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Objectives

  • Explain how the Greeks knew that the Earth is spherical (S11/12PS-IVa-38).

  • Cite examples of astronomical phenomena known to astronomers before the advent of telescopes (S11/12PS-IVa-41).

  • Explain how Brahe's innovations and extensive data collection in observational astronomy paved the way for Kepler's discovery of his laws of planetary motion (S11/12PS-IVb-44).

Aristotle’s View of Motion

  • Two Types of Motion:

    • Terrestrial Motion: Pertains to the movement of any object on Earth.

    • Celestial Motion: Refers to the movement of any object beyond Earth.

  • Three Types of Terrestrial Motion According to Aristotle:

    • Natural Motion: Determined by the nature of an object’s composition.

    • Violent Motion: Happens when an object is acted upon by an external force.

    • Alteration: Refers to qualitative change in motion.

The Celestial Sphere

  • Ancient Cosmology: Earth was believed to be enclosed in a rotating celestial sphere, with the sun, moon, stars, and other celestial objects attached to it.

  • Key Points of the Celestial Sphere:

    • North celestial pole: Point directly over Earth’s North Pole.

    • South celestial pole: Point directly over Earth’s South Pole.

    • Celestial equator: Projection of Earth’s equator onto the celestial sphere.

Sun’s Apparent Path and Equinoxes

  • Ecliptic: The sun’s apparent path through the celestial sphere.

  • Equinox: Occurs when the sun's position in the ecliptic intersects with the celestial equator, resulting in equal lengths of day and night.

    • Two Equinoxes Per Year:

    • Vernal Equinox: March.

    • Autumnal Equinox: September.

Solstices

  • Solstice: Happens when the sun’s position in the ecliptic reaches its northernmost or southernmost point relative to the celestial equator.

    • Summer Solstice: Occurs in June; the longest day of the year.

    • Winter Solstice: Occurs in December; the longest night of the year.

Obliquity of the Ecliptic

  • Obliquity: Refers to the angle of inclination of Earth’s equator with respect to the orbital plane, approximately 23.5ext°23.5^ ext{°}.

  • Historical Context:

    • Hipparchus of Nicaea (190-120 BCE) to Claudius Ptolemy (90-168 CE) considered this phenomenon relevant in understanding celestial mechanics.

  • Ptolemy's Contribution: Proposed the ecliptic of the sun and planets lie at an angle to Earth’s axis.

Earth’s Motion

  • Types of Motion:

    • Diurnal Motion: Daily rising and setting of the sun.

    • Annual Motion: Apparent shift in the location of stars throughout the year.

    • Precession of the Equinoxes: Refers to the gradual change in the orientation of Earth's axis, occurring at a rate of one degree every century. A full cycle takes approximately 26,000 years.

  • Sidereal Year vs. Tropical Year:

    • Sidereal Year: Time for the sun to return to the same point relative to the fixed stars.

    • Tropical Year: Time taken for the sun to return to an equinox.

Precession Mechanisms

  • Lunisolar Precession: Caused by the gravitational forces of the sun and moon on Earth; spans approximately 26,000 years.

  • Planetary Precession: Influenced by gravitational interactions with other planets.

  • Terminology Change (2006): IAU redefined "lunisolar precession" and "planetary precession" to "precession of the equator" and "precession of the ecliptic" respectively, leading to the term general precession for the combined effect.

Historical Concepts of Earth’s Shape

  • Mesopotamian Mythology: Believed Earth to be a flat disk floating on the ocean with a spherical sky above.

  • Greek Understanding: Philosophers such as Plato and Aristotle offered physical and observational evidence for a spherical Earth:

    • Aristotle’s Arguments:

    • Every part of Earth tends to be compressed towards the center, forming a sphere.

    • Observations of southern constellations rising above the horizon as one travels south.

    • The shadow of Earth on the moon is always round during a lunar eclipse.

Philosophical Perspectives

  • Plato’s View: Pythagoras conceptualized heaven as a perfect circle; Plato aligned this with celestial motions being perfect and circular.

  • Saving the Appearances: Plato’s allegory of the cave illustrates the quest to understand underlying realities versus perceptions, a key aspect of his philosophy.

Competing Models of the Universe

  • Geocentric Model: Earth at the center of the universe.

  • Heliocentric Model: Sun at the center of the universe.

Eudoxus’ Model

  • Eudoxus (480-355 BCE): First geocentric model using celestial spheres based on Plato’s notion of circular motion.

    • Model Characteristics:

    • Homocentric spheres with 27 spheres total: 1 for background stars, 3 for the sun, 3 for the moon, and 4 for each of the five known planets (Mercury, Mars, Venus, Jupiter, Saturn).

Aristotle’s Model

  • Refinement of Eudoxus’ Model:

    • Callippus added spheres to account for irregular planetary motion, culminating in 34 spheres.

    • Aristotle expanded this model to 56 spheres, introducing the concept of Prime Mover as the initiator of celestial motion.

Ptolemy’s Model

  • Ptolemy's Contribution:

    • Advanced the geocentric model, providing accurate explanations of celestial motion with terms such as epicycles and deferents:

    • Deferent: Circular path for planetary motion around Earth.

    • Epicycle: A smaller circle along which a planet moves around its deferent.

    • Conceptualized uniform circular motion.

  • Mechanisms of Motion:

    • Considered three factors influencing the apparent speed of planets:

    • The epicycle of the planet.

    • Observer’s eccentric positioning (off-center observation).

    • The equant, a point equidistant from Earth to the circle's center, guiding the motion

Aristarchus’ Model

  • Aristarchus of Samos (319-230 BCE): Proposed a heliocentric model with the sun at the center of the universe, claiming it was much larger than Earth.

  • Key Work: "On the Sizes and Distances of the Sun and the Moon," utilizing geometry based on Earth’s shadow during a lunar eclipse.

  • Challenges: Faced skepticism due to prevailing geocentric consensus; concepts contradicted contemporary beliefs.

Legacy of Aristarchus

  • Neglected Hypothesis: Despite initial rejection, only cited later by Archimedes in "The Sand Reckoner," not gaining traction for 2000 years.

  • Reappraisal in the Modern Era: Aristarchus’ heliocentric view validated eventually.

Copernicus’ Model

  • Nicolaus Copernicus (1473-1543): Advocated for heliocentric model, explaining retrograde motion based on combined motions of Earth and planets.

  • Key Propositions:

    • Celestial motions are uniform, infinite, circular, or composite of circles (epicycles).

    • Sun as the center of the universe, planets revolve around the sun, including fixed stars.

    • Explains Earth’s motion accounting for retrograde motion and seasonal changes due to Earth's axial tilt.

The Copernican Revolution

  • Support from Key Figures: Observational work by Galileo Galilei (1564-1642), Tycho Brahe (1546-1601), and Johannes Kepler (1571-1630) reinforced the Copernican model.

Galileo’s Astronomical Discoveries

  • Galileo Galilei: Known as the father of modern astronomy, used telescopic observations to support heliocentric theory.

  • Key Discoveries:

    • Lunar Craters: Challenged the belief of a perfect moon; craters observed through telescope indicated imperfections.

    • Phases of Venus: Demonstrated that Venus exhibited phases akin to the moon, inconsistent with the geocentric model.

    • Moons of Jupiter: Discovered four largest moons; acknowledged them as celestial bodies orbiting Jupiter, named by Simon Marius: Io, Europa, Ganymede, Callisto.

    • Sunspots: Observed dark spots on the sun, showing that the sun rotates, supporting Copernican views.

    • Supernova Observation: Recorded two supernovas, observations refuted Aristotle’s belief in unchanging celestial materials, highlighting dynamism in the universe.