Lecture 5: Science Methods, Misuse and Madness

"Let no one ignorant of geometry enter my door."

Plato, The Republic

Navigation Options

You may :
  • Go to the Astro 105 Main Menu
  • Go to the Class Schedule
  • Look at the Review Questions for Lecture # 5
  • Go to the Lecture # 4 Master Page
  • Go to the Lecture # 6 Master Page

    • Date: September 13, 1994
    Reading Assignment: pp. 32-39

    Description : Introduction to Ancient Greek astronomy.

    Objectives

  • Students should understand why the ancient Greeks believed the Earth to be round.
  • Students should be able to understand and use a method to determine how large the Earth is.
  • Students should understand the differences between the geocentric and heliocentric model.
  • Students should understand what an epicycle is and why it is used.
  • Students should understand triangulation and parallax.

    • Lecture Outline

    Slide # 1: Lecture 4: Science Methods, Misuse and Madness

  • Click here for subtitle
  • The Scientific Method
  • Experiments and Statistics
  • Science and Society
  • Fringe Sciences and Pseudo-Sciences
    • Slide # 2: Pseudo Sciences Slide # 3: Lecture 5: Dead Greeks
  • Measuring Distances
  • The Size of Earth
  • Apparent Motion of Planets
  • The Geocentric Model
    • Slide # 4: Measuring Distances
  • How do you measure how far it is to a distant object?
    • Slide # 5: Measuring Distances
  • How would you measure the distance across a large river?
    • Slide # 6: Measuring Distance
  • Swimming may not be a wise idea.
    • Slide # 7: Triangulation
  • Construct a right triangle across from a fixed reference point
    • Slide # 8: Triangulation Slide # 9: Triangulation
  • By using trignometry or similar triangles, you can calculate the distance acro
    • Slide # 10: Triangulation of Objects in Space?
  • Celestial objects are much farther away
  • We must
  • Use as very large baselines in our triangle
  • Be able to measure very small angles
    • Slide # 11: Large Baselines : Earth Slide # 12: Large Baselines : Earth Slide # 13: Large Baselines : Earth Slide # 14: Views from the Observers Slide # 15: View from the Observers
  • The two observers see the object in two different positions
  • The shift is due to PARALLAX
    • Slide # 16: Large Baselines : Earth's Orbit
  • A very large baseline is need to measure the parallax of stars
    • Slide # 17: The Parallax of Stars
  • We have measured the parallax of stars
  • The parallax angle is less than 1 arcsecond
  • less than 1/3600 degrees!!!
  • Impossible to see without telescopes
    • Slide # 18: How do you know the Earth is round? Slide # 19: A Lunar Eclipse
  • The Earth's Shadow is always Round during a Lunar Eclipse
    • Slide # 20: Aristotle
  • Theorized the Earth must be round from Observations of Lunar Eclipses
  • Predicted that the star's visible would change for observers at different lati
  • Confirmed the prediction based on other observations
    • Slide # 21: Aristarchus
  • Determined the Sun is much further away than the Moon
  • Determined the relative sizes of Earth, Moon and Sun
    • Slide # 22: The Sun is further away than the Moon Slide # 23: Aristarchus' Results
  • The Sun is 19 times further away than the Moon
  • (Actually, it is about 400 times further away)
    • Slide # 24: Relative Sizes of Sun, Moon, Earth
  • The Sun is 19 times further away than the Moon
  • The Sun and Moon are to be the Same Angular Size
  • The Moon is about 3/8 the Size of the Earth's Shadow
    • Slide # 25: The Results
  • The Sun is 19 times farther than the Moon
  • (Actually about 400 times further)
  • Sun is 7 times larger than the Earth
  • (Actually about 109 times larger)
    • Slide # 26: The Size of Earth
  • How do you measure how big the Earth is?
    • Slide # 27: The Size of Earth
  • Two Observers have different Zenith Points
    • Slide # 28: The Size of Earth
  • If a star is overhead for one observer, it will not be overhead for the other.
    • Slide # 29: The Size of Earth Slide # 30: The Size of Earth Slide # 31: A Simplified Diagram Slide # 32: Measuring the Size of Earth
  • Find a place where the Sun is directly overhead
  • Go to another place and measure the angle between overhead and the Sun's posit
  • Measure the distance between the two points.
    • Slide # 33: Measuring the Size of Earth Slide # 34: The Size of Earth
  • This measurement was first done by Eratosthenes in about 200BC
  • He measured the distance and angle between
  • Alexandria
  • Aswan Egypt
  • His accuracy was better than 1%
    • Slide # 35: How do the Planets move in the Sky? Slide # 36: Where are the Planets Right Now? Slide # 37: What Planets were known to the Ancients?
  • Mercury
  • Venus
  • Mars
  • Jupiter
  • Saturn
    • Slide # 38: Planet Means "Wanderer"
  • Planets change positions relative to the background stars
  • Predicting the Position of the Sun, Moon and Stars was easy
  • Planets seemed to follow a different set of rules
    • Slide # 39: Outer Planets- The View From Earth Slide # 40: Retrograde and Direct Motion
  • Most of the time, planets travelled across the sky West to East
  • Direct Motion
  • a few months every year, the outer planets travel East to West
  • Retrograde Motion
    • Slide # 41: The Geocentric Model- A Description
  • The Earth is at the Center
  • All planets, the Sun and the stars revolve around the Earth
  • No stellar parallax
    • Slide # 42: The Geocentric Model Slide # 43: The Geocentric Model- the Rules
  • planets move on perfect circles
  • planets move at uniform speed
    • Slide # 44: Retrograde Motion?
  • Additional circles were needed to make planets reverse direction
  • Epicycles were introduced
    • Slide # 45: Epicycles Slide # 46: Epicycles
  • one epicycle for each planet explained most of retrograde motion
  • more observations made more circles needed
    • Slide # 47: Epicycles Out of Control Slide # 48: Epi-epi-epicycles
  • Ptolemy introduced a model of the solar system with 80 circles
  • Accepted model 140BC to 1543AD
    • Slide # 49: Why was this model believed?
  • It explained all the motions of the planets
  • It predicted NO stellar parallax
    • Slide # 50: Lecture 5: Dead Greeks
  • Measuring Distances
  • The Size of Earth
  • Apparent Motion of Planets
  • The Geocentric Model