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The Motion of Planets Birth of Modern Astronomy OR How Nerds Changed the World!!! Theory? Hypothesis? Law? Scientific Method?

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How is science done? Observations Experiments Explanations Theories Laws Repeat

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Assumptions of Early Models Geocentric - Earth in the middle Everything orbits the Earth Stars are located on the Celestial Sphere Everything moves in uniform circular motions

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The Greeks Anaximander –Celestial sphere rotates around the earth Pythagoras –Earth is a sphere Eudoxus –Planet motion accounted for by separate spheres Aristotle –Complete model of the universe (4 elements) –Perfect heavens Apollonius –epicycles

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The Time of Aristotle

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Model of the Universe All things in the universe go to their Natural Place ElementNatural MotionProperties EarthFalls downDry, Cold AirRises upWet, Hot WaterFalls downCold, Wet FireRises upHot, Dry

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Hellenistic (Greek) Periodic Table

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Retrograde Motion

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The problem of Retrograde Motion: Apollonius The motion of these spheres did not account for retrograde motion. Apollonius introduces ‘epicycles’ –Roughly meaning ‘cycles within’

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What is an epicycle? The Center of of epicycle revolves around the earth The planet spins along the epicycle at the same time. Earth Deferent Epicycle Mars

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Enter the Roman: Ptolemy Brought it all together Added the equant to adjust the model to match observations Wrote “The Mathematical Compilation” Destruction of Library of Alexandria –(Europe lost almost all it’s written knowledge) The Arab Scholars called it “Almagest” (“the greatest”) This is how they came to know it once the work returned to Europe.

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Earth Deferent Epicycle Mars Equant Claudius Ptolemy (87-165)

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The Dark Ages

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Nicolaus Copernicus ( ) Errors building up Must be a better way! Let’s try a Heliocentric system! Not any better though

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Tycho Brahe ( ) Comet – beyond the Moon Supernova – far away Naked eye observations of planets Accuracy through repetition Best observations of planetary positions Hired “nerd” to help calculate model Died….

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Johannes Kepler ( ) Worked for Brahe Took data after his death Spent years figuring out the motions of the planets Came up with… Three Laws of Planetary Motion

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1. Planets move in elliptical orbits with the Sun at one foci Sun Foci (sing. Focus) PerihelionAphelion Average distance from the Sun = 1 Astronomical Unit (1 A.U.)

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2. Planets move faster at perihelion than at aphelion. 1 Month

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3. Period is related to average distance P = period of the orbit a= average distance P 2 = k a 3 Longer orbits - greater average distance Need the value of k to use the formula k depends upon the situation Can be used for anything orbiting anything else

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Special version of Kepler’s third Law – If the object is orbiting the Sun P – measured in years, a – measured in A. U., then…. P 2 = a 3

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Galileo Galilei ( ) Knew of Copernicus’s & Kepler’s work Used a telescope to look at the sky What did he see?

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The Moon was an imperfect object Venus has phases

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Jupiter has objects around it Saturn is imperfect The Sun is imperfect

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Isaac Newton ( ) The ultimate “nerd” Able to explain Kepler’s laws Had to start with the basics - The Three Laws of Motion

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1. Law of Inertia - Objects do whatever they are currently doing unless something messes around with them.

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2. Force defined F=ma F=force m=mass a=acceleration (change in motion)

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3. For every action there is an equal and opposite reaction. The three laws of motion form the basis for the most important law of all (astronomically speaking) Newton’s Universal Law of Gravitation

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F=force of gravity G=constant M 1, M 2 = masses R=distance from “centers” Gravity is the most important force in the Universe

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Newton’s Revisions to Kepler’s Laws of Planetary Motion: Kepler’s 1 st and 2 nd Laws apply to all objects (not just planets) 3 rd Law rewritten: 4π2 and G are just constant #s (they don’t change) M 1 and M 2 are any two celestial bodies (could be a planet and Sun) Importance: if you know period and average distance of a planet, you can find mass of Sun (2 x kg) or any planet! Mass of Sun is kg Mass of Earth is kg Mass of Mr. J is 100 kg! WOW!

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