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ASTR 340
Origin of the Universe
SUPPLEMENT #1
Spring 2004
Dennis Papadopoulos
January 27, 2004
l. Questions, Scales and Objects
What this course will cover started billions of years ago. Man looked at the sky probably
as early as he came into existence. Everybody has, at one time or another gazed at the
stars and pondered at least a bit on the mysteries of the universe and man’s place in it.
This course will attempt to cover the fascinating story of the evolution of the universe. It
is a story which is more enthralling since everybody can participate in observing many of
the astronomical bodies. The history abounds with contributions made by amateurs with
as little instrumentation as the naked eye or a looking glass. Sumerian, Chinese, Korean,
Egyptians and most prominently ancient Greeks recorded and interpreted the
observations. With the knowledge accumulated from the course you will be able to
answer questions such as
“Where did we come from?”
“How was the universe created and evolved to its present stage?”
“Can we learn more about the basic laws of physics from the observable effects
they had on the structure of the universe?”
“How did galaxies and clusters of galaxies formed and how they evolved?”
“Can massive stars or galaxy size aggregates collapse to form black holes,
liberating enormous amounts of energy?”
“How do stars and star clusters form and die and how they interact with stellar
matter?”
2. Large Scale Structures
Over the years and after many false stars the story can today be summarized as following.
The Earth that we live on is simply one of a family of planets revolving around the Sun.
The Sun itself is nothing more than an ordinary star in the huge stellar system – the Milky
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Way – which is our galaxy. Similarly, the Milky Way is merely one galaxy among the
vast number of galaxies that stretch to the edge of the visible universe. Some of them so
far distant that light take billions of years to reach us. In fact the observable universe is
1027 meters across. Against this background the Earth, which has a radius of 6000 km (6
 106 m), seems very insignificant. How much more insignificant is the man! [Figs. 2.12.6].
Figure 2.1: The Solar system
The Sun is only one among 1011 stars bound together by gravity into a large cluster of
stars called galaxy (Fig.2.2 & 2.3). The stars of the galaxy revolve about its center as the
planets revolve about the Sun. The Sun itself participates in its rotating motion, with a
period of 2  108 years. The galaxy is flattened by its rotation to a pancake like disk
whose thickness is roughly 1/5 of its diameter. The Sun is located about 3/5 of the way
out from the center to the edge. Looking up we see so many stars that we cannot
separate, but blend together into a luminous band stretching across the Sky, called the
Milky Way.
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Figure 2.2: Our Galaxy – The Milky Way
Figure 2.3: Stars in our Galaxy – Galactic Center
Milky Way.
Figure 2.4: Neighboring Galaxies – The Local Group
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Within the galaxy the stars are separated from one another by about 5  1013 km which
correspond to 5  y. The 5 m Palomar Telescope has within its range 1010 other galaxies,
each of comparable size as our own and with a comparable number of stars. The average
distance between the galaxies of 106 y . The extent of the visible universe as seen with a
5 m telescope is 1010 y .
The nearest galaxy to ours is the Andromeda galaxy 3  106  y away (Fig. 2.5).
Figure 2.5: The Andromeda Galaxy
Figures 2.6-2.10 show the garden variety of galactic shapes, with the distribution of
shapes depending in a way that is not completely understood on the evolution of galaxies.
Our galaxy has arms of younger stars and gas that appear to spiral out from the center.
Figure 2.6: Spiral Galaxy – M100 at the Virgo Cluster
The majority of galaxies do not show any spiral features and are not flattened disks they
take the form ellipsoids such as shown in Figure 2.7.
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Figure 2.7: Elliptical Galaxy – M87 in the center of the Virgo Cluster
Some galaxies are neither ellipsoids nor spirals. Some of these are obviously objects
distorted by the presence of near-by galaxies and have irregular shapes or other shapes
(2.8-2.9)
Figure 2.8: Irregular Galaxy- The Large Magellanic Cloud
Figure 2.9 Lenticular Galaxy
Some galaxies show evidence for the generation of enormous amounts of energy from the
vicinity of their nucleus. Figures 2.10 shows a galaxy known as NGC4261 that has
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gigantic radio frequency jets emerging from its nucleus and a Hubble Telescope image of
its central region where a black hole is suspected to exist.
Figure 2.10: Radio frequency jets and black hole in the center
Galaxies are preferentially found in groups or larger agglomerations called clusters. The
Local Group consists of our own galaxy, the Andromeda and several smaller satellites,
including the Magellanic Clouds. Clusters contain from 3 to 104 galaxies each. Clusters
of galaxies are the largest known systems of organized matter and thus terminate the
hierarchy of structure in the universe. The physics behind some of the clustering will be
addressed later on in the course.
Figure 2.11: Virgo an irregular cluster is the nearest large cluster of galaxies (103-104
stars)
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Figure 2.12: The Coma cluster has concentrated core and well defined spherical structure
Figure 2.13: Fornax – A small cluster of spirals and ellipticals near our Local Group
Recent deep red-shift surveys reveal a very bubbly structure to the universe with galaxies
primarily confined to sheets and filaments. Voids with size of 25 Mpc are the dominant
feature (Figure 2.14).
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Figure 2.14: Survey to 2% of the distance to the edge of the observed universe. Galaxies
are plotted as white points. Filamentary, sheet like structures and bubble like voids are
evident.
3. Small Structure
While we discussed the large length scale structure the key aspect of astrophysics and its
link to physics is the coupling of the large and small scales.
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For a long time the atom whose size is only 10-10 m was thought as the building block of
matter. In the 1930’s we found that the atom is composed of even smaller objects such as
electrons, protons and neutrons.
We all have heard of the atom or the electron. “How big is the atom?” “Is it much
smaller than a speck of dust?”
The correct answer is that the size of a speck of dust is to the size of an atom, about one
tenth of what the earth is to a speck of dust.
How can we confirm that such small entities exist? No one picked up an electron to
measure it. As we will later see, we cannot even localize it. How do we even know that
it exists? The evidence is indirect. During 150 years from the late eighteenth century to
the beginning of the twentieth a great variety of experiments were conducted on the flow
of electricity through liquids and gases. The existence of the electron was not proved
conclusively by any single one of them. However the majority of them could be easily
explained assuming that the current was carried by a stream of small particles, each
bearing its own electric charge. A conviction was gradually built up that the electron
exists.
The next question was how large it is and how much electric charge each electron
carries? The clearest answer came from an experiment conducted by Robert Millikan of
the University of Chicago, in the early twentieth century. Millikan made a particularly
simple experiment. An atomizer created a mist of very fine droplets of oil just above a
small hole in the top of a container. A smaller number of them fell through the hole and
slowly drifted towards the bottom. Their motion could be observed by illuminating them
from one side and projecting them against a dark backdrop. By applying an electric field,
Millikan, found that some droplets were responding to it, because they had picked up
extra electrons in the atomizing procedure. By studying their motion he managed to
deduce the amount of electric charge carried by an electron. It turned out to be small (1.6
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 10-19 Cb). It takes a flow of over 1014 electrons per second to light a 10 Watt bulb.
This discovery was relatively recent (1914).
The electron and two sister particles the proton and the neutron are the building blocks of
all matter that can exist in free state over macroscopic time scales.
The proton was
identified in 1920 and the neutron in 1932. They are 1840 times heavier than the electron
but still extremely light. The electron mass m2  9  10-31 kg, while the proton and
neutron mass mp  mn  1.6  10-27 kg. The three particles combine in an amazingly
simply way to produce the objects we see and feel. A strong force of attraction, nuclear
force, binds neutrons and protons together to form a compact body, the nucleus, with size
about 10-15 m. The protons are positively charged while the neutron has not charged.
Thus, the nucleus is positively charged. Electrons are attracted to the nucleus and circle
around it in a fashion similar to the planets around the Sun. Together the electrons and
the nucleus form the atom (Fig. 3.1). It has a radius of 10-10 m. To get an idea of the size
of the atom, note that if each atom in a table had the size of a grain of sand the table
would be 3000 km long.
The comparison of the atom with a grain of sand implied that it is solid. In fact it is
mostly empty space. The solid part, (nucleus) has a radius of 10-15 m, while the electrons
from a diffuse shell with radius of 10-10 m. If the outer shell electrons were the size of the
Astrodome the nucleus will be smaller than a ping-pong ball.
Matter is composed of three fundamental building -blocks: a light particle called the electron and two relatively heavy
particles, each 1840 times as massive as the electron, called the neutron and the proton. The neutrons and protons are
bound very tightly into a compact mass called the nucleus. Electrons are attracted to the nucleus by the
positive
charge of the protons and circle in orbits around it under the influence of this attraction. Together the nucleus and
orbiting electrons form the atom. An atom of carbon consists of six electrons circling a nucleus of six protons and six
neutrons. The diameter of a typical atom is one hundred-millionth of an inch.
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Figure 3.1: Structure of the atom
If the atoms are empty space what holds material things together? Why does a table top
resist when you push it with your finger? The reason is that the outside wall of the table
consists of electrons. So does the outside of your finger. Where they meet, strong force
of electric repulsion prevents the electrons in your fingertip from pushing past the
outermost electrons of the top of the table into the empty space within each atom. Fast
atomic projectiles can penetrate or even break the atom.
Atoms are joined together in groups of molecules, such as water, which consists of two
atoms of hydrogen to one atom of oxygen (H2O). Large numbers of atoms or molecules
together from solid matter. There are more than 1021 atoms in one cm3 of solid matter,
which is approximately the number of grains of sand in all oceans of the earth.
The earth is a large collection of atoms bound together into a ball of rock and iron with a
6000 km radius and a weight of 6  1024 kg . It is one of the planets bound to the solar
system (Fig. 2.1). The Sun has a mass 700 times the combined mass of all planets. Like
the atom at least on a superficial basis the Sun is surrounded by the planets that revolve
about it at great distances leaving a large volume of empty space.
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4. Forces – Chemical Elements
The groups of objects discussed above are held together by only three fundamental
forces. A nuclear force, an electromagnetic force and a gravitational force. Towards the
end of the course we will examine attempts to unify all these forces. Furthermore, in our
current cursory examination we consider only one nuclear force, the strong one. The
weak nuclear force will be discussed later on.
The most power force, which binds neutrons and protons together into the nucleus of the
atom. This force binds the nucleus into a very compact body with density in excess 1011
kg/cm3. The next strongest force is the electromagnetic (em) force which is about 100
times weaker than the nuclear force. This force binds together the electrons to the
nucleus to form atoms, and binds atoms together into solid matter. Least powerful is the
force of gravity. It is 1038 times weaker than the nuclear force. Nonetheless it is the
force that produces bound systems such as the earth and the moon, the solar system, the
galaxy and the galactic clusters.
Gravity is the simplest basic force since it is always attractive. The em force can be
attractive or repulsive. Both forces drop with distance as 1/r2. The nuclear force is
attractive but is short range. Namely it drops with distance as 1/r 2 e  r/ro where ro  10-15
m is the radius of the nucleus.
The simplest atom, hydrogen, consists of a single electron circling around a nucleus of a
single proton. Hydrogen makes up 90% of all matter in the universe. The next atom,
deuterium, has again one electron but its nucleus is composed of one neutron and one
proton bound by the nuclear force.
The chemical properties of the elements are
dependent on the number of electrons they have.
Thus chemically hydrogen and
deuterium behave similarly.
After hydrogen, the second most abundant element in the universe is helium. Helium
usually exists on the earth in the form of a gas. It is lighter than air, once had a wide use
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in dirigibles, and is still used in children'’ balloons. The nucleus of a helium atom
contains two neutrons and two protons. Since each proton can attract one electron to
itself, an atom of helium has two electrons circling in orbit around the nucleus.
Hydrogen and helium together constitute approximately 99 percent of the matter in the
universe. All other elements make up the remaining one percent. Among the electrons in
this fast one percent, the most abundant is the critically important substance oxygen. An
atom of oxygen is composed of a nucleus containing eight neutrons and eight protons,
around which eight electrons circle. Other nuclei exist with still greater numbers of
neutrons and protons. In each case, the complete atom is formed when the nucleus has
circling around it a number of electrons equal to the number of protons it contains. In the
heaviest elements, such as lead and gold, the nucleus contains approximately 200
neutrons and protons, surrounded by up to 92 electrons arranged in a complicated array
of orbits of many different sizes. The atoms of uranium are the largest, heaviest and most
complicated of all. It consists of a nucleus containing 146 neutrons and 92 protons,
surrounded by 92 electrons.
Altogether there exist 92 different kinds of nuclei and 92 corresponding kinds of atoms,
stretching from hydrogen to uranium. These elements, in various combinations, make up
all the varieties of matter – animal, vegetable and mineral – which exist in the universe.
5. A Brief History
A way of measuring the completeness of our knowledge is to ask how far back can we
trace evolution of matter or to put it in another way, how close can we get to the actual
moment of creation. At any time in history a FOLKLORE was developed to provide an
explanation as to how the world came into existence.
Originally the creation folklore rested around the deeds of gods whose whims, battles, or
needs caused the world and its human inhabitants to be created and to perform according
to their wishes. The key question asked in the search for understanding was “who?”.
The search was confined to the earth and its surrounding constellation of stars and
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planets.
Astrology was the result of thinking that attributed the positions of the
constellation members and of the known planets to the wishes of this “who”. Very soon
however geometric patterns became apparent and were used by ancient Greeks,
Phoenicians etc. as navigation aids.
As early as the sixth century BC philosophers in the Green colonies along the eastern
Mediterranean had switched the question from “Who?” to “How””. They are trying to
explain how the elements of earth, fire, air and water interact to produce the “cosmos”
they were able to observe. The prevailing thinking was that the (cosmos) earth was the
center of the Universe. Under the philosophical influence of Pluto and with the empirical
observations of nature Aristotle formulated a model of the universe which consisted of
spheres nested within spheres with the earth at the center. Each sphere corresponded to a
planet and the Sun, with axes and directions of rotation adjusted to approximate their
observed motions (Fig. 5.1). The outer sphere was the sphere of the stars which were
considered as invariant.
Figure 5.1: The Aristotelian Universe
A major problem with the model was the existence of retrograde motion, i.e. motion at
which a planet moving in one direction appears to stop and then change direction of
motion. Typical of such an orbit was the orbit of Mars. Later on Ptolemy managed to
develop an improved model of the cosmos. He accomplished it by adding epicycles (5.2
and 5.3) and eccentrics in the motion of the bodies on their spheres, so as to reconcile
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theory and observation. This is nothing more than an empirical model of the cosmos,
which worked with surprising accuracy. It was a geocentric model. However, in practice,
even this was not enough to account for the detailed motion of the planets on the celestial
sphere! In more sophisticated epicycle models further "refinements" were introduced:

In some cases, epicycles were themselves placed on epicycles, as illustrated in the
adjacent figure.

In actual models, the center of the epicycle moved with uniform circular motion,
not around the center of the deferent, but around a point that was displaced by
some distance from the center of the deferent.
That ancient astronomers could convince themselves that this elaborate scheme still
corresponded to "uniform circular motion" is testament to the power of three ideas that
we now know to be completely wrong, but that were so ingrained in the astronomers of
an earlier age that they were essentially never questioned:
1. All motion in the heavens is uniform circular motion.
2. The objects in the heavens are made from perfect material, and cannot change
their intrinsic properties (e.g., their brightness).
3. The Earth is at the center of the Universe.
These ideas concerning uniform circular motion and epicycles were catalogued by
Ptolemy in 150 A.D. His book was called the "Almagest" (literally, "The Greatest"), and
this picture of the structure of the Solar System has come to be called the "Ptolemaic
Universe".
Figure 5.2: Ptolemaic Epicycle
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Figure 5.3: More complex epicycle
At the same time another Greek Aristarchos from the Greek island of Samos proposed the
first heliocentric model, i.e. a model where all the planets rotate about the Sun. His
motivation came from the results of an ingenious method for measuring the relative
distances of the Moon and Sun (see problem set #1), which were indicative that the Sun
was much more massive than the earth; it was then more plausible to suppose that the
more massive body would be the true center of the known cosmic rather than the earth.
A heliocentric model naturally accounts for retrograde motion. The system proposed by
Aristarchos was not accepted by his contemporaries.
Following the dark ages during which time all scientific ideas were suppressed by
religious dogma, the heliocentric system was rediscovered by Copernicus (Figure 5.4).
The Copernican system despite having placed correctly the Sun at the center was not less
intricate than Ptolemy’s due to its insistence on having circular orbits. It was necessary
to introduce Ptolemaic epicycles into the model and to move the center of the universe to
a point little away from the Sun to conform to the charts. Even in its compromised form
it did not make more accurate predictions than the Ptolemaic. Exactly how the planets
moves about the Sun, with exactly what motion to be the subject of a great philosophical
debate during the fifteenth century. A major breakthrough in the way of thinking was
caused by Tycho Brahe. His idea was that the philosophical debate about nature should
give way to measurement.
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Figure 5.3: The Copernican Universe
The nature of the motions of the planets would be best resolved if the actual positions of
the planets in the sky were measured with sufficient accuracy. This was a breakthrough –
that to find something out, it is better to perform some careful experiment followed by
careful calculations rather than carry on deep philosophical arguments. To a certain
extent it was the beginning of modern science. Pursuing this idea, Tycho Brahe studied
the positions of the planets for many years in his observatory on the island of Hven, near
Copenhagen. He made voluminous tables, which were then studied by the mathematician
Kepler, after Tycho’s death. Kepler discovered from the data some very beautiful and
remarkably simply laws regarding planetary motions.
The fundamental change in
thinking was that the planets instead of having circular motions they were following
elliptical motions which the Sun at one of its two foci (Fig. 5.4). Kepler also noted that
while a planet’s velocity changes during its years, so that it moves more rapidly when
close to the Sun than when further away, its motion obeys a simple mathematical rule.
Each planet sweeps out equal areas in equal times (Fig. 5.5). Finally, give years later,
Kepler stated one more rule. The cube of the mean distance of each planet from the Sun
is proportional to the square of the time it takes to complete one orbit (Fig. 5.6). As we
shall see later on this was the beginning of the concept of the gravitational force.
Kepler’s laws today are utilized in studying everything from orbits of artificial satellites,
to binary star systems and orbits of galaxies across clusters of galaxies.
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Figure 5.4: The orbits of the planets are ellipses, with the Sun at one focus of
the ellipse.
Figure 5.5: The line joining the planet to the Sun sweeps out equal areas in
equal times as the planet travels around the ellipse.
Figure 5.6: The ratio of the squares of the revolutionary periods for two
planets is equal to the ratio of the cubes of their semi-major axes:
On the observational side of the next break was Galileo’s use of the telescope to observe
the heavens. He first looked at the moon and discovered rocks, mountains and craters,
contrary to the Aristotelian smooth surface expectations.
He then, turned his
observations to Jupiter and discovered four moons orbiting giant planet, their positions
changing perceptibly within a few hours of observations. Thus, Jupiter constituted a
Copernican mini-solar system, and a proof that the earth was not unique in having a
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moon. He next observed a bright white planet, Venus, and he found that he exhibited
phases like the moon, and it appears much larger when in the crescent phase than when in
the full phase. The obvious explanation (Fig. 5.7) is that Venus stands nearer to the Sun
than the Earth and its big face occurs when it is on the far side of the Sun. The greatest
surprise was the stars. The telescope suggested, as the unaided eye could not, that the sky
has depth and the stars are not studded along the inner surface of the Aristotelian sphere,
but range out deep into space. We can thus say that the zero order exploration of the
solar system was completed.
Figure 5.7: Venus’s phases
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The complete picture of our solar system as we understand it today is summarized in
Table I. It is interesting to note a peculiar law when we look at the relative distances
between the Sun and the planets. It was discovered in 1772, by the German astronomer
Bode and it is known as Bode’s law. If we take the number 0, 3, 6, 12, 24, 48, 96, 92 and
384, where each number after 3 is double the preceding one, add the number 4 and divide
by 10, we find .4, .7, 1.0, 1.6, 2.8, 5.2, 10.0, 19.6 and 38.8. We find that with the
exception of 2.8 where there is no planet and of Neptune the laws holds true (see Table
I). The gap at 2.8 forced an intensive search for a planet. No planet was discovered.
However, the search revealed a large number of rocks (over 400000) each few km’s
across, which are in orbit near 2.8. It is called the asteroid belt. Whether Bode’s law has
any physical significance is not yet clear. We should finally mention that in the solar
system there are comets, one of them being Halley ’s Comet which has a 75 year period.
The nucleus of the ice like comets is few km’s, while a hell of a few thousand kilometers
and a tail of a few million kilometers accompanies them.
There are also meteors
(shooting stars), which are trails of tiny pieces of matter (meteoroids) rushing, through
space and burned up by friction as they get into the atmosphere.
Following Copernicus and Kepler, it did not take long to realize that the stars were bodies
like the Sun. The fact that they appeared fixed in the sky was, rightly, taken to indicate
that they lie very far from our solar system. By 1750, only a century after Galileo had
been forced to recant the Copernican doctrine at his trial for hearsay in 1633, the English
astronomer Thomas Wright put forward the idea that the appearance of the Milky Way
was evidence that the stars near the solar system are arranged in a flat dislike structure.
We now call this structure the Milky Way galaxy (from the Greek
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Table I
Planet
Mercury
Venus
Earth
Mars
Jupiter
Saturn
Uranus
Neptune
Pluto
Mean Distance
from Sun AU
.39
.72
1.0
1.5
5.2
9.5
19.
30.
39.
Equatorial
Radius
RE
.38
.95
1.0
.53
11.
9.4
4.4
3.9
2.6
Gravitational
Mass ME
.055
.81
1.0
.11
318
95.
15.
17.
.0023
Mean
Density
gr/cm3
Sid.
Period
Axial
Rot
Day
Max
T
C
5.4
5.1
5.5
3.0
1.3
88 Days
225 Days
365 Days
687 Days
11 3/4
58
247
1
1
.41
400
350
60
25
-140
.7
1.0
1.7
.8
Years
29 1/2
84 Days
165 Days
248 Days
.43
.51
.66
6.4
-160
-210
-230
?
1 AU – 1.5  1013 cm, RE = 600 km, ME = 2.5  1016 kg
word “galacticos”; gala is milk in Greek). It is a collection of some 10 billion (10 10)
stars, of which our own Sun has been explored extensively, since it is the star that we can
observe best. How many other planetary systems exist in the Milky Way galaxy is still
unknown.
If the Sun is part of a collection of stars arranged in a certain way, it is natural to ask
whether other such collections exist in the Universe. Debate on this question went
throughout the late eighteenth and nineteenth centuries. It centered on faint patches of
light on faint patches of light in the sky known as nebulae, of which there are many.
One, in the (galaxy) constellation Andromeda had been known to Arab and Persian
astronomers since the tenth century. The famous astronomer Sir William Herschel and
Immanuel Kant suggested that some of these nebulae might be galaxies. Yet there are
many nebulae in the sky that are not galaxies. For example there are clouds of gas (more
appropriately of plasma) that are illuminated by stars located in their interior, having the
appearance of galaxies. Such nebulae are clearly in our galaxy and strong arguments
were made against “assigning” large distances to any other nebulae in the sky. A key
argument was centered on the fact that flashes of extreme strength were occasionally seen
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originating in some nebulae.
If a large distance was assigned to them one had to
conclude that no source of energy known in the 19th century could have produced them.
Today we know that these flashes were supernovae and that the source of energy is the
conversion of large amounts of matter into energy. Since this was then unknown the
question of whether some nebulae were distant galaxies or merely clouds within the
Milky Way remained open.
The resolution to the puzzle came again by measurement. In 1923 the 100 inch (2.5 m)
telescope was completed in Mount Wilson, CA.
The discriminating power (i.e.
resolution) of the new telescope was such that it was possible to resolve individual stars
in the Andromeda nebula. The types of stars Hubble saw were similar to the ones in our
galaxy; in particular he was able to isolate several stars of the type known as “Cepheid
variables” (pulsating stars) which we will study later on.
These are stars whose
brightness varies periodically with time over periods of weeks or months.
It was also
known that the time average luminosity <L> was proportional to their period
~
2

L
~  . Since the amount of light we receive on the earth scales as 1/R2 where
R is the distance to the emitting object, knowledge of the luminosity value <L> from the
measurement of the period  could tell us the distance to the object. By observing the
Cepheid variable stars in the Andromeda nebula Edwin Hubble was able to show that the

stars, and hence the nebula, must be a million light years away 10 6 y
1 y  3.15  10
7


 3  1010 cm  9.45  1017 cm . Since the Milky Way is only 105 y
across, the only possible conclusion was that the Milky Way was one of many galaxies in
the universe. Since that time the number of known galaxies is larger than 106 and its
growth does not seem to be slowing down. Just as those who followed Copernicus had to
surrender the concept of the earth and the solar system as the center of the universe,
twentieth century scientists have to abandon the concept of uniqueness of the Milky Way.
It turns out that it is a rather typical galaxy with nothing distinguishable more than the
fact that we live in it. The next breakthrough following the establishment of the existence
of other galaxies was accomplished also by Hubble.
His studies revealed another
important and surprising thing. It appeared that the distance between the Milky Way and
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other galaxies was increasing; that other galaxies on both sides of the Milky Way were
moving away from us. Furthermore, the further away from us the galaxy in question the
gaster its recession speed. The technique used for this measurements is known as the
“redshift” and is based on a universal wave phenomenon known as Doppler effect which
we will discuss in detail in the next lecture (examples are the pitch of the whistler of a
passing train higher as it approaches, drops when it moves away; the radar detector used
for speed control).
This profound observation was consistent with the concept of a universal expansion of
the universe, with all galaxies receding from each other. Knowing the separation of
galaxies at the present time and the recession speed, allows us to mentally “run the film
in reverse”; that is let the galaxies move closer and closer together. This in principle
allows us to infer from the present position of the galaxies the amount of time that has
elapsed since the matter in the universe existed in a highly compact state. The number
we find this way is called the “Hubble time” or the “Hubble age” and represents a rough
guess at the age of the universe.
Measuring this number accurately requires both good instrumental resolution and good
calculations. When Hubble produced its first measurement he put it to one billion (109)
years, which about one order of magnitude smaller than the currently accepted value of
10-20 billion years (1-2  1010 years). At that point the age of the earth as determined by
geological (radioactive dating) measurements was thought to be several billion years. Of
course it is impossible for the earth to be older than the universe. As mentioned this
discrepancy was later corrected by more accurate observations which essentially place
the age of the universe to 1.5  1010 years  50%. The 50% uncertainty is not important
to modern cosmology.
The only force presently acting on outward moving galaxies is gravitational attraction of
the rest of the galaxies. Since the gravitational laws are well established we are able to
trace the expansion backwards in time.
We cannot, however, use this sort of
extrapolation all the way to the origin. At early stages in the expansion the density of the
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matter was so great that other forces (e.g. such as electromagnetic and nuclear forces,
which we will study later in detail, become dominant and are expected to plan the major
role. Our task in this course is to combine the understanding of physics as is emerging
with the astronomical observations to race back the history of the universe to as short as
possible times, which today approach somewhere between 10-30 – 1040 seconds.
6. Physics and Astronomy
The correlation and interplay between physics and astronomy cannot be overemphasized.
In fact, astronomy got physics started by showing the beautiful simplicity of the motions
of the stars and planets, the understanding of which marked the beginning of physics.
Today the roles have been reversed and physics is leading astronomy. However, with the
introduction of modern powerful instrumentation such as the space telescope or new xray detectors the roles might be again reversed.
A telling example of the physics-astronomy interplay is connected with remarkable
discovery that
“stars are made of atoms of the same kind as those on earth”.
How was that discovered? Atoms emit light which has a characteristic frequency typical
of the particular atom. This is similar to the timbre of a musical instrument, which has
definite pitches (i.e. sound frequencies). The trained ear has the discriminating power to
tell them apart. When, however, we look at light we cannot do the same because the eye
is not as highly a resolving instrument as the ear. With an instrument similar to the
prism, which we call a spectroscope, we can analyze the frequencies (i.e. colors) of the
light waves and thus see the signals emitted by various atoms in stars. As a matter o fact
Helium was discovered in the sun before it was found in the earth as was technetium
which was found in tertian cool stars. The fact that stars have similar atoms with the
earth allows us to make great progress. We know a lot about the behavior of atoms under
high temperatures but not great densities. However, although we cannot reproduce on
earth stellar conditions, statistical mechanics which is based on fundamental physics laws
allows us to calculate what will happen. So physics helps astronomy. Strange as it
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seems, we understand better the distribution of matter inside the sun than in the interior of
the earth. What is going on inside a star is better understood than one might guess from
the difficulty of having to look through a little dot because physics taught us how to
calculate what atoms in the stars should do in most circumstances.
Another important discovery was the origin of the energy that makes stars burn. It was
“nuclear fusion”. Namely at extremely high temperatures hydrogen in the stars “burns”
and produced large amounts of energy while it converts into helium. Furthermore,
ultimately, the manufacturing of various chemical elements, called nucleosynthesis,
proceeds in the centers of stars starting from hydrogen. The stuff we are made, was
“cooked” once in a star and pit out. How do we know this? Because there is a clue. The
proportion of different isotopes, the ratio of C12 to C13 etc, is something that is preserved
in chemical reactions. The proportion are purely the result of nuclear reactions. Looking
again through spectral lines at the proportions in the stars we find that they are similar to
the earth. Namely the furnace where the elements were cooked was like the one in the
stars. We can thus conclude that most probably the elements were “made” in the stars
and thrown out in explosions which we call novae and supernovae.
7. Time Scales
Let us again ask the question. What is time? Webster defines “time” as a “period”.
When we look at a “period” it defined it as “time”. Not very useful. Maybe we can face
the fact that we cannot define time in the dictionary sense and just say that it is what we
already know it to be: it is how long we wait!!
What really matters is not how we define it but how we measure it. One way to measure
time to utilize something periodic. For example a day, but of course in an average sense.
Pendulum was perhaps the first modern periodic instrument to measure short times. If its
length is kept constant the swing amplitude small then it oscillated 3600  24 times in
day. We present below in Table 1 the times that we will deal in this course. The span
over 42 orders of magnitude. It is obviously impossible to use a conventional clock to
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measure the short or the large times. For the short times the LC oscillator is a good
possible down to 10-12 sec (picosecond). An important issue is calibration. This is
usually accomplished by increasing the
TIMES
MEAN
LIFE OF
YEARS SECONDS
1018
9
10
????????
Age of universe
Age of earth
U238
15
10
Earliest man
106
1012
Age of pyramids
3
Ra326
10
109
Age of U.S.
Life of a man
H3
1
106
10
1
10-3
10-6
One day
Light goes from sun to earth
One heart beat
Period of sound wave
Period of radiowave
10-9
10-12
10-15
Light travels one foot
Period of molecular rotation
Period of atomic vibration
3
Neutron
Muon
-meson
o-meson
-18
Light crosses an atom
-24
Period of nuclear vibration
Light crosses a nucleus
????????
10
10-21
10
Strange particle
Table 1
frequency one order of magnitude at a time and comparing the oscilloscope traces.
Modern “lasers” techniques have gone to times shorter than 10-12 sec but with some
uncertainty in the calibration.
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Much shorter times require different techniques which in essence amount to a different
definition of the unit of time. These techniques are based on observing the distance
elapsed between two events that occurred on a moving object. For example if the
headlights of a moving automobile were turned on and off and if we know the position
where they turned on (x1) and the turned off (x2) and the speed (u) of the automobile we
know that
Δt 
x 2  x1
u
In the last few years this technique has been used to measure the lifetime of the  meson.
Measuring with a microscope the tracks left on photographic emulsions by impinging 
mesons it was seen that they traveled on the average 10-7 m before disintegrating. Since
their velocity is close to c their third lifetime  is

10 7
 3  10 16 sec .
8
3  10
Extensions of such techniques to shorter times will be discussed later.
It is obvious how to measure longer times as long as we are talking about periods of
thousand years. For longer times a different kind of clock is used. This is the radioactive
decay of active substances. We define as half life H of a radioactive substance the time
it takes for the radioactivity I to be reduced to half its value. Thus if we know that, say a
piece of wood, had contained an amount of radioactivity Io when it was formed and that it
now contains an amount I1 we can find the elapsed time t by solving the equation
1
 
2
t / H

I1
Io
Of course this assumes knowledge of H which can easily be measured in the laboratory.
Fortunately there are few cases that we know the radioactivity of an object when it was
formed. Such a case is C14 which is contained in a small fraction is CO2. If we measure
the total content of C in an object we know that a fraction of it was originally the
radioactive C14; C14 has H = 5000 years. By careful measurement of the amount of I left
after 20 H we can “date” organic objects which grew as long as 100000 ago. For longer
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times are uranium which has a radioactive isotopic with H 109 years. This technique
applied to rocks and meteorites dates the age of the earth as 5.5  109 years.
8. Length Scales
What about measuring distances? Table 2 represents again 42 orders of magnitude of
sizes. Let us start with large distances. How, for example, do we measure the height of
the shuttle in orbit. A simply way to do this has been known for very long and it is called
triangulation. It is shown in Fig. 8.1, distance L a part we have all the necessary elements
to find height h as well as x1 and x2 by simple geometric relations. The typical height of
the shuttle is 300 km. A similar technique gives a distance of 4  105 km for the moon.
More recently laser and radar ranging techniques have been used to measure the location
of satellites, the moon and several of the planets.
These techniques are based at aiming a radar or laser signal at the object and measuring
the time  it takes to receive the backscattered signal. The distance x is then x = ½ c.
Figure 8.1: By measuring the angles with respect to the shuttle from two locations on the
ground with a known distance L, we have all the necessary information to determine the
height of the shuttle and its distance from the two locations.
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DISTANCES
LIGHTYEARS
METERS
????????
1027
Edge of universe
109
1024
106
To nearest neighbor galaxy
1021
To center of our galaxy
103
1018
To nearest star
1
1015
Radius of orbit of Pluto
1012
To the sun
10
9
10
6
10
3
To the moon
Height of a Sputnik
1
103
Height of a TV antenna tower
Height of a child
A grain of salt
10-6
A virus
10
-9
Radius of an atom
-12
10
10-15
Radius of a nucleus
Table 2
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