Physical Science

1. D A N I E L B O Y L E & A U D R E Y V I T T E R
The Copernican Model &
Kepler’s Laws

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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’

13. 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

14. 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

15. 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

16. 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...”

17. 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”

18. 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

19. 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

20. 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

21. 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

22. 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

23. Questions?

24. Works Cited
 Kuhn — The Structure of Scientific Revolutions
 Kuhn — The Copernican Revolution
 Cushing — Philosophical Concepts in Physics
 Koestler— Sleepwalkers