Astronomical
Distances
Blendon Middle School
April 13, 2010
Dr. Uwe Trittmann
Otterbein College
Astronomical Distances
• Locations in the sky are easy to measure: 2
angles
• Distances from observer are hard (one
length)
 Together they give the location of an
object in three-dimensional space
The Trouble with Angles
• Angular size of an object cannot tell us its actual
size – depends on how far away it is
• Sun and Moon have very nearly the same angular
size (30' = ½) when viewed from Earth
Angles and
Size
Without Distances …
• We do not know the size of an object
• This makes it hard to figure out the “inner
workings” of an object
• We can’t picture the structure of the solar
system, galaxy, cosmos
The Universe is structured on
different length scales
Stars
nebulae
molecular clouds
star clusters
THE UNIVERSE
clusters
and
superclusters
galaxies
like the
Milky Way
quasars
Sun
planets
terrestrial
jovian
Solar System
black holes
pulsars
moons
comets
meteors
asteroids
dust
voids
Big  ----------------------------- small
Powers of Ten
– From Man to Universe 0
10 meters
=1 meter
The Human
Scale
Street Size
3
10 meters
=1000 m
= 1 km
Harbour
City Size
4
10 meters
= 10,000 m
=10 km
Chicago
Planet Size: thousands of km
• 1000 km = 1,000,000 m = 1 million meters
Star Size: 1,000,000,000 m
=1 billion meters
• The Sun (a typical star): diameter 1.4 million km.
Solar System
Scale
Venus, Earth, Mars
Orbits
1011 meters
=100,000,000,000m
=100,000,000 km
= about 1 A.U. (Astronomical Unit)
Farther out: Nebulae – Where stars
are born...
… and die !
• How big ARE these?
• They APPEAR tiny!
Black Holes – Dead Stars
• How big is a black hole?
Galaxies
• How big is a galaxy?
• Are all galaxies the same size?
Clusters of Galaxies
• What is the distance between galaxies?
The Universe
• How big is the Universe?
• Does this question make sense?
• If yes, can we answer it while living IN the universe?
Different lengths scales 
Different length units
• Human scale: meters (yards)
– Human height: 1.8 m
• Geographical scale: kilometers (miles)
– Distance to Cincinnati: 100 mi
• Solar system scale: Astronomical Unit
– Distance Earth-Sun: 1 A.U.
• Intragalactic scale: lightyears (parsecs)
– Next star: 4 lightyears
• Intergalactic scale: millions of lightyears (Megaparsecs)
– Andromeda galaxy: 2.2 million lightyears = 0.67 Mpc
• Cosmological Scale: billions of ly (Gigaparsecs)
– Edge of observable universe: about 15 billion ly
Different lengths scales 
Different length measurements
•
•
•
•
Human scale: yardstick
Geographical scale: triangulation
Solar system scale: Radar ranging
Intragalactic scale:
– Close stars: stellar parallax
– Far: spectroscopic parallax
• Intergalactic scale:
– Close: Variable stars
– Far: Tully-Fisher relation
• Cosmological Scale: Hubble’s Law
Astronomical Distance
Measurements
• Fundamental technique uses
triangulation:
• Objects appear to move with
respect to background if
looked at from different
vantage points
• Try looking at you thumb with
only your left, then right eye
• The more the thumb jumps,
the closer it is!
• Measure “jump”, get distance
• See: Link, Link 2
Distances to the Stars
•
•
Measurements ½ year apart!
Parallax can be used out to
about 100 light years
The bigger the parallactic
angle, the closer the star!
•
–
–
•
A star with a measured parallax
of 1” is 1 parsec away
1 pc is about 3.3 light years
The nearest star (Proxima
Centauri) is about 1.3 pc or 4.3
lyr away
–
Solar system is less than 1/1000
lyr
Insight
• Some stars are close to us (4 ly), other are
far away (1000 ly)
• This means that some stars appear dim but
are actually very bright
• That means that stars have different sizes,
temperatures, life expectancy…
Our Stellar Neighborhood
Scale Model
• If the Sun = a golf ball, then
–
–
–
–
–
Earth = a grain of sand
The Earth orbits the Sun at a distance of one meter
Proxima Centauri lies 270 kilometers (170 miles) away
Barnard’s Star lies 370 kilometers (230 miles) away
Less than 100 stars lie within 1000 kilometers (600 miles)
• The Universe is almost empty!
• Hipparcos satellite measured distances to nearly 1
million stars in the range of 330 ly
• almost all of the stars in our Galaxy are more distant
Luminosity and Brightness
• Luminosity L is the total power
(energy per unit time) radiated
by the star, actual brightness of
star, cf. 100 W lightbulb
• Apparent brightness B is how
bright it appears from Earth
– Determined by the amount of
light per unit area reaching Earth
– B  L / d2
• Just by looking, we cannot tell
if a star is close and dim or far
away and bright
Brightness: simplified
• 100 W light bulb will look
9 times dimmer from 3m
away than from 1m away.
• A 25W light bulb will look
four times dimmer than a
100W light bulb if at the
same distance!
• If they appear equally
bright, we can conclude that
the 100W lightbulb is twice
as far away!
Same with stars…
• Sirius (white) will look 9
times dimmer from 3
lightyears away than from 1
lightyear away.
• Vega (also white) is as
bright as Sirius, but appears
to be 9 times dimmer.
• Vega must be three times
farther away
• (Sirius 9 ly, Vega 27 ly)
Distance Determination Method
• Understand how bright an object is
(L)
• Observe how bright an object appears (B)
• Calculate how far the object is away:
B  L / d2
So
L/B  d2 or
d  √L/B
Understand Star Brightness:
Classify Stars by their
Temperature (Color)
Class
O
B
A
F
G
K
M
Temperature
30,000 K
20,000 K
10,000 K
8,000 K
6,000 K
4,000 K
3,000 K
Color
blue
bluish
white
white
yellow
orange
red
Examples
Rigel
Vega, Sirius
Canopus
Sun,  Centauri
Arcturus
Betelgeuse
The hotter  the bluer!
ColorLuminosity
Correlation
• Hertzprung-Russell
Diagram is a plot of
absolute brightness
(vertical scale)
against spectral type
or temperature
(horizontal scale)
• Most stars (90%) lie
in a band known as
the Main Sequence
Spectroscopic Parallax
• From the color of a
main sequence star
we can determine its
absolute brightness
• Then, from the
apparent brightness
compared to absolute
luminosity, we can
determine the
distance d  √L/B
Insight
• We now know how far away stars are, so we
know how big they are, and we can
understand how they work.
• We understand how big our galaxy is
(100,000 ly) and that some “nebulae” are
galaxies like our own
Sizes of Stars
• Dwarfs
– Comparable in
size, or smaller
than, the Sun
• Giants
– Up to 100 times
the size of the Sun
• Supergiants
– Up to 1000 times
the size of the Sun
• Note: Temperature
(Color) changes!
Galaxies are close together –
compared to their size
The Local Group
The Virgo Cluster
Aside: What are stars made out of ?
• 90% of the universe is Hydrogen
• The rest is mostly Helium
• How do we know? By identifying the
fingerprints of the elements, aka the light
they send out!
Spectral Lines – Fingerprints of the Elements
• Can use this to
identify
elements on
distant objects!
• Different
elements yield
different
emission spectra
Origin of Spectral Lines: Emission
Heated Gas emits light at specific frequencies
 “the positive fingerprints of the elements”
Origin of Spectral Lines: Absorption
Cool gas absorbs light at specific frequencies
 “the negative fingerprints of the elements”
Use Spectra to measure the Size of the Universe
• Measure spectrum of
galaxies and compare to
laboratory measurement
• lines are shifted towards red
• This is the Doppler effect:
Red-shifted objects are
moving away from us
Using Redshift: Hubble’s Law
• The final rung on the cosmic
distance ladder
• Hubble’s observations (1920’s):
– Light from distant galaxies is redshifted
– The more distant the galaxy, the
greater the red-shift
• Interpretation:
– Galaxies are moving away from us
– More distant galaxies are moving
faster
• The universe is expanding,
carrying the galaxies with it!
Hubble’s Law
Velocity = H0  Distance
Distance = Velocity /H0
• H0 = (65 ± 15) km/sec/Mpc is Hubble’s constant
• Compare to distance = velocity  time
• Appears the universe “exploded” from a single point in
the past – the Big Bang
• Age of the universe is 1/H0 or about 14 billion years
The Latest Surprise
• Type Ia Supernovae are
standard candles
• Can calculate distance
from brightness
• Can measure redshift
• General relativity gives us distance as a
function of redshift for a given universe
Supernovae are further away than
expected for any decelerating (“standard”)
universe
Supernova
Data
magnitude
• Solid line is
best fit to data
redshift
Expansion of the Universe
• Old lore:
–
–
–
–
Either it grows forever
Or it comes to a standstill
Or it falls back and collapses (“Big crunch”)
In any case: Expansion slows down!
Surprise of the year 1998
(Birthday of Dark Energy):
All wrong! It accelerates!
Additional Material
Powers of Ten
– From Man to Universe 0
10 meters
=1 meter
The Human
Scale
Powers of Ten
– From Man to Universe 1
10 meters
=10 meters
Lawn and
Blanket
Powers of Ten
– From Man to Universe 2
10 meters
=100 meters
Highway and
Boats
Powers of Ten
– From Man to Universe -
103 meters
=1000 m
Harbour
Powers of Ten
– From Man to Universe 4
10 meters
=10 km
Chicago
Lakeshore
Powers of Ten
– From Man to Universe 5
10 meters
=100 km
Chicago &
L. Michigan
Powers of Ten
– From Man to Universe 6
10 meters
=1000 km
Lake
Michigan
Powers of Ten
– From Man to Universe -
107 meters
=10000 km
The Earth
Powers of Ten
– From Man to Universe 8
10 meters
=100000 km
Earth in
Space
Powers of Ten
– From Man to Universe -
109 meters
=1000000km
Moon Orbit
Powers of Ten
– From Man to Universe 1010 meters
Part of Earth’s
Orbit around
the Sun
Powers of Ten
– From Man to Universe -
1011 meters
= ca. 1 A.U.
(Astronomical Unit)
Earth’s Orbit
Powers of Ten
– From Man to Universe 12
10 meters
Inner Planets’
Orbits
Powers of Ten
– From Man to Universe -
1013 meters
Outer Planet’s
Orbits
Powers of Ten
– From Man to Universe -
1014 meters
Solar System
in Space
Powers of Ten
– From Man to Universe -
1015 meters
The Sun “a bright star”
Powers of Ten
– From Man to Universe 16
10 meters
= ca. 1 ly
(light year)
The Sun “just another star”
Powers of Ten
– From Man to Universe -
1017 m
= ca. 10 ly
Distinct Stars
Powers of Ten
– From Man to Universe -
1018 m =
100 ly
Sun in center;
Arcturus (α Tauri)
Powers of Ten
– From Man to Universe -
1019 m =
1000 ly
A cloud of Stars
- making up constellations
Powers of Ten
– From Man to Universe 20
10 m
= ca.10000 ly
Clouds - made
out of Stars
Powers of Ten
– From Man to Universe 1021 m
=100000 ly
The Milky Way
– Our Galaxy
Powers of Ten
– From Man to Universe -
1022 m
=1,000,000 ly
The Milky Way
in Space
Powers of Ten
– From Man to Universe -
1023 m
6
= 10 x 10 ly
The Local Group
of Galaxies
Powers of Ten
– From Man to Universe 24
10 m
=
8
10
ly
The Virgo Cluster
of Galaxies
(incl. the local Group)
Powers of Ten
– From Man to Universe 1025 m
9
= 10 ly
The Universe:
Many clusters of
galaxies – and even
more empty space
The “old” Planets
Mercury
Venus
Mars
Jupiter
Saturn
The “new” Planets
Uranus (1781)
Neptune (1846)
Pluto (1930)
(“dwarf planet”
since 2006)
Kepler’s Third Law: Relating Orbits
The square of a planet’s orbital period is proportional to the cube of its
orbital semi-major axis:
P 2  a3
a
Planet Semi-Major Axis
Mercury
0.387
Venus
0.723
Earth
1.000
Mars
1.524
Jupiter
5.203
Saturn
9.539
Uranus
19.19
Neptune
30.06
Pluto
39.53
(A.U.)
Jupiter: 53 / 122 = 125/144 ~ 1
P
Orbital Period
0.241
0.615
1.000
1.881
11.86
29.46
84.01
164.8
248.6
(Earth years)
Eccentricity ____
0.206
0.007
0.017
0.093
0.048
0.056
0.046
0.010
0.248
P2/a3
1.002
1.001
1.000
1.000
0.999
1.000
0.999
1.000
1.001
The Problem with Kepler’s Third Law
• The square of a planet’s orbital period is proportional to the
cube of its orbital semi-major axis:
P 2  a3
• But: everything is expressed in “Earth units”, i.e.
one Earth year, and one Earth-Sun distance.
• Problem: How big are these units?
Practical Problem: Determine the
Sun’s Diameter?
• Trickier than you might think
• We know only how big it appears
– It appears as big as the Moon
• Need to measure how far it is away
– Kepler’s laws don’t help (only relative
distances)
• Without knowing its size, we don’t know
how much energy it can produce, so we
can’t figure out how the Sun “works”
Solution: relate to distances on Earth
or fundamental constants
• Use two observations of Venus transit in
front of Sun
– Captain Cook in the 1700s
– Hard and not very precise (100,000 km)
• Modern way: bounce radio signal off of
Venus (measure traveling time of light)
– In the 1960s, very precise (few centimeters)
Insight
• Sun is 109 times bigger than Earth
• Up to the 1930s no mechanism was known
to produce so much energy
• Know now that the Sun fuses hydrogen to
helium
More Insight: Understanding
Variable Stars yields another Method
• Two useful types:
– Cepheids
– RR Lyrae
• Again, method uses insight to get absolute
brightness, then concludes distance from
apparent brightness
Cepheids
•
•
•
•
•
Named after δ Cephei
Period-Luminosity Relations
Used as “standard candles”
“yard-sticks” for distance measurement
Cepeids in Andromeda Galaxies established
the “extragalacticity” of this “nebula”
Cepheids
• Henrietta Leavitt (1908) discovers the
period-luminosity relationship for
Cepheid variables
• Period thus tells us luminosity, which
then tells us the distance
• Since Cepheids are
brighter than RR Lyrae,
they can be used to
measure out to further
distances
Properties of Cepheids
• Period of pulsation: a few days
• Luminosity: 200-20000 suns
• Radius: 10-100 solar radii
Properties of RR Lyrae Stars
• Period of pulsation: less than a day
• Luminosity: 100 suns
• Radius: 5 solar radii
• Extends the cosmic
distance ladder out
as far as we can see
Cepheids – about 50
million ly
• In 1920 Hubble used
this technique to
measure the distance
to Andromeda
(about 2 million ly)
• Works best for
periodic variables
Distance Measurements
with variable stars
Cepheids and RR Lyrae: Yard-Sticks
• Normal stars undergoing a
phase of instability
• Cepheids are more massive
and brighter than RR Lyrae
• Note: all RR Lyrae have the
same luminosity
• Apparent brightness thus
tells us the distance to
them!
– Recall: B  L/d2
Insight: How does our Galaxy look like?
Other Galaxies
• Edwin Hubble identified single stars in the
Andromeda nebula (“turning” it into a
galaxy)
• Measured the distance to Andromeda to be
1 million Ly (modern value: 2.2 mill. Ly)
• Conclusion: it is 20 times more distant than
the milky way’s radius  Extragalacticity!
 Old theory (Milky Way is the universe)
falsified!
The Tully-Fisher Relation
• A relation between the rotation speed of a spiral galaxy
and its luminosity
• The more mass a galaxy has the brighter it is  the
faster it rotates  the wider the spectral lines are
• Measuring rotation speed allows us to estimate
luminosity; comparing to observed (apparent)
brightness then tells us the distance
Electromagnetic Spectrum
Energy:
low

medium

high
Electromagnetic Radiation:
Quick Facts
• There are different types of EM radiation, visible
light is just one of them
• EM waves can travel in vacuum, no medium needed
• The speed of EM radiation “c” is the same for all
types and very high ( light travels to the moon in 1
sec.)
• The higher the frequency, the smaller the
wavelength ( f = c)
• The higher the frequency, the higher the energy of
EM radiation (E= h f, where h is a constant)
Visible Light
• Color of light determined
by its wavelength
• White light is a mixture
of all colors
• Can separate individual
colors with a prism
Three Things Light Tells Us
• Temperature
– from black body spectrum
• Chemical composition
– from spectral lines
• Radial velocity
– from Doppler shift
Temperature Scales
Fahrenheit
Centigrade
Kelvin
459 ºF
273 ºC
0K
32 ºF
0 ºC
273 K
Human body
temperature
98.6 ºF
37 ºC
310 K
Water boils
212 ºF
100 ºC
373 K
Absolute zero
Ice melts
Black Body Spectrum
• Objects emit radiation of all frequencies,
but with different intensities
Ipeak
Higher Temp.
Ipeak
Ipeak
Lower Temp.
fpeak<fpeak <fpeak
Cool, invisible galactic gas
(60 K, fpeak in low radio
frequencies)
Dim, young star
(600K, fpeak in infrared)
The Sun’s surface
(6000K, fpeak in visible)
Hot stars in Omega Centauri
(60,000K, fpeak in ultraviolet)
The higher the
temperature of an object,
the higher its Ipeak and fpeak
Activity: Black Body Radiation
•
•
•
•
•
Pick up a worksheet
Form a group of 3-4 people
Work on the questions on the sheet
Fill out the sheet and put your name on top
Hold on to the sheet until we’ve talked about
the correct answers
• Hand them in at the end of the lecture or during
the break
• I’ll come around to help out !
Kirchhoff’s Laws: Bright lines
Heated Gas emits light at specific frequencies
 “the positive fingerprints of the elements”
Kirchhoff’s Laws: Dark Lines
Cool gas absorbs light at specific frequencies
 “the negative fingerprints of the elements”
Kirchhoff’s Laws
1. A luminous solid or liquid (or a sufficiently dense
gas) emits light of all wavelengths: the black body
spectrum
2. Light of a low density hot gas consists of a series
of discrete bright emission lines: the positive
“fingerprints” of its chemical elements!
3. A cool, thin gas absorbs certain wavelengths from
a continuous spectrum
 dark absorption ( “Fraunhofer”) lines in
continuous spectrum: negative “fingerprints” of its
chemical elements, precisely at the same
wavelengths as emission lines.
Spectral Lines
• Origin of discrete spectral
lines: atomic structure of
matter
• Atoms are made up of
electrons and nuclei
– Nuclei themselves are made up
of protons and neutrons
• Electrons orbit the nuclei, as
planets orbit the sun
• Only certain orbits allowed
Quantum jumps!
• The energy of the electron depends on orbit
• When an electron jumps from one orbital to
another, it emits (emission line) or absorbs
(absorption line) a photon of a certain energy
• The frequency of emitted or absorbed photon is
related to its energy
E=hf
(h is called Planck’s constant, f is frequency)