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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” - PowerPoint PPT Presentation
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DANIEL BOYLE & AUDREY VITTER
The Copernican Model & Kepler’s Laws
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 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 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 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) Premature baby, sickly
Lutheran Witch ties
1591: Graduated from University of Tubingen Scholarship to study Theology Formation of Copernicus
beliefs1594: Professorship of
astronomy in Graz, Styria
Mysterium Cosmographicum
The Sacred Mystery of the CosmosGod made the universe with a mathematical beauty
Five Pythagorean regular polyhedral
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 error by eight minutes of arc
Threw out modelWanted a “dynamically”
explained model Explain Mars orbital
movement in “steady motion”
Development of the New Model
First step: Earth’s orbital
Thales’ method of Greek geometry Two fixed points: Sun and
Mars “An idea of true genius” –Einstein
Kepler’s Second Law In their orbits around the
sun, the planets sweet out equal areas in equal times
http://www.keplersdiscovery.com/Earth.htmlhttp://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” 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 First Law
The planets move in elliptical orbits with the sun at a focus
Second Law 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 The light intensity decreases with the square of the
distance Later became the principle of the camera obscura
Harmonices Mundi
Harmony of the WorldRelates his findings about the concept of congruence
with respect to diverse categories of the physical domain: 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 inconsistenciesThird Law:
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 RevolutionsKuhn — The Copernican RevolutionCushing — Philosophical Concepts in PhysicsKoestler— Sleepwalkers