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