Unit 2: Copernicus, Keppler, Galileo, Newton, & Einstein

copernicus’ heliocentric system

• planets on circles around sun

  • not ellipses nor spheres

• problem: planet’s orbits are ellipses

  • fixed this with minor epicycles

copernicus’ model and parallax

stars had to be exceedingly far away

ptolemy

• geocentrism

• very “complicated”

copernicus

• heliocentric

• less complicated

copernicus + ptolemy

• models had similar level of accuracy

• used epicycles, copernicus used less

• perfect circles

G. bruno (1548)

proposes that Sun is one star out of an infinite number

new inventions in baroque era

• telescope

• air pump

tycho barhe

• postions of planets

• worked without telescope

• stellar and planetary positions

• comets and novas are extralunar

• shows that stars can change (supernova of 1572)

• proves that comets are superlunar

the closer an object is…

• the more shifted it appears wrt the fixed stars

  • tycho measures parallax 0 for Great comet of 1577 and supernova of 1572

  • objects must be beyond the moon: change without circular motion—contradicts aristotle

kepler’s question

how are things happening?

kepler’s construction of the orbit of mars

triangulated position of mars using Brahe’s data

kepler’s 3 laws

1. law of ellipses

2. law of equal areas

3. harmonic law

law of ellipses

1. orbits of planets are ellipses, with the sun at one focus

2. a = semimajor axis

3. e = eccentricity

law of equal areas

an imaginary line connecting the sun to any planet sweeps out equal areas of the ellipse in equal times

harmonic law

tycho’s hybrid solar system model

• sun orbits earth

• planets orbit sun

scientific method

• francis bacon, descartes, galileo

• yields conclusions that are independent of the individual

  

• conclusions are based on observation

aristotle’s model of the cosmos

heavenly bodies are perfect, smooth, and unchanging

galileo’s telescopes

• 1st: 3x magnifying

• last: 32x

galileo findings

1. moutains and craters on the moon

2. moons of jupiter

3. sunspots

4. phases of venus

5. milky way is made up of stars

6. ears of saturn

why are phases of venus at odds with the geocentric epicycle model?

venus would not appear “full” as the moon does

issac newton question

why are things happening

newton’s 3 laws of motion and law of universal gravitation explain…

kepler’s laws

inertia

an object at rest remains at rest, and an object in motion remains in motion at a constant speed and in a straight line unless acted upon by a force

force and acceleration

F = ma

action and reaction

for every action, there is an equal and opposite reaction

acceleration

• rate of change of velocity

• change in speed or direction

barycenter of earth and moon

• moon doesn’t orbit earth’s center and earth doesn’t stay still

• earth and moon orbit each other about the barycenter

why inverse quadratic

the influence “thins out” as the distance from the source increases (scales like area)

compromise of orbital motion

planet moves in curved orbit

hooke’s polygon model

continual pulls towards the center

it takes a … force to make a higher speed move in an orbit

stronger

newton’s law explains

• baseball, cannonball, water motion

• tides

• atoms

• moon around earth

1919 eddington experiment

• Einstein’s theory of relativity correctly predicted that gravity would bend light

• comparing photographs and measuring tiny distances on glass plates under a microscope

results of eddington experiment

1. gravity is not a force, it is the curvature of spacetime

2. space, time, matter, and energy are all connected

3. objects and light follow curved spacetime

spacetime

1. 3 spatial dimensions

2. 1 time dimension

3. space and time are linked together

4. mass and energy warp spacetime to produce gravity

GPS

• GPS must account for relativity

• satellite’s motion and distance from earth’s gravity alter their time wrt on earth