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Cosmic Distance Ladder
What’s Up There in the
Measuring the Distances
There is no one single
method that works in all
distance scales.
Measuring the distance is
a hard problem in
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
Distances of Planets
• Kepler’s third law give only the ratios of the
• 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
• 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
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
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
Measuring Venus transit times to determine solar parallax
• The astronomical unit is precisely determined
with the transit method.
• Also by radar ranging.
• 1AU=150 Million km=1.5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.
Distances of planets
• Once 1AU is
determined, the
distances of all
planets can be found
from Kepler’s third
• Actually not a law, an
emprical relation
that has to be
explained by the
underlying physics.
Distances of Stars
• How do we know the distances of stars?
• Parallax!
Stellar Parallax
• Different orbital positions
of the Earth causes nearby
stars to appear to move
relative to the more distant
• 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
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
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 a Measure of
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)
• 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):
• Parallax angle = 0.5 arcsecond=>d=2 pc
• Proxima Centauri has a parallax of 0.771
arcsecond. This implies that its distance
is d= 1.295 pc.
• 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
Bessel (1838)
• Successfully measured the
parallax of the star 61 Cygni.
• This was considered as the
conclusive evidence that the
Earth was in motion.
Astronomical Angular
• Easy yardstick: your hand held at arms’ length
– fist subtends angle of  5°
– spread between extended index finger and thumb 
• 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
Distance Units
• Light Year (ly): the distance light can
travel in one year = 9.46E17
cm=6.324X104 AU
• Parsec (pc) = 3.26 ly = 3.08X1018 cm
• Astronomical Unit (AU) = 149.6E13 cm
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
Size of the Milky Way
• 100 pc is a small fraction of the size of
the Galaxy (diameter 100.000 light years.)
• How do we know the distances of galaxies,
clusters of galaxies etc if the parallax
method does not work?
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 Einstein’s Universe (1916) was a universe
of stars.
Standard Candles
• A standard candle is an astronomical
object that has a known luminosity.
• Luminosity=power (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.
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
Cepheid Variables: A Standard
• 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 intrinsic luminosity.
• Measuring the period of light
fluctuations (easy) allows the object's
absolute luminosity to be determined.
Cepheids as Variable Stars
Modern calibration of the
Cepheid P-L relation in the
Magellanic clouds, yields:
M I  2.96(log P 1)  4.9
here the period P is measured in days,
and the magnitude is measured in the I
Henrietta Leavitt
• One of the woman computers at Harvard
• Established of the period-luminosity relation
for variable stars.
• Along with Annie Jump Cannon and Cecilia
Payne-Gaposchkin, Leavitt represents an early
generation of early 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
Through painstaking comparison
of numerous photographic plates
of the Magellanic Clouds, she
identified thousands of variable
Photo Caption: Henrietta Leavitt at her
Photo credit: The Harvard College
Great Debate Solved (1924)
• Edwin Hubble determined a Cepheid
Variable in Andromeda Galaxy.
• Used Leavitt’s method to find the
• Andromeda is much distant than the
estimated size of our galaxy!
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.
Some Elements of the Universe
Open Clusters
• Few thousand
stars formed
at the same
• Gravitationall
y looselt
• Usually less
than a few
million years
Pleiades Open Cluster
The Solar Neighborhood
The 30 closest stars to the Sun:
Globular Clusters
• Spherical collection
of stars
• Strongly bound by
• Orbits the galactic
• 150 currently known
globular clusters in
the Milky Way, with
perhaps 10–20 more
• Concentrated in the
halo of the galaxy
• Old stars
Our galaxy
Our Position in the Milky Way
Andromeda Galaxy:Our
2.5 million light-years away
Local Group
Galaxies do not
stand alone.
They are in
A few million lightyears.
• Local group is
a member of a
called Virgo
• So galaxy
clusters form
Part of the Virgo super-cluster.
Some 60 million lightyears.
Large Scale Structure
• Large scale
structure is
made up of
• Each dot
represents a
• Superclusters
form filaments
and walls around
Billions of lightyears.
Age of the Universe
The universe is about 13.7 Billion years old.