Ast 207 F2005 Oct-08Ast 207 F2008Weighing a Galaxy—31 Oct• Change in syllabus– What are galaxies made of? (Today & next week)– Important events in the history of the universe• Formation of helium (Done)• Universe becomes unionized (Later)• Galaxies and stars form (Later)• Wed, Nov 26: No classAst 207 F2008Test 202550751004 8 12 16 20 24 28ScorePercentileAverage on test 2: 19.7/31 = 64%Average on test 1: 61%4.03.02.01.0Ast 207 F2008AndromedaAst 207 F2008SombreroAst 207 F2005 Oct-08Ast 207 F2008M51Ast 207 F2008M87Ast 207 F2008Galaxy cluster A2218Ast 207 F2008Galaxies• The Milky Way is our galaxy.– The sun is halfway from the center of the Milky Way.– We see the Milky Way as a band of light.• Spiral galaxies are made of– billions of stars–gas– dust– dark matter• The sky is covered by distant galaxies.Ast 207 F2005 Oct-08Ast 207 F2008Weighing a Galaxy• What is the mass of a galaxy?– Answer before 1974: Mass is that of stars & gas– Actual answer: Most mass is not that of star & gas• Most mass is dark• Dark mass is less concentrated.• Today: How to measure massNGC 3672www.astro.princeton.edu/~frei/Gcat_htm/Catalog/CJpeg/n3672.jpgVera Rubin 1928-cwp.library.ucla.edu/images/rubin.1.jpgFritz Zwicky 1898-1974www.astrosurf.org/lombry/Images/zwickyf.jpgb1974: Mass herea 1974: Most mass hereAst 207 F2008Weighing Eros• Near Earth Rendezvous (NEAR) orbited the asteroid Eros (and landed). http://near.jhuapl.edu•Eros– 20mi long, 8mi wide (size of Lansing)• Gravity is 1000 times weaker– You can leap 1000 times farther•½v2=g h– Speed limit is 20mph•v2=g R• On Earth, a ball dropped 1m takes 0.45s. How long would that take on Eros?•½v2=g h; v=g t; t=(2h/g)1/2• t = 0.45s (1000)1/2 =14s1. How can you measure the mass of Eros with the satellite (without landing)?Ast 207 F2008Weighing the Sun• To find mass of sun, measure period T & size R of a planet’s orbit.–Kepler’s3rdLawGM = 4π2R3/ T2–M = R3/ T2for R in AU, T in years, and M in solar masses.2. Under influence of the gravity of the sun, a planet moves a given distance. If the time is short, the mass of the sun is A. greater.B. less. An orbitEarthSunGalaxyTime is shorterDrops 1mA ballEarthErosBehavior if more massiveMotionTest objectMassAst 207 F2008Weighing a Galaxy• To find mass of sun, measure period T & size R of a planet’s orbit.–Kepler’s3rdLawGM = 4π2R3/ T2–M = R3/ T2for R in AU, T in years, and M in solar masses.3. Under influence of the gravity of the sun, a planet moves a given distance. If the time is short, the mass is greater. Write an equivalent statement for the galaxy NGC 3672Year is shorterAn orbitEarthSunGalaxyTime is shorterDrops 1mA ballEarthErosBehavior if more massiveMotionTest objectMassAst 207 F2005 Oct-08Ast 207 F2008Use Doppler effect• Kepler’s Law needs modification since period of sun’s motion around Milky Way is 200 Myr.Mass = R3/ T2= R (R/ T)2Mass = R v2• Doppler effect for measuring speed.– No need to wait to see motion.– Speed is imprinted in the light.Most mass here.not where stars are.Ast 207 F2008Doppler Effect: Measuring velocities• Recall redshift & expansion of U– Wavelength changes b/c U expands– Wavelength changes if light source is moving–v = c (λreceived/ λemitted-1)– If motion is away (v>0),• λreceived> λemitted, redshift– If motion is toward (v<0),• λreceived< λemitted, blueshift• Motion across line of sight cannot be measured with Doppler effect. Key idea.Viewed from here,λ unchanged.Line of sightAst 207 F2008Weighing using Doppler effect• Measure period T & size R of a planet’s orbit to find the mass M–Kepler’s3rdLaw–GM ∝ 4π2R3/ T2–M= R3/ T2for R in AU, T in years, and M in solar masses.•M ∝ R v2– Measure velocity with Doppler effect. Useful in astronomy.– Periods of sun’s orbit is 200Myr.• Under influence of the gravity of a mass, a test object moves a given distance. If the time is short, the mass is greater.1. Alien astronomers want to measure the mass of the sun using the Doppler effect of light emitted by Jupiter. If the mass of the sun is greater, they would measure a shift in wavelength.A. smallerB. biggerYear is shorterAn orbitEarthSunGalaxyTime is shorterDrops 1mA ballEarthErosBehavior if more massiveMotionTest
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