Ancient Greeks and Spherical Earth

The Greek Discovery of Earth's Spherical Shape

• When ships sail away, the hull disappears first, followed by the mast and sails.
• A flat earth would make the entire ship appear smaller as it sails away.
• The curved shape of the disappearing ship suggests a curved surface to the Earth.
• Earth's shadow on the moon is always circular.
• Only a sphere can cast a round shadow regardless of orientation.
• When traveling north or south, new stars become visible, while others disappear.
• On a flat Earth, the same stars would be visible everywhere.
• Eratosthenes compared the sun's angle at 2 cities during noon, measured the angle difference, and used geometry to estimate Earth's size.

Early Greek Models of the Universe

• Anaximander of Miletus (610-546 BCE) described Earth as a free-floating cylinder in space, and isn't held up by a deity.
• Anaximander introduced the concept of the Aperion (infinite/boundless), suggesting the universe has no defined limits.
• Anaximander relied on natural laws rather than mythology.
• Anaximander proposed that celestial bodies make full circles around Earth, laying the foundation for later models.
• Pythagoras (600 BCE) believed numbers and geometric relationships governed the cosmos.
• Pythagoras was one of the first to propose that Earth is a sphere based on observations of celestial bodies.
• Pythagoras used the shape of the sun and moon and ships disappearing over the horizon as evidence.
• Pythagoras introduced the term "cosmos" to describe an orderly universe.
• Pythagoras views were more mystical rather than scientific, but influenced later astronomers.

Saving the Appearances

• Plato believed all celestial motion was perfectly circular.
• Plato realized he couldn't explain planetary retrograde motion/backward motion.
• Plato encouraged astronomers to develop models that "saved appearances"/matched observations.

Concentric Spheres

• Eudoxus developed the first mechanical explanation and sought to save appearances.
• Eudoxus proposed a model with 27 spheres in total.
• Each planet and star is carried by its own sphere.
• Each sphere rotates at a different speed and in a different direction.
• Eudoxus attempted to account for retrograde motion, but the model was purely mathematical.
• Eudoxus model was ignored because it was inaccurate and didn't follow observations.

Prime Mover

• Aristotle adopted Eudoxus's model.
• Aristotle added buffering spheres between celestial spheres and an outermost sphere called the Prime Mover.
• The order of planets/heavenly bodies from Earth out: Earth, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn.
• Earth was the center, and everything else moved around it.
• Aristotle considered circular motion the perfect form of motion, contrasting with the imperfect, linear motion observed on Earth.

First Heliocentric Model

• Aristarchus proposed the sun was the center of the universe.
• In Aristarchus model Earth and other planets revolve around the sun.
• Aristarchus model was a radical departure from the geocentric models.
• Aristarchus model wasn't widely accepted during his time.

Ptolemaic Model

• Ptolemy's model was the most popular geocentric.
• To explain retrograde motion, Ptolemy introduced epicycles.
• In Ptolemy's model, a planet moved in a small circular orbit, which moved along a larger circular orbit (deferent) around Earth.
• Ptolemy's model became the standard for over 1,400 years.
• Ptolemy's model accurately predicted planetary positions despite conceptual flaws.

Heliocentric Revolution

• Copernicus revived the heliocentric model, marking the birth of modern astronomy.
• Copernicus model explained retrograde motion more simply by suggesting that Earth and other planets moved around the sun.
• There was resistance to the idea of the heliocentric model.
• The heliocentric model contradicted religious teachings and lacked observable evidence like stellar parallax.

Tychonic Model

• Tycho Brahe created a hybrid between geocentric and heliocentric models.
• In Tycho Brahe's model Earth remains stationary at the center of the universe
• In Tycho Brahe's model the Sun and Moon orbit Earth.
• In Tycho Brahe's model other planets orbit the sun.
• Served as a compromise between the 2 models.
• Matched observations better than Ptolemy's model but still rejected heliocentrism.
• Provided precise astronomical data.
• Used by Johannes Kepler to develop laws of planetary motion.

Galileo Contributions

• The Dutch Invention (1608) was the first telescope was invented by Hans Lippershey.
• The original Dutch telescope had only 3x magnification.
• The origianl Dutch telescope was only used for navigation and military purposes.
• Galileo improved the lens design thus improving the clarity.
• Galileo's improved telescope had higher magnification, from 3x to 20x then 30x.
• Galileo had better image quality.
• Galileo ground his own lenses, making clearer and sharper images.
• Galileo discovered lunar craters.
• The moon's surface was observed to be rugged and covered with craters, mountains, and valleys.
• Galileo challenged the Ptolemaic Models.
• Showed that Celestial bodies aren't perfect and unchanging.
• Galileo contradicted Aristotelian Physics, showed that heavens were not fundamentally different from earth.
• Galileo showed that Earth and heavens were made rom the type of matter.

Discovered Phases of Venus

• Galileo observed that Venus went through phases, like the moon.
• Galileo's observations are a challenge to the Ptolemaic Model.
• Venus was believed to orbit the earth.
• Galileo's discovery is evidence for the heliocentric model
• Galileo showed that some planets revolve around the sun.
• Galileo showed that the motions of celestial objects were more complex than the geocentric model predicted.

Discovered the Moons of Jupiter

• Galileo discovered 4 moons orbiting Jupiter.
• Galileo's discovery is a challenge to the Ptolemaic Model.
• Galileo contradicted the geocentric model, which stated all celestial bodies were supposed to orbit the earth
• Galileo's discovery showed that Earth was not the only center of motion in the universe.
• Galileo's discovery weakened the belief that everything revolved around the Earth.
• Galileo's discovery led to Kepler's Law of Planetary motion.

Discovered Sunspots

• Galileo observed dark spots on the sun's surface, which changed in size and position over time.
• Galileo's discovery is a challenge to the Ptolemaic model, which stated that the sun and celestial bodies were perfect divine and unchanging
• Galileo showed that the sun was dynamic, not a flawless and unchanged light source
• Galileo showed that celestial bodies undergo changes
• Galileo further weakened Aristotle's claim.

Discovered Supernova

• Galileo observed a bright new star in the night sky that later faded.
• Galileo's discovery is a challenge to the Ptolemaic Model, which suggested that the heavens were eternal and unchanging
• Galileo's discovery showed that stars could change, appear, or disappear
• Galileo provided direct evidence that celestial bodies could change.
• Galileo showed that same physical law applied to space and earth
• Galileo encouraged astronomers to question old beliefs

Discovered the Apparent Size of Stars

• Galileo observed that stars were actually distinct point of light at varying distances.
• Galileo's discovery is a challenge to the Ptolemaic Model, which statedstars were embedded in a fixed celestial sphere, equidistant from earth
• Early evidence of the vast scale of the earth
• Strengthen the heliocentric model

Tycho Brahe Contributions

• Known for his highly precise, systematic astronomical observation without the aid of a telescope
• Designed advanced instruments to measure planetary position with high accuracy rates
• Hybrid Model Discovery: Earth remained at the center with the Sun and Moon orbiting it, however all other planets orbited the sun and not the earth
• Exposed the weakness of the Ptolemaic Model
• Planetary orbits didn't perfectly match circular predictions
• Laid the foundation for the Laws of Planetary Model

Johannes Kepler Contributions

• Mathematician of the cosmos
• Built on Tycho Brahe's data to develop a mathematical model of planetary motion
• Improved Copernicus's heliocentric model by providing mathematical precisions to planetary orbits and eliminated the need for circular orbits
• Proved that planets move in elliptical orbits, eliminating the need for epicycles
• Laws
• Ellipses: Planets move in elliptical orbits around the sun with the sun is positioned off center, closer to one end of the ellipsis.
• Challenged the belief in perfect circular orbits and explained the planetary motion more accurately, which eliminated the need for epicycles
• Equal Areas: Planets move faster when closer to the sun (perihelion) and vice versa (aphelion).
• Proved that planetary speeds change, explained seasonal changes, and refuted Aristotle's idea of uniformity.
• Harmonies: The square of a planet's orbital period is proportional to the cube of its average distance from the Sun. Allowed astronomers to predict planetary positions, provided a mathematical relationship between a planet's distance from the Sun and the time it takes to complete 1 orbit and provided a foundation for newton's laws of gravitation

Understanding Motion

• The change in position of an object over time, resulting in movement and displacement with respect to time

History of Motion

• Aristotelian: Used observation and deduction to explain natural phenomena, introducing 2 types of motion
  • Natural: An object ten to return to its natural state based on its composition, such as a heavy object falling downward and a lighter objects rising upward
  • Violent: A cause is necessary for an object to move; once that runs out, the object will return to tis natural state
• Any motion that required an external force to sustain it, where object stop mothing when force is removed
• Limitations: Aristotle couldn't explain why object in motion keep moving unless stopped and believe heavier objects fall faster than lighter ones.
  • Aristotle couldn't account for inertia, where the speed at which an object falls is proportional to its weight
  • Aristotle couldn't explain projectile motion correctly and believed that when an object is thrown, it moves forward only because air pushes it

Galilean Mechanics

• First to use controlled experiments to study motion, building the idea of motion from observing experiments and highly doubted Aristotle's views on motion
• Falling Object Experiment
  • He dropped 2 metal balls of different weights from the Leaning Tower of Pisa
  • With no air resistance, all objects fall at the same rate regardless of mass, but real world conditions = air resistance can slow down lighter objects and was later confirmed with vacuum experiments

Inclined Plane Experiment

• Rolling balls down inclined plans to slow down the motion and study acceleration
• Objects in motion accelerate uniformly, and the object in motion stay in motion unless acted upon by an external force

Directions of Motion

• Horizontal:
• Aristotle required continuous force to stay in motion, where motion stops when force is removed
• Galileo stated objects stay in motion unless acted upon by friction or another force, where there no external forces act, an object will continue moving at a constant velocity indefinitely
• Vertical:
• Aristotle believed the heavier object fall faster because the contain more Earth, and objects thrown upward return to the ground because they seek their natural place
• Galileo stated the All objects fall at the same rate in the absence of air resistance, the object accelerate as they fall due to gravity, not because of their composition and Projectile motion is a combination of constant horizontal motion and accelerated vertical motion due to gravity

Projectile Motion

• Problem: Aristotle's incorrect idea was object thrown forward eventually love their motion and fall straight down, in which no one correctly explained why cannonballs, arrows, or thrown objects followed a curved path
• What Galileo Did: Studied projectile motion using inclined planes to slow down the movement and analyze patterns where rejected Aristotle's Impetus Theory
• Newtonian Mechanics
  • Theory claimed that an external force was
  • 3 Laws of Motion:
    • Law of Inertia: Objects will keep moving unless acted upon by a force, the object resist changes in their state of motion, resulting in contradictions w/ Aristotle
    • Law of Acceleration: An object is directly proportional to the force applied and inversely proportional to its mass, where acceleration depends on force and mass, described by F = ma
  • Law of Action - Reaction: Every action there is an equal opposite reaction, explaining motion interactions

Acceleration

• Change in velocity over time, where if the object speeds up = positive, and the object slows down = negative
• Object changes directions, and even is speed remains constant, where the opposite signs = slowing down and same signs = speeding up
• Follows the formula: A = delta v / delta t, where A = accelerations, V = change in velocity and T = change in time

Kinematics

• Branch of physics that studies the possible motion of a body or system of bodies
• Equations will describe motion in terms of displacement, velocity, acceleration, and time
• Newton/s laws explain why motion happens
• Equations describe how objects move when forces act on them
• Allow us to predict velocity and displacement without explicitly calculating force