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Lecture 5 Outline • Einstein’s “Theory of Gravity” • Discussion about Size and Shape of the Milky Way • Lecture on Size and Shape of the Milky Way – Curtis’ Method – Shapley’s Method – Whom would you believe? • Providing Feedback Einstein Principle of Equivalence Acceleration pulls you down No Gravity!! ONLY acceleration Need New Theory of Gravity, "General Relativity" Difference between Newtonian Theory of Gravity and General Theory of Relativity • Newtonian: The Sun creates a gravitational field that exerts a force upon the Earth, which, in turn, causes it to orbit around the Sun rather than move in a straight line • General Relativity: The Mass-Energy Distribution of the Sun changes the geometry of space-time. The Earth is in free motion (no forces acting on it!) and travels on a geodesic of space-time. But because space-time is curved around the Sun, the Earth orbits the Sun. From the Special Theory of Relativity to the General Theory of Relativity Newtonian Mechanics – 3 space coordinates -- no time coordinate no relation between event 1 and event 1 need the Special Theory of Relativity need frames of reference -- need Lorentz Transformation However: Galaxy is accelerating due to -- other galaxies around it -- expansion of the Universe “Acceleration” is due to “forces” Include “forces” into the Theory of Special Relativity General Theory of Relativity Task of General Relativity Couple Geometry to the Mass distributions and motions How does matter affect the Geometry of Space-Time? How do particles move in this Geometry? (no forces!) 8G Gij 2 Tij c Stress Energy Tensor Geometry described by Robertson Walker Metric A constant dr 2 2 2 2 2 dS c dt R (t ) r d sin d 1 kr2 2 2 2 2 Test of General Relativity Eclipse in 1917 • • Curvature strongest in vicinity of dense and massive objects (black holes are theoretical playgrounds for relativity people) Einstein Ring The Castle on the Mall in Washington, D.C., as viewed from the Natural History Museum Now we place a black hole with the mass of Saturn over the middle of the Mall, and view the Castle through the resulting gravitational lens. Questions of Antiquity & Today • • • What is the Cosmos that we live in? What is our Position in the Cosmos? What is the fate of our Cosmos? Still quite an Art to explain this. Today’s Lecture again. Last third of course _____________________________ cos·mos (kŏzʹməs, -mŏs´, -mōs´) 1. 2. 3. The universe regarded as an orderly, harmonious whole. An ordered, harmonious whole. Harmony and order as distinct from chaos. And the Saga continues Cosmologies based on Observations and our Understanding No Planets – Wondering Star Flat Earth Geocentric Heliocentric Stars = Suns Galaxy Also kept changing More spheres were added Model was refined Model & Theory Applies only to our Solar system Solar System and other Stars embedded in our Galaxy Clusters of Galaxies All Galaxies, luminous and dark matter as far as we can see next Horizons are Broadened -orSize of Universe increases Horizons are Broadened -orHuman Understanding increases? Broadening Horizons? Earth? Solar System? Galaxies? Universe? ???? http://antwrp.gsfc.nasa.gov/diamond_jubilee/debate.html Great Debates in Astronomy The Scale of the Universe (1920); Curtis, Shapley The Distance Scale to Gamma-ray Bursts (1995); Paczynski, Lamb The Scale of the Universe (1996); Tammann, van den Bergh The Nature of the Universe (1998); Peebles, Turner The Milky Way Galaxy roughly looks like this Side view of our Galaxy Top View of our Galaxy Position of the Earth & Side View of Galaxy Discussion • How could you determine the Shape and Size of the Universe? • Let’s start with the Shape and Size of the Milky Way… 360o Picture of the Milky Way How can we determine the Size and Shape of our Universe? Mid 17th Century Thomas Wright: Two concentric spheres outside the solar system that incorporate all the stars. Milky Way = band of stars; perpendicular less stars Look around you band of stars puts sun in the middle Kant – end of 17th Century faint fuzzy nebulae are “Island Universes of stars sort of like our Solar System” philosophized --- Parsons 72 inch telescope “nebulae” of stellar systems How can we determine the Size and Shape of our Universe? Mid 18th Century Herschel: Count stars in all directions using telescope Assume uniform stellar density more stars imply “larger” in that direction estimate distances to “edge” Get better telescopes – more data size of universe Increased slightly How can we determine the Size and Shape of our Universe? Turn of Century Dutch Astronomer Kapteyn used parallax to determine distances to nearest stars. calibrate distances combine with data on star counts more quantitative model (often regarded as the first real model of the universe) 10 kpc in diameter by 2 kpc in thickness (Or 30,000 by 6,000 lyrs) Number Counts and the Kaptyn Universe (Sun in the Center) 10 kpc Curtis – Shapley Debate, ~1920 • How BIG is our Universe? • What is the overall SHAPE of our Universe? • What are the “Spiral Nebulae”? Opponents were chosen to represent differing views Curtis • Look at Nova Novae – brightening by ~8 mag sudden onset of H and He burning on the surface of the white dwarf All Novae have roughly the same Light Curve and Brightness at Maximum What is special about Novae? Get distances to “nebulae” Can figure out their luminosity at maximum brightness (M) Measure brightness (m) Get distance modulus (m-M) ==> Get distance! m M 5 log D 5 Apparent magnitude Absolute Magnitude Distance Curtis – blue stars & novae Curtis Claim • Galaxy Size ~ 10 kpc x 2kpc (small Galaxy, same as Kapteyn) use data on star counts & parallaxes and spectral types and intrinsic brightness of blue stars • Sun at the Center of flat lens Also Sun • “Spiral Nebulae” are outside our Galaxy • “Spiral Nebulae” are systems of stars, i.e., other galaxies • Slipher’s spectroscopic measurements high radial velocities • Showed photos of spiral nebulae – with absorbing bands What are Globular Clusters? Shapley was leader on studying globular clusters Detecting the Expansion of the Universe Method employed by Hubble: Use Cepheid Variables in Globular Clusters Method still used today What are Cepheid Variables? • "Pulsating Stars“ • A phase in the life of massive stars: – – Unstable Stars (not in Hydrostatic Equilibrium) He-burning core, on their way to becoming a giant (supergiant) star the second time around Distances and Cepheid Variables What are Cepheid Variables? • "Pulsating Stars" • Unstable Stars (not in Hydrostatic Equilibrium) • He-burning core, on their way to becoming a giant (supergiant) star the second time around How do you get their Luminosity? Period Luminosity relationship Big stars pulsate slowly, Small stars pulsate fast Measure Period Get Luminosity Measure m Calculate m-M Calculate distance… What is special about these stars? Can figure out their luminosity (M) Through Period-Luminosity Relationship Measure brightness (m) Get distance modulus (m-M) ==> Get distance! m M 5 log D 5 Apparent magnitude Absolute Magnitude Distance Procedure • • • • • • • • Take picture after picture Compare brightness of stars Find variable stars Re-observe those stars night after night Plot magnitude against time of observation Get period Deduce luminosity Determine distance modulus, then distance ==> very tedious Distributions of Globular Clusters (Bohlin) Globular Clusters – Shapley Claim • Galaxy Size ~ 100 kpc (large) (10 times larger than Kaptyn) • Center of Galaxy shifted by 20 kpc • BIG == The Galaxy is our entire universe!! Also • Galaxy contains “Spiral Nebulae” • Spiral nebulae are “minor objects” of gaseous content • Galaxy is so large that it contains the entire Universe Notes on spiral nebulae • Van Maanen – internal rotational velocities of spiral nebulae • If outside the Galaxy big fast motion (fraction of speed of light) – Thus spiral nebulae must be closer… Why is the Curtis-Shapley Debate important? • Combines philosophical and scientific thought • Uses scientific Methodology to solve the problem (Who produces better data; who gives better interpretations?) Irony of the Debate • Sun moved away from the Center of the Galaxy – Shapley is right • There are other galaxies outside our own – Curtis was right BUT: Both were wrong too about different aspects of the debate. • • Curtis: Novae mostly in Disk -- Dust causes extinction (stars look dimmer than they really are) under-estimate distances Shapley: Cepheids: Wrong Period Luminosity Relation over-estimate distances Problem of Dust and Extinction • Novae appear fainter than they really are – Curtis m M 5 log D 5 should really be brighter light is blocked by dust distance should be farther Problem with Cepheids variables • • Two types of cepheids – Cepheids in globular clusters and in galactic clusters • • Globular clusters are older Galactic clusters are younger metal rich Different period luminosity relationship m M 5 log D 5 Absolute Magnitude is really fainter Distance too large The Milky Way Visual Wavelengths Near IR – Look through the Dust at Old Stars The Final Picture Resolution of the Shapley-Curtis Debate 1924 – Hubble: Use Cepheid Variables in M31 distances Next Big discovery concerning Size of Universe • 1970’s Quasars • Universe expanded by a factor of ten overnight… • 20years later Hubble space telescope HDF Motion away from us • • All galaxies are moving away from us Does this put us at the center of the universe?