1B1BThe CopernicanThe CopernicanRevolutionRevolutionThe Birth of Modern Science
1B1BWhat do we see in the sky?• The stars move in the sky but notwith respect to each other• The planets (or “wanderers”)move differently from stars– They move with respect to the stars– They exhibit strange retrogrademotion• What does all this mean?• How can we explain thesemovements?• What does the universelook like?
1B1BGeocentric(Ptolemaic) System• The accepted model for1400 years• The earth is at the center• The Sun, stars, andplanets on their spheresrevolve around the earth: explains daily movement• To account for unusual planetary motion epicycles wereintroduced• Fit the Greek model of heavenly perfection – spheres arethe perfect shape, circular the perfect motion
1B1BHeliocentric (Copernican) System• Sun at center (heliocentric)• Uniform, circular motion– No epicycles (almost)• Moon orbited the earth, the earthorbited the sun as another planet• Planets and stars still on fixedspheres, stars don’t move• The daily motion of the starsresults from the Earth’s spin• The annual motion of the starsresults from the Earth’s orbit
1B1B• In the heliocentric model, apparentretrograde motion of the planets is a directconsequence of the Earth’s motion
1B1BGeocentric vs. Heliocentric• How do we decide betweentwo theories?• Use the Scientific method:– These are both explanationsbased on the observation ofretrograde motion– What predictions do the modelsmake?– How can these predictions betested?
1B1BPhases ofVenus• Heliocentricpredicts thatVenus shouldshow a full phase,geocentric does not• Unfortunately, thephases of Venuscannot be observedwith thenaked eye
1B1BGeocentric vs. Heliocentric• Against heliocentric– It predicted planetary motions and events no better thanthe Geocentric system– The earth does not move (things do not fly off)– The earth is different from the heavens (from Aristotle –the heavens are perfect and unchanging) and cannot bepart of the heavens• For heliocentric– Simplified retrograde motion, but epicycles werenecessary to account for the planets’ changing speed– The distances to the planets could be measured. Thesedistances were ordered, and therefore aestheticallypleasing to the philosophy of the day
1B1BStellar Parallax• Parallax caused by the motion ofthe earth orbiting the Sun• Not observed with the naked eye• The heliocentric model predictsstellar parallax, but Copernicushypothesizes that the stars are toofar away (much farther than theearth from the Sun) for theparallax to be measurablewith the naked eye
1B1BMisconceptions1. The Copernican model has a force between the sunand the planets. Actually, the natural motion of thecelestial spheres drove the planetary motions.2. The Copernican model was simpler than thePtolemaic one. In fact, though Copernicuseliminated circles to explain retrograde motion, headded more smaller ones to account fornonuniformities of planetary motions.3. The Copernican model predicted the planetarymotions better. Because both models demandeduniform motion around the centers of circles, bothworked just about as well – with errors as largeas a few degrees at times.
1B1BGalileo Galilei• Turned a telescope toward the heavens• Made observations that:– contradicted the perfection of the heavens• Mountains, valleys, and craters on the Moon• Imperfections on the Sun (sunspots)– Supported the heliocentric universe• Moons of Jupiter• Phases of Venus – shows a full phase
1B1BTycho Brahe• Had two sets of astronomicaltables: one based on Ptolemy’stheory and one based onCopernicus’.• He found that both tables’predictions were off by daysto a month.• He believed that much bettertables could be constructedjust by more accurate observations.• Tycho’s homemade instruments improvedmeasurement precision from ten minutes of arc(which had held since Ptolemy) to less than one
1B1BThe skies change• Tycho observed 2 phenomena thatshowed the heavens DO change:– In November 1572, Tycho noticeda new star in the constellationCassiopeia– Comet of 1577• Prior to this sighting,comets were thought to be atmosphericphenomena because of the immutabilityof the heavens• But neither the star nor the comet changed position asthe observer moved, as expected for atmosphericphenomena
1B1BJohannes Kepler• Kepler succeeded Tycho as the Imperial mathematician(but at only 1/3 the salary of the nobleman)• Kepler worked for four years trying to derive the motionsof Mars from Brahe’s observations• In the process, he discovered that the plane of the earth’sorbit and the plane of Mars’ (and eventually the otherplanets) passed through the sun• Suspecting the sun had a force over the planets, heinvestigated magnetism• While this is not true, it did lead him to the idea ofelliptical orbits• “With reasoning derived from physical principlesagreeing with experience, there is no figure left forthe orbit of the planet except a perfect ellipse.”
1B1BAstronomia nova• Published in 1609, The New Astronomy was justthat, it revolutionized the field• It predicted planetary positions as much as tentimes better than previous models• It included physical causes for the movement ofthe planets• The ideas of the Greeks were gone – the heavensno longer were perfect, immutable, or differentfrom the earth
1B1BKepler’s first Law• The orbital pathsof the planetsare elliptical (notcircular), withthe Sun at onefocus.
1B1BKepler’s second law• An imaginaryline connectingthe Sun to anyplanet sweepsout equal areasof the ellipse inequal intervalsof time.
1B1BKepler’s Third Law• The square of aplanet’s orbitalperiod isproportional tothe cube of itssemi-major axis.• Kepler orbit demonstration:http://csep10.phys.utk.edu/guidry/java/kepler/kepler.html
1B1BOther Solar System Bodies• Kepler derivedhis laws for the 6planets known tohim. The lawsalso apply to the 3discoveredplanets and anyother bodyorbiting the Sun(asteroids, comets,etc.)
1B1BA force for planetary motion• Newton proposes a force which controls themotion of the planets – GRAVITY• The larger the mass, the larger the force ofgravity• The further the distance, the smaller the forceof gravity• Kepler’s third law can be derived fromNewton’s law of gravity• F = GMm/r2= mg