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How Far Away Are The Stars?. Distances in the Solar System. Kepler’s Third Law relates period and distance Defines a relative distance scale One accurate distance determines everything. The Streetlight Analogy: What can the prisoner learn about the outside world?. Parallax.

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distances in the solar system
Distances in the Solar System
  • Kepler’s Third Law relates period and distance
  • Defines a relative distance scale
  • One accurate distance determines everything
  • Nearby Lights Appear to Change Position as the Observer Moves
  • Can Triangulate to get distance
  • Can determine true brightness of lights
parallax and the distances of stars
Parallax and the Distances of Stars
  • Stars appear identical all over Earth
  • They do show slight parallax shift from opposite sides of Earth’s orbit
parallax pre 1997
Parallax: pre-1997
  • Parallax is tiny - was once used as argument against motion of the Earth
  • One second of arc = size of a quarter at 5 km (3 mi.)
  • Parallax angle of nearest star (4.3 l.y.) is 0.75”
  • Accuracy limited by Earth’s atmosphere
  • Fairly accurate to 30-40 l.y., rough to 100
  • Named for ancient Greek astronomer who catalogued the stars
  • High Precision Parallax Collecting System
  • Launched by European Space Agency, 1989
  • Data Collection 1989-1993
  • Data Analysis 1993-1997
the hipparcos data
The Hipparcos Data
  • 118,218 stars measured: parallax and motion
  • 22,396 accurate to 10% - a 20-fold improvement
  • Stars out to 200-300 l.y. are known to within 10%
  • 30,000 more accurate to 20%
  • All pre-Hipparcos distance data is obsolete
gaia the next generation
GAIA: the Next Generation
  • To be placed in Earth-Sun L2 point
  • Measure a billion stars out to 100,000 l.y.- 1% of entire galaxy
  • Transmit 1 Mb every 8 seconds for five years
  • Accuracy of five micro-seconds (width of a human hair at 2,500 miles)
  • Data could be available by 2020
beyond parallax
Beyond Parallax
  • More Distant Lights Show Little Parallax
  • We know how much light nearby lights emit
  • Can use this to estimate distance of faraway lights

In nearby towns, lights of known type and brightness can be observed

  • Use brightness to estimate distance

We know how much light a town emits per block

  • Can estimate the distance of towns even when individual lights cannot be seen

Once we have a good idea how big and bright a typical city is, we can estimate the distance to faraway cities


Nearby clusters of cities allow us to gather statistics

  • Statistics can estimate distances to faraway clusters of cities
  • At these distances, some small cities can no longer even be seen.
  • Sometimes a big fire will outshine the rest of the city
  • Distant fires can be used as distance estimators
  • Sometimes a fire is visible even if the city is too faint to see
the cosmic distance scale
The Cosmic Distance Scale
  • Makes use of different indicators for different distances
  • Each increase in distance builds on previous distances
  • Faraway distances are only as accurate as nearer distances
distances in our galaxy
Distances in our Galaxy
  • Parallax (to 300+ l.y. with Hipparcos)
  • Spectroscopic Parallax (Brightness of stars of known types and absolute brightness)
  • Moving Cluster Method
    • Radial motions of stars from Doppler Effect
    • Transverse motions measured directly
    • Assume velocity distribution uniform
variable stars
Variable Stars
  • Henrietta Leavitt, 1917
  • Measured Magellanic Cloud stars - a lot in a small space
  • Unexpected discovery- some variables have uniform properties
  • Magellanic Cloud stars all about same distance away (170,000 l.y.)
variable stars as yardsticks
Variable Stars as Yardsticks
  • RR Lyrae Stars
    • Have distinctive light variation curve
    • All about 100 times as luminous as Sun
  • Cepheid Variables
    • The brighter, the longer the period
    • Think of a bell ringing
extragalactic yardsticks standard candles
Extragalactic Yardsticks (“Standard Candles”)
  • Cepheids (Governed specifications for Hubble Space Telescope)
  • Supernovae
  • Brightest Galaxy in Cluster
  • Hubble Parameter (25 km/sec/m.l.y. - implies age of universe = 12 billion years)