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Friday, Oct. 31Syllabus, class notes, and homeworks are at:www.as.utexas.edu  courses  AST 301, LacyReading for this week: chapter 11The Wednesday help session is in GRG 424 at 5:00 (forthe entire semester).Our ScheduleAug 27: Ch 1+App A The Scale of the CosmosSep 3: Ch 2+3 The Sky, Cycles in the SkySep 8: Ch 4 The Origin of Modern AstronomySep 15: Ch 5 TelescopesSep 19: Exam #1, Ch 1-5Sep 22: Ch 6 Starlight and AtomsSep 29: Ch 7 The SunOct 6: Ch 8 The Family of StarsOct 13: Ch 9 The Formation and Structure of StarsOct 20: Ch 10 The Lives and Deaths of StarsOct 24: Exam #2, Ch 6-10Oct 27: Ch 11 Neutron Stars and Black HolesNov 3: Ch 12 The Milky Way GalaxyNov 10: Ch 15 CosmologyNov 17: Ch 16 The Origin of the Solar SystemNov 24: Ch 17 The Terrestrial PlanetsDec 1: Ch 18 The Outer Solar System Dec 5: Exam #3, Ch 10-12,15-19Topics for this weekCompare the two types of supernova: how do they differ inthe cause of the explosion and in what is left behind?Describe neutron stars.Describe pulsars.Why do neutron stars rotate so quickly?Why couldn’t white dwarfs or other stars rotate as quickly?Define ‘escape speed’.Describe black holes.What evidence do we have that there is a very massiveblack hole at the center of the Milky Way?RelativityEinstein showed that Newton’s laws aren’t valid whenobjects move at speeds near the speed of light.When an object moving at nearly the speed of light is givenenergy it doesn’t go much faster. Instead it gets moremassive.He also showed that it is better to look at gravity not as aforce, but as a distortion of space around massiveobjects, making objects that come near massive objectsfollow curved paths.That is his explanation for the fact that Galileo’s two ballsfell together. They were both following the natural paththrough curved space.Black HolesIf massive objects follow apparently curved paths throughspace because space-time is curved by gravity, lightmust also be affected by gravity.In fact, if an object is dense enough that escape speedfrom its surface is greater than the speed of light, lightwill not be able to escape from the object.This is a black hole.The theory of General Relativity says that if a mass M isinside of a radius R withthe mass will all fall to the center, and not even light willever get out.22cRGM=It’s not so badAlthough you need to use General Relativity to calculatethe paths of objects near a black hole, farther away youcan still use Newton’s laws.If the Sun collapsed into a radius of 3 km it would be ablack hole.But the Earth would still orbit it just like it does now.General Relativity give the same predictions as Newton’slaws is long as you are far enough from an object thatthe orbital speed is much less than the speed of light.Gas orbiting around the center of the Milky WayWhen I was a graduate student, I observed ionized gasnear the center of the Milky Way.From the Doppler shift, I could measure the speed of themotion of the gas.The gas closer to the center was moving faster.Gas at about 1.7 pc (5 ly) from the center moves at about100 km/s.Gas at about 1/6 pc (0.5 ly) moves at about 300 km/s.Gas orbits around massive objects according to Kepler’slaws just like solid objects do.Gas orbiting around the center of the Milky WayWe used an infrared emission line of ionized neon toobserve the ionized gas near the center of the Milky Wayand measure its Doppler shift.Gas at about 1.7 pc (5 ly) from the center moves at about100 km/s.Gas at about 1/6 pc (0.5 ly) moves at about 300 km/s.We can use these numbers with Kepler’s 3rd law tocalculate the mass that the gas is orbiting around.M = a3 / P2 and P = (2πa) / vso M = v2 a / (2π)2 (if you use the right units for v and a)Mass in the Center of the Milky Waydistance speed period mass1.7 pc 100 km/s 110,000 yr 4x106 Msun1.0 pc 125 km/s 50,000 yr 3.5x106 Msun0.5 pc 170 km/s 18,000 yr 3x106 Msun0.2 pc 270 km/s 5,000 yr 3x106 MsunThere are lots of stars near there (that’s why the massinside of 1.7 pc from the center is greater than the massinside of 0.2 pc) but there can’t be 3x106 stars inside of0.2 pc.We argued that there is a 3x106 Msun black hole there.But astronomers weren’t convinced that gravity was theonly force causing the gas to orbit.Stars orbiting around the black holeRecently astronomers have observed stars orbiting aroundthe center, and they think that only gravity could makethem orbit.They come to the same conclusion we did.See


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