Chapter 10.

Copernicus and Kepler

10.1. The Ptolemaic System

• Assumptions underlying Ptolemaic system
  • Heaven is spherical in form and rotates as a sphere
  • Earth is spherical
  • Earth is situated in "middle of heavens" like a center
  • Earth is a point in comparison to size and distance of sphere of fixed stars
  • Earth does not participate in any motion, neither rotation nor revolution
• Mathematics of Ptolemaic system
  • Orbits are perfect circles (Plato)
  • Planets move on epicycles, which move on deferents; adjustable radii and periods of motion
  • Eccentric deferent and equant
• Success of Ptolemaic system
  • Provided accurate enough description of what could be observed with instruments of that day
  • Predicted future paths of planets; when discrepancies arose, flexible enough that could be tinkered with to remove problem
  • Explains naturally why fixed stars show no annual parallax
  • In most details coincided with Greek philosophical and physical doctrine concerning nature of Earth and celestial bodies
  • By medieval period became part of Christian theology; appropriate places for Earth and God
  • Consistent with medieval physics based on natural motion, natural place, etc.
  • Had common-sense appeal; consistent with perception that Sun, Moon, stars are "moving around us"

10.2 Copernicus' Heliocentric System

• Nicolaus Copernicus (1473-1543), Polish
  • Raised by uncle, who later became bishop
  • Studied mathematics, philosophy astronomy, and astrology at University of Krakow in Poland
  • Studied law and medicine at Universities of Bologna and Padua in Italy
  • Practiced medicine after his return to Poland
  • Later in life he was elected a Canon of Ecclesiastical Law by the Church
  • His book, On the Revolutions of the Heavenly Orbs, published in 1543
• Assumptions underlying Copernican system
  • Heaven and Earth are spherical in form
  • Sun is situated in "middle of heavens" like a center with Earth and planets orbiting Sun; Moon orbits Earth
  • Earth is a point in comparison to size and distance of sphere of fixed stars; system not infinite, since "God must have his place"
  • Earth rotates about internal axis in addition to revolving about Sun
• Mathematics of Copernican system
  • Orbits are perfect circles
  • Earth and Moon move on circles
  • Planets move on epicycles, which move on deferents (fewer epicycles than Ptolemaic system)
  • No equant
• Copernicus' arguments for heliocentric concept
  • As plausible as geocentric argument
  • Coincided with theological dogma
    • Observable world symbol of working of God's mind
    • To find symmetry and order in apparently chaotic sensory data viewed as act of reverence and proof of Deity
  • Quantitative material in his book; predictive accuracy of Ptolemaic and Copernican systems about same
  • Rotation of Earth is no more incomprehensible than rotating celestial sphere which is much larger
  • Parallax not observable because of immense distances of sphere of stars
  • Reduction of number of elements of Copernican system compared to Ptolemaic
• Arguments offered to Copernicus against heliocentric concept
  • Theological dogma concerning immobility and central position of Earth (Joshua 10:13)
  • Damage to Aristotelian physics, which was more than just a physical system of the world; had become Church orthodoxy - an article of faith
  • Parallax in a finite universe acceptable; infinite universe not an acceptable concept, contrary to theological dogma
  • Copernican system offered no observation which was explainable only by it and not by Ptolemaic system
• Feature's of modern science to be found in Copernicus' work
  • Economy of concepts and assumptions (Plato, William of Ockham)
  • Simplicity of formulation (Thales - unity, order, and beauty)
  • Applicability to a variety of problems

10.3. Copernican Cosmology

• Two-sphere geometry, very large but not infinite, centered on Solar System
• Terrestrial and celestial physics may not be the same
• Mathematics is the language of nature
• Heliocentric motion
• Copernican system (Copernicus, 1540 to Galileo, 1640)
• Matter is probably composed of four elements--earth, water, air, fire; void may or may not exist; space is where matter exists

10.4. After Copernicus

• Tycho Brahe (1546-1601), Danish nobleman
  • Constructed observatory (naked-eye) on island of Hveen, about 32 km northeast of Copenhagen with financial aid of King Frederick II
  • Constructed most accurate naked-eye observing instruments ever used
  • Many years of consistent observations to accuracy of 1 minute of arc for planets and stars
  • Published his own cosmology; planets orbit Sun, but Sun and Moon orbit Earth
  • Tychonian cosmology never seriously considered and made no impact on cosmological thought
• Girdano Bruno (1548-1600), Italian philosopher
  • Traveled through Europe lecturing on Copernican system
  • Argued that boundaries of Universe are infinitely far away
  • Our Solar System is but one of infinitely many
  • For his outspoken heresies, tried by Inquisition, burned at the stake in 1600
• William Gilbert (1540-1603), English natural philosopher
  • Physician to Queen Elizabeth I
  • Published De magnete in 1600
  • Performs experiments on magnetic effects
  • Said to have shown experimentally that magnetized sphere keeps up constant rotation
  • Ascribes Moons motion round Earth to magnetic forces
  • Lays experimental foundation for concept of "action-at-a-distance"
• Francis Bacon (1561-1626), English natural philosopher
  • Emphasized observation and induction, Novum Organum of 1620
  • "Now for grounds of experience--since to experience we must come--we have as yet had either none or very weak ones; no search as been made to collect a store of particular observations sufficient either in number, or in kind, or in certainty to inform the understanding, or in any way adequate.... Nothing duly investigated, nothing verified, noting counted, weighed, or measured, is to be found in natural history; and what in observation is loose and vague, is in information deceptive and treacherous."
  • "But my course and method, as I have often clearly stated and would wish to state again, is this--not to extract works from works or experiments from experiments, as an empiric, but from works and experiments to extract causes and axioms, and again from those causes and axioms new works and experiments, as a legitimate interpreter of nature."

10.5. Johannes Kepler (1571-1630), German

• Born in German town of Weil der Stadt; sickly and bitter childhood
• Graduated from University of Tübingen
• Taught mathematics and astronomy in Graz, Austria
• Became assistant and successor to Tycho Brahe in Prague
• Strongly influenced by metaphysical viewpoint associated with Pythagorean and "neo-Platonic" tradition
• Lifelong question as to clockwork that governed the celestial machinery; firmly convinced that mathematical relations existed that could make sense of the planetary system
• Had Brahe's observations of planets
• Published in 1609, New Astronomy, containing his first two laws of planetary motion; published in 1619, The Harmonies of the World, containing his third law
• Developed laws of planetary motion (kinematics laws) from Brahe's data on Mars
• Boldly extended laws derived from basically Mars to all planets, regarding his laws as universal--very imaginative step
• Believed that magnetic forces by Sun responsible for orbital motion of planets
• Anticipates Newton's cause and effect concept
• Rejects notion of an infinite universe without center or edge..."one finds oneself wandering in this immensity in which are denied limits and center, and therefore also all determinate places."
• Died at age 60, in poverty, sickly and having endured years of persecution for his liberal Protestant views
• Although having elements of Greek science about his work, Kepler first of modern scientists

10.6. Kepler's Laws of Planetary Motion

• Kepler's First Law (Law of Elliptic Orbits)
  • Each planet moves in an elliptic orbit around the Sun with the Sun occupying one foci.
• Kepler's Second Law (Law of Areas)
  • The imaginary line connecting any planet to the Sun sweeps over equal areas in equal intervals of time.
• Kepler's Third Law (Harmonic Law)
  • The square of any planet's orbital period (sidereal) is proportional to the cube of its mean distance (semi-major axis) from the Sun.
  • Mathematical statement: P = k(a)[E(3/2)]
  • Example: If a is measured in astronomical units (AU = semi-major axis of Earth's orbit) and the sidereal period in years (Earth's sidereal period), then the constant k in the mathematical expression for Kepler's third law is equal to 1, and the mathematical relation becomes P[E(2)] = a[E(3)]