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Astronomy 350 Cosmology Professor Lynn Cominsky Department of Physics and Astronomy Offices: Darwin 329A and NASA EPO (707) 664-2655 Best way to reach me: [email protected] March 4, 2003 Lynn Cominsky - Cosmology A350 1 Is the Universe really expanding? Take a look at the handout How do you interpret the 3 graphs? Try to draw graphs of a Universe that has Static galaxies (not moving) Turbulent galaxies (random motion) Rotating galaxies (like the planets around the Sun) Uniformly contracting galaxies March 4, 2003 Lynn Cominsky - Cosmology A350 2 Cepheid variables and Nebulae In 1923, Hubble used new Mt. Wilson 100 inch telescope to observe Cepheid variables in the nearby “nebula” Andromeda. He recognized that the fuzzy patches called nebulae were actually distant galaxies, outside of our own Milky Way This relation was calibrated by Hertzsprung and Shapley L =K P1.3 March 4, 2003 Lynn Cominsky - Cosmology A350 3 Hubble Law The Hubble constant Ho = 558 km s -1 Mpc -1 is the slope of these graphs Compared to modern measurements, Hubble’s results were off by a factor of ten! March 4, 2003 Lynn Cominsky - Cosmology A350 4 Redshift and Doppler Shift Redshift z is a non-relativistic approximation that relates the Doppler shift to the velocity of the object Redshift is determined by comparing laboratory wavelength lo to observed wavelength l z March 4, 2003 = Dl lo = l - lo lo Lynn Cominsky - Cosmology A350 = v c 5 Hubble Law v = Ho d = cz where v = velocity from spectral line measurements d = distance to object Ho = Hubble constant in km s-1 Mpc -1 z is the redshift Space between the galaxies expands while galaxies stay the same size March 4, 2003 Lynn Cominsky - Cosmology A350 6 Measuring Distance and Time If the Universe expands at a constant rate v = Hod and d= vt Solving for t, we find the age of the Universe: t = 1/Ho = 9.78 x 109 y h-1 where h = Ho/(100 km s-1 Mpc-1) Current value for Ho is 68 km s-1 Mpc-1 So the age of the Universe is ~14 x 109 y March 4, 2003 Lynn Cominsky - Cosmology A350 7 Expanding Universe Expanding Universe of Students The farther things are, the faster they are moving away Expanding Universe of Dots Why it looks as though you are at the center of the expanding universe March 4, 2003 Lynn Cominsky - Cosmology A350 8 Doppler shifting spectral lines When a star or galaxy is moving, its spectral lines are Doppler shifted by Dl = lobs – llab The redshift Z = Dl/llab The velocity of the star or galaxy is found from the redshift using v = ZAVG c H and K lines March 4, 2003 Lynn Cominsky - Cosmology A350 9 Hubble constant You will plot the velocities (km/sec) vs. the distances (Mpc) that you obtain from a sample of galaxies The slope of this line is known as the Hubble constant – it is given in km/sec/Mpc H = v/D March 4, 2003 Lynn Cominsky - Cosmology A350 10 The age of the Universe The age of the Universe is the inverse of the Hubble constant Age = 1/H = D/v But H must be in the correct units! D must be in km V must be in km/sec This will give you the age of the Universe in seconds To convert to years, divide by 3.15 x 107 March 4, 2003 Lynn Cominsky - Cosmology A350 11 Web Resources CLEA Astronomy Laboratories http://www.gettysburg.edu/academics/physics/clea /CLEAsoft.overview.html Hubble diagram http://physics.ucsd.edu/students/courses/fall2001/ physics5/notes/ch17/sld005.htm Thanks also to Dr. Gordon Spear for providing his Hubble Law Lab spreadsheet! March 4, 2003 Lynn Cominsky - Cosmology A350 12 Web Resources Astronomy picture of the Day http://antwrp.gsfc.nasa.gov/apod/astropix.html Imagine the Universe http://imagine.gsfc.nasa.gov Ned Wright’s ABCs of Distance http://www.astro.ucla.edu/~wright/distance.htm Prof. Pogge’s class notes at OSU http://www-astronomy.mps.ohio-state.edu/~pogge/Ast162/Unit4/nebulae.html March 4, 2003 Lynn Cominsky - Cosmology A350 13