Transcript Boyle-Vitter: Copernicus and Kepler

The Copernican Model &
Kepler’s Laws
DANIEL BOYLE & AUDREY VITTER
Scientific Paradigms
 According to Thomas Kuhn paradigms are
“universally recognized scientific achievements that,
for a time, provide model problems and solutions for
a community of researchers”
 “Successive transition from one paradigm to another
via revolution is the usual developmental pattern of
mature science.”
 Transition to a heliocentric model of the universe is
an example of paradigm shift
The Aristotelian Paradigm
 2 Sphere Universe (Celestial and Terrestrial)
 4 terrestrial elements: Earth, Water, Air and Fire
 Each terrestrial element tends towards a natural place
 Earth is naturally located at the center of the universe
 One celestial element: Ether
 Celestial bodies are immutable and move in uniform circles
Nicolaus Copernicus
 Born in Torun, Poland in 1473
and raised by his uncle
 Established an observatory at
Frauenburg, and developed a
reputation as an astronomer
 Invited to the 1514 Lateran
Council to discuss calendar
reform
 Major works include
Commentariolus, Narratio
Prima, and De Revolutionibus
De Revolutionibus
 Most of Copernicus’ work
prior to De Revolutionibus
was circulated as manuscripts
 De Revolutionibus was
completed in 1530, but was
not published until 1543 while
Copernicus was on is death
bed
 Georg Rheticus and other
friends were instrumental in
convincing Copernicus to
publish his revolutionary
work
Religious Climate
 Copernicus was hesitant to publish any of his work
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considering that it could be viewed as heretical
Osiander’s preface to De Revloutionibus appeals to
the instrumental character of astronomy
It is likely that Copernicus actually saw his model as
representative of reality
Protestants felt the Copernican model was
incompatible with scripture
Counter-Reformation Catholicism bans De
Revloutionibus in 1616
Pros of the Copernican Model
 Problems of retrograde
motion and varying
brightness are solved
 Proximity of the inner
planets to the sun is
explained
 Simple proof for order of
the planets can be
derived
 Fit to observation
Cons of the Copernican Model
 Features more epicycles than Ptolemaic system
 Does not completely eliminate equants
 Expands the universe to account for lack of stellar
parallax
 Deconstructs Aristotelian physics
Is the Copernican Model revolutionary?
 Copernicus retains uniform circular motion
 Copernicus was largely attempting to repair
problems with the Ptolemaic, not to overthrow
Aristotelian cosmology
 “The significance of De Revolutionibus lies, then,
less in what it says itself than what it caused others
to say”- Kuhn
Tycho Brahe
 Born in 1546 in present
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day Sweden, and raised by
his grandfather
Lost his nose in a duel, and
replaced it with gold
Was said to own a
clairvoyant dwarf
It is rumored that Tycho
had an affair with the
Danish Queen
Died as a result of holding
his bladder too long
Tycho’s Work
 Witnessed a new supernova in 1572 which cast doubt
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on celestial immutability
Built an observatory commissioned by King Fredrick
II of Denmark in 1576
Observed a comet in 1577, which he proved was
above Earth’s atmosphere
Considered the greatest naked eye observer, his
predictions of planetary position were within 4 arc
minutes of actuality
The accuracy and volume of his work opened the
door for Kepler’s laws
The Tychonic Model
 Tycho noted the
improvements that came
with the Copernican
model
 He was unable, however,
to accept that Earth was
in motion
 Tycho devised a system
that was kinematically
equivalent to
Copernicus’
Johannes Kepler
 December 27, 1571: Born
in Weil der Stadt,
Württemberg (Germany)
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Premature baby, sickly
 Lutheran
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Witch ties
 1591: Graduated from
University of Tubingen
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Scholarship to study Theology
Formation of Copernicus
beliefs
 1594: Professorship of
astronomy in Graz, Styria
Mysterium Cosmographicum
 The Sacred Mystery of the Cosmos
 God made the universe with a mathematical beauty
 Five Pythagorean regular polyhedral
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Reflect God’s plan through geometry and symmetry
First Model
 Why did the outer planets move more slowly?
 Saturn vs. Earth
 Later rejected
 Initially blamed the discrepancies on errors in Copernicus' tables
 http://www.uff.br/cdme/kepler/kepler-html/kepler-en.html
New Chapter
 ~1658: Counter-revolution occurred
 1660: Left Prague to work for Tycho
 Kepler made a bet that he could understand Mars’ orbit in
eight days—took him eight years
 1601: Tycho died
 Kepler took all his data under his care.
 "I confess that when Tycho died, I quickly took advantage
of the absence, or lack of circumspection, of the heirs, by
taking the observations under my care, or perhaps
usurping them...”
Ptolemy Model
 Ptolemy Model
 Used Tycho’s data to backup
model
 Precision allows error to be seen
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error by eight minutes of arc
Threw out model
 Wanted a “dynamically”
explained model
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Explain Mars orbital movement
in “steady motion”
Development of the New Model
 First step: Earth’s orbital
 Thales’ method of Greek
geometry
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Two fixed points: Sun and
Mars
“An idea of true genius”
–Einstein
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 Kepler’s Second Law
 In their orbits around the
sun, the planets sweet out
equal areas in equal times
http://www.keplersdiscovery.com/Earth.html
http://astro.unl.edu/naap/pos/animations/kepler.swf
Mars’ Orbital
 “Oval” shape
 Deviated by 0.00429 of the
radius (AC)
 AC/MC = 1.00429
 Secant(CMS) = 1.00429
 Later stated as an
“ellipse”
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Sun at one focus
 Kepler’s First Law
 The planets move in
elliptical orbits with the sun
at a focus
Astronomia nova
 1609: Findings were
published
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First Law
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The planets move in
elliptical orbits with the sun
at a focus
Second Law
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In their orbits around the
sun, the planets sweet out
equal areas in equal times
Gravity and Optics
 Gravity
 A mutual tendency between material bodies toward contact
 The waters of the oceans being attracted by the moon’s
gravitational pull caused tides
 Optics
 Focused on this topic after Galileo found four new planets by
looking through lenses into the night sky
 1611: Published Dioptrice, a basic work on optics
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The light intensity decreases with the square of the distance
 Later became the principle of the camera obscura
Harmonices Mundi
 Harmony of the World
 Relates his findings about the concept of congruence
with respect to diverse categories of the physical domain:
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regularities in three-dimensional geometry
the relationships among different species of magnitude
the principles of consonance in music
the organization of the Solar System.
 Full of errors and inconsistencies
 Third Law:
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The distance a planet is from the sun, cubed, is directly proportional
to the time it takes to complete the orbit, squared.
The distance a planet was located from the sun directly determined
the time it took that planet to revolve around the sun
Questions?
Works Cited
 Kuhn — The Structure of Scientific Revolutions
 Kuhn — The Copernican Revolution
 Cushing — Philosophical Concepts in Physics
 Koestler— Sleepwalkers