It appears to me that they who in proof of anyassertion rely simply on the weight ofauthority, without adducing any argument insupport of it, act very absurdly. I, on thecontrary, wish to be allowed freely toquestion and freely to answer you withoutany sort of adulation, as well becomes thosewho are in search of truth.- Vincenzo Galilei (Galileo’s father)Ozymandias, by Percy Bysshe ShelleyI met a traveller from an antique landWho said: "Two vast and trunkless legs of stoneStand in the desert.Near them on the sand,Half sunk, a shattered visage lies, whose frownAnd wrinkled lip and sneer of cold commandTell that its sculptor well those passions readWhich yet survive, stamped on these lifeless things,The hand that mocked them and the heart that fed.And on the pedestal these words appear:`My name is Ozymandias, King of Kings:Look on my works, ye mighty, and despair!’Nothing beside remains. Round the decayOf that colossal wreck, boundless and bare,The lone and level sands stretch far away.Diagram of the Inner Solar SystemTop ViewDiagram of the Inner Solar SystemSide ViewOuter Solar System: Top ViewOuter Solar System: Side ViewSome Fun Links• http://csep10.phys.utk.edu/guidry/java/kepler/kepler.html• http://galileoandeinstein.physics.virginia.edu/more_stuff/flashlets/kepler6.htm• http://www.physics.sjsu.edu/tomley/Kepler12.html• http://janus.astro.umd.edu/javadir/orbits/ssv.html• http://janus.astro.umd.edu/SolarSystems/How Fast is the Earth Moving?• Orbit is approximately circular (e=0.017) with a radiusof r=1.5×1010 meters. Circumference of orbit is2πr= 9.4×1010 meters.• Orbital period is P=1 year = 3.2×107 seconds.• Velocity,v = 2πr/P = 9.4×1010 meters/ 3.2×107 secondsv = 3.0×104 meters/second = 30 km/s• Be careful that you don’t fall off :)Galileo Galilei (1564-1642)http:/www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Galileo.htmlThe First “Modern” ScientistGalileo’s work was characterized byinnovative experiments, careful and farreaching analysis, and sophisticatedmathematics. He contributed to a widerange of scientific investigations, inaddition to astronomy. He generalizedresults in a way that had not been donebefore and, along with Kepler, paved theway for Newton. When Newton said thathe stood on the shoulders of giants, hewas talking about Galileo.• In April 1609, a spyglass wasmade in Paris with amagnification of 3.• Galileo pointed this to theheavens.• Thus motivated he made an 8power by August and a 20power by October.Galileo’s Discoveries• The moons of Jupiter• Sunspots• Mountains on the Moon• Phases of Venus• Previously unseen starsOur Moon is bumpyIt is not the perfect sphereexpected in the divine heavens.Galileo’s DrawingsJupiter has MoonsGalileo’s sketchesJupiter’s Galilean SatellitesGalileo discovered 4moons of Jupiter, Io,Europa, Ganymede,and Callisto finding,in effect, a mini solarsystem and provingthat at least someobjects do not orbitthe Earth.The GalileoSpacecraftorbitedJupiter for ~ 5yearsThe Milky Way is made of Stars!Using his telescope Galileocould see many more starsthan were visible to the nakedeye. In the drawing to theright, Galileo shows hisobservations of the new starsalong with the brighter stars.The stars visible to the nakedeye are outlined foremphasis. Galileo reasonedcorrectly that the Milky Waywas made up of thousands ofthese dim stars.Phases of VenusPtolemy’smodelVenus doesnot have a fullphase asGalileoobserved.Copernicus’ Model: Venus has a full phase.Galileo the HereticIn 1632 Galileo published the DialogueConcerning the Two Chief World Systemsin which he advocated the heliocentric(Copernican) view of the Universe.“My dear Kepler, what would you say ofthe learned here, who, replete with thepertinacity of the asp, have steadfastlyrefused to cast a glance through thetelescope? What shall we make of this?Shall we laugh or shall we cry?” -Letter from Galileo Galilei to Johannes KeplerSalviati, Sagredo, and Simpliciodiscuss the Universe.Galileo on TrialGalileo was a vocaladvocate of theCopernican system.The church ordered himto be silent, but Galileorefused, choosinginstead to ridicule thechurch authorities. Hewas put on trial,threatened with torture,and made to recant.Thereafter he was keptunder house arrest forthe remainder of his life.The Catholic Church reopened the Galileo Trial in 1992 and reversedits decision.Galileo’s Incline Plane ExperimentsNeed to measure the changeof distance with time.Measurement of time:1) Heartbeat too irregular,2) Pendulum too awkward,3) Lute just right.Strings were stretchedacross the path of the ballclose enough to hear atwang. Then they wereseparated to give twangsat equal intervals.How do objects fall?Galileo’s Pendulum Experiments• Pendulums nearly return to theirrelease heights• The period is independent of thebob weight• The period is independent of theamplitude• The square of the period isproportional to the length• Lighter pendulums come to restfaster than heavy ones.Galileo contemplating haleHale stones of different sizes fell at the same speedGalileo searched for mathematicallaws that described the motion offalling bodies, much as Keplerdiscovered mathematical lawsdescribing the motion of planets.His results included:•Objects fall at the same speed independent ofmass.*• The distance traversed by a falling objectincreases as the square of the time.* This contradicts Aristotle’s theories, whichwere the still thoughts of the day.Describing MotionDescribing Motion• Position, x– The distance from one place to another– Vector: has magnitude and direction– Units: meters (miles)• Velocity, v– Change in position with time– Vector: magnitude (speed) and direction– Units: meters/second (miles/hour)• Acceleration, a (we use the symbol g for gravitationalacceleration)– Change in velocity with time– Vector: magnitude and direction– Units: meters/second2 (miles/hours/second)Constant Acceleration v = *distance/time = d/tThen: d = v tFrom diagram, averagevelocity v = ½ gtAnd, d = v t = ½ g t2Start: v = 0End: v = gt* Note this is the change of distance over thechange in timeConstant Acceleration• The acceleration of falling objects on Earth is constantat g=9.8 m/s2. Falling objects speed up as they fall (thevelocity increases) but the acceleration stays the same.• The velocity of an object, starting at rest, after travelinga time t
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