Earth's Shape, Solstices, Eclipses & Geocentric Model

• Oblate spheroid is the shape of the Earth.
• A solstice is when the Sun reaches its highest or lowest point in the sky at noon during the summer and winter.
• An eclipse is the obscuring of light from one celestial body by another.
• Heliocentrism is an astronomical model where the Earth and planets revolve around the Sun.
• Geocentrism is a theory where Earth is assumed to be at the center of the solar system or universe.

Background

• Mesopotamians in the 6th century BC described the Earth as a flat disk in the ocean with a spherical sky.

Models of the Universe

• Models are categorized as either geocentric (Earth-centered) or heliocentric (Sun-centered).
• In the geocentric model, the Earth is at the center, and planets/heavenly bodies revolve around it.
• The Earth and other heavenly bodies were assumed to be spheres in geocentric models.
• Pythagoras and Plato entertained the idea of a spherical Earth, but lacked concrete evidence.
• In the heliocentric model, the Sun is at the center, and heavenly bodies (including Earth) revolve around it.
• Around 320 BC, Artistotle argued the sphere is perfect, the heavens are a region of perfection, and the Earth's components would press into a round form.
• The Earth's shadow is always circular during a lunar eclipse.
• The Pole Star appears higher in the sky when traveling north.

Greeks and the Spherical Earth

• Around 500 BC, Greeks believed the Earth was round; Pythagoras and his pupils proposed it first.
• Between 500 to 430 BC, Anaxagoras supported Pythagoras, claiming during a lunar eclipse the Earth casts a circular shadow on the Moon.
• Around 340 BC, Artistotle listed arguments for a spherical Earth including: positions of the North Star, shape of the Moon and the Sun, and the disappearance of ships over the horizon.

Observations That Suggest a Spherical Earth

• The North Star was thought to be at a fixed position, but Greeks found it closer to the horizon near the equator.
• Aristotle argued that if the Sun and Moon were spherical, then the Earth was likely spherical.
• When traveling away, ships disappeared hull first, as if being enveloped by water.

Size of the Spherical Earth

• Ancient scholars calculated the spherical Earth's circumference.
• Eratosthenes provided the most accurate measurement of the Earth's size.
• Vertical objects in Syene, Southern Egypt, did not cast shadows at noon during the summer solstice, suggesting the sun was overhead.
• But in Alexandria, Northern Egypt, a vertical object did cast a shadow at noon during the summer solstice, suggesting the sun was not overhead.
• Eratosthenes determined the Sun's angle with the vertical by measuring the shadow a vertical stick cast.
• He found the Sun made a 7.2° angle from the vertical in Alexandria while 0° in Syene.
• To explain the difference, he proposed that the light rays coming from the Sun are parallel, and the Earth is curved.
• Eratosthenes computed the Earth's circumference to be about 250,000 stadia or ~ 40,000 kilometers.
• Greeks concluded the Earth was a sphere based on:
• Earth casting a circular shadow on the Moon during lunar eclipses.
• The North Star's position changing depending on observer location.
• The Moon and Sun being spherical.
• Sailing ships disappearing hull first.
• The angle of the Sun with the vertical direction varying by location during the summer solstice.

Greek Astronomers and Their Models

• Eudoxus of Cnidus (400 BC), a mathematician, devised a system of concentric spheres to explain the movements of the sun, moon, and planets.
• Aristotle patterned his model of the universe after Eudoxus, believing it to be spherical and finite.
• He perceived the Earth was stationary at the center because it was too big to move.
• Aristarchus (BCE-230 BCE) created a heliocentric model, placing the sun at the center.
• He proposed that the sun and fixed stars were at rest, while the Earth revolved around the sun.
• Claudius Ptolemaeus (Ptolemy) believed the Earth was at the center, and planets revolved around Earth in perfect circles at a constant velocity.
• Ptolemy's geocentric model was more refined with planets revolving on epicycles (small spheres) that moved around the deferent (large spheres).
• He added that stars belonged to a celestial sphere beyond planetary spheres.
• Nicolaus Copernicus (1473-1543), was a Polish astronomer who accepted Aristarchus/heliocentric model.
• He delayed publishing his work out of fear of condemnation; it was published a year before his death.
• Copernicus believed in the heliocentric model because he saw loopholes in Ptolemy's model.
• Tycho Brahe (1546-1601) was a Danish astronomer who made planetary observations.
• Unlike Copernicus, Brahe believed in a geocentric universe that differed slightly from Ptolemy's.
• In Brahe's Tychonic System, the Earth was at the center, and the Moon and the Sun revolved around it, while all other planets revolved around the Sun (geoheliocentric system).