Lecture 3: Ancient Astronomy

Lecture Overview

• Ancient history of astronomy, exploring early observations and cultural interpretations.

• Geocentric model: The historical belief that Earth is the stationary center of the universe, with all celestial bodies orbiting it.

• "Flat Earth" model: The historical belief that Earth is a flat disc or plane, typically supported by limited local observations.

• Scientific method: The systematic approach to understanding the natural world through observation, hypothesis, experimentation, and revision of theories.

Scientific Method in Astronomy

• Astronomy evolves through evidence-based replacement of theories, demonstrating the self-correcting nature of science. For instance, the geocentric model was replaced by the heliocentric model due to accumulating observational evidence.

• Learns and applies critical thinking and skepticism, constantly questioning assumptions and evaluating empirical data before accepting conclusions.

• Highlights our understanding of celestial bodies, including planets, stars, galaxies, and larger cosmic structures, using advanced tools like optical telescopes, radio telescopes, and space probes.

Historical Context

• Modern humans emerged approximately 300,000 years ago; recorded history, enabled by writing, began around 5,000 years ago.

• Major astronomical advancements occurred significantly in recent centuries, particularly from the Renaissance onwards with the invention of the telescope and the formulation of classical mechanics by Newton.

• Expanded knowledge: Our understanding has grown from a solar system-centric view to recognizing the Milky Way as just one of billions of galaxies in a vast and expanding universe, leading to discoveries of phenomena like black holes, dark matter, and dark energy.

Ancient Astronomy

• Early views often linked celestial objects to deities and spiritual beliefs, influencing daily life, rituals, and seasonal festivals (e.g., sun gods, moon goddesses).

• Data collection and analysis became possible with the development of writing and mathematics (around 5,000 years ago), allowing for systematic recording and interpretation of celestial events.

• Ancient civilizations used astronomy for practical purposes like agriculture (creating calendars to predict planting and harvesting seasons based on solstices and equinoxes), navigation, and timekeeping.

Contributions of Babylonian and Chinese Astronomy

• Babylonian data (Moon and planets) was meticulously mapped for predictive purposes, especially for lunar eclipses (documented as early as ~400 BC). They developed sophisticated mathematical methods and astronomical tables (ephemerides) and discovered cycles such as the Saros cycle for predicting eclipses.

• Chinese records dating back to 2000 BC included detailed observations of eclipses, comets (e.g., Halley's Comet), and guest stars (supernovae), many of which are still used by modern astronomers. They also observed sunspots and used astronomy for calendrical reform and imperial prognostication.

Hipparchus and Axial Precession

• Established an observatory around 150 BC (likely on the island of Rhodes) and compiled one of the earliest comprehensive star catalogs, listing about 850 stars with their positions and brightness.

• Developed the first known system for stellar brightness, a scale of apparent magnitude, where 1^{st} magnitude stars were the brightest and 6^{th} magnitude stars were the faintest visible to the naked eye. This logarithmic scale is still the basis of modern magnitude systems.

• Discovered axial precession, the slow wobble of Earth's rotational axis, similar to a spinning top. This wobble causes the North Celestial Pole to shift its position over approximately 26,000 years, slowly changing which star appears as the "North Star" over millennia.

Evidence of Earth's Sphericity

• Flat Earth Beliefs: Historically common and intuitive due to the limited scope of human sensory perceptions, as the Earth appears flat on a local scale.

• Greeks (notably Pythagoras for philosophical reasons, and Aristotle based on observations) were among the first to establish and provide evidence for Earth's sphericity.

• Proofs:

  • Lunar eclipses: During a lunar eclipse, Earth's shadow cast upon the Moon is always circular, regardless of Earth's orientation, which is consistent with a spherical object. A flat disc would project an elliptical shadow in most cases.

  • Visibility of stars at different latitudes: As one travels north or south, different constellations become visible or invisible. For example, the North Star appears higher in the sky the further north one travels and eventually disappears below the horizon when one crosses the equator, indicating a curved surface.

  • Satellite images: Modern advancements provide direct photographic and video evidence of Earth's spherical shape from space.

  • Disappearing ships at horizon: When a ship sails away, its hull disappears below the horizon before its mast, as if it's sinking into the water. This phenomenon is caused by the Earth's curvature.

Eratosthenes' Measurement of Earth's Circumference

• Used shadows in two different Egyptian cities (Syene, modern Aswan, and Alexandria) to calculate the Earth's circumference with remarkable accuracy.

• Methodology: On the summer solstice, he observed that the Sun's rays shone directly down a well in Syene (indicating no shadow at noon). In Alexandria, measured to be approximately 800 km (5,000 stadia) north of Syene, a vertical pole cast a shadow. He measured the angle of this shadow to be about 7.2^ ext{o}.

• Calculation: Assuming the Sun's rays are parallel and the Earth is a sphere, he reasoned that the angle of the shadow (7.2^ ext{o}) was equal to the angular distance between Syene and Alexandria on Earth's surface. Since 7.2^ ext{o} is 1/50th of a full circle (360^ ext{o} / 7.2^ ext{o} = 50), he multiplied the distance between the two cities by 50 to find the Earth's circumference: 800 ext{ km} imes 50 = 40,000 ext{ km}.

• Findings: His calculated value of approximately 40,075 km (or 250,000 stadia) was exceptionally close to the actual circumference of Earth, which is about 40,075 km at the equator (2 ext{π}r ).

1. Two practical uses of astronomy in the ancient world were:

   • Agriculture: Ancient civilizations used astronomy to create calendars that predicted planting and harvesting seasons based on solstices and equinoxes.

   • Navigation and Timekeeping: They also used celestial observations for navigation and to keep track of time.

2. Five different ways to prove that the Earth is round are:

   • Lunar eclipses: Earth's shadow cast on the Moon during a lunar eclipse is always circular, consistent with a spherical object.

   • Visibility of stars at different latitudes: Different constellations become visible or invisible as one travels north or south, and the North Star's apparent height changes with latitude, indicating a curved surface.

   • Satellite images: Direct photographic and video evidence from space clearly shows Earth's spherical shape.

   • Disappearing ships at the horizon: The hull of a ship disappears before its mast as it sails away, due to the Earth's curvature.

   • Eratosthenes' measurement: The methodology and success of Eratosthenes' experiment rely on the Earth being a sphere and provided an accurate measurement of its circumference.

3. Stellar parallax is the apparent shift in the position of a nearby star against the background of more distant stars, caused by the Earth's orbit around the Sun. The Greeks did not observe this parallax. Without the ability to detect this tiny shift (because stars are much farther away than they could comprehend and their instruments weren't precise enough), they concluded that if the Earth revolved around the Sun, stars should appear to shift. Since no such shift was observed, they incorrectly reasoned that the Earth must be stationary, and therefore, the Sun (and all other celestial bodies) must orbit a stationary Earth. They were missing the crucial information that stars are extraordinarily far away, making the parallax angle too small to be observed with the naked eye or ancient instruments.

4. Eratosthenes measured the circumference of the Earth using observations of shadows in two different Egyptian cities. On the summer solstice, he noted that the Sun's rays shone directly into a well in Syene (modern Aswan), meaning there was no shadow at noon. In Alexandria, located approximately 800 km north of Syene, he measured the angle of the shadow cast by a vertical pole at the same time. Assuming the Sun's rays were parallel, he reasoned that the angle of the shadow in Alexandria was equal to the angular distance between Syene and Alexandria on the Earth's curved surface. By determining this angle was a specific fraction of a full circle, he could then multiply the ground distance between the cities by the reciprocal of that fraction to find the Earth's total circumference.

5. Precession is the slow wobble of Earth's rotational axis, similar to the wobble of a spinning top. This wobble causes the North Celestial Pole (the point in the sky directly above Earth's North Pole) to gradually shift its position in a circle over a period of approximately 26,000 years. As the North Celestial Pole shifts, different stars appear to be the 'North Star' over millennia, and the apparent positions of all other stars also slowly change over these vast time scales.

6. When planets move "in retrograde," they do not actually move backward in their orbits. This phenomenon is an apparent motion caused by the relative speeds and positions of Earth and the other planet as they orbit the Sun. When Earth, on its faster, inner orbit, overtakes an outer planet, or when an inner planet catches up to Earth on its faster orbit, the perspective from Earth makes the other planet appear to temporarily reverse its direction across the sky before resuming its normal prograde motion. Ecologically, astrologers may assign special significance to this. However, from an astronomical perspective, retrograde motion is a natural and predictable consequence of orbital mechanics in a heliocentric system and does not have any special significance beyond being an optical illusion caused by our changing viewpoint.

7. Epicycles were small circles whose centers moved around a larger circle called a deferent. In Ptolemy's geocentric model, planets were thought to move along these epicycles, which themselves moved along the deferent around the Earth. Ptolemy introduced them to solve the problem of explaining the observed retrograde motion of planets (their apparent backward movement in the sky), as well as variations in planetary brightness and speed, all while maintaining the core belief that Earth was the unmoving center of the universe. While epicycles allowed Ptolemy's model to predict planetary positions with reasonable accuracy for centuries, they technically did "solve" the immediate observational problem of explaining retrograde motion within a geocentric framework, though they made the model incredibly complex.

8. Two ways in which Ptolemy's model of the solar system is incorrect are:

   • Geocentric nature: Ptolemy's model placed the Earth (geocentric) at the center of the universe, with all other celestial bodies orbiting it, which is incorrect. The Sun is the center of our solar system (heliocentric).

   • Inaccurate orbital paths: His model used complex combinations of perfect circles (deferents and epicycles) to describe planetary motion. While it could approximate observations, planets actually follow elliptical orbits, as later discovered by Kepler, not circular paths or combinations of circles.