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Part 1: Early Cosmological Ideas
Topics:
Introduction
The Birth of "Scientific" Cosmology
Aristotle & Ptolemy
The "State of the Universe" for the Greeks
The "Dark" Millennium
The Recovery of W. European Science
Introduction
The word Cosmology is from the Greek kosmos (world)
and logia (from legein: to speak).
All civilizations (probably) developed
some form of "cosmology". Indeed
all civilizations (we know about)
seem to have "Creation myths" of
some sorts.
In the earliest civilizations (& up to
very recent times) cosmology was
primarily (often totally) a branch of
religion/myth.
Introduction
Certainly many (all ?) ancient
civilizations performed
astronomical observations of
various levels of sophistication from the neolithic observatories
(eg.Stonehenge), to written reports
(eg. The Chinese, Egyptians, etc).
..a little humility required ?
Many earlier beliefs & models may seem "silly" or "absurd" now.
Our beliefs and our scientific methods are "clearly far superior" - aren't they ?
However it worth reminding ourselves from the very start that we have not
figured everything out yet !! (dark matter, cosmic acceln, WIMPs, MACHOS etc)
Many variations on Mythological/Cosmological Ideas, but many with themes
not so different from our own:
Cosmic Birth Myths
Big Bang
Sages, Shamen…
Newton, Einstein, Hawking
Unseen Forces/laws
Gravity, Weak, Strong etc
Unchangeable destiny
Unchangeable destiny
Whims of the Gods
Ultimately understandable
AND we should not underestimate the struggles/difficulties early thinkers had attempting to
explain the universe within their various cultural, religious & technological environments….
..a little humility required ?
Imagine life before telescopes…
Earth seems flat and motionless
Sun, Moon, planets, stars move in sky (East to West)
Strange things appear (comets, meteors)

The Greeks are generally credited with promoting the idea that the
universe was understandable using logic, and could be described
by mathematics.
This is a huge leap forward, and the basis of all science today
Birth of "Scientific" Cosmology
By ~400BCE, generally thought that the universe worked & evolved
through "natural" processes that can be observed on Earth.
...Divine intervention is not required (at least in the "running" of the universe).
Consensus - there are no limits to what can be observed & understood
(again, at least not concerning the "running" of the universe),
theories could be postulated,
predictions made,
theories revised as necessary
Cosmology was really a branch of philosophy at the time,
but the Empirical Scientific Method was developing.
Birth of "Scientific" Cosmology
The Greeks understood that the Earth is a sphere:Observation of ships sailing over the horizon
Observation of Earths shadow on the moon during lunar eclipses
Geocentric Spheres
Only five planets were known to the Early Greeks
(Mercury, Venus, Mars, Saturn, Jupiter).
Thus early Greek cosmologists believed they had to account for
8 celestial entities -the 5 planets, the Sun, the Moon, and the "Stars".
Cosmologies were all "naturally"
Geocentric
(centered on the Earth)
Cosmologies generally included
perfect spheres
(Sphere count: Pythagoras of Samos,(c.530BCE) 8)
Aristotle (c.350 BCE)
The physical universe was finite - beyond the outer
sphere of the stars was the (non-material) spiritual realm.
Reasoned that that this "universe" must be unique
(& have a single center), and have existed for
eternity (& in a steady-state).
Believed celestial bodies move in
perfect circles
Forced to increase the number of spheres due
to refined observations of planetary motion
(Sphere count: Aristotle,(c.350BCE) 55)
Hipparchus (c.125 BCE)
Constructed a catalog of close to 1000 stars.
Discovered precession (1 degree/century)
- the change of the position of the stars with time
(now known to be due to the precession of the Earth's axis).
In 134 BCE he discovered a new star (a nova),
...in direct contradiction to the paradigm that the "heavens" were unchanging.
Refined distances to (& hence size of) the Moon (via Parallax)
...made the first step determining the scale of the "cosmos"
Suggested that the Sun appeared to be much larger than the Earth.
...some aesthetic concerns for a geocentric universe
… but these were generally ignored…
Parallax
...the apparent change of position
of a (closer) object as measured
against the positions of more
distant object(s) due to the
movement of the observer.
A Parsec is defined as the distance of an object that exhibits
parallax of 1 arcsec (Easy to remember since the word parsec is a
construction from parallax and arcsec)
1 parsec = 3.085678 x 1016 m = 3.26 light years
Larger parallax = smaller distance
Hipparchus, Parallax & the Moon
Hipparchus of Rhodes estimated the distance to the Moon from
measurements taken during a solar eclipse in189BCE.
eclipse was
"full" in Hellespont
(NW. Turkey),
partial in Alexandria
(Egypt)
20% of the Sun's disk remained visible in Alexandria
Since 20% of the Sun's disk corresponds to 6 arcmins,
then by estimating the distance between the cities
one can derive the distance of the Moon.
Hipparchus estimated distance (4.5 to 5.2) x 108 m
(c.f. modern value of 3.8 x 108 m)
First attempt to scale the cosmos
Ptolemy (c.150)
His (13 volume) master work
Megale Syntaxis ("Great Compilation")
Is usually known as by the arab translation
Almagest ("The Greatest")
Extended the system of Aristotle,
sticking "religiously" to the ideas of
a geocentric cosmology,
the perfection of spheres
a finite universe.
(There is an on-going debate whether he stole/plagiarized Hipparachus' data !)
[e.g. see Schaefer, Sky & Telescope 2002 Feb issue, p39]
Ptolemy & Epicycles
(Bothun, Fig1.2)
The key elements are
the epicycle to account for the retrograde
motion of the planets
the deferent (main circle) to
account for the brightening &
speeding-up of the planets at
some times.
relative tilts between the various planes,
Large number of parameters
(for 8 celestial objects)
The “equant” is the point from which ang. vel
of epicycle ~const)
The model was able to make accurate predictions
Remained the "standard" cosmological model
for 1400 years
Math as a Parameterization
Contrary to the Greek ideas that Nature is
simple, perfect, beautiful
In the middle ages some thinkers started suggesting that
the Ptolemaic system of eccentrics/epicycles
do not actually exist,
...but are merely convenient mathematical descriptions
of celestial motion & reality (not reality itself)
Note: The concept of Nature being simple, perfect, beautiful
can be argued to be back with some modern theories (!)
The Ptolemy Monopoly
Alan W. Hirshfeld, in
"Parallax - The Race to Measure the Cosmos"
“In a sense, Ptolemy was the Bill Gates of his day.
His Ptolemaic "operating system", despite its known
deficiencies, grew to dominate - in fact, monopolize the astronomical market place."
Rise of the Scientific Method
The modern Scientific Method
observations, theory, predictions, tests/revisions...
Roger Bacon (c.1250) helps popularize the scientific method
in W.Europe,
William of Ockham (or Occam; c.1300) suggests entities should not be
“multiplied unneccessarily”, leading to (interpreted as)
Ockham's Razor:
the simplest (most succinct) theory is more likely
to be correct, and certainly a better working model
(to attempt) to disprove first.
Other Early Cosmologies (?)
It should be remembered that our knowledge of history
is solely dependent us on having written records
Also few (if any) of the original works survive,
so we must rely on later works (true & complete reporting ?)
Who knows what ideas have been lost...
One (radical) idea that was not developed (apparently ignored)
is due to Aristarchus (c280BCE - between Aristotle & Ptolemy)
a Heliocentric universe - the Earth orbiting the Sun (!)
Recap
The following should be remembered:
Cosmology one of the oldest philosophies/sciences
Many ancient cosmologies grappled with some of the same deep
philosophical questions we still ponder with today.
The Greeks first (we think)
reasoned that Universe was formed by natural processes
which could be observed, understood/explained by mathematics
Developed the Empirical Scientific Method
Developed a geocentric system (Pythagoras of Samos, c.550BCE;
Aristotle,c.350BCE) culminating with that of Ptolemy,c.150
involving a complex arrangement of spheres & epicycles.
Reason and beauty/perfection were a strong influence of their
thoughts.
The universe was reasoned to be finite but eternal/unchanging
Recap
Greeks thought Earth was stationary, if it were moving, wouldn’t we
feel a sense of motion (great winds, loose objects whizzing by us etc)
Recap (cont)
Mathematics (ie. the Ptolemaic system) seen as a parameterization,
By c.1400, the Ptolemaic (geocentric) system had remained
essentially unchallenged as the cosmology for 1300 years
You should be familiar with
the concept of Parallax
the basics of how the Ptolemaic system works
(how epicycles, deferent etc account for retrograde
motion).
the concept of Ockham's Razor
Again, a detailed knowledge of names, dates and places is not required
However, you should be familiar with at least the names & approximate
dates of Aristotle (c.350BCE) and Ptolemy (c.150).
Foundatn of Modern Cosmo
Continuing…
The Earth moves from Center Stage
And Then the Apple Dropped…
Summary at the beginning of the C20th
State of the Universe, 1400
By 1400, the geocentric cosmology of Aristotle & Ptolemy
(based on concentric spheres, epicycles etc) had been
essentially unchallenged for well over a thousand years.
However, in the 15th & 16th centuries, following the years of the
"Black Death" & centuries of strife, the start of the Renaissance
in W.Europe finally allowed scientific & technological progress.
Rumblings of Discontent
In c.1430, Nicholas de Cusa published
On Learned Ignorance
In which he suggested
the universe is infinite
(the universe does not have a center,
the pattern of stars would look the
same at all locations.
all motion is relative,
& that the Earth might not be stationary
Homogeneity & Relativity
Earth moves from Center Stage...
The suggestion by Nicholas de Cusa (c.1430) that
the Earth might not be stationary,
was supported by Leonardo da Vinci (c1490),
who amongst many (!) other things also suggested
the Earth moves (rather than the Sun).
However it was not until 1543 when
Nicholas Copernicus publishes his
Revolutionibus Orbium Coelestium
(The Revolution of the Celestial Spheres)
that this idea was put of a more rigorous
footing.
Heliocentric Cosmology
Copernicus suggested
the planets rotate (on circles)
around a central Sun
….with "slower" planets being
further from the Sun.
Heliocentric Cosmology
Copernicus also acknowledged
the Earth rotates on its axis
A “Good” (Simpler) Model
The heliocentric model of Copernicus obviously could be used
to make predictions, that could be compared to observations.
It was simpler than the model of Ptolemy that it replaced.
However,
it’s predictions were not any better than those of Ptolemy’s model
unless (much smaller) epicycles were added
The Cosmological Principles
One important aspect of Copernicus’ work - he took
his heliocentric model, went further and made a model
for the cosmos by saying, lets assume several things,
then use observations to test whether this is a good
model
Cosmological principles are the assumptions which allow us
to deduce the whole of nature on the basis of the observable to
the unobservable. Not surprisingly, any study of cosmological
principles must combine elements of astronomy, physics and
philosophy.
The Copernican Cosmological Principle
This is sometimes simply referred to as simply
“The Cosmological Principle”
The Copernican Cosmo Principle
The Copernican Cosmological Principle is a logical
extension of the the Copernican theory that the Earth is
not the center of the universe.
Thus the Earth is not "special", thus the "laws of
nature" on (or around) Earth are not special.
It is essentially a philosophical
requirement/simplification necessary/assumed for all
modern cosmologies:
- our laws of physics are otherwise "irrelevant"
The CCP itself
The Copernican Cosmological Principle is that
On a large scale, the universe is both
homogeneous and isotropic (in 3-D space),
and has/will always be so.
Note that the statement "has/will always be so" refers to the
universe continuing to display the properties of homogeneity &
isotropy.
The CCP does not imply that any actual observable parameter
(e.g. the density of matter in the universe) will remain constant with
time. Indeed, the CCP allows the properties of the universe to
evolve with time, but states that at any given time the universe will
be both homogeneous and isotropic (in 3-D space).
The CCP again
Another way of expressing
the Copernican Cosmological Principle is that ...
observers
will see identical properties & laws everywhere- homogeneity
will NOT see any preferred direction - isotropy
i.e. this was the suggestion that we do not
occupy a special place in the universe
Homogeneity/Isotropy
homogeneous - same properties everywhere
isotropic - no special direction, uniform in all directions
homogeneous but
not isotropic
isotropic but not
homogeneous
The CCP - an analogy
A (small) sentient being living in the center of a "perfect" loaf of
bread…!
There may be obvious structure on small scales (air bubbles
etc), but on the large scale the loaf can be considered
uniform and isotropic
The laws of physics (e.g. which caused the dough to rise)
are the same throughout the loaf.
The loaf might still be rising - but (in this perfect loaf) this
happens
uniformly & following then same laws throughout the loaf
The CCP Evidence for & against
The best support for the Copernican Cosmological Principle is
the Cosmic Microwave Background (CMB), which is isotropic
to 1 part in 105
The obvious observational evidence against the Copernican
Cosmological Principle seems to be the structure seen in the
universe on a variety of scales
(stars, galaxies, clusters, super-clusters..the cosmic web)
This is why the qualifier "On a large scale.." is required to be
added to the principle.
The question them becomes a question of scale (now large is
"large" ?), and whether the observed structures on large scales
are indeed representative of the universe on these scales (or
are "perturbations" which "happen” to be visible to us).
Recap
We are up to 1400
We briefly mentioned the ideas of Nicholas de Cusa
Homogeneity & Relativity
We discussed the Heliocentric system of Nicholas Copernicus
We then discussed the Copernican Cosmological Principle
On a large scale, the universe is both
homogeneous and isotropic (in 3-D space)
What have we learned?
•
How can we distinguish science from non-science?
• It’s not always easy, but science generally exhibits at least three
hallmarks.
•
(1) Modern science seeks explanations for observed phenomena that
rely solely on natural causes.
•
(2) Science progresses through the creation and testing of models of
nature that explain the observations as simply as possible (Ockhams
Razor)
•
(3) A scientific model must make testable predictions about natural
phenomena that would force us to revise or abandon the model if the
predictions do not agree with observations.
What have we learned?
•
What is a theory in science?
•
•
A model that explains a wide variety of observations in terms of just a
few general principles, which has survived numerous tests to verify its
predictions and explanations.
How were astronomy and astrology related in the past, and are
they still related today?
• Astronomy and astrology both grew out of ancient observations
of the sky. Astronomy grew into a modern science. Astrology
has never passed scientific tests and does not qualify as science
(ALTHOUGH EARLY ON IT HELPED US DEVELOP
ASTRONOMY).
What else have we learned?
•
Copernicus created a Sun-centered model of the solar
system designed to replace the Ptolemaic model, but
was more fundamentally correct yet it was no more
accurate because he still used perfect circles.
Tycho Brahe (c.1570))
Also famous for having lost his nose in a swordfight
Tycho Brahe (c.1570)
did accept that the (other) Planets
move around the Sun
but did not accept that the Earth & Stars
move around the Sun
Why ?
… Falling bodies fall towards the Earth
... The lack of Stellar Parallax
What was his problem ?)
Falling Bodies fall towards the Earth
Indeed if you throw something vertically upwards,
it falls vertically downwards (to the same spot)
Tycho Brahe reasoned this surely meant
the Earth was the center of the universe
Tycho Brahe was unable to detect (by naked-eye) Stellar Parallax
and reasoned that in a Copernican system this would require
the Stars to be so far away they would have to be
"unreasonably" large/bright.
Tycho Brahe the observer
Tycho Brahe was primarily an observer
a Supernova
position did not change (so it was not a comet or meteor),
- lack of Parallax must be in one of the “outer spheres”
-therefore the outer sphere of stars does change!
a Comet
position did not change significantly throughout the night.
- lack of Parallax, must lay beyond the orbit of the Venus
Observed positions of Mars twice-daily
which implied its orbit intersects that of the Sun.
- apparent crossing/smashing of the “crystalline spheres”
“there are no solid spheres "holding" the celestial bodies”
- observations that strengthened the rejection of the cosmology of
Aristotle & Ptolemy
Tycho Brahe - his contribution
So, even though Tycho Brahe never found the “right” model…
… his observations did play a major role in the final
rejection
of the notions of Aristotle/Ptolemy that
the celestial bodies are carried by crystalline spheres,
with everything beyond the Moon eternal & unchanging.
In addition Tycho Brahe also actually published his data !
In particular his twice-daily measurements of the position of Mars
provided Johannes Kepler with a crucial database a few years later.
Johannes Kepler (1571-1630)





Greatest theorist of his
day
a mystic
there were no heavenly
spheres
forces made the planets
move
Modifications to
Copernicus idea showed
heliocentric models were
correct
Kepler’s Laws - #1
1
Each planet’s orbit around the Sun is an ellipse, with
the Sun at one focus.
Properties of an Ellipse
a + b = constant
The amount of "flattening" of the
ellipse is termed the eccentricity
All ellipses have eccentricities
lying between zero and one.
e=ratio; dist. between foci
compared to major axis
Kepler’s Laws - #1
1
Each planet’s orbit around the Sun is an ellipse, with
the Sun at one focus.
Kepler's Laws:
Kepler's First Law:
1Each
planet’s orbit around the Sun
is an ellipse, with the Sun at one
focus.
Kepler's Third Law: The squares of
the periods of the planets are proportional to
the cubes of their semi-major axes:
Kepler's Second Law: Line
joining planet and the Sun sweeps out
equal areas in equal times
Kepler’s Laws
2
A convenient unit of measurement for periods is in Earth years, and
a convenient unit of measurement for distances is the average
separation of the Earth from the Sun, which is termed an
astronomical unit and is abbreviated as AU. If these units are used
in Kepler's 3rd Law, the denominators in the preceding equation are
numerically equal to unity and it may be written in the simple form
Kepler’s 3rd Law: version 2
This equation may then be solved for the period P of the
planet, given the length of the semi-major axis axis,
or for length of the semi-major axis, given the period of the planet
Kepler’s Laws
3
As an example of using Kepler's 3rd Law:
3
let's calculate the "radius" of the orbit of Mars (that is, the length of the
semi-major axis of the orbit) from the orbital period. The time for Mars to
orbit the Sun is observed to be 1.88 Earth years. Thus, by Kepler's 3rd
Law the length of the semi-major axis for the Martian orbit is
Second example, let us calculate the orbital period for Pluto, given
that its observed average separation from the Sun is 39.44
astronomical units. From Kepler's 3rd Law
Galileo Galilei (1564-1642)


First man to point a telescope at
the sky
wanted to connect physics on
earth with the heavens
Galileo’s Observations



Galileo saw shadows cast by
the mountains on the Moon.
He observed craters.
The Moon had a landscape;
it was a “place”, not a perfect
heavenly body.
Galileo’s Observations



Galileo discovered that
Jupiter had four moons of
its own.
Jupiter was the center of its
own system.
Heavenly bodies existed
which did not orbit the
earth.
Ptolemy:
•
-recap
What was the Ptolemaic model?
•
Ptolemy’s synthesis of earlier Greek ideas about the
geocentric universe, which was a sophisticated (or
some may say incorrect and overly complex) model
which, most importantly, allowed prediction of
planetary positions.
Epicycles ‘explained’
retrograde motion…but of
course this was not
physically a correct model
(by far!!!).
•
In use for ~1500 years!!)
Galileo’s observation of the phases of Venus was the
final evidence which buried the geocentric model.
Geocentric
No gibbous or full phases!
Heliocentric
All phases are seen!
His astronomical work got him in trouble with
the Church!Galileo observed all phases!
KEPLER:
•
-recap
What are Kepler’s three laws of planetary motion?
•
•
•
(1) The orbit of each planet is an ellipse with the
Sun at one focus.
•
(2) As a planet moves around its orbit, it
sweeps out equal areas in equal times.
•
(3) More distant planets orbit the Sun at slower average speeds,
following a precise mathematical relationship (P2 = R3).
KEPLER:
•
3rd law -recap
(3) More distant planets orbit the Sun at slower average speeds,
following a precise mathematical relationship (P2 = R3).
This version of 3rd Law can use *any* units
for P and R (hours, years, weeks, km, feet
etc etc
This version of 3rd Law is
simpler, because we are
constrained to use years
and AU
Rearranged versions ‘isolate’ P or
R
All you need is to be able to use
the the squared and cubed
buttons on your calculator, plus
the square-root  or cube-root 3
buttons
KEPLER:
3rd law -recap
Rearranged versions ‘isolate’ P or R
All you need is to be able to use the the “squared” and “cubed” buttons
on your calculator, plus the square-root  or cube-root 3 buttons
Calculate R cubed (RxRxR) then
take the square-root of that
number
Calculate R squared (RxR) then
take the cube-root of that number
What else have we learned?
•
Copernicus created a Sun-centered model of the solar system
designed to replace the Ptolemaic model, but was more
fundamentally correct yet it was no more accurate because he still
used perfect circles.
•
Tycho provided observations used by Kepler to refine the model by
introducing orbits with the correct characteristics.
•
Galileo’s experiments and telescopic observations (sunspots,;
craters on moon; moons of Jupiter, phases of Venus…)
•
--overcame remaining objections to the Copernican idea of the
Earth is a planet orbiting the Sun.