Phys Sci WW3

The Greek Discovery of Earth's Spherical Shape

• Ships Disappearing Over the Horizon

  • When ships sailed away, their hull disappeared first, then the mast, and sails

  • A flat earth would cause the entire ship to shrink/appear smaller

  • This suggested a curved surface

• The Shape of Earth's Shadow on the Moon

  • The earth's shadow on the moon was always circular

  • Only a sphere always casts a round shadow, regardless of orientation

• Difference in the Night Sky by Location

  • When traveling north or south, new stars appeared while other disappeared blow the horizon

  • A flat earth would have the same visible stars everywhere

• Eratosthenes' Measurement of Earth's Circumference

  • Compared the sun's angle at 2 cities at noon

  • Measured the angle difference and used geometry to estimate Earth's size

Early Greek Models of the Universe

• The Beginning

  • Anaximander of Miletus

  • 610-546 BCE

  • Described earth as a free floating cylinder in space

    • Isn't held up by a deity

  • Introduced the concept of the Aperion (infinite/boundless)

    • Suggested the universe had no defined limits

  • Relied on natural laws rather than mythology

  • Proposed that celestial bodies made full circles around earth

    • Laid the foundation for later models

• Mathematical Approach

  • Pythagoras

  • 600 BCE

  • Believed numbers and geometric relationships governed the cosmos

  • One of the first who proposed that the earth is a sphere based on observation of celestial bodies

    • Also used the disappearing ships + he sun and moon appeared round as evidence

  • Introduced the term cosmos to describe an orderly universe

  • Views were more mystical rather than scientific

    • Influenced later astronomers tho

• Saving the Appearances

  • Plato

  • Believed all celestial motion was perfectly circular

  • Couldn't explain planetary retrograde motion/backward motion

  • Encouraged astronomers to develop models that "saved appearances"/matched observations

• Concentric Spheres

  • Eudoxus

  • First mechanical explanation

  • First to save appearances

  • Proposed that there were 27 spheres in total

    • Each planet and starts being carried by its own sphere

    • Each sphere rotating at a different speed and in a different direction

  • Attempted to account of retrograde motion but the model was purely mathematical

    • Was ignored because it wasn't accurate and didn't follow observations

• Prime Mover

  • Aristotle

  • Adopted Eudoxus model

    • Added buffering spheres between celestial spheres and an outermost sphere that was the domain of what he called the Prime Mover

  • Order of the planets and heavenly bodies from earth out: Earth, Moon, Mercury, Venus, Sun, Mars, Jupiter, Saturn, …

    • Earth was the center and everything else moved around it

  • Considered circular motion to be the perfect form of motion

    • Was in contrast to the imperfect linear motion observed on earth

• First Heliocentric Model

  • Aristarchus

  • Famous for proposing that the sun was the center of the universe

    • Earth and their planets revolved around the sun

  • Was a radical departure from the geocentric models

  • Wasn't widely accepted and was ignored by other Greek astronomers at the time

• Ptolemaic Model

  • Ptolemy

  • Most popular geocentric model

  • To explain retrograde motion, he introduced the concept of epicycles

    • Planet moved in a small circular orbit which moved long a larger circular orbits (deferent) around the earth

  • Became the standard for over 1,400 years

    • Accurately predicted planetary positions despite its conceptual flaws

• Heliocentric Revolution

  • Copernicus

  • Revival of heliocentric model

  • Birth of modern astronomy

  • Explained retrograde motion more simple by suggesting that earth and other planets moved around the sun

  • Resistance to the idea

    • It contradicted religious teachings and lacked observable evidence like stellar parallax

• Tychonic Model

  • Tycho Brahe

  • Hybrid between geocentric and heliocentric models

    • Earth remains stationary at the center of the universe

    • Sun and moon orbit the earth

    • Other planets orbit the sun

  • Why was this model important

    • 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

• Early Telescope

  • The Dutch Invention (1608)

  • First telescope was invented by Hans Lippershey

    • Only has 3x magnification

    • Only used for navigation and military purposes

  • Galileo's improvement

    • Lens design

      • Improved the clarity

    • Higher magnification

      • From 3x to 20x then 30x

    • Better image quality

      • Ground his own lenses, making clearer and sharper images

• Discover Lunar Craters

  • Observed that moon's surface was rugged, covered with craters, mountains and valleys

  • Challenged the Ptolemaic Models

    • Celestial bodies were perfect and unchanging

    • Contradicted Aristotelian Physics

      • Heavens were fundamentally different rom earth

  • Impact

    • Earth and heavens were made from the type of matter

• Discovered Phases of Venus

  • Observed the Venus went though phases, like the moon

  • Challenge to Ptolemaic Model

    • Venus was believed to orbit the earth

  • Impact

    • Evidence for the heliocentric model

      • Some planets revolve around the sun

    • Motions of celestial objects were more complex than the geocentric model predicted

• Discovered the Moons of Jupiter

  • Discovered 4 moons orbiting Jupiter

  • Challenge to the Ptolemaic Model

    • In geocentric model, all celestial bodies were supposed to orbit the earth

  • Impact

    • Earth was not the only center of motion in the universe

    • Weakened the belief that everything revolved around the Earth

    • Lead to Kepler's Law of Planetary motion

• Discovered Sunspots

  • Observed dark spots on the sun's surface that changed in size and position over time

  • Challenge to the Ptolemaic model

    • The sun and celestial bodies were perfect divine and unchanging

  • Impact

    • Sun was dynamic, not a flawless and unchanged light source

    • Celestial bodies undergo changes

    • Further weakened Aristotle's claim

• Discovered Supernova

  • Observed a bright new star in the might sky that later faded

  • Challenge to the Ptolemaic Model

    • Suggested that the heavens were eternal and unchanging

    • Stars couldn't change, appear, or disappear

  • Impact

    • Direct evidence that celestial bodies could change

    • Same physical law applied to space and earth

    • Encourage astronomers to question old beliefs

• Discovered the Apparent Size of Stars

  • Observed that stars were actually distinct point of light at varying distances

  • Challenge to the Ptolemaic Model

    • Stars were embedded in a fixed celestial sphere, equidistant from earth

  • Impacts

    • Ealy 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

• Importance

  • 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

  • Eliminated the need for circular orbits

• Proved that planets move in elliptical orbits

• Discovery eliminated the need for epicycles

• Laws

  • Law of Ellipses

    • Planets move in elliptical orbits around the sun

      • The sun is positioned off center, closer to one end of the ellipsis

    • Importance

      • Challenged the belief in perfect circular orbits

      • Explain the planetary motion more accurately

      • Eliminated the need for epicycles

  • Law of Equal Areas

    • Planets move faster when closer to the sun (perihelion) and vice versa (aphelion)

    • Importance

      • Proved that planetary speeds change

      • Explained seasonal changes

      • Refuted Aristotle's idea of uniformity

  • Law of Harmonies

    • The square of a planet's orbital period is proportional to the cube of its average distance from the Sun

    • Importance

      • Allowed astronomers to predict planetary positions

      • A mathematical relationship between a planet's distance from the Sun and the time it takes to complete 1 orbit

      • Provided a foundation for newton's laws of gravitation

Understanding Motion

• The change in position of an object over time

• Movement

• Displacement with respect to time

History of Motion

• Aristotelian

  • Used observation and deduction to explain natural phenomena

  • Introduced 2 types of motion

    • Natural

      • Object ten to return to its natural state based on its composition

      • Heavy object fall downward

      • Lighter objects rise upward

    • Violent

      • A cause is necessary for an object to move

        • Once it runs out, the object will return to tis natural state

      • Any motion that required an external force to sustain it

      • Object stop mothing when force is removed

  • Limitations

    • Couldn't explain why object in motion keep moving unless stopped

      • Didn't account for inertia

    • Believed heavier objects fall faster than lighter ones

      • The speed at which an object falls is proportional to its weight

    • Couldn't explain projectile motion correctly

      • 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

• Built the idea of motion from observing experiments

• Highly doubted Aristotle's views on motion

• Falling Object Experiment

  • He dropped 2 metal balls of different weights from the Leaning Tower of Pisa

  • Findings

    • With no air resistance, all objects fall at the same rate regardless of mass

    • Real world conditions = air resistance can slow down lighter objects

    • Later confirmed with vacuum experiments

• Inclined Plane Experiment

  • He rolled balls down inclined plans to slow down the motion and study acceleration

  • Findings

    • Objects in motion accelerate uniformly

    • Object in motion stay in motion unless acted upon by an external force

Directions of Motion

• Horizontal Motion

  • Aristotle

    • Objects required a continuous force to stay in motion

    • Motion stopes when force is removed

  • Galileo

    • Objects stay in motion unless acted upon by friction or another force

    • If no external forces act, an object will continue moving at a constant velocity indefinitely

• Vertical Motion

  • Aristotle

    • Heavier object fall faster because the contain more Earth

    • Objects thrown upward return to the ground because they seek their natural place

  • Galileo

    • All objects fall at the same rate in the absence of air resistance

    • Object accelerate as they fall due to gravity, not because of their composition

    • Projectile motion is a combination of constant horizontal motion and accelerated vertical motion due to gravity

Projectile Motion

• Problem

  • Aristotle's incorrect idea

    • Object thrown forward eventually love their motion and fall straight down

  • Implication

    • 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

  • Rejected Aristotle's Impetus Theory

    • Theory claimed that an external force was

Newtonian Mechanics

• 3 Laws of Motion

  • Law of Inertia

    • Objects will keep moving unless acted upon by a force

    • Object resist changes in their state of motion

    • Contradictions w/ Aristotle

  • Law of Acceleration

    • An object is directly proportional to the force applied and inversely proportional to its mass

    • Acceleration depends on force and mass

      • F = ma

  • Law of Action - Reaction

    • Every action there is an equal opposite reaction

    • Explains motion interactions

Acceleration

• Change in velocity over time

• Velocity

  • Object speeds up

    • Positive

  • Object slows down

    • Negative

  • Object changes directions

    • Even is speed remains constant

• Opposite signs = slowing down

• Same signs = speeding up

• Formula

  • A = delta v / delta t

    • A = accelerations

    • V = change in velocity

    • 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

• Why Use Kinematics?

  • 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