The Copernican Model Keplers Laws DANIEL BOYLE AUDREY

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 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 � http: //www. uff. br/cdme/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 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 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” 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