Cosmic Distance Ladder
What’s Up There in the Universe
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.
• Calibration
Kepler’s laws 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.
Astronomical Unit (AU): The Earth-Sun distance = 150 Million km=1.5E13 cm
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.
Aside: 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
Caution: NOT to scale
A
Apparent Position of Foreground
Star as seen from Location “B”
“Background” star
Foreground star
B (6 months later)
Earth’s Orbit
Apparent Position of Foreground
Star as seen from Location “A”
Parallax as Measure of
Distance
Background star
Image from “A”
P
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)
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): d=1/p
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
Distance Units
• Light Year (ly): the distance light can travel
in one year = 9.46E17 cm=6.324E4 AU
• Parsec (pc) = 3.26 ly = 3.08E18 cm
• Astronomical Unit (AU) = 149.6E13 cm
Bessel (1838)
• Successfully measured the
parallax of the star 61 Cygni.
• This was considered as the
conclusive evidence that the
Earth was in motion.
Example
• The Sun has a parallax of 90 degrees
• Proxima Centauri has p=0.77233 thus it is
at a distance of d=1.295 pc
Limits of Parallax Method
• Refraction caused by the atmosphere limits the
accuracy to 0.01 arcseconds.
• d=1/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
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
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.
Transit of Venus
• It does not
occur very
often because
the plane of
the orbit of the
Earth is tilted
by 3.4°.
Three consecutive days of close conjunction between the Moon and Venus.
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 via
Measuring Venus transit times to determine solar parallax
Open Clusters
• Few thousand
stars formed
at the same
time
• Gravitationally
looselt bound
• Usually less
than a few
hundred
million years
old
Pleiades Open Cluster
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 10–20 more
undiscovered
• Concentrated in the
halo of the galaxy
• Old stars
Milky
Way
Our galaxy
Our Position in the Milky Way
Andromeda Galaxy:Our Neighbour
2.5 million light-years away
Local Group
Galaxies do not
stand alone.
They are in
groups
A few million lightyears.
Abell
Super-Clusters
• Local group is
a member of a
supercluster
called Virgo
• So galaxy
clusters form
superclusters.
Part of the Virgo super-cluster.
Some 60 million lightyears.
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.
Age of the Universe
The universe is about 13.7 Billion years old.
Standard Candles
• How do we know such distances if the
parallax method does not work?
• A standard candle is an astronomical
object that has a known luminosity.
• Flux = Luminosity/4d2
• Measure the flux received on Earth and
calculate the distance.
We Can Not See the Sky in all
Wavelengths
Why?
Adaptation
Multiwavelength astronomy
• All-sky views at various
wavelengths
• Images are centered on
the Milky Way galaxy,
which dominates the
views
Gamma Ray
X-ray
Visible
Stars are only one ingredient
in a galaxy!
Infrared
Radio WavesImages from NASA
The Young Stars in Orion viewed at
different wavelengths
optical (HST)
X-Ray (Chandra)
infrared (2MASS)
infrared (2MASS)
Radio (VLA --image courtesy
of NRAO/AUI )
Star Brightness measured in
“Magnitude” m
• Uses a “reversed” logarithmic scale
• Smaller Magnitudes  Brighter Object (“golf
score”)
–
–
–
–
–
Sun: m  -27
Full Moon: m  -12
Venus (at maximum brilliancy): m  -4.7
Sirius (brightest distant star): m  -1.4
Faintest stars visible to unaided eye: m  +5 to +6
Star Brightness measured in
“Magnitude” m
• Decrease of 1 magnitude object brighter by
factor of 2.5
– decrease of 5 magnitudes from one star to another star 
increase in brightness by factor 100
– decrease of 2.5 magnitudes from one star to another 
increase in brightness by factor 10
F
m  2.5  log10  
 F0 
F, F0: number of photons received per second from
object and from reference source, respectively.
Magnitudes and Human Vision
– Sensitivity of human vision is limited (in large part) by
the length of time your brain can wait to receive and
interpret the signals from the eye
• How long is that?
• How do you know?
Time between movie frames = 1/24 second
Time between video frames = 1/30 second
•  Eye collects light for about 1/20 second before
reporting to brain
– What if your retina could store collected signal over
much longer times before reporting to the brain?
Magnitude scale
Spectrum