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Aristotle (384-322 BC) showed Earth is
round,
way before Columbus!
• Shadow of earth on moon always part of a circle.
• ``Sinking” ship as it is seen going to sea.
• Walk north, NCP is higher in the sky.
Eratosthenes’ 200 BC calculation of
size of earth
• Aristotle’s geocentric theory.
Going beyond the Earth to get distance of the Moon
Must use parallax (similar to binocular vision).
Two eyes on
opposite parts of
Earth
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Ptolemy(200 AD) discusses previous work.
4000 miles radius of Earth
Earth radius/(2π orbit radius) = Angle p / 360o.
60 Earth radii distance from p≈ 1o.
240,000 miles or about 1.3 light second travel
time.
• Stilted conversation between astronauts and
President Nixon.
Aristarchus (310--230BC) proposed
that Earth went around Sun, way
before Copernicus.
• Shadow of round Earth on Moon.
• Deduced Moon is about 1/3 size of Earth
(Modern 1/4)
• Aristarchus studied times 3rd Q, new, 1stQ
of the Moon versus 1st, full, 3rd.
• Found Sun was at least 21x Moon’s
distance
• As revealed by solar
eclipse, the sun and moon
are about the same
ANGULAR SIZE.
• But the sun is a lot bigger
by a factor equal to ratio
of distances.
• Aristarchus’ results:
• Sun is 21xMoon’s distance or 21xsize of
Moon
• Moon is 1/3 the size of the earth.
• Sun is 21x(1/3)~7 x size of the earth. Modern
value ~100>>Earth!
• Concluded such a big sun couldn’t circle earth.
Aristarchus’ idea was rejected.
Parallax from one side of Earth’s orbit to other was expected. Stars too
far and parallaxes to small for ancient Greeks to accept or measure.
Largest p < 1/3600 degree.
Ptolemy’s
125 AD book
Almagast
• Elaborated geocentric
theory to
quantitatively
account for and
predict observed
motions of planets,
“wanderers” in the
sky.
• Seven wanderers:
Sun, Moon, Mercury,
Venus, Mars, Jupiter,
Saturn. 7 objects.
Renaissance:
Nicolaus Copernicus
(1473–1543)
• Revived sun-centered
idea ignoring failure to
observe parallax.
• Simpler model than
earth-centered
• Simpler calculations and
could calculate relative
sizes of planet orbits.
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New!
Copernicus
could calculate
relative sizes of
planet orbits.
Know
“maximum”
elongation angle
at Earth
SunPlanetEarth
angle is 90o
Triangle gives
dist. PlanetSun in
AU
Also did for
Mars, Jupiter,
Saturn
• Copernicus calculated the sizes of the planets’ orbits
RELATIVE to the Earth’s orbit size (1 AU).
• Death bed publication, why?
Believing the Earth circled
the Sun was dangerous.
Giordano Bruno burned at
stake in 1600
• ``There is a single general space, a single vast
immensity which we may freely call void: in it are
innumerable globes like this on which we live and
grow.”
• ``I await your sentence with less fear than you pass
it. The time will come when all will see as I see.”
The Distance of the Nearest Star
• Recall Copernicus found relative distances
of planets in solar system.
• Copernicus calculated the sizes of the
planets’ orbits RELATIVE to the Earth’s
orbit size (1 AU).
• But exactly how big is the Earth’s orbit and
the solar system in miles or km?
• To 1700’s AU very poorly known.
Basilica of San Petronio, a solar observatory
1576
by Egnatio Danti, a mathematician and Dominican friar
Aristarchus: 1 AU = 1520 Earth radii
1650 Giovanni Cassini (France) found that Sun was much farther and
Solar System much bigger than previously thought >17,000 Earth radii.
Expanded Solar System (universe) over 10x
Cassini’s San Petronio method
• Noon Sun (black solid line) is farther south or
lower from overhead (red) at both summer and
winter solstices than it would be if infinitely far
away (dashed lines)
• Differences permit calculation of Sun’s distance in
Earth radii.
Halley is famous for
calculating the 75 yr
elliptical orbit of “Halley’s
comet” and predicting its
1758 return.
Haley had an idea to more
precisely measure the AU
in Earth radii.
• Halley’s parallax transit method. Venus crosses the Sun along
different lines depending on the latitude of the observer on the Earth.
• The lines differ by no more than 44 seconds of arc on disk.
• Exaggerated in the drawing. The Sun is half a degree, 40 times the
max difference).
1761,1769
transits
observed from
all over Earth,
even Tahiti!
• First accurate results, 1%
• 93 million mi, 150x106 km.
• Space probes, radar 23,500
Earth radii within meters.
• 8 minutes blissful
ignorance if Sun vanishes!
The long quest for stellar parallax
• German astronomer Karl
Bessel.
• Visual observation, special
telescope.
• First accurate measuremnt of
parallax of star 61 Cygni in
1838.
• Tiny, about 0.3 seconds of
arc. One arc sec= 1/3600 o
Tiny parallaxes
simplify
calculating
distance.
• Nearest star (besides the Sun) has a parallax of 0.75
sec of arc, less than 1/3600 of a degree= 1 arc sec.
• Distance in parsec = 1/parallax in arc sec.
• Distance = 1/0.75 = 1.33 parsecs
• 1 parsec = 3.26 light years or 206,265 AU
• One light year = 6 trillion miles.
Nearest star amazingly far away.
• The double star in the
figure, Alpha,Proxima
Centaurus.
• 1.3 pc away, four light
years travel time.
• Our info about it is over
4 years out of date!
Next “Expansion” Galileo’s
Starry Messenger
http://www.rarebookroom.org/Control/galsid/index.html
The Milky Way and the Pleiades as
seen with the telescope.
• All sky photo
• Meteor
shower.
• MW circles
whole sky.
• Galileo found
the MW was a
multitude of
dim stars.
• Bright stars
uniform over
the sky.
Thomas Wright in 1750 clarified
Galileo’s discovery.
• Bright stars scattered uniformly over sky.
• Milky Way divides the sky into two equal
halves.
• We are in mid-plane of a somewhat thick
disk of stars.
• Nearby stars above, below, and to sides
make up bright stars on sky.
• Stars so distant they appear as haze, mark
out the disk plane.
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Bright
& *
dim*
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Bright only.
No dim stars
in this direction.
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Bright only.
No dim stars
in this direction.
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1785 Herschel surveyed and found our
place in MW Galaxy
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Looked in different directions w. telescope
Counted # of stars of diff apparent magnitudes
Assumed all were like the sun
Plotted number versus distance in different directions.
Disk a few thousand light years in size. Wrong!!
Sun in center. Wrong!!
• This is a mosaic of visual photos of the entire sky.
• Dust lanes that block view of galaxy center misled Herschel.
• Also more H gas than dust.
True Size & Place
• Early 20th century, Harlow
Shapley
• Undergrad journalism at U.
of Missouri, Columbia
• Wanted to take an
archeology course one
semester. It wasn’t offered
(but astronomy was).
• Became director of Harvard
College Observatory.
In 1920’s, Shapley’s
method
• Estimated distances of globular star clusters above
and below the absorbing dust of the Milky Way
disk. (eg 47 Tuc >106 stars, 50 pc).
• Used RR Lyrae variable stars as ``distance
indicator”.
• Periods of <1day and 100x Sun’s luminosity.
• Got distances from RR Lyrae intensity and
luminosity.
• Most globular clusters are seen on one side of the sky
• Shapley plotted their directions and distances
• A spherical swarm whose center is in the direction of
the nearby stars of the constellation Sagittarius.
• Center ~30,000 light years away.
Modern MW Map
• Disk has mostly stars, galactic clusters of stars (like
Pleiades) + some H, He gas, and dust.
• Halo has swarm of globular clusters, scattered old stars,
and other unknown objects.
• Nuclear bulge is mostly stars + some gas, dust.
Galaxies: A big
step beyond.
• Initially were
``nebulae,” fuzzy
patches of light beyond
the solar system.
• Messier cataloged ~100
in 1700’s for comet
hunters.
• M31 is #31 in the list.
• Herschel in early
1800’s cataloged
1000’s in New General
Catalog e.g. NGC205
Study of nebulas via spectroscope.
• Some showed emission line spectra
– These were clouds of thin gas in our galaxy.
– Mostly hydrogen
– Supernova ejection or gas which may form stars later.
• Others had continuous spectra with absorption lines.
– Like a star’s spectrum. Figure below
– Astronomers were uncertain about these.
– Collection of stars or one star and reflecting dust?
• Shapley’s RR Lyrae stars
(100xSun)
not luminous enough to
use outside MW Galaxy
• Herietta Leavitt(Harvard)~1915
• Cataloged 1000’s of variable
stars!
• Found a new variable 10,000 x
Sun, Cepheids
• Useful outside MW gal.
Cepheid
Variables
An Example of a
Cepheid Variable
in MW Galaxy.
• Are pulsating giant
stars
• Very distinctive
because of their
brightness variation >
1 day up to 50 days.
• Leavitt found Cepheid
variable stars, in a
satellite galaxy of MW.
• All at same distance.
• Found “periodluminosity” relation,
• Observe P, know
luminosity, compare to
intensity.
• Can thus estimate
distance of the galaxy
Getting M31’s Distance
• 1920’s Edwin Hubble observed
what was called the ``Great
Nebula in Andromeda” Top
photo.
• IDed Cepheid variables.
• Hubble’s negative photo=>
• Var! marks his exciting
discovery of a Cepheid.
• Compared M, m to get distance
M31’s huge
distance from
Cepheids
• The graph shows magnitudes
of 20 day Classical Cepheids
if they were at 10 pc (~33
lyr), -5.
• Hubble found M31’s 20 day
Classical Cepheid apparent
magnitudes are +20.
• 1010 times less intense.
• 3x106 lyr
Math details 33 ly x √(1010 )
reversing the inverse square law.
Expanding the
Andromeda “Nebula”
• The farther away, the bigger the physical size
• Modern result Andromeda Nebula, M31, is
780,000 pc, 780 kpc,
• 2.4 million LY away, far outside MW Galaxy
• Radio observations => disk ~3o in angular
diameter.
• 3o/360o= Size/(2πx2.4 million LY)
• Size about 126,000 LY in diameter.
• Andromeda Galaxy, bigger than Milky Way
Galaxy.
• But this info is two million yr old
Systems of galaxies: The Local Group
• ~Several million light years across=One million pc
Beyond Local
Group
Virgo Cluster
~50,000,000 LY
17,000 kpc away
Over 1000 galaxies
7 million LY size
12x size moon.
Giant E, M87, center
.
• 1920’s Edwin Hubble and Milton Humason worked
together at Mt Wilson observatory. Hubble getting
distances of galaxies and Humason getting spectra.
• Expected to find some coming toward us, some away.
• That’s what they and others found for nearby galaxies.
• But when they got distances and spectra of more distant
galaxies, Hubble noticed a pattern.
Redshift-Distance
Correlation
• Hubble used distance indicators
(variable stars, novae, supernovae
etc) to estimate distance.
• Humason got spectra. Identified
characteristic element lines (eg
Calcium)
• Measured wavelength compared to
sample on earth.
• They found larger redshifts the
larger a galaxy’s distance.
Measuring
Redshifts
• Distances are in Millions
of pc= 3.26 million LY
on x axis.
• Pair of dark Calcium
absorption lines in
spectra.
• V=0 wavelengths
indicated by blue lines.
• Red arrows=red shifts.
• Calculated velocities in
km/s are plotted on y
axis.
First graph data Hubble made pointing
out the pattern.
More distant
galaxies have
larger
redshifts
(velocities
away).
Distance is
most
uncertain
quantity.
The velocity-distance relation:
Real expansion
• Are we at rest and all galaxies flying away from us?
• No! Doppler shifts are relative. Don’t know what’s
moving.
Implications of recession
• Galaxies jammed together in past.
• When ? E.g. car 120 miles away at 60 mi/hr left
about 120/60≈2 hr ago.
• Hubble law, a galaxy D kpc away, recession V
km/s.
• Left us, D/V billion years ago.
• The universe had a beginning.
• Einstein thought this was not the case.
• Math note: 1 kpc in km / 1 km/s ≈ 1 billion yrs
Early Evidence for Origin of Universe
• In 1826, Olber pointed out a problem with a
perpetual unchanging universe:
• It would incinerate the earth!
• Why? The number of stars inside progressively
larger imaginary spheres or cubes increases with R3
• Intensity of the light from each star on earth
2
1
/
R
decreases like
• The product of these two, the total intensity
increases as R . Light from a large volume would
be enough to burn up the earth.
• Less mathematical
description.
• In an unchanging,
perpetual universe, all
lines of sight from the
earth would eventually
intersect the surface of
a star.
• The entire sky should
be as bright as the
photosphere of the
sun!
• No dark night sky!
Why aren’t we incinerated?
• In 1848, Edgar Allen Poe (of all people)
suggested a solution.
• The universe had to have a finite age.
• The limited speed of light would prevent the
light of stars more distant than the age of
the universe (in light years) from reaching
us.
Age problem from Hubble’s initial plot
• Hubble law, a galaxy 1.9 Mpc=1,900 kpc away,
recession V=HxD=1000km/s.
• Left us, 1,900 kpc/1000km/s≈2 billion years ago.
• Problem: Radioactive dating of Earth & Solar
System 4.5 billion yr
• Math note:
1 kpc in km / 1 km/s ≈
1 billion yrs
An under appreciated astronomer
• Walter Baade born, educated in
Germany.
• Came to US in 1931 to Mount Wilson
Observatory, home of the world's largest
telescope (100”).
• During WWII, he, an enemy alien, was
confined to Los Angeles County with
almost unlimited use of the most
powerful telescope in the world.
• Lights of LA were briefly darkened.
• Early 50’s, corrected and enlarged
Hubble’s distances so Universe older
than Earth.
Modern velocity vs distance relation.
• V=HD
• H=Hubble
constant ≈72
km/s per Mpc.
• Much less
steep.
• Age =D/V=
1/H
• Age ≈ 14
billion yr. >
Earth or Solar
System
Critical density of the universe?
Analogy with ball thrown
upward from surface of earth.
Go up and return
Fly away forever (escape)
Return or escape depends on
speed of ball, radius of earth,
and mass of earth.
Since density is mass/volume,
whether returns or escapes
depends on speed of ball and
DENSITY of earth.
• Galaxy receding with speed,
v, from center of an
expanding sphere of
galaxies of radius, r, is
attracted to the sphere
center determined by r,
sphere density, ρ, and
gravitational constant, G.
• Critical density depends
only on current local
Hubble constant H=v/r
• ρcritical = 3H2/ [8Gπ]
Future?
``Bottom line” numbers
• If the density is 9x10-27 kg/m3 then the
galaxies will just barely recede forever
despite gravitational action of matter and
dark matter.
• This is called the ``critical density.”
• This universe is called the ``flat universe.”
• Present day density (luminous and dark
matter) is only ~1/4 the critical density.
Some galaxies’ Δλ/λ= z>1! Why?
Time increases
downward
Time 1 Milky Way
2
I see it
3
COSMIC red shift for
expansion. Not Doppler.
“Rubber sheet”stretches λ
while wave travels
Quasar emitting
White dwarf supernovas permit estimate of
still larger distances of galaxies
Measure Doppler shift=> speed of recession
Compare apparent magnitude and known absolute magnitudes to
estimate distances like we discussed for Cepheids.
Get recession velocities of galaxies at larger distances and back in time
Redshift vs. Distance:
Type I SN (dots)
Redshift cz in km/s
500000
400000
300000
200000
• Line is uniformly
100000
expanding universe
0
(no gravity deceleration,
0
5000
10000
15000
no acceleration)
Distance in 10 light years
• Horizontal axis also past time.
• Accelerating universe points would be below curve
• Gravitationally decelerating points would be above the
curve.
• Observed SN are below the line=>
Acceleration due to new component “dark energy.”
which began to dominate ~5 billion years ago.
6
Separation/
today’s
separation
between
galaxies
vs time
• Red
curve
best fits
SNI
data
What was it like at
origin?
• Extrapolate back what’s
happening in MW galaxy
today.
• Today uniform H, He gas is
forming into concentrated
masses (stars).
• In past, more H, He gas, fewer
stars.
• Galaxy collapsed from H, He
gas cloud.
What was it like back then? Part
II
• Today supernova heavy element enrichment of H,
He. Galaxies receeding.
• Long ago, uniform gas H, He of our galaxy was
all jammed together (compressed) with gas of
others.
• Initially, gas expanded as part of universe
expansion.
• Compressed gas hotter than expanded gas later.
• Initially hot, compressed H, He gas.
The universe
then and now
• Then: Just hot H, He
gas.
• Now: Galaxies made of
stars, planets, you, me.
The ``Big Bang” origin of the
universe
• Initially, hot compressed H, He gas
• This expanded rapidly in what astronomers
call the ``Big Bang”
• To really prove this, you would need to see
the universe back then.
• You would need a time machine!
• In 1948 George Gamow, pointed out that
we did have such a ``time machine.”
Use of the time machine
• Finite speed of light creates a time machine.
• The sun is 8 light minutes away, we see the sun as it
was 8 minutes ago.
• The nearest star, 4LY away, as it was 4 years ago.
• Andromeda galaxy as it was about 2 million yr ago.
• If we look ~14 billion LY away, expect to see
universe in its early, hot, compressed, uniform gas
state.
Universe at different distances & times
• Imagine a sphere
about 14 billion
LY in radius
• Milky Way
Galaxy in center.
• We see this part
as the universe is
now.
• We see edge as it
was right after
Big Bang 14
billion years ago.
The universe becomes transparent
• The early universe was composed of lots of
energetic photons which keep protons (H+ nuclei)
from combining with e- . Not transparent.
• After ~300,000 yr expansion, photons and gas cool
to ~3000 K.
• H+ & e- combine to make H atoms. Transparent.
• We do not see the
hot glow of 3000K
gas with our time
machine.
• Instead, expansion
of the universe
would cause a
``red shift.”
• Visual λ of the hot
gas will become
much longer λ
microwave
radiation.
3000K=>3K.
14 billion ly to here
• 1960’s Penzias (right) & Wilson (left) worked at
Bell Labs studying the sky’s radio brightness.
• They accidently discovered the red-shifted Big
Bang radiation, a weak uniform microwave
glow.
• Tedious, careful work.
Intensity
versus
wave
length plot
of what
they found.
• The familiar continuous spectrum of hot, thick gas.
• Originally at visual wavelengths from ~3000K gas.
• Red-shifted to 0.1cm APPEARS to be 3K gas. “3
degree Kelvin radiation.”
Uniform 3K radiation
• Remove local MW dust thermal emission and motion of Sun in
Galaxy, in Local Group, Local Group motion toward Virgo Cluster.
• Result is uniform through 4 digits.
Tiny 3K
variations
• COBE also found tiny variations in 3K, 0.0003 K
temperature fluctuations.
• Represent slightly denser regions of the gas, the creation
of first structure in the universe.
• George Smoot, the principal investigator for COBE in a
famous quote called this plot ``the face of God.”
Improvement on COBE,
WMAP Observations
can be used to check past density of universe
• WMAP observations indicate a critical density of
matter in universe at time of 3K emission.
• Gravitation of dark matter, matter, photons,
neutrinos just equal to critical density to expand
forever.
• Later dark energy dominates.
• Origin
• Inflation stretches to
critical density.
• H, He + light elements made in Big Bang.
• 3 K radiation now (3000 K then)
• Electrons and H nuclei combine=> space transparent
• Gravity (mostly dark matter’s) dominates
deceleration => formation of galaxies
• Dark energy dominates recent & future expansion.
The future
• No big crunch in future.
• Nice not to have a fiery death
• Having all the stars eventually stop shining is
depressing.
• But that won’t happen for trillions of years
and … who knows what we (or somebody else)
might be like (or do) in a trillion years.
We have seen a history of “expansion”. What does it
mean? That’s up to you!