Age and Shape of the Universe Today s Lecture Chapter 18 pages 428 453 Hubble Time Geometry of the Universe Fate of the Universe for different geometries Dark Energy Hubbles s Law V H0d H0 H naught Hubble s constant now but it changes with time H0 71 4 km s Mpc Hubble s constant is for now and doesn t tell you anything about the past or future This does NOT imply that the speed of a given galaxy increases with time Velocity increases with distance By fitting a line we find that All galaxies are moving away from us Are we the center of the Universe s expansion NO There is no unique center Simple analogy a rubber band with dots drawn on it 1 cm 2 cm 2 cm 4 cm Now stretch the rubber band For any given dot it appears as if everything is expanding from it Another good analogy is the expansion of a balloon with stickers on it What is the universe expanding into A 4th physically inaccessible dimension Expanding coordinate grid Linear relationship between speed and distance is consistent with no center As the expansion continues the average density of the Universe decreases R the scale factor is getting larger with time R can be thought of as the average distance between galaxy clusters Going backward in time to R 0 the density and temperature must have been REALLY high BIG BANG But when did it occur Estimating when the Universe began If V constant the d Vt but sense V H0d d V x 1 H0 VT0 This gives us the Hubble Time T0 1 H0 Examples If H0 50 km s Mpc then T0 20 Gyr If H0 71 km s Mpc then T0 13 7 Gyr But this is just an estimate because it assumes a constant speed The Hubble Time is an upper limit The Hubble Time assumes a constant speed with time If speed is decreasing with time because gravity is slowing down the expansion then you have actually gone further at earlier times The age of the Universe must therefore be smaller than T0 But coincidentally the addition of Dark Energy makes T0 a very good approximation we ll discuss this later The Hubble Time is an upper limit If the speed is decreasing with time then the age t0 T0 R R Big Bang Big Bang now 0 t0 T0 now t 0 T0 t0 t Measuring distances to galaxies 1 Angular size approximate 2 Apparent brightness b L 4 d2 If you know L and measure b then you can calculate d Some objects have known L Cepheids supergiants globular clusters novae galaxies especially Type Ia SNe These are the standard candles Measuring and applying H0 Obtain distances and redshifts of many galaxies at different distances determine H0 Then 1 H0 is the maximum possible age of the Universe Also knowing H0 we can deduce distances of distance galaxies Problem must account for deviation from the Hubble flow uniform expansion to measure H0 accurate for example we are falling into the Virgo cluster of galaxies Cosmological Principle Mathematically study cosmic expansion with Einstein s General Theory of Relativity Assumptions Uniform On largest size scale Universe is homogenous same average density and isotropic looks the same in all directions This uniformity of the Universe is called the COSMOLOGICAL PRINCIPLE Evidence The largest structures appear to be superclusters Cosmic black body radiation is the same everywhere we ll discuss this later Note Average density of the Universe can change with time A Uniform Universe Homogenous same average density Isotropic looks the same in all directions Homogenous but NOT isotropic matter lined up Homogenous and isotropic Einstein s infamous Cosmological Constant It used to be thought that the Universe was static Hubble hadn t discovered expansion of the Universe yet Galaxy 1 Einstein needed an anti gravity make the Universe static Once Hubble made his discovery Einstein called the biggest blunder of his career Gravity Galaxy 2 Temporarily assume 0 The expanding universe decelerates because of gravity Three possibilities that depend on the average density of matter and energy in the Universe average Depend M average critical where critical 3H02 8 G 9 5 x 10 30 g cm3 for H0 71 km s Mpc If M 1 Expansion eventually reverses Big Crunch If M 1 Expansion stops at t infinity If M 1 Expansion never stops completely Spatially flat M 1 Described by Euclidean geometry Given a line blue and a point there is ONE parallel lines green Simplest case infinite in volume also called open but could be finite Expands forever but just barely v 0 as t Critical Universe average critical Positive curvature M 1 Described by spherical geometry Given a line blue and a point are NO parallel lines green Finite in volume closed but had no boundaries no edge Like the surface of a sphere but in 3 dimensions called a hyper sphere Expansion slows down and ends with Big Crunch average critical Negative curvature M 1 Described by hyperbolic potato chip geometry Given a line blue and a point there are infinitely many parallel lines green Simplest case infinite in volume open but could be finite Expands forever asymptoting to a constant v v constant as t average critical Flat Area r2 Spherical Hyperbolic r2 r2 How to measure M 1 Measure average density and then compute M ave crit See if M 1 1 or 1 2 Measure expansion rate long ago see how fast the Universe is decelerating talk about later 3 Measure geometrical properties of the Universe a Sum of angles in a triangle not practical b Parallel lines not practical c Count the number of galaxies as a function of distance V 4 3 r3 if flat If double the distance then 8 times
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