REVIEW

Last: 15. A Brief History of the Universe

Much of what we know of the universe can be organized into a handfull of big themes.

Themes

  • Scientific Method
  • Copernican Principle
  • Orbital Motion & Gravity
  • Distance Scales
  • Cosmic Geography
  • Stellar Evolution
  • Origin of Elements
  • Expanding Universe

Scientific Method

Scientists develop ideas by the following general method:

  1. Observe the world and pose a question to be answered
  2. Develop a tentative answer — a hypothesis
  3. Deduce predictions assuming this hypothesis is true
  4. Test predictions; if they're not confirmed, go back to #1 or #2

A hypothesis which has been used to make many successful predictions — and which has not predicted anything we don't actually observe — advances to the status of a theory.

As a rule, theories are valid for some range of situations, but fail outside this range. We generally expect theories to fail if pushed too far. These failures inspire newer and more general theories which include older theories as special cases.

Copernican Principle

The Earth is Not the Center

Outer planets appear to move backwards whenever the Earth passes them on the inside as both planets orbit the Sun. For a time before and after the moment of opposition, when the planet is directly opposite the Sun, its motion is retrograde. As this animation shows, planets don't actually reverse their motion about the Sun; they only seem to do so because we are observing from a moving point of view.  
2003: Mars Retrograde Animation [NASA]

The Earth is a Planet Among Many



Moon, Mars, and Earth to scale

The Sun is a Star Among Many

We can compare the Sun with other nearby stars. It turns out that some are much more luminous than the Sun, some are like the Sun, and most are much less luminous than the Sun. For a sample of the 150 stars nearest the Sun, this table shows how many we find in various ranges of luminosity (measured in units of LSun).

  From
(LSun)
  To
(LSun)
  Number
of Stars
   
  10.0   100.0   4   Vega: L=50LSun
  1.0   10.0   14   αCen: L=1.5LSun
  0.1   1.0   25   τCet: L=0.46LSun
  0.01   0.1   21     
  0.001   0.01   57     
  0.0001   0.001   29     
  View of the solar neighborhood

The Milky Way is a Galaxy Among Many

All-sky view of MW
COBE view of MW
The Needle galaxy

The Universe is the Same Everywhere


Expansion from MW   Expansion from Galaxy 2   Expansion from Galaxy 3
Observed from MW   Observed from Galaxy 2   Observed from Galaxy 3

The expansion looks the same no matter where we are: all observers see other galaxies moving away from their galaxy, with speeds proportional to distances. The expansion of the universe does not define a center.

The Laws of Physics are the Same Everywhere

The unification of terrestrial and celestial physics began when ancient people first applied geometry to astronomy. Some key results:

Note: we also believe that the laws of physics don't change with time. This hypothesis is constantly being tested by observations of distant galaxies.

Orbital Motion & Gravity

We can summarize the motion of celestial objects by saying that ``Everything Falls''.

Kepler's Laws

  Law I: The orbit of a planet is an ellipse with the Sun at one focus.
  • The planet is closest to the Sun at perihelion, and furthest at aphelion.
  • At its widest point, the distance across the ellipse is 2a, where a is the semi-major axis.
  Ellipse with sun at focus
Kepler's laws [Wikipedia]
  Law II: A line drawn from the Sun to a planet sweeps out equal areas in equal times.
  • In other words, (area swept out) ⁄ (time elapsed) is a constant for each orbit.
  • This constant is now called angular momentum, and Law II states that angular momentum is conserved.
Ellipse with star at focus
Kepler's laws [Wikipedia]
  Law III: For all planets, P2 ⁄ a3 = 1 yr2 ⁄ AU3, where P is the period and a is the semi-major axis.

Question 16.1

Kepler's second law implies that a planet moves

  1. fastest when close to the Sun, and slowest when far away.
  2. slowest when close to the Sun, and fast when far away.
  3. at a constant speed at all times.
  4. any darn way it wants to.

Problem 16.1

Consider an asteroid with an elliptical orbit. Suppose that at perihelion (smallest distance) it's 2 AU from the Sun, while at aphelion (greatest distance) it's 6 AU from the Sun. (a) Sketch the orbit, showing the Sun and the empty focus. (b) How far is the empty focus from the Sun? (c) Calculate the asteroid's orbital period P in years. (d) Indicate the places where the asteroid is moving slowest and fastest, and calculate the ratio of fastest to slowest speed.

Laws of Falling Bodies

I. All bodies fall at the same rate, regardless of their composition or weight.   Galileo's experiment at the leaning tower (http://physics.nad.ru/Physics/English/top10.htm)
 
II. The total distance D  a falling body travels is proportional to the square of the time t  it has been falling:

D = g t 2 ⁄ 2     where     g = 10 m ⁄ s2
  Galileo's experiment with acceleration.
Physics for the Enquiring Mind, Ch. 19, Fig. 1

Orbits. a


A ball falls to Earth

Consider what happens to a ball released 200 km above the surface of the Earth. The law of falling bodies tells us that

in 60 s, it falls 18 km = (10 ms2) (60 s)2 ⁄ 2
in 120 s, it falls 72 km = (10 ms2) (120 s)2 ⁄ 2
in 180 s, it falls 162 km = (10 ms2) (180 s)2 ⁄ 2

Orbits. b


A ball falls on a parabola

If we give the ball some sideways velocity, the law of inertia tells that it keeps this sideways velocity as it falls; thus, the distance to the right is proportional to time.

Orbits. c


Multiple parabolas starting from 200 km

If we increase the sideways velocity, the ball falls further and further from where it started.

Orbits. d


A circular orbit from 200 km

Finally, when the sideways velocity reaches about 8 km/s, something almost magical happens: the surface of the Earth curves away just enough that the ball maintains its starting height of 200 km!

With this sideways velocity, the ball is finally in a circular orbit. It completes one orbit in about 90 minutes. This is a typical period for a satellite in a low orbit about the Earth.

`The secret of flying is to throw yourself at the ground and miss.' -- Douglas Adams

Distance Scales

The key idea of a distance scale is to use a known distance to measure one which is unknown — and often much larger than the known distance. In this way we build up an idea of distances to extremely distant objects.

The Size of the Earth


Simultaneous observations at two places -- Alexandria and Syene -- enabled Eratosthenes to calculate the size of the Earth:

R =  1

2 π 
 DAS  360°

θ 

He got a radius of 3800 miles, a remarkably accurate result! (The modern value is R = 3963 miles.)
Evidence for a spherical earth
Physics for the Enquiring Mind, Ch. 14, Fig. 14

Parallax: Theory

Parallax measurement from Earth

To measure the distance from the Earth (E) to a planet (P), observations are made at two different places. Suppose that one observation is made with P exactly overhead and aligned with a distant star. The other observation is made with P on the horizon; the angle between P and the distant star is θ.

The distance D from E to P can be calculated in terms of the Earth's radius, R:

D =  1

2 π
 R  360°

θ

You may recognize this equation -- or something like it -- from before. Eratosthenes used it to calculate the size of the Earth. Now the same relationship is being used to calculate distances to planets!

Question 16.2

In the parallax equation just described, the quantity

 R  360°

θ

represents:

  1. the radius of a circle
  2. the number of triangles in a circle
  3. the circumference of a circle
  4. the diameter of a circle

Parallax: Distances in the Solar System

On October 1, 1672, Mars passed in front of a moderately bright star. Realizing that this presented an opportunity to measure the distance to Mars, Cassini organized simultaneous observations from Paris (Europe) and from Cayenne (South America).

Mars from Paris Mars from Cayenne
  Giovanni Cassini
Giovanni Cassini [Wikipedia]

According to Kepler's model, Mars was 0.43 AU at this time. Cassini used the observed parallax and the known distance between Paris and Cayenne to to determine the distance to Mars, and find a value for 1 AU (which was 8% too small):

DMars = 6.0×107 km = 0.43 AU AU = 1.38×108 km

Parallax: Reaching for the Stars

To measure stellar distances, a baseline much larger than the Earth is required. The Earth's orbit provides a suitable baseline for measuring distances to nearby stars; observations made 6 months apart are separated by a baseline of

AU = 2.99×108 km .

Over the course of a year, a nearby star appears to trace a small oval in the sky when compared to more distant ones. By measuring the parallax angle p (defined as half the long axis of this oval), the distance D to the star can be found:

D =  1

2 π
(1 AU 360°

p
= 1''

p
 pc

where 1 pc = 206265 AU.

  Measurement of stellar parallax

Question 16.3

If we were to measure the parallax of a star from Mars (semi-major axis a = 1.5 AU) instead of the Earth, we would get

  1. the same parallax angle p.
  2. a parallax angle 50% larger.
  3. a parallax angle 50% smaller.
  4. a distance 50% larger.
  5. a distance 50% smaller.

Inverse Square Law: Theory

To map the Milky Way we need to measure distances far beyond the reach of parallax. We use the inverse-square law: the apparent brightness B of a standard candle of known luminosity is inversely proportional to the square of its distance D.   The inverse-square law

Suppose we observe two stars and know that they have the same luminosity. Star 1 has brightness B1 at distance D1, and star 2 has brightness B2 at distance D2; then

D2 : D1 = √B1 : √B2

Another way to express the same relationship is

D2  =  D1  ×  √(B1 ⁄ B2)

Question 16.4

How does the apparent brightness of a star depend on its distance?

  1. The apparent brightness is independent on distance.
  2. The apparent brightness is proportional to distance.
  3. The apparent brightness is inversely proportional to the distance.
  4. The apparent brightness is inversely proportional to the square of the distance.

Inverse Square Law: Main-Sequence Stars

When we plot surface temperature T against apparent brightness B for stars in the Hyades and the Pleiades, we find that both clusters contain stars on the main sequence. However, the main sequence in the Hyades appears about 8.5 times brighter than the main sequence in the Pleiades:

BH = 8.5 × BP

  Temperature-brightness diagram

Using the inverse-square law, we can find the distance to the Pleiades:

DP  =  DH  ×  √(BH ⁄ BP)  =  46.3 pc  ×  √(8.5)  =  135 pc

Inverse Square Law: Cepheid Variable Stars

To determine if Andromeda was another ``island universe'' -- a galaxy like the Milky Way -- we needed to find out its distance. For this we had to find more luminous objects which could be used as standard candles. A special kind of star, known as a Cepheid variable, turned out to be just what was required.

Cepheid variables are giant stars. Instead of shining steadily, they vary in brightness, following a regular pattern. The time a variable star takes to go through one cycle is known as its period.

Cepheid have a number of advantages as standard candles:

  • Easily recognized
  • Extremely luminous
  • Luminosities can be measured
  Light curve of a Cepheid

Question 16.5

Two cepheid variable stars with the same period will also have

  1. the same distance.
  2. the same color.
  3. the same luminosity.
  4. the same apparent brightness.
  5. the same mass.

Inverse Square Law: Supernovae

To directly measure distances to far-away galaxies we need more powerful standard candles. Type Ia Supernovae — thermonuclear explosions triggered when white dwarf stars collpase — can be used as `standard bombs'; they are
  • very luminous, and therefore visible at extremely large distances
  • easy to recognize — a bright point of light suddenly appearing in a distant galaxy is almost certainly a supernova
  • well-standardized, because they occur when the mass of a white dwarf reaches 1.4 MSun
  SN Ia in a distant galaxy

With such powerful candles it became possible to measure changes in the expansion rate of the universe. We expected to find that the expansion was slowing down due to gravity. Instead...

Distance Scales: Summary

Using each new distance measurement to help determine the next one, we've developed the ability to measure distances to the edge of the visible universe:

Using the Earth as a baseline, parallax provided the distance to the Sun; using that distance as a baseline, it yielded distances to the nearby stars. These results provided a way to measure main-sequence luminosities and get distances to star clusters; cluster distances, in turn, enabled us to measure Cepheid variable luminosities and get distances to nearby galaxies; finally, galaxy distances allowed us to measure luminosities of Type Ia SN.

distances to astronomical objects

Cosmic Geography

A basic knowledge of some key celestial objects is part of this course.

The Earth: Internal Structure

The core of the Earth is composed of iron and related elements. In contrast, the mantle is largely composed of lighter rocks in a semi-soft state.

When the Earth formed, it was melted throughout and the heavy elements sank to the center. Planets with this kind of structure are said to be differentiated.

  Internal structure of Earth
Earth's Interior [Views of the Solar System]

The Earth: Internal Activity

Heat generated by radioactive decay drives convective flows in the outer core and mantle; this accounts for the Earth's magnetic fields and plate tectonics.

When a fluid is heated from the bottom and cooled at the top, convection develops: warm fluid rises to the top, cools, and sinks back to the bottom. This transports heat very efficiently.   Simulation of Convection
Mantle convection [H. Schmeling]
Earth's magnetic field is created in its molten outer core by a combination of (1) rotation, (2) convection, and (3) electrical conduction. Mercury, despite its slow rotation, also produces a magnetic field; Mars apparently did when it was young and active.   The Earth and a bar magnet
Magnetic Field of the Earth [hyperphysics]

The Earth: Surface Features

Surface features on the Earth — and other planets — are created by several different processes.

Question 16.6

In this simplified diagram of the Earth, which region is

• composed of semi-soft rock flowing slowly due to convection?

• composed of solid iron and similar elements?

• the origin of the Earth's magnetic field?

• solid, but constantly rearranged by the motion of material below it?

  The Earth's internal structure

The Sun: Internal Structure

The Sun's interior is made up of the same mix of hydrogen and helium as its surface. Below the visible surface, three main regions can be defined. These are the core, where energy is produced, a radiative zone, where this energy travels as radiation, and a convective zone, where energy travels by convection.   Structure of the sun

The Sun: Energy Production

Within the Sun's core, the weight of the overlying material compresses the gas to a density and temperature of

ρ = 150 gm ⁄ cm3 ,

T = 1.5×107 K .

Under these conditions, the hydrogen in the core of the Sun is slowly transmuted into helium. About 0.7% of the hydrogen used in these reactions is converted to energy:

E = Mc 2 .

  Nuclear fusion in the sun
Proton-proton chain reaction [Wikipedia]

Question 16.7

In this simplified diagram of the Sun, which region

• gives off the visible light we actually see?

• transports energy via radiation?

• is the origin of the Sun's magnetic field?

• is the source of the Sun's energy?

  The Sun's internal structure

The Solar System: Overview

The Solar System can be divided into two zones. Bodies in the inner zone are composed mostly of rock and metal, while those in the outer zone consist largely of gas and ice.

The inner solar system   The outer solar system
Inner Solar System: Mercury, Venus, Earth, Mars and asteroids.   Outer Solar System. Left: Jupiter, Saturn, Uranus, Neptune, Pluto, a comet, and the Kuiper belt. Right: The Oort cloud.

The Solar System: Inventory

Question 16.8

In this simplified diagram of the Solar System (not to scale!), which

• orbits are occupied by earth-like planets?

• orbit is typical of a comet?

• region contains the asteroids?

• orbits are occupied by gas giants and water worlds?

  Layout of the solar system

The Milky Way: Structure

Edge-on diagram of the Milky Way

Plotting positions of globular clusters showed that they form a swarm centered not on the Sun but rather on a point about 8500 pc = 8.5 kpc away. Once this was understood to be the center of the Milky Way galaxy, the big picture became clear.

The Milky Way: Populations & Components

Pop'n Where? Age
(Gyr)
``Metals''
(heavy
elements)
Orbits
I Disk 0 to 10 Like Sun Circular,
flat
II Bulge
& Halo
10 to 12 Less
than Sun
Elongated,
tilted
  orbits in Milky Way

Besides these two stellar populations, there is a third component of the Milky Way: dark matter. This stuff is not stars and is probably not any form of ordinary matter (ie, composed of atoms). The dark matter is probably distributed like the halo and may represent as much as 90% of the Milky way's mass.

Question 16.9

In this simplified diagram of the Milky Way,

• where is the Sun?

• which region contains stars on circular orbits?

• which letter labels a globular cluster?

• which region includes the halo?

• which regions contain old stars? (Note: there's more than one correct answer.)

  Layout of the milky way

Stellar Evolution

The lives of stars are constant struggles against gravity; nuclear reactions provide a temporary energy source which halts contraction for a while.

A gas sphere held together by gravity heats up and contracts as it radiates energy:

T ∝ 1 ⁄ R .

  A sphere of gas heating up

Hydrogen `burning' (4H → He + energy) begins when the core of the star reaches a temperature of about 107 K. This process is stable; if reactions produce too much energy, the core expands and cools off, reducing the rate of energy production.

Stars producing energy by burning hydrogen to helium in their cores are on the main sequence.

Stellar Evolution: The Main Sequence

On a plot of surface temperature against luminosity, we find a swath of stars crossing from lower right to upper left. This is the main sequence (red curve). The main sequence is a mass sequence; low-mass stars are cool and dim, while high-mass stars are hot and luminous.

The amount of time a star spends on the main sequence depends on its mass: low-mass stars live a long time (~1010 yr or more), while high-mass stars have shorter lifetimes (as little as a few 106 yr).

  HR diagram with models & tracks
Galaxies in the Universe, Ch. 1, Fig. 4

Stallar Evolution: Red Giants

When all the hydrogen in a star's core has been burned to helium, the star begins a dramatic transformation.

An inert helium (He) core sits at the star's center. The core is hot, so energy flows out; in response, it contracts (black arrows), releases gravitational energy, and gets even hotter! Hydrogen burning (4 H → He) continues in a shell around the core.

The total amount of energy produced by the star is now much greater than it was when the star was on the main sequence, and the envelope of the star must expand (red arrows) to handle this energy flow. The surface temperature drops from white-hot to red-hot.

  Evolution after H exhaustion

From an external point of view, the star becomes both brighter and cooler; it swells up to about 100 times its main sequence size, becoming a red giant.

Late Stages of Low-Mass Stars

A low-mass star has four stages of nuclear burning: main sequence (MS), red giant (RG), horizontal branch (HB), and asymptotic giant (AG).   Key stages in life of solar-mass star

At each stage, key properties of a M = 1 MSun are:

Stage Age
(109 yr)
Diam.
(AU)
Lumin.
(LSun)
Nuclear Reactions
MS 10.9 0.01 2 4 H → He (core)
RG 12.2 1 2000 4 H → He (shell)
HB 12.3 0.1 100 4 H → He (shell) 3 He → C (core)
AG 12.4 2 5000 4 H → He (shell) 3 He → C (shell)

Question 16.10

To ignite helium requires temperatures of ~108 K; how do stars generate the energy required to reach such temperatures?

  1. Carbon burning.
  2. Hydrogen burning.
  3. Gravitational contraction.
  4. Radioactive decay.

Stellar Evolution: White Dwarfs

Why doesn't the core of a low-mass star continue contracting, and heat up enough to burn C/O?

A new form of pressure stops contraction.

Core ejects envelope (→ planetary nebula) and remains behind as central star:

No energy sources -- bare core gradually cools off.

Origin of Elements: Supernovae

Main types of supernovae

There are two possible ways in which stars can explode and return new elements to interstellar space. Both involve a critical mass limit, the Chandrasekhar mass.

Origin of Elements: The Chandrasekhar Mass

Recall that quantum mechanics requires electrons to move with speeds inversely proportional to the radius of a star:

v  ∝  1 

R 
 .

Also, recall that the more mass a white dwarf has, the smaller its radius. Therefore, the higher the mass of a white dwarf, the faster its electrons must move.

Now, if a star supported by degeneracy pressure is too massive, the electrons would be required to move faster than light. Nothing can move faster than light, so degeneracy pressure cannot support stars above a certain mass. This mass, first computed by Chandrasekhar, is 1.4 MSun.

Origin of Elements: Type II Supernovae

Stars with more than 10 times the Sun's mass reach very high internal temperatures and can burn heavier elements:

Reactants Temperature
(°K)
Products
12C + 12C 6×108 24Mg, 23Mg + n, 23Na + H, 20Ne + He, 16O + 2 He
20Ne + He 1.2×109 24Mg
16O + 16O 1.5×109 32S, 31S + n, 31P + H, 28Si + He, 24Mg + 2 He
32S, 28Si, He ~3×109 56Fe, 56Co, 56Ni

Each stage of burning yields less energy, and the iron-group elements (Fe, Co, Ni) yield no energy at all.

As burning proceeds, a degenerate core of Fe builds up at the center of the star. When it reaches the Chandrasekhar limit, it collapses and triggers an explosion.

 
Structure of 20 M_sun star

Origin of Elements: Type Ia Supernovae

A white dwarf orbiting a another star may gain mass from its companion. The stolen mass forms an accretion disk around the white dwarf and slowly spirals in toward the center.   Mass transfer to a white dwarf

When the white dwarf gains enough mass to exceed the Chandrasekhar limit, it begins to collapse. But the carbon and oxygen making up the white dwarf begin to burn as it collapses, and this releases so much nuclear energy that the star is completely destroyed. The nuclear reactions synthesize large amounts of iron-group elements, and some heavier elements as well.

Origin of Elements: Cosmic Abundances

Some elements are more common than others; the pattern of abundances reflects the origins of different elements.
  • Li, Be, B are rare; they are produced in the early universe, as is most He.
  • C and O are products of Type II SN, as are other light elements with even numbers of protons.
  • Iron-group elements (Fe, Co, Ni) are common products of Type Ia SN.
  • Elements beyond the iron group require energy to create; mostly produced in Type Ia SN, they are rare.
  • Pb is more common than other heavy elements; it's produced when heavier ones (eg, Th, U) decay.
  Abundances of elements
Abundance of Elements [GreenSpirit]

Expanding Universe: Hubble's Law

Standard candles enable us to measure galaxy distances to many 100 mpc. When a galaxy's distance d is plotted against its recession velocity v = cz (where z is the redshift), a simple relation emerges:

v = H0 d ,

where Hubble's constant has the value H0 = 72 km ⁄ sec ⁄ Mpc.

This yields two key conclusions: (1) the universe is expanding, and (2) the expansion began ~13.6×109 yr ago.

  Hubble diagram

Expanding Universe: ``Dark Energy''

Extending the distance-velocity diagram to very distant galaxies shows the expansion is speeding up!

To prevent gravity from slowing the expansion, some form of `antigravity' is needed. The most promising possibility is a repulsive force associated with empty space itself (Einstein's `cosmological constant'). This force becomes more and more effective as the universe expands, because the expansion creates more and more empty space.

A possible recipe for the universe contains about 5% ordinary matter, 25% dark matter, and 70% `dark energy' — in effect, energy associated with this form of antigravity.

  Accelerating expansion
Dark energy [physicsweb]

Expanding Universe: The Microwave Background

The oldest light we can detect comes from a time long before the first stars and galaxies formed. This is an almost perfectly uniform sea of microwave photons coming from all directions. The spectrum of this radiation is a perfect match to a `black-body' with a temperature of 2.725 K — the temperature of the universe today.   COBE/FIRAS data and black-body spectrum
Ned Wright's Cosmology Tutorial [UCLA]

Nothing in the present universe produces radiation so perfectly matched to a black-body spectrum. This radiation is a relic of a time when the entire universe was a black body, with a temperature of about 3000 K.

Expanding Universe: Concordance

Fluctuations in the microwave radiation provide key information about cosmology. For example, `lumps' in the microwave sky tend to have angular sizes of about 1°, implying that the universe has no overall curvature. (These fluctuations also serve as the `seeds' of galaxy formation.)   Microwave fluctuations
WMAP Data Product Images [NASA]

The net result is a `best bet' model of the universe!

Expanding Universe: Light Element Formation

When the temperature of the universe had fallen to 109 K (∼100 sec after the universe began), ps outnumbered ns by a ratio of about 7:1. At this temperature, ps and ns could start combining to build up atomic nuclei. The first reaction produced `heavy hydrogen' (2H, a.k.a. deuterium or D) via

p + nD + γ

As in stars, D gets involved in other reactions as soon as it forms. Thus almost all of the D quickly combined to produce helium (4He).

  Nucleosynthetic reactions

Within a few minutes, almost all the available ns had combined with ps, yielding 25% by mass of 4He. Other reactions produced tiny amounts of other light elements, mostly leftover D and lithium (7Li).

Expanding Universe: Inflation

The original `Big-Bang' model for the formation of the universe left a few questions: Why is the universe the same everywhere? Why is space `flat'? Why are exotic particles like monopoles not common?

Inflation provides one answer to all three of these questions. The idea is that when the universe was about 10-35 sec old, Einstein's cosmological `constant' could have become very large, creating a powerful antigravitational force. This would have caused the universe to expand exponentially, increasing its size by a factor of 1050 or more.   Inflation vs standard theory

Expanding Universe: Inflationary Answers

If inflation actually occurred, it would provide answers to the horizon, flatness, and monopole problems:

In addition, inflation could account for the tiny variations in density needed to produce the microwave background fluctuations and the large-scale structure of galaxies and clustwers we observe today.

Last: 15. A Brief History of the Universe

Joshua E. Barnes (barnes@ifa.hawaii.edu)
Last modified: December 6, 2006
http://www.ifa.hawaii.edu/~barnes/ast110_06/review.html
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