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Celestial Distances A Galaxy 150 Million Light Years From Earth
February 14, 2006 Astronomy 2010
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Distance and Motion of Stars
To infer luminosity, mass, and size from observations we need to know the distance to a star. Distance units for stars: light year (LY): distance light travels in one year 1 LY = 9.46 x 1012 km Rigel 775 LY, Betelgeuse 1,400 LY Proxima Centauri 4.2 LY nearest parsec: 1 pc = 3.26 LY Motion of the star relative to the Sun (Ch. 16): radial motion: star moves along line of sight proper motion: star moves across celestial sphere February 14, 2006 Astronomy 2010
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Stellar Distances How can we measure such great distances?
We use several techniques, useful at different scales, with each scale connecting to the next, like the steps of a ladder. Precise determination of the metre. Radar measurements of distances to planets to determine the astronomical unit (AU). Parallax measurements of nearby stars Variable stars H-R diagram Red shift and supernovae (later chapters) February 14, 2006 Astronomy 2010
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Parallax Effect wavy motion: parallax effect period of 1 year
distance to star is 6.0 LY type M straight line is the star's proper motion February 14, 2006 Astronomy 2010
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What is Parallax? nearby star appears to move back and forth compared to more distant stars Barnard's star: 6.0 LY parallax depends on distance use it to measure distance February 14, 2006 Astronomy 2010
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Parallax on the Earth View object from 2 vantage points
Determine distance using trigonometry Object appears to shift positions compared to the far off background Angular shift, called the parallax: angle of a triangle and the distance between the two vantage points is one side of the triangle how far away is the tree? measure baseline distance B with a meter stick measure parallax angle p use trigonometry to derive distance February 14, 2006 Astronomy 2010
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Parallax for Stars Need Earth-Sun distance View Sun and Venus
why we need A.U. View Sun and Venus measure Venus-Earth distance using radar measure angular distance between Sun and Venus in 1st quarter phase use trigonometry to derive Earth-Sun distance Now you know how far Earth travels in year – baseline distance February 14, 2006 Astronomy 2010
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Parallax Distance measure angular shift p
know baseline distance (1 AU) trigonometry star distance d February 14, 2006 Astronomy 2010
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Parsecs Distances to the stars in units of astronomical units are huge, a more convenient unit of distance called a parsec is used abbreviated “pc”. parsec = distance of a star that has a parallax of one arc second using a baseline of 1 astronomical unit. 1 parsec = 206,265 AU = 3.26LY. Nearest star is ~1.3 parsecs from the Sun. February 14, 2006 Astronomy 2010
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Trigonometry Use basic trigonometric relations.
Used by modern surveyors to measure great distances (also called surveyor's method). d : distance b : baseline p : angle b p d February 14, 2006 Astronomy 2010
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Parallax at Large Distances (but not too large)
For Earth-based measurements one can write: d = (1AU) / tan(p), Where angle p is the parallax measured in arc seconds And d is the distance in parsecs. The farther away the object is, the less it appears to shift. Since the shifts of the stars are so small, arc seconds are used as the unit of the parallax angle. 3,600 arc seconds in just one degree. The ball in the tip of a ballpoint pen viewed from across the length of a football field is about 1 arc second. February 14, 2006 Astronomy 2010
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More parsecs Conversion of parsecs to LY
1 parsec = 3.26 light years. Which unit to use to specify distances: a light year or a parsec? Both are fine and are used by astronomers. Using a parsec for the distance unit and an arc second for the angle, we can express the relation between distance and parallax in the simple form: p = 1/d and d=1/p February 14, 2006 Astronomy 2010
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What about more distant stars?
parallax fails for stars > 1000 LY away baseline of 1 AU is too small Variable Stars: Cepheids and RR Lyrae The luminosity of these stars can be determined by measuring the time it takes them to vary in brightness. Apparent brightness and luminosity tell us the distance. Outline What are Cepheid Variable Stars? Why do they vary? How is their variation related to luminosity. February 14, 2006 Astronomy 2010
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Cepheid Variables large yellow pulsating stars first: Delta Cephei
Discovered by John Goodricke in 1784 magnitude changes over 5.4 day cycle hundreds known periods range from 3 to 50 days average luminosities are 1,000 to 10,000 LSun February 14, 2006 Astronomy 2010
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Cepheid Variable Stars
luminosity time Polaris, the North Star, is a Cepheid Variable variation of 10% of magnitude (10% of luminosity) period of 4 days pulsation decreases over time Cepheid variable stars are in a flickering phase of life February 14, 2006 Astronomy 2010
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Why Cepheid Variables Vary
pulsations: changes in color and spectral class temperature varies doppler shift of spectra size varies luminosity changes when temperature and area change cloud pressure from hot gas weight from gravity normal stars: balance of pressure and gravity variable stars: pressure and gravity out of synch February 14, 2006 Astronomy 2010
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Period – Luminosity Relationship
Henrietta Levitt (1908): systematic search found many Cepheid variables including hundreds in the Magellanic Clouds The Magellanic Clouds are nearby “dwarf” galaxies All stars in the Magellanic Clouds are roughly same distance away -- like observing the Moon from Earth found: brighter Cepheids have longer periods Calibrate distance scale: nearby Cepheid Variables within parallax distance February 14, 2006 Astronomy 2010
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150 Million Light Years away
February 14, 2006 Astronomy 2010
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February 14, 2006 Astronomy 2010
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Distance from Spectral Types
close star (within our galaxy) – parallax variable star – if you find one alternative: spectral class + HR diagram spectrum temperature spectral lines broad classes supergiants bright giants giants subgiants main sequence HR diagram luminosity luminosity distance February 14, 2006 Astronomy 2010
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Summary Determine the metre
Use the metre to determine the astronomical unit (AU) Use the AU and stellar parallax to measure stars out to about 300 LY with satellite measurements, like Hipparcos Use the period-luminosity relationship for variable stars to measure distances out to 100million LY. Calibrate with nearby variables. Often the distance measured is to a cluster of stars or another galaxy. February 14, 2006 Astronomy 2010
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Summary (cont’d) For distant stars that are not variable and don’t have a nearby variable star, use the temperature - luminosity relation of the H-R diagram. Does require some work to determine if the star is main sequence, dwarf, or giant. Later we will see the use of red shift and supernovae to measure the largest distances. February 14, 2006 Astronomy 2010
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Discussion Question How would you explain how far away even the nearest star is to your Mother/Father/Sister/Brother? February 14, 2006 Astronomy 2010
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