112http://stardate.org/radio/program/delta-lyrae3 Explain what is meant by the parallax of a star, how wemeasure it and use it to find the distance to a star. Define brightness, parallax effect, arc second, parsec, apparentmagnitude, absolute magnitude.Describe the methods used to determine: temperature,luminosity, radiusLearning goals:4Questions:Questions:Which stars are the brightest?Which stars are putting out the mostwatts? (energy per second)NEED TO KNOW:NEED TO KNOW:DistancesThe most fundamental andaccurate (within a certain range)means of finding distances ismeasuring the parallaxes of stars.25You already know about the parallax effect:http://video.google.com/videoplay?docid=976314958746443105#docid=-871826109299127679• Define brightness, parallax effect, arc second, parsec, apparent magnitude, absolute magnitude6Definitions:Definitions:Arc Degree, Arc Minute, Arc Second• Define brightness, parallax effect, arc second, parsec, apparent magnitude, absolute magnitude7Define 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? ANSWERS: 360, 60, 60, 3600; 1,296,0002 pi; 206,265 arc sec/rad8PARSEC: 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 Unit• Define brightness, parallax effect, arc second, parsec, apparent magnitude, absolute magnitudeSmall angle formula for distance in AU’s:39 Works accurately for stars within about200 pc (Hipparchos satellite) Biggest problem: measuring the minisculeshift of a star against more distant stars• Define brightness, parallax effect, arc second, parsec, apparent magnitude, absolute magnitude! 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 ly10Define parallax11Depends On:• Distance• LuminosityHow the star looks to US HERE ON EARTH.• Define brightness, parallax effect, arc second, parsec, apparent magnitude, absolute magnitude10 times farther away100 Watt 1000 Watt1 Watt! 1000times farther away2 x farther away, 1/4 as bright3 x farther away, 1/9 as brightInverse square law:12 Every 5 magnitudesdifference means 100 xdifference in brightness One magnitude differenceis 2.512 times in brightness.(2.5125 = 100)• Define brightness, parallax effect, arc second, parsec, apparent magnitude, absolute magnitude413When you see only “magnitude,” that means APPARENT magnitude.1. The magnitude (m) of star A is 1, the magnitude (m) of star B is6. 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 isstar D than star C? (Or, equally stated, how many times dimmeris star C than star D?)a) 10 b) 24 c) 100 d) 10,0003. The Sun is the brightest star in the sky, with an apparentmagnitude of about -26.5 Sirius is next in line, with an apparentmagnitude of -1.5; how many times brighter is the Sun thanSirius?a) 25 b) 28 c) 100,000 d) 10,000,000,00014Absolute magnitude is the apparent magnitude a star would haveif its distance = 10 parsecs.Relates luminosities: Stars placed on common scale.Smaller the absolute magnitude number, the more luminous thestar.! m " M = 5log(dpc) " 5M = m " 5log(dpc) + 5• Define brightness, parallax effect, arc second, parsec, apparent magnitude, absolute magnitude15! m " M = 5log(d) " 5d = 10m "M +55! distance in parsecs =10 RAISED TO THE POWER OF m " M + 55# $ % & ' ( 16Main Sequence Star (dwarf) VSub-Giant IVGiant IIIBright-Giant IISupergiant IWe estimate the luminosityof a star by measuring howbroad the absorption lines arein its spectrum.At a given temperature, theless luminous stars haveatoms colliding a lot morethan in the giant stars.• Describe the methods used to determine: temperature, luminosity, radius517LuminosityHighLowTemperatureHighLow18Tutorial: Apparent and Absolute Magnitudes19Depends on•Size (radius, R)•Temperature! L = 4"R2( ) #T4• Describe the methods used to determine: temperature, luminosity, radius! R "LT4=1T2L! T "LR24=1RL4. . . or if you know the luminosity:20( ) 442TRL!"=Put luminosity and radius and temperature together with reasoning:1. Rigel is much more luminous than Sirius B, even though theyhave the same temperature. Which star has the greater surfacearea? A) Rigel B) Sirius B C) not enough information2. Two stars have the same luminosity but one is larger than theother. Which star has the higher temperature?A) the smaller star B) the larger star C) not enough information3. The stars Rigel and Betelgeuse have the same luminosity, but thetemperature of Betelgeuse is much lower. Which star has thegreater surface area? A) Betelgeuse B) Rigel C) Help!621Learning goals:Describe the 3 kinds of binary star systemsSpectroscopic binaryVisual binaryEclipsing binarySummarize the basics of how the mass of a star is foundState what an H-R Diagram is and why the information inferredfrom it is important to the study of starsExplain what is meant by the mass-luminosity relationship andwhy the “main-sequence” for stars is significant22The orbit of a binary star system depends on gravity and the extentto which one star can accelerate the other: a = F/m.ABC•Describe the 3 kinds of binary star systems23Center of Mass in a Binary Star System•Describe the 3 kinds of binary star systems24Spectroscopic BinaryWe determine the orbit by measuring the Doppler shiftsof the stars.•Describe the 3 kinds of binary star systemsObserving Star B (not A)725Real observations of one of thesets of stars of Mizar - Mizar AAhttp://www.nofs.navy.mil/projects/npoi/science/mizarmov.gifVisual Binary26Eclipsing BinaryWe measure periodic eclipses. For eclipsing binaries, wealso get a direct measurement of the radii.•Describe the 3 kinds of binary star systems27Direct mass measurements are possible only forstars in binary star systems.! p2=4"2Ga3M1+ M2( )M1+ M2( )=4"2Ga3p2 p = period (seconds) a = average separation (meters)Masses will be in kilograms•Summarize the basics of how the
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