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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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How Far Away Are The Stars?

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How far away are the stars

How Far Away Are The Stars?

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

The streetlight analogy what can the prisoner learn about the outside world

The Streetlight Analogy: What can the prisoner learn about the outside world?



  • 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  • All pre-Hipparcos distance data is obsolete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

How far away are the stars

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

  • Use brightness to estimate distance

How far away are the stars

  • We know how much light a town emits per block

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

How far away are the stars

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

How far away are the stars

  • 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

Spectroscopic parallax

Spectroscopic Parallax

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)

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