Download Celestial Distances

Chapter 18:
Celestial
Distances
A Galaxy
150 Million Light Years
From Earth
February 14, 2006
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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.
1. Precise determination of the meter.
2. Radar measurements of distances to planets to
determine the astronomical unit (AU).
3. Parallax measurements of nearby stars
4. Variable stars
5. H-R diagram
6. 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).
b
d
tan p
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 d=1/p
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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.
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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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luminosity
Cepheid Variable Stars
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
pressure
from hot
gas
cloud
weight
from
gravity
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 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 observing
the Moon from Earth
 found:
brighter Cepheids have
longer 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 (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.
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Discussion Question
 How would you explain how far away even the
nearest star is to your
Mother/Father/Sister/Brother?
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