Slide 1Slide 2Slide 3Clicker Question:Clicker Review:Slide 6Slide 7Slide 8Slide 9Slide 10Slide 11Slide 12Slide 13Slide 14Slide 15Slide 16Slide 17Slide 18Slide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Slide 27Slide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39From Aristotle to NewtonThe history of our knowledge about the Solar System (and the universe to some extent) from ancient Greek times through to the beginnings of modern physics.Eratosthenes Determines the Size of the Earth in about 200 B.C.SyeneAlexandriaSun's rays7.2o SNEarthHe knows the distance between the two cities is 5000 "stadia”, where 1 stadia = 6.25 kmFrom geometry then,7.2o 360o Earth's circumference 5000 stadia ==> circumference is 250,000 stadia, or 40,000 km.So radius is:40,000 km2 = 6366 km(very close to modern value, 6378 km!)Clicker Question:Who was the first person to use a telescope to make astronomical discoveries?A: AristotleB: BraheC: KeplerD: GallileoE: NewtonClicker Review:What time of day does the first quarter moon set?A: 6amB: noonC: 6pmD: midnightE: Never sets"Geocentric Model" of the Solar SystemAristotle vs. Aristarchus (3rd century B.C.) Aristotle: Sun, Moon, Planets and Stars rotate around fixed Earth. Ancient Greek astronomers knew of Sun, Moon, Mercury, Venus, Mars, Jupiter and Saturn. Aristotle: But there's no wind or parallax.Difficulty with Aristotle's "Geocentric" model: "Retrograde motion of the planets".Aristarchus: Used geometry of eclipses to show Sun bigger than Earth (and Moon smaller), so guessed that Earth orbits the Sun. Also guessed Earth spins on its axis once a day => apparent motion of stars.Aristarchus: Yes, sirWhat are some reasons that the geocentric model of the universe seems to make intuitive sense?•It doesn't feel like we are moving – wouldn't there be a wind or something?•Why would things fall down and not towards the center of the universe?•Why don't we see stellar parallax?Planets generally move in one direction relative to the stars, but sometimes they appear to loop back. This is "retrograde motion".But if you support geocentric model, you must attribute retrograde motion to actual motions of planets, leading to loops called “epicycles”.Ptolemy's geocentric model (A.D. 140)Geocentric model fails to account for phases of VenusHeliocentric model easily accounts for phases of Venus"Heliocentric" Model● Rediscovered by Copernicus in 16th century.● Put Sun at the center of everything.● Much simpler. Almost got rid of epicycles.● But orbits circular in his model. In reality, they’re elliptical, so it didn’t fit the data well.● Not generally accepted at the time.Copernicus 1473-1543Illustration from Copernicus' work showing heliocentric model.Copernican model was a triumph of the Scientific MethodScientific Method:a) Make high quality observations of some natural phenomenonb) Come up with a theory that explains the observationsc) Use the theory to predict future behaviord) Make further observations to test the theorye) Refine the theory, or if it no longer works, make a new one- Occam’s Razor: Simpler Theories are better-You can prove a theory WRONG but not RIGHTObservationTheoryPredictionPlanets generally move in one direction relative to the stars, but sometimes they appear to loop back. This is "retrograde motion".12345671234567EarthMarsApparent motion of Mars against "fixed" stars******JanuaryJulyGalileo (1564-1642)Built his own telescope.Discovered four moons orbiting Jupiter => Earth is not center of all things!Discovered sunspots. Deduced Sun rotated on its axis.Discovered phases of Venus, inconsistent with geocentric model.Kepler (1571-1630)Used Tycho Brahe's precise data on apparent planet motions and relative distances.Deduced three laws of planetary motion.Kepler's First LawThe orbits of the planets are elliptical (not circular) with the Sun at one focus of the ellipse.Ellipseseccentricity = (flatness of ellipse) distance between foci major axis lengthKepler's Second LawA line connecting the Sun and a planet sweeps out equal areas in equal times.Translation: planets move fasterwhen closer to the Sun.slowerfasterKepler's Third LawThe square of a planet's orbital period is proportional to the cube of its semi-major axis. P2 is proportional to a3 or P2  a3 (for circular orbits, a = b = radius).Translation: the larger a planet's orbit,the longer the period.abSolar System OrbitsOrbits of some planets (or dwarf planets):Planet a (AU) P (Earth years)Venus 0.723 0.615Earth 1.0 1.0Pluto 39.53 248.6 P2 is proportional to a3 or, using Earth years and AU P2 = a3At this time, actual distances of planets from Sun were unknown, but were later measured. One technique is "parallax""Earth-baseline parallax" uses telescopes on either side of Earth to measure planet distances.Newton (1642-1727)Kepler's laws were basically playing with mathematical shapes and equations and seeing what worked.Newton's work based on experiments of how objects interact.His three laws of motion and law of gravity described how all objects interact with each other.Newton's First Law of MotionEvery object continues in a state of rest or a state of uniform motion in a straight line unless acted on by a force.Newton's First Law of MotionDEMO - Smash the HANDNewton's Second Law of MotionWhen a force, F, acts on an object with a mass, m, it produces an acceleration, a, equal to the force divided by the mass.a = Fm or F = maacceleration is a change in velocity or a change in direction of velocity.Newton's Second Law of MotionDemo - Measuring Force and AccelerationNewton's Third Law of MotionTo every action there is an equal and opposite reaction.Or, when one object exerts a force on a second object, the second exerts an equal and opposite force on first.Newton's Third Law of MotionDEMO: Cart or HeliocopterNewton's Law of GravityFor two objects of mass m1 and m2, separated by a distance R, the force of their gravitational attraction is given by:F =G m1 m2 R2F is the gravitational force.G is the "gravitational