ASTR 150 & ERTH 105 F25 WEEK 3 HISTORY KEPLERS LAWS ann new

ERTH 105 OL S22: Voyage Through the Solar System

Introduction

  • Course Overview
    • Focus: Exploration of scientific thinking and its application to planetary science.
    • Relevance: Understanding roots of modern science in ancient practices.

Scientific Thinking

  • Definition: Scientific thinking involves systematic observation and experimentation akin to everyday problem-solving methods.
  • Components:
    • Observation
    • Trial-and-error experiments

Roots of Modern Science in Ancient Astronomy

  • Significance: Modern scientific practices are deeply influenced by ancient astronomy.
  • Timekeeping systems have origins in ancient astronomical observations.
Ancient Knowledge
  • Evidence from France: Cave paintings dated back to 18,000 B.C.E. suggest early humans had knowledge of lunar phases, evidenced by the depiction of 29 dots representing lunar cycles.

Ancient Greek Science (3.2)

Goals for Learning
  • Understand why modern science is traced back to Greek contributions.
  • Explore Greek explanations for planetary motion.
Contributions of Ancient Greeks
  • Modeling Nature: Greeks were pioneers in creating models to explain natural phenomena without reliance on myth or supernatural elements.
    • Their geocentric model placed Earth at the center of the universe.
Eratosthenes (c. 240 B.C.E)
  • Measurement Method:
    • Distance from Syene to Alexandria: Approximately 5000 stadia.
    • Angle of Sun's shadow in Syene: 7°.
  • Calculation of Earth's Circumference:
    • Formula: 7360⋅circumference of Earth=5000 stadia\frac{7}{360} \cdot \text{circumference of Earth} = 5000 \text{ stadia}
    • Rearranged: circumference of Earth=5000⋅3607 stadia\text{circumference of Earth} = 5000 \cdot \frac{360}{7} \text{ stadia}
    • Approximate Result: 250,000 stadia.
    • Comparison: Modern value of Earth's circumference is approximately 40,100 km; conversion shows that 250,000 stadia ≈ 42,000 km.
Greek Explanations of Planetary Motion
  • Geocentric Model:
    • Earth is stationary and at the center.
    • Heavenly bodies were theorized to move in perfect circles.
  • Challenges: Explaining the retrograde motion of planets proved difficult.
Retrograde Motion
  • Definition: An apparent reversal of a planet's movement in the sky, noticeable over a period (e.g., Mars appearing to stop, move backwards, and resume forward motion).
  • Greek Misinterpretations: The Greeks rejected the actual explanation, partly due to their inability to detect stellar parallax.
Stellar Parallax and its Implications
  • Observation Limitation: Stars are excessively far, making parallax imperceptible to the naked eye.
  • Rejection of Heliocentrism: The Greeks concluded either:
    1. Stars are insufficiently distant.
    2. Earth is stationary despite evidence suggesting otherwise, maintaining debate on Earth-centered versus Sun-centered systems.
Ptolemaic Model
  • Ptolemy's Contributions (A.D. 100-170): Developed a refined geocentric model sufficient for narratives lasting 1500 years.
  • Almagest: Arabic translation of Ptolemy's work showcasing the depth of Greek astronomical insight.
  • Retrograde Motion in Ptolemy's Model: Suggested planets sometimes moved backward in a deferent circle around Earth.

Preservation of Greek Knowledge

  • Islamic Scholars: Preserved and expanded upon Greek knowledge especially in mathematics and astronomy.
  • House of Wisdom: Established by Al-Mamun in Baghdad around A.D. 800 as a pivotal academic institution.
  • European Renaissance Influence: The fall of Constantinople in 1453 enabled Eastern scholars to migrate to Europe, aiding in the revival of classical knowledge.
Summary of Greek Contributions
  • Model Development: Greeks emphasized that predictions must align with empirical observations, creating foundational scientific methodology.
  • Ptolemaic Planetary Motion Explanation: Models depicted planets moving in small circles (epicycles) as they orbited Earth (deferents).

The Copernican Revolution (3.3)

Learning Goals
  • Analyze how Copernicus, Tycho Brahe, and Johannes Kepler challenged the geocentric model.
  • Explain Kepler's three laws of planetary motion.
  • Discuss Galileo's role in reinforcing the Copernican model.
Copernicus (1473-1543)
  • Background: A priest and lawyer; educated in multiple prestigious universities, forming the first sun-centered model.
  • Personal Discovery: Lacked experimental evidence but proposed heliocentrism.
Tycho Brahe (1546-1601)
  • Key Contributions: Compiled precise naked-eye measurements of planetary positions (accuracy within one arcminute).
  • Limitations: Despite recognizing planets revolved around the Sun, he did not detect parallax, thus clinging to a geocentric view.
  • Collaboration with Kepler: Hired Kepler, allowing him to fine-tune the understanding of planetary motion.
Johannes Kepler (1571-1630)
  • Initial Hypothesis: Attempted to fit Tycho's observations using circular orbits but found discrepancies.
  • Shift to Ellipses: A recognition of an 8-arcminute discrepancy shifted his perspective towards elliptical orbits, leading to revelatory conclusions in astronomy.
Definition of an Ellipse
  • General Characteristics:
    • Represents shape differing from a circle based on eccentricity.
    • Focus points defined as the two fixed points to maintain the shape.
Kepler’s Laws of Planetary Motion
  • First Law: The orbit of each planet is an ellipse with the Sun at one focus.
  • Second Law: A line segment joining a planet and the Sun sweeps out equal areas