Chapter 18: Celestial Distances

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Chapter 18Celestial Distances
A Galaxy 150 Million Light Years From Earth
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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

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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 meter.
• 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)

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Parallax Effect

• wavy motion parallax effect
• period of 1 year
• distance to star is 6.0LY
• type M
• straight line is the star's proper motion

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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

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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

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Parallax for Stars

• Need Earth Sun distance
• why we need AU
• 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

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Parallax ? Distance

• measure angular shift p
• know baseline distance (1 AU)
• trigonometry ? star distance d

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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.

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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
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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.

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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 d1/p

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What about more distant stars?

• parallax fails for stars gt 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.

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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

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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

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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

• normal stars balance of pressure and gravity
• variable stars pressure and gravity out of synch

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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 observingthe Moon
  from Earth
• found brighter Cepheids havelonger periods
• Calibrate distance scale nearby Cepheid
  Variables within parallax distance

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150 Million Light Years away
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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

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Summary

• Determine the meter
• Use the meter 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.

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Summary (contd)

• For distant stars that are not variable and dont
  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.

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Discussion Question

• How would you explain how far away even the
  nearest star is to your Mother/Father/Sister/Broth
  er?