aristotle (384-322 bc) showed earth is round, way before columbus! shadow of earth on moon always...

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

• 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.

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’sStarry 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.

• Bright only.• No dim stars• in this direction.• * * * * * * * * * * * * * * • Bright * * * * * * * * * * * *• & * * * * * * * * * * * * *• dim* * * * * * * * * * * * *• * * * * * * * * * * * * * *• Bright only.• No dim stars• in this direction.

1785 Herschel surveyed and found our place in MW Galaxy

• 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?

Cepheid Variables

• 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.

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 “period-luminosity” 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

• Intensity of the light from each star on earth decreases like

• The product of these two, the total intensity increases as . Light from a large volume would be enough to burn up the earth.

3R

2/1 R

R

• 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.

Future? • 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]

``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.

Time increases downward

Some galaxies’ Δλ/λ= z>1! Why? COSMIC red shift for • expansion. Not Doppler.• “Rubber sheet”stretches λ• while wave travels •

• Time 1 Milky Way Quasar emitting

• 2

• I see it

• 3

White dwarf supernovas permit estimate of still larger distances of galaxies

Measure Doppler shift=> speed of recessionCompare 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)

• Line is uniformly expanding universe (no gravity deceleration, no acceleration)• 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.

Separation/today’s

separation between galaxiesvs 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.

3000K=>3K. 14 billion ly to here

• 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.

• 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!