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The Copernican Revolution
Scotland: 4,000-year-old stone circle; the Moon rises as shown here every 18.6 years.
What did ancient civilizations
achieve in astronomy?
• Daily timekeeping
• Tracking the
seasons and calendar
• Monitoring lunar
cycles
• Monitoring planets
and stars
• Predicting eclipses
• And more…
Mexico: model of the Templo Mayor
England: 1550 BC
Our mathematical and scientific
heritage originated with the
civilizations of the Middle East
Why does modern science trace
its roots to the Greeks?
• Greeks were the first
people known to make
models of nature.
• They tried to explain
patterns in nature without
resorting to myth or the
supernatural.
Greek geocentric model (c. 400 B.C.)
• This is a very important
step in understanding the
natural world.
What shape is the Earth?
Prove it!
Eratosthenes measures the Earth (c. 240 BC)
Measurements:
Syene to Alexandria
distance ≈ 5000 stadia
angle = 7°
Calculate circumference of Earth:
7/360  (circum. Earth) = 5000 stadia
 circum. Earth = 5000  360/7 stadia ≈ 250,000 stadia
Compare to modern value (≈ 40,100 km):
Greek stadium ≈ 1/6 km  250,000 stadia ≈ 42,000 km
APPARENT RETROGRADE MOTION OF THE
PLANETS
We see apparent retrograde
motion when we pass by a
planet in its orbit.
Easy for us to explain today:
occurs when we “lap” another
planet (or when Mercury or
Venus laps us).
But very difficult to explain if
you think that Earth is the
center of the universe!
In fact, ancients considered
but rejected the correct
explanation …
Why did the ancient Greeks reject the real
explanation for planetary motion?
Their inability to observe stellar parallax was a major factor.
p
tan p = 1AU/d (AU)
For small angles:
d
p = 1/d
Here p is in radians,
but there are 206265
arcseconds in 1 radian.
1 AU
If the angle p = 1 second of
arc then d =206265 AU. We
define this distance to be 1
parsec (pc). Can you show
that 1 pc = 3.26 light-years?
Not to scale
The Greeks knew that the lack of observable
parallax could mean one of two things:
1. Stars are so far away that stellar parallax is
too small to notice with the naked eye
1. The Moon is 30 minutes of arc and the eye can
separate objects about 1 minute of arc apart
2. Earth does not orbit the Sun; the Earth is
the center of the universe
With rare exceptions such as Aristarchus, the Greeks
rejected the correct explanation (1) because they
did not think the stars could be that far away
Thus setting the stage for the long, historical showdown
between Earth-centered and Sun-centered systems.
Explaining retrograde motion with the Geocentric model
Arabic translation of Ptolemy’s work named Almagest
(“the greatest compilation”)
Ptolemy
Most sophisticated geocentric model
was that of Ptolemy (A.D. 100-170).
Sufficiently accurate to remain in use
for 1,500 years.
The Copernican Revolution
Our goals for learning:
• How did Copernicus, Tycho, and Kepler
challenge the Earth-centered (geocentric)
idea?
• What are Kepler’s three laws of planetary
motion?
• How did Galileo solidify the Copernican
revolution?
How did Copernicus, Tycho, and Kepler
challenge the Earth-centered idea?
Copernicus (1473-1543):
• Proposed Sun-centered model
(published 1543)
• Used model to determine layout of
solar system (planetary distances in AU)
But . . .
• He had the right idea, yet Copernicus
still assumed that the orbits of the
planets were perfect circles and so his
heliocentric model was no more
accurate than Ptolemy’s geocentric
model in predicting planetary positions!
Danish astronomer Tycho Brahe (1546-1601)
• Compiled the most accurate (one
arcminute) naked eye measurements
ever made of planetary positions.
• He still could not detect stellar
parallax, and thus still thought Earth
must be at center of solar system (but
recognized that other planets must go
around the Sun)
• Hired Johannes Kepler, who later
used these detailed observations to
discover the truth about planetary
motion.
Brahe’s observatory was visual – before the telescope –
and really a giant protractor for measuring angles.
Johannes Kepler (1571-1630)
• Kepler first tried to match Tycho’s
observations with circular orbits
• But an 8-arcminute discrepancy
led him eventually to ellipses…
“If I had believed that we could
ignore these eight minutes [of
arc], I would have patched up
my hypothesis accordingly. But,
since it was not permissible to
ignore, those eight minutes
pointed the road to a complete
reformation in astronomy.”
What is an ellipse?
The semi-major axis is also the
“average” distance from the focus.
An ellipse looks like an elongated circle
Eccentricity and Planetary Orbits
• Define c to be the distance from the center
to either focus
• Define a to be the semi-major axis length
• The eccentricity e of an ellipse is then
e = c/a
[ For a circle e = 0 because c = 0]
 Perihelion distance = a(1 – e)
a
c
 Aphelion distance = a(1 + e)
Earth: e = 0.017; a = 149.6 million km; closest = 147.1 million km
and farthest = 152.1 million km. Note that a is the average.
Eccentricity of an Ellipse
Kepler’s Three Laws of Planetary Motion?
Kepler’s First Law: The orbit of each planet around
the Sun is an ellipse with the Sun at one focus.
NOTE: None of the planets have orbits as elliptical as this, only some comets.
Kepler’s Second Law: As a planet moves around
its orbit, it sweeps out equal areas in equal times.
 this law means that a planet travels faster when it is nearer to the
Sun and slower when it is farther from the Sun.
Kepler’s Third Law
More distant planets orbit the Sun at slower
average speeds, obeying the relationship
p2 = a3
p = orbital period in years
a = avg. distance from Sun in AU
If a = 1 AU then 13=1 and p2=1 therefore p=1 (year).
Graphical version of Kepler’s Third Law
p2 plotted against a3
v plotted against a
Planet’s average speed is v = 2πa/p (circumference of orbit divided by
period), so v2 = (2π)2 a2/p2 but p2 = a3 so, v2 = (2π)2 a2/a3 = (2π)2/a,
thus v = 2π/√a. Using v in km/s then v = 30/√a.
Thought Question:
An asteroid orbits the Sun at an average distance
a = 4 AU. How long does it take to orbit the Sun?
A.
B.
C.
D.
4 years
8 years
16 years
64 years
Hint: Remember that p2 = a3
An asteroid orbits the Sun at an average distance
a = 4 AU. How long does it take to orbit the Sun?
A.
B.
C.
D.
4 years
8 years
16 years
64 years
We need to find p so that p2 = a3
Since a = 4, a3 = 43 = 64
Therefore p = 8, p2 = 82 = 64
How did Galileo Galilei solidify the Copernican revolution?
Galileo (1564-1642) overcame major
objections to Copernican view. Three
key objections rooted in Aristotelian
view were:
1. Earth could not be moving because
objects in air would be left behind.
2. Non-circular orbits are not “perfect”
as heavens should be.
3. If Earth were really orbiting Sun,
we’d detect stellar parallax.
Overcoming the first objection (nature of motion):
Galileo’s experiments showed that objects in
air would stay with a moving Earth.
• Aristotle thought that all objects naturally come
to rest.
• Galileo showed by experiment that an object will
stay in motion unless a force acts to slow it down.
• Galileo proved this with countless experiments
involving falling and rolling objects.
Overcoming the second objection (heavenly perfection):
• Tycho’s observations of a comet
and a supernova (new star) already
challenged this idea.
• Using his telescope (1609), Galileo
saw:
• Sunspots or “imperfections” on
the Sun
• Mountains and valleys on the
Moon (proving it is not a perfect
sphere)
Overcoming the third objection (parallax):
• Tycho thought he had measured stellar distances, so lack
of parallax seemed to rule out an orbiting Earth.
• Galileo showed stars must be much farther than Tycho
thought — in part by using his telescope to resolve the
Milky Way into countless individual stars.
 If stars were much farther away, then lack of detectable
parallax was no longer so troubling.
 The eventual discovery of the tiny angular shifts in a star’s
position due to parallax as the Earth orbits the Sun required more
than another century of technology development to make much
bigger telescopes.
Galileo’s observations of phases of
Venus proved that it orbits the Sun and
not Earth.
Galileo saw four moons
orbiting Jupiter, proving
that not all objects orbit
the Earth
The Nature of Science
Our goals for learning:
• How can we distinguish science from
nonscience?
• What is a scientific theory?
The previous example of the evolution of ideas from the
false geocentric model to the true heliocentric model
leads us nicely to a discussion of the Scientific Method.
The idealized Scientific Method
• Based on proposing and
testing hypotheses through
careful and repeated
experiments
• hypothesis = educated guess
• Around the time of Galileo
there was a fundamental shift
away from mere speculation
and towards tangible
experimental evidence.
Hallmarks of Science: #1
Modern science seeks explanations for
observed phenomena that rely solely on
natural causes.
(A scientific model cannot include divine intervention)
Example: Kepler sought a natural explanation for
observations made by Tycho.
Hallmarks of Science: #2
Science progresses through the creation and
testing of models of nature that explain the
observations as simply as possible.
(Simplicity = “Occam’s razor”)
Occam’s principle states that “all things being equal, the simplest
explanation tends to be the right one.” The heliocentric model is
simpler than the geocentric one.
Hallmarks of Science: #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.
Example: each of the competing models offered predictions that were
tested. Kepler’s model worked best. Kepler’s model can still be tested. In
fact, slight discrepancies found at much later dates led to new discoveries,
such as Einstein’s theories…
What is a scientific theory?
• The word theory has a different meaning in
science than in everyday life.
• In science, a theory is NOT the same as a
hypothesis, it is NOT a guess, rather:
• A scientific theory must:
— Explain a wide variety of observations with a few
simple principles, AND
— Must be supported by a large, compelling body of
evidence.
— Must NOT have failed any crucial test of its validity.
Scientific Theories
•
•
•
•
•
•
•
The theory of gravity
The theory of electromagnetism and light
The theory of atoms
The theory of evolution by natural selection
The theory of relativity
The theory of plate tectonics
The quantum theory
Other modes of reasoning
• Appeal to authority – weak because does not rely on experimental
evidence and advance predictions, even if the authority figure is a
famous scientist.
• Opposing advocates (the legal system) – good in principle if both
sides present all the evidence and argue rationally for the truth.
Fails in practice because each advocate presents only those facts
that support their position.
• Myths, superstitions and divine intervention – weakest of all
because there is no rational way to seek truth when explanations
are attributed to unseen and unknowable forces. Today, after
millennia of study, no belief systems based on superstitions stand
the test of experiment.
• The Scientific Method, especially in modern times where many
scientists of equal skill compete to verify facts by experiment, is
the most powerful method of obtaining new knowledge.
What have we learned?
• How can we distinguish science from nonscience?
– Science: seeks explanations that rely solely on
natural causes; progresses through the creation
and testing of models of nature; models must
make testable predictions
• What is a scientific theory?
– A model that explains a wide variety of
observations in terms of a few general principles
and that has survived repeated and varied testing