Early Astronomy & Retrograde motion

Astronomy around the World

• Babylonians, Assyrians, and Egyptians:

  • Egyptians adopted a calendar based on a $365\text{-day}$ year around $3000$ years ago.

  • Tracked the predawn rising of the star Sirius to predict the annual flooding of the Nile River.

• Chinese Astronomers:

  • Determined the year length around the same time as the Egyptians.

  • Recorded comets, meteors, sunspots, and "guest stars" (sudden supernovae explosions).

• Mayan Culture:

  • Developed a complex calendar based on the orbital motion of Venus.

• Polynesians:

  • Used celestial navigation to travel hundreds of kilometers across open ocean.

• Prehistoric Britain:

  • Built stone circles like Stonehenge (around $2800\,\text{BCE}$) to align with solar and lunar motions.

Early Greek Cosmology and Earth's Shape

• Cosmology Defined: The study of the basic structure, origin, and evolution of the universe.

• Arguments for a Spherical Earth:

  • Pythagoras ($2500$ years ago): Suggested Earth was spherical based on the philosophical belief that spheres represent perfect geometric forms.

  • Aristotle ($384\text{--}322\,\text{BCE}$):

  • Lunar Eclipses: Observed that Earth's shadow on the Moon during a lunar eclipse is always round. Only a sphere consistently casts a circular shadow.

  • Stellar Visibility: Noted that moving south reveals stars not visible further north and decreases the altitude of the North Star, proving motion over a curved surface.

• Additional Proofs of Earth's Curvature:

  • Ships sailing into the distance disappear hull-first over the horizon.

  • Spacecraft photos confirm Earth is round from all perspectives.

  • Time zones experience different solar positions simultaneously.

Stellar Parallax and Heliocentric Ideas

• Aristarchus of Samos ($310\text{--}230\,\text{BCE}$): Proposed that Earth rotates and orbits the Sun (heliocentric model).

• Stellar Parallax:

  • The apparent shift in direction of an object caused by the change in position of the observer.

  • Ancient Greeks could not detect stellar parallax because stars are vastly farther away than they imagined, leading them to reject the heliocentric concept in favor of a stationary Earth.

Measurement of Earth by Eratosthenes

• Eratosthenes ($276\text{--}194\,\text{BCE}$):o

  • Successfully measured Earth's circumference around $200\,\text{BCE}$ using geometry.

  • Observations on Solstice Noon:

  • At Syene: Sunlight struck the bottom of a vertical well directly overhead ($0^\natural$ zenith angle).

  • At Alexandria ($5000\,\text{stadia}$ north): Sunlight cast a shadow making an angle of $7^\circ$ (or $\frac{1}{50}$ of a full circle) with the vertical.

  • Calculation: Earth's circumference = $50 \times 5000\,\text{stadia} = 250{,}000\,\text{stadia}$ (within $1\%$ to $20\%$ of the actual value of $40{,}000\,\text{km}$).

Hipparchus and Precession

• Hipparchus (c. $150\,\text{BCE}$):

  • Created an accurate star catalog containing approximately $850$ stars.

  • Developed the apparent magnitude system to classify stars by visual brightness.

  • Precession:

  • Discovered that the position of the celestial poles changes continuously over time.

  • Caused by the gravitational tug of the Sun and Moon on Earth's equatorial bulge, making Earth wobble on its axis.

  • Completes one full precession cycle every $26{,}000\,\text{years}$.

Ptolemy’s Geocentric System

• Claudius Ptolemy (c. $140\,\text{CE}$):

  • Compiled Greek astronomical knowledge into the Almagest.

  • Retrograde Motion: The temporary apparent westward motion of a planet across the sky, caused when faster-moving Earth overtakes an outer planet in orbit.

  • Ptolemy's Geocentric Model:

  • Preserved the geocentric (Earth-centered) view and required circular motions.

  • Epicycle: A small circle on which a planet revolves.

  • Deferent: A larger circle around Earth along which the center of the epicycle travels.

  • Equant Point: An offset center point used to explain non-uniform motion while maintaining geometric circularity.