Cosmic Distance Ladder

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Cosmic Distance Ladder

• Whats Up There in the Universe

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Measuring the Distances

• There is no one single method that works in all
  distance scales.
• Measuring the distance is a hard problem in
  astronomy.
• Infact there is succession of methods whose
  domain of validities overlap.
• Each rung of the ladder provides information that
  can be used to determine the distances at the
  next higher rung.
• We need to calibrate each method in the domain of
  overlap.

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Distances of Planets

• Keplers third law give only the ratios of the
  distances
• Although by the 17th century astronomers could
  calculate each planet's relative distance from
  the Sun in terms of the distance of the Earth
  from the Sun, an accurate absolute value of this
  distance had not been calculated.

P2ka3
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Astronomical Unit

• Astronomical Unit (AU) Average distance between
  the Earth and the Sun.
• Appropriate unit for giving distances in the
  Solar System.
• No constant of proportionality if P is measured
  in years and a is measured in AU.

P2a3
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Conjunction
Conjunction two celestial bodies appear near one
another in the sky. Mostly one of the objects is
the Sun and the other is one of the planets
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2004 Transit of Venus

• The duration of such transits is usually measured
  in hours (the transit of 2004 lasted six hours).
• occur in a pattern that repeats every 243 years,
  with pairs of transits eight years apart
  separated by long gaps of 121.5 years and 105.5
  years.

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Transit of Venus

• It does not occur very often because the plane of
  the orbit of the Earth is tilted by 3.4.

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Three consecutive days of close conjunction
between the Moon and Venus.
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Solar Paralax by Venus Transit

• The technique is to make precise observations of
  the slight difference in the time of either the
  start or the end of the transit from widely
  separated points on the Earth's surface.
• The distance between the points on the Earth can
  then be used as to calculate the distance to
  Venus and the Sun.

Measuring Venus transit times to determine solar
parallax
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AU

• The astronomical unit is precisely determined
  with the transit method.
• Also by radar ranging.
• 1AU150 Million km1.5?1013 cm
• The Earth is actually 147 104 753 km away from
  the Sun on the 29th of December and 152 091 803
  km away from the Sun on the 30th of June.
• The currently accepted value of the AU is 149 597
  870 691 ? 30 metres.

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Distances of planets

• Once 1AU is determined, the distances of all
  planets can be found from Keplers third law.
• Actually not a law, an emprical relation that has
  to be explained by the underlying physics.

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Distances of Stars

• How do we know the distances of stars?
• Parallax!

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Stellar Parallax

• Different orbital positions of the Earth causes
  nearby stars to appear to move relative to the
  more distant stars.
• The annual parallax is defined as the difference
  in position of a star as seen from the Earth and
  Sun, i.e. the angle subtended at a star by the
  mean radius of the Earth's orbit around the Sun.

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Parallax and distance

• Only direct measure of distance astronomers have
  for objects beyond solar system is parallax
• Parallax apparent motion of nearby stars against
  background of very distant stars as Earth orbits
  the Sun
• Requires images of the same star at two different
  times of year separated by 6 months

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Parallax as a Measure of Distance
P
Background star
Image from A
Image from B 6 months later

• P is the parallax
• typically measured in arcseconds
• Gives measure of distance from Earth to nearby
  star (distant stars assumed to be an infinite
  distance away)

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Parsec

• The parsec is the distance for which the annual
  parallax is 1 arcsecond.
• A parsec equals 3.26 light years.
• Distance (in parsecs) is simply the reciprocal of
  the parallax angle (in arcseconds) d1/p

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Examples

• Parallax angle 0.5 arcsecondgtd2 pc
• Proxima Centauri has a parallax of 0.771
  arcsecond. This implies that its distance is d
  1.295 pc.

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Example

• The Sun has a parallax of 90 degrees.
• Why?

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Bessel (1838)

• Successfully measured the parallax of the star 61
  Cygni.
• This was considered as the conclusive evidence
  that the Earth is in motion.

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Astronomical Angular Yardsticks

• Easy yardstick your hand held at arms length
• fist subtends angle of ? 5
• spread between extended index finger and thumb ?
  15
• Easy yardstick the Moon
• diameter of disk of Moon AND of Sun ? 0.5 ½
• ½ ? ½ 1/60 radian ? 1/100 radian ? 30 arcmin
  1800 arcsec

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Distance Units

• Light Year (ly) the distance light can travel in
  one year
• 1 ly 9.46E17 cm6.324X104 AU
• Parsec (pc) 3.26 ly 3.08X1018 cm
• Astronomical Unit (AU) 149.6E13 cm

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Limits of Parallax Method

• Refraction caused by the atmosphere limits the
  accuracy to 0.01 arcseconds.
• d1/p??d?p/p2
• Reliable measurements, those with errors of 10
  or less, can only be achieved at stellar
  distances of no more than about 100 pc.
• Space-based telescopes are not limited by this
  effect and can accurately measure distances to
  objects beyond the limit of ground-based
  observations.
• E.g. Hipparcos 0.001 arcseconds

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Size of the Milky Way
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Question

• 100 pc is a small fraction of the size of the
  Galaxy (diameter 100.000 light years.)
• We can only measure the distances of a small
  fraction of stars in our galaxy with the paralax
  method.
• How do we know the distances of galaxies,
  clusters of galaxies etc if the parallax method
  does not work?

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Great Debate (1920)

• Is the Galaxy the whole Universe?
• Are the spiral nebulae other galaxies or are
  they just gas clouds in the Galaxy?
• A universe of stars or a universe of galaxies?
• Great Debate between Heber D. Curtis and Harlow
  Shapley.
• Even Einsteins Universe (1916) was a universe of
  stars.

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Standard Candles

• A standard candle is an astronomical object that
  has a known luminosity.
• Luminositypower (measured in Watts)
• Or rather ergs/s (cgs system prefered in
  astronomy).
• Flux Luminosity/4?d2
• Measure the flux received on Earth and calculate
  the distance.

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Woman Computers
A group of women computers a the Harvard
College Observatory circa 1890, directed by Mrs.
Williamina Fleming (standing). Photo credit The
Harvard College Observatory
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Cepheid Variables A Standard Candle

• A cepheid variable is a young star of several
  solar masses and roughly 104L? whose luminosity
  changes periodically.
• The period of a Cepheid variable is related to
  its luminosity.
• Measuring the period of light fluctuations (easy)
  allows the object's absolute luminosity to be
  determined.

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Cepheids as Variable Stars
Modern calibration of the Cepheid P-L relation in
the Magellanic clouds, yields
here the period P is measured in days, and the
magnitude is measured in the I band.
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Henrietta Leavitt

• One of the woman computers at Harvard
  Observatory.
• Established the period-luminosity relation for
  variable stars.
• Along with Annie Jump Cannon and Cecilia
  Payne-Gaposchkin, Leavitt represents an early
  generation of female astronomers who, serving as
  astronomical computers doing meticulous and
  demanding work around the turn of the 20th
  Century, received little credit for their
  contributions until much later.

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Through painstaking comparison of numerous
photographic plates of the Magellanic Clouds, she
identified thousands of variable stars.
Photo Caption Henrietta Leavitt at
her desk. Photo credit The Harvard
College Observatory.
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Great Debate Solved (1924)

• Edwin Hubble determined a Cepheid Variable in
  Andromeda Galaxy.
• Used Leavitts method to find the distance.
• Conclusion Andromeda is much distant than the
  estimated size of our galaxy!

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Summary of Distance Ladder
Note that beyond the Virgo cluster, even very
bright stars like Cepheids become unresolved and
we see only the integrated light from galaxies.
Further away than this, we must determine
distances using the redshift of galaxies.
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Some Elements of the Universe
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Open Clusters

• Few thousand stars formed at the same time
• Gravitationally loosely bound
• Usually less than a few hundred million years old
  

Pleiades Open Cluster
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The Solar Neighborhood
The 30 closest stars to the Sun
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Globular Clusters

• Spherical collection of stars
• Strongly bound by gravity
• Orbits the galactic core
• 150 currently known globular clusters in the
  Milky Way, with perhaps 1020 more undiscovered
• Concentrated in the halo of the galaxy
• Old stars

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Milky Way
Our galaxy
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Our Position in the Milky Way
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Andromeda GalaxyOur Neighbour
2.5 million light-years away
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Local Group
Galaxies do not stand alone. They are in groups
A few million lightyears.
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Abell
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Super-Clusters
Part of the Virgo super-cluster. Some 60 million
lightyears.

• Local group is a member of a supercluster called
  Virgo
• So galaxy clusters form superclusters.

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Large Scale Structure

• Large scale structure is made up of
  superclusters.
• Each dot represents a supercluster.
• Superclusters form filaments and walls around
  voids.

Billions of lightyears.
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Age of the Universe
The universe is about 13.7 Billion years old.