PHYSICAL SCIENCE

• Tycho Brahe


  Danish astronomer (1546-1601) from a rich noble family, fascinated by astronomy and dedicated his life to recording planetary positions ten times more accurately than previous work
• Tycho Brahe's Observatory


  • King of Denmark gave Tycho an island with many families and money to build an observatory
  • Tycho's aim was to confirm his own picture of the universe, with the Earth at rest, the sun going around the Earth, and the planets going around the sun
• Tycho Brahe's works


  • 1572 book "De Nova Stella" showing position of 1572 supernova
  • Observations of 1577 comet revealing no measurable parallax, implying it was beyond the moon
• Tycho's Instruments


  • Uraniborg was Tycho's astronomical observatory and alchemical laboratory, built from 1576-1580
• Tycho Brahe clung firmly to the notion of perfectly circular orbits for all heavenly bodies
• Johannes Kepler was the first to break from Tycho's theory into Kepler's Laws of Planetary Motion
• Kepler's First Law (Law of Ellipses)

  Planets move in elliptical orbits with the sun at one of the foci
• Kepler's Second Law (Law of Equal Areas)

  Line from the sun to a planet sweeps with equal areas in equal time
• Kepler's Third Law (Law of Periods/Harmonies)

  The square of the periods (T) of the planets are proportional to the cube of their mean distances (R) from the sun. T^2 = k R^3, where k is a constant
• Kepler's Third Law describes the motion and distance of objects in the solar system
• Kepler's Third Law


  • Earth's sidereal year (T) and distance (R) both equal 1, so T^2 = R^3
• The average distance from the Earth to the sun is 1 astronomical unit (AU)
• Solving for planet's mean distance from sun using Kepler's Third Law

  Given: T = 200 days

  Use T^2 = k R^3 to solve for R
• Tycho Brahe's discoveries and data paved the way for Kepler's laws of planetary motion, which are close to our present model of the solar system
• Greeks made major contributions in philosophy, science, and math
• Golden Age of early astronomy centered in Greece
• Geocentric view


  Earth at center of universe, motionless sphere
• Celestial sphere


  Transparent, hollow sphere beyond planets where stars travel daily
• Oblate spheroid


  • Earth's shape has bulging equator and squeezed poles
• Solstice


  Either two times in the year (summer and winter), sun's highest/lowest point in sky at noon, longest/shortest days
• Eclipse


  Obscuring light from one celestial body by passage of another
• Heliocentrism


  Earth and planets revolve around the Sun
• Geocentrism


  Earth is assumed to be at the center of solar system/universe
• Around 500 B.C. Greeks believed Earth round, not flat
• Pythagoras and pupils proposed spherical Earth
• 500-430 B.C. Anaxagoras supported spherical Earth through lunar eclipse shadow observation
• Around 340 B.C. Aristotle listed arguments for spherical Earth: North Star position, Sun/Moon shape, disappearing ships
• North Star


  Position varied closer to equator
• Shape of Sun and Moon

  Spherical, suggesting Earth also spherical
• Disappearing Ships


  Hull disappeared before sail as if it was being enveloped by the water until it completely disappeared, suggesting curvature of the Earth
• Eratosthenes calculated Earth's circumference accurately
• Eratosthenes' method


  1. Observation: Vertical object in Syene in Southern Egypt cast no shadow during summer solstice, but in Alexandria in North Egypt it did

  2. Measured angle Sun made with vertical direction

  3. Alexandria Sun angle 7.2° from vertical, Syene 0°

  4. Hypothesis: Light rays parallel, Earth curved

  5. Result: Earth's circumference approximately 250,000 stadia about 40,000 kilometers
• Anaxagoras explained moon phases as reflection of sunlight, only half sphere illuminated at a time due to its spherical shape, visible part changes periodically
• Eudoxus proposed fixed spheres carrying Sun, Moon, five planets, and stars, revolving around stationary Earth
• Aristotle believed Earth spherical due to curved shadow during lunar eclipses, considered Earth center of universe with planets and stars on concentric, crystalline spheres
• Aristotle disagreed with flat Earth belief, used North Star position, ship observation, eclipse shadow to prove Earth's curvature
• Aristotle lived in ancient Greece more than 300 years before the Common Era (or Before Christ)
• Aristotle was the Father of Natural Science, centuries after his death, his methods formed basis of scientific method
• Aristarchus was the first to propose heliocentric view, sun center of universe, calculated sun-moon distance with geometric principles but with small measurements and observational errors
• Eratosthenes determined Earth's size by observing noonday sun angles in Syene and Alexandria using geometric principles, assumed same longitude