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
• 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
• Stars appear
identical all over
Earth
• They do show slight
parallax shift from
opposite sides of
Earth’s orbit
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
Hipparcos
• 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
• 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• All pre-Hipparcos distance data is obsolete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
• 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
• 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.
Disasters
• 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
• 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
• 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
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
• 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”)
• 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)