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 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  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

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  Used Tycho’s data to backup model  Precision allows error to be seen  error by eight minutes of arc  Threw out model Wanted 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

Mars’ Orbital “Oval” shape  Deviated by of the radius (AC)  AC/MC =  Secant(CMS) = 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 World Relates 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 inconsistencies Third 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 Revolutions Kuhn — The Copernican Revolution Cushing — Philosophical Concepts in Physics Koestler— Sleepwalkers