towards the modern view

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Brief review of last time: Og through Tycho Brahe Early Science 1 Reading: Chap. 2, Sect.2.4, Ch. 3, Sect. 3.1 Homework 3: Due Tomorrow and Mon.

posted soon Greek Astronomy: perfect, immutable heavens, with Earth at the center uniform circular motions - epicycles computational scheme consistent with observations The Renaissance Copernicus -

experiments 2nd stick in Aristotle s eye - Venus phases, Jupiter s moons 3rd stick in Aristotle s eye - experiments refute Aristotle s physics towards the modern view 1200s: Ptolemy s method off by

1580: Tycho Brahe precise positions of planets stars are fixed, therefore very distant sky is not immutable 1609: Galileo astronomer: telescope studies show Copernicus right physicist: experiments

1 Brief review of last time: Og through Tycho Brahe Early Science 1 Reading: Chap. 2, Sect.2.4, Ch. 3, Sect. 3.1 Homework 3: Due Tomorrow and Mon. Homework 4: Now available, due next recitation cycle, or next Thurs. for fast grading. Exam 1: Tuesday, Sept. 26; review sheet up, practice questions etc. posted soon Greek Astronomy: perfect, immutable heavens, with Earth at the center uniform circular motions - epicycles computational scheme consistent with observations The Renaissance Copernicus - Sun to the center Tycho Brahe - detailed observations to test Copernican model 1 stick in Aristotle s eye - heavens are changeable & imperfect Galileo - telescope views of planets + physics experiments 2nd stick in Aristotle s eye - Venus phases, Jupiter s moons 3rd stick in Aristotle s eye - experiments refute Aristotle s physics towards the modern view 1200s: Ptolemy s method off by several degrees response: add more epicycles : Copernicus moved sun to center -----> Revolutionary! 1580: Tycho Brahe precise positions of planets stars are fixed, therefore very distant sky is not immutable 1609: Galileo astronomer: telescope studies show Copernicus right physicist: experiments with Gravity A model from history of overcoming adversity. Johannes Kepler ( ) Son of a reckless soldier of fortune and the undisciplined and ill-educated daughter of the burgomeister of Eltingen (1927 Encyclopedia Brittanica). Recovered from smallpox at age 4, with crippled hands, and eyesight permanently impaired. Enrolled in seminary at age 13, entered university at age 17. Gave up theology for science professorship (in Ptolemaic astrology) at Gratz, Austria. Because of religious disturbances in Gratz, took job with Tycho in Prague. Succeeded him in 1601 as court astronomer or mathematician. Picked up the study of Mars. Long struggle with traditional orbit models, though from early on he considered the Law of Areas. Finally stumbled on a model that behaved like an ellipse. Published Astronomia Nova in 1609 with an orbit for Mars and his first 2 laws. Got a telescope in 1610 and did optical studies (theory of refraction). Published De Harmonice Mundi in 1619 with the third law and a theory of the harmony of the spheres. Mother arrested for witchcraft in 1620 (Wurttemberg). Linz beseiged, obtained permission to move his Rudolphine Tables types to Ulm. Published in Statue in Linz (from Wikipedia)

1610 - Johannes Kepler mathematician and klutz used Tycho s data on the motion of Mars: with no circular motion bias to discover Kepler s Laws of Planetary Motion These are simple empirical laws

2 Johannes Kepler mathematician and klutz used Tycho s data on the motion of Mars: with no circular motion bias to discover Kepler s Laws of Planetary Motion These are simple empirical laws explaining planetary motion, derived from data only, with no preconceptions. 5 Kepler s Law #1 Planets orbit the sun in ELLIPTICAL orbits around the sun, with the sun at one focus of the ellipse. abandonment of perfect circular motion 6 Anatomy of an ellipse DEFINITION where your distance from two fixed points adds up to a constant FOCI - the two reference points MAJOR AXIS longest dimension of ellipse contains foci usually refer to semimajor axis a ECCENTRICITY measure of the flatness of the ellipse e= (distance between foci) / 2a e = 0 for a circle (semimajor axis = radius) 0 e 1 for an ellipse e = 1 for a parabola 7 The Earth s orbit is an ellipse 8

3 Kepler s Law #2 9 A line joining the planet to the Sun sweeps out equal areas in equal times. abandon concept of constant speed Kepler s Law #3 The Law of Periods: Period 2 = (semimajor axis) 3 P 2 = a 3 (P in years, a in A.U.) 10 Bigger orbit (larger a) > longer Period planet moves faster when closer to the Sun Kepler s 3rd Law Kepler s 3rd Law Planet P[y] a[a.u.] P 2 a 3 P 2 /a 3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune Planet P[y] a[a.u.] P 2 a 3 P 2 /a 3 Mercury Venus Earth Mars Jupiter Saturn Uranus Neptune

13 1666: Isaac Newton 14 mathematician: Invented calculus as a youth.

basis of Modern Science Apple falls -> Earth and apple attract each other Moon and Earth

.. If moon moves sideways as it falls, it could forever circle the Earth.

would fly away in straight lines Newton s theory of gravity explains -simply- the orbits of

4 : Isaac Newton 14 mathematician: Invented calculus as a youth... SYNTHESIZED: Galileo s Experiments + Kepler s Laws + Calculus into Physical Laws; the basis of Modern Science Apple falls -> Earth and apple attract each other Moon and Earth attract each other, too If moon moves sideways as it falls, it could forever circle the Earth... If moon moves sideways as it falls, it could forever circle the Earth... Newton s Legacy Force of Gravity pulls planets towards Sun without gravity, planets would fly away in straight lines Newton s theory of gravity explains -simply- the orbits of the planets Understanding motions of the planets was the principal discovery of astronomy from prehistory through Improved observations ( technology ) demanded more precise models of the Solar System This precision was approached by complex models (epicycles, etc.) but achieved by discovery of the underlying simplicity: Gravity

Newton s Laws: Newton #1: The Law of Inertia 17 18 A body moves at a constant velocity unless an unbalanced force acts on it Velocity: speed and direction example: 65 mph southbound an external push

= mass x acceleration Acceleration: (rate of) change in velocity = (rate of) change in speed and/or direction examples: 0mph to 60 mph in 12 seconds (accel.) 60 to 0 in 10 seconds (decel.

5 Newton s Laws: Newton #1: The Law of Inertia A body moves at a constant velocity unless an unbalanced force acts on it Velocity: speed and direction example: 65 mph southbound an external push or pull Force: something that changes a body s velocity something that changes body s speed and/or direction Inertia: resistance to change in velocity Newton s Laws: Newton #2: The Law of Force Force = mass x acceleration Acceleration: (rate of) change in velocity = (rate of) change in speed and/or direction examples: 0mph to 60 mph in 12 seconds (accel.) 60 to 0 in 10 seconds (decel.) Inertia: a=f/m turning left at the light (change in direction) bigger mass: smaller accel. for same force inertia: resistance to acceleration by a force example: linebackers are big, wide receivers are small example: shot put vs. golf ball 19 mass vs. weight mass < > inertia weight < > force 20

6 Newton s Laws: When one body exerts a force on a second body, the second body exerts an equal force, in the opposite direction, on the first. Example: a rocket 21 Newton #3: Law of Action and Reaction Gravity is a central force: strength drops with distance2 a universal force: same form everywhere a cosmic force: inherent property of matter 22 Newton s Law of Universal Gravitation Apple falls -> Earth and apple attract each other Moon and Earth attract each other, too If moon moves sideways as it falls, it could forever circle the Earth... Body 1: expanding gas jet < F F > Body 2: rocket Force of gravity pulls planets towards Sun (Newton s 2nd law) without gravity, planets would fly away in straight lines (Newton s 1st law) Newton s Derivation of Kepler #3 Gravitational force pulling planets toward sun F toward = GMm a 2 centrifugal force pulling planets away from sun F away = mv2 a 23 (Newton s law of Universal Gravitation) or, since v = 2πa P F away = m4π2 a P 2 If forces equal, then distance between doesn t change! GMm a 2 = m4π2 a P 2... or... P 2 = a 3 ( 4π 2 this is Kepler s Third Law! GM ) a constant

Looping Planets. towards the modern view. Ptolemy s computational scheme for celestial motion

Looping Planets. towards the modern view. Ptolemy s computational scheme for celestial motion Reading: Chap. 2, Sec. 2.2, 2.4 Homework 3: Due Friday/Monday Exam 1: 2 weeks from today: Tuesday, Sept. 26, in the evening Public lecture: Tomorrow night 8 p.m., Great Hall, Memorial Union "Water Exploration