PowerPoint PresentationSlide 2Learning goals:Slide 4Slide 5Slide 6Slide 7Slide 8Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.Slide 10Inverse square law for lightSlide 12Slide 13Slide 14Slide 15Slide 16Define brightness, apparent and absolute magnitudeSlide 18Slide 19Slide 20The H-R DiagramRelationship between absolute magnitude and luminosity - bring in the Sun!LuminositySlide 241QuickTime™ and a decompressorare needed to see this picture.2http://stardate.org/radio/program/delta-lyrae3 Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.Define arc second, parsec. Define brightness, apparent magnitude, absolute magnitude.Describe the methods used to determine the temperature, luminosity, and radius of a star.Learning goals:Learning goals:4Questions:Questions:Which stars are the brightest?Which stars are putting out the most watts? (luminosity = energy per second)NEED TO KNOW:NEED TO KNOW:DistancesThe most fundamental and accurate (within a certain range) means of finding distances is measuring the parallaxes of stars.5You already know about the parallax effect:•Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.Demonstrating parallaxParallax of Stars6Define arc secondHow many degrees in a circle? How many arc minutes in a degree? How many arc seconds in an arc minute?How many arc seconds in a degree?How many arc seconds in a circle?__?__ radians = 360 degrees1 radian = 57.3 degreesHow many arc seconds in 1 radian? 360, 60, 60, 3600; 1,296,000; 2 pi; 206,265 arc sec/rad7PARSEC: Parallax ARc SECondA star having a parallax of 1 arc second is 1 parsec away1 parsec (pc) = 3.26 light years1 kiloparsec (1 kpc) = 1000 pc; 1 megaparsec (1 Mpc) = 1,000,000 pc Baseline is 1 Astronomical UnitSmall angle formula for distance in AU’s:• Define arc second, parsec8 Works accurately for stars within about 200 pc (Hipparchos satellite) Biggest problem: measuring the miniscule shift of a star against more distant stars€ parallax = 0.75 arcsecondsdistance = 10.75=1.3 pc = 4.3 ly€ parallax = 0.15 arcsecondsdistance = 10.15= __?__ pc = __?__ ly€ parallax = 0.0015 arcsecondsdistance = 10.0015= __?__ pc = __?__ ly6.7 22667 2170 ly•Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.9•Explain what is meant by the parallax of a star, how we measure it and use it to find the distance to a star.10Using SIMBAD to find the parallaxes of the stars of Exercise 2QuickTime™ and a decompressorare needed to see this picture.41 Cygni data (partial)Parallax = 4.24 ± 0.16 mas or 0.00424 ± 0.00016 arc secondsDistance = 1/parallax = 1/0.00424 = 236 pc or ~770 ly11Inverse square law for lightInverse square law for lightQuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.p. 49412How the star looks to US HERE ON EARTH.QuickTime™ and a decompressorare needed to see this picture.10 times farther away100 Watt 1000 Watt1 WattsQuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.QuickTime™ and a decompressorare needed to see this picture.€ 1000times farther away2 x farther away, 1/4 as bright 3 x farther away, 1/9 as bright• Define brightness, apparent magnitude, absolute magnitude€ apparent brightness = L4πD2€ apparent brightness = L4πD213 Every 5 magnitudes difference means 100 x difference in brightness One magnitude difference is 2.512 times in brightness.(2.5125 = 100)QuickTime™ and a decompressorare needed to see this picture.• Define brightness, apparent magnitude, absolute magnitude14When you see only “magnitude,” that means APPARENT magnitude.1. The magnitude (m) of star A is 1, the magnitude (m) of star B is 6. How many times brighter is A than B?a) 5 b) 10 c) 100 d) 10002. m of star C is 12, m of star D is 2: How many times brighter is star D than star C? (Or, equally stated, how many times dimmer is star C than star D?)a) 10 b) 24 c) 100 d) 10,000•The Sun is the brightest star in the sky, with an apparent magnitude of about -26.5 Sirius is next in line, with an apparent magnitude of -1.5; how many times brighter is the Sun than Sirius?a) 25 b) 28 c) 100,000 d) 10,000,000,00015Using SIMBAD to find the apparent magnitudes of the stars of Exercise 2QuickTime™ and a decompressorare needed to see this picture.41 Cygni data (partial)V = apparent magnitude through “visual” filterThink of it as mv .QuickTime™ and a decompressorare needed to see this picture.UVIR16Absolute magnitude is the apparent magnitude a star would have if its distance = 10 parsecs.Relates luminosities by “placing” stars on common scale.Smaller the absolute magnitude number, the more luminous the star.€ m − M = 5log10(dpc) − 5M = m − 5log10(dpc) + 5• Define brightness, apparent magnitude, absolute magnitude41 Cygni dpc = 236 parsecsmv = 4.016€ Mv= mv− 5log10(dpc) + 5Mv= 4.016 − 5log10(236) + 5Mv= 4.016 − 5(2.37) + 5 = −2.8What does the answer tell you?17Define brightness, apparent and absolute magnitudeDefine brightness, apparent and absolute magnitude18Supergiant IBright-Giant IIGiant IIISub-Giant IVMain Sequence Star (dwarf) VWe estimate the luminosity of a star by measuring how broad the absorption lines are in its spectrum. At a given temperature, the less luminous stars have atoms colliding a lot more than in the giant stars.• Describe the methods used to determine temperature, luminosity, radius19LuminosityHighLowTemperatureHighLow20Using SIMBAD to find the parallaxes of the stars of Exercise 2QuickTime™ and a decompressorare needed to see this picture.41 Cygni data (partial)F5 Iab21The H-R The H-R DiagramDiagram€ L = 4πR2( ) σT422Relationship between absolute magnitude and luminosity Relationship between absolute magnitude and luminosity - bring in the Sun!- bring in the Sun!€ MSun− Mstar= 2.5log10LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟MSun− Mstar( )2.5= log10LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟10MSun−Mstar( )2.5=10log10LstarLSun ⎛ ⎝ ⎜ ⎞ ⎠ ⎟10MSun−Mstar( )2.5=LstarLSunLstarLSun=10MSun−Mstar( )2.5LstarLSun=104.74 −(−2.8)( )2.5=1070€
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