Physics 406 Course Review J.V. Hollweg, E. Möbius Bring the review with you each day to class. You may insert comments of your own. Some space has been left at the end of each major sub-chapter. These review sheets should be used to study for the exams. Many exam questions will be directly based on these pages. They are not to be memorized, but they should serve as a guide to what you are expected to understand. However note, the Review won't replace the book! As you can see it uses a “sound bite” format. Therefore, read your course book!!! Ask questions, if you don't understand what is in the Review!!! • Consult your course book • Ask questions in class. They are appreciated!! Revised E. Möbius, 1/2003 0. Roots of Astronomy and our View of the World Why does Man study Astronomy? organize time (plan the year) -> clock, calendar, seasons understand how the world is built -> model of the universe - We face discussions between Science and Religion Where do we come from? - We are confronted with the limitations of Science Will we ultimately understand ”everything”? In astronomy almost all sciences are used Mathematics -> sizes, "language for modeling" Physics -> understand processes Chemistry -> composition of planets and comets Geology -> appearance and evolution of planets Meteorology -> planetary atmospheres Biology -> life on Earth and elsewhere? Contents of the Universe Planets, moons, comets Sun and stars, gas nebulae Clusters of stars, galaxies, clusters of galaxies Learning goals • Astronomy spans all sciences, in particular all branches of physics • Physics is the art to measure objects and processes • Science is a never-ending enterprise • Contents of the universe 2 I. Use of Scientific Methods Chapter I. is to be used as a Compendium throughout the Course. We browse through it now and fill in some blanks when we use the tools in the following Chapters. 1) To Measure Means to Compare We measure an unknown quantity by comparison with a known quantity. A. Powers of ten Large and small numbers are presented easier as powers of ten: e.g.: 2,300 -> 2.3 . 103; 0.000,000,2 -> 2 . 10-7 B. Geometry a) Length: Basic Unit: m (cm, km) Compared with a meter stick (original meter, Paris) Size and Distances of Planets inin the Solar System Geometric model 1:10,000,000,000 _________________________________________________________________ Reality Model Size Distance Size Distance in km in km in cm in m _________________________________________________________________ Sun 1.4 . 106 13.9 Mercury 4880 5.8 . 107 0.05 5.8 2 steps up Venus 12100 1.0 . 108 0.12 10.8 7 steps up Earth 12760 1.5 . 108 0.13 15.0 Rear of auditorium Mars 6800 2.3 . 108 0.07 22.8 Tree in front of auditorium Jupiter 143800 7.8 . 108 1.44 77.8 UNH bookstore Saturn 120000 1.4 . 109 1.20 143. EOS (Morse Hall) Uranus 50800 2.8 . 109 0.51 287. Hood House Neptune 49500 4.5 . 109 0.50 450. Tin Palace Pluto 2300 5.9 . 109 0.02 590. Young's Restaurant _________________________________________________________________ Closest Star: LY a Centauri 4.34 4.1 . 1013 4,108,799 San Francisco _________________________________________________________________ 3 Further units derived from Length: -> Area = Length * Length m * m = m2 Used for example for Surface of objects E.g.: circle 2x in radius -> area of circle: 2*2 = 4 x as large!! -> Volume = Length * Length * Length m * m * m = m3 Used for example for Volume of objects E.g.: sphere 2x in radius -> volume of sphere: 2*2*2 = 8 x as large!! b) Angles: Degrees (360o per circle) (90o right angle) Minutes (60' per degree) Seconds (60'' per minute) c) Distance/Size determination in Astronomy: To get distances and sizes in astronomy we use angle measurements and a baseline. Skinny triangle: (in Astronomy always a "skinny triangle") i) Distance r known ii) Observer separation d known r obs.1 r observer q d d q obs.2 "Parallax" -> Determine i) Size d ii) Distance r of an astronomical object q = 360⋅ d = 57.3⋅ d by measuring q, plugging into: 2p r r and solving for d or r "Parallax" is a fundamental method to measure distances in Astronomy. Useful length units in astronomy: Longest Baseline for Parallax: 1 AU [Astronomical Unit = Earth - Sun distance] = 1.5 108 km Distance from which 1 AU is seen as 1 arcsec 1 Parsec = distance giving a Parallax of 1 arcsec = 3.1 1013 km = 3.26 LY Distance based on the speed of light 1 LY [Light-year = distance light travels in 1 year] = 9.5 1012 km 4 C. Action: a) Time Basic unit: sec (second), hour, day Time is measured by comparing with a regular motion. Method Type of Clock Accuracy sun throwing a shadow -> sun clock -> hours sand flowing through an orifice -> sand clock -> minutes mechanical pendulum -> mechanical clock -> second oscillation of crystal -> quartz clock -> fractions of second b) Velocity: Derived Unit: m/sec km/h Distance traveled per unit time: Velocity = Distance/Time Change of velocity (acceleration, deceleration) Derived Unit: m/sec/sec = m/sec2 Velocity change/unit time: Acceleration = Velocity/Time D. Substance Chapter IV a) Mass "amount of material" Basic Unit: kg (kilogram) Compared with original kg (Paris) Mass articulates itself in two ways: Inertial mass mi resists the attempt to move it Gravitational mass mg ability of objects to attract one another mi = mg Einstein's General Theory of Relativity Note: Do not confuse Mass with Weight!! Weight means a force in a given gravitation (e.g., on Earth) Mass of the same body remains the same, but its Weight may vary from location to location (on Earth, Moon or in free space)!!! Unit: see Force (or 1 kilopond (kp) = 1 kg on Earth) b) Mass density: = mass/volume Derived Unit: kg/m3 -> Idea of planet's interior: rock + iron core -> denser than rocks or of stars' interior -> compressed gas or neutron stars -> denser than atomic nuclei c) Force ability to pull or push an object (to change its motion) Derived Unit: kg * m/sec2 = Newton (N) in Chapter IV d) Energy Ability to change motion or generate heat Derived Unit: kg*m2/sec2 = Joule in Chapter IV Types of energy: Gravitational, kinetic (motion), heat all interchangeable (in principle): For example: Falling object vaporizes rock -> explosion -> round crater Gravitation fi Motion fi Heat 5 e) Pressure = Force per area in Chapter VIII Derived Unit: N/m2 = Pascal ≈ 1/50 Pounds/foot2 Holds things up against gravity: Atmospheres: pressure = weight of overlying atmosphere Stars: internal oven keeps material above in balance Black holes: no pressure high enough to keep it from collapse? f) Temperature Average energy per molecule in Chapter VI, VIII Basic Unit: Kelvin = Centigrade + 273 (starts with 0 degree!!) 0 Kelvin = -273 Celsius = - 404 Fahrenheit 273 Kelvin = 0 Celsius = 32 Fahrenheit Provides ability for gas to resist gravity fi Determines properties of atmospheres hot sun has an extended atmosphere warm earth's atmosphere is only tens of miles deep hot and small Mercury with its weak gravity lost its atmosphere Determines life of stars Stars form from collapse of cool interstellar clouds ("stellar nurseries") Nuclear Fusion possible in hot interior of stars ("ignition temperature") System of Units Basic Units Length 1 Meter Time 1 Second Mass 1 Kilogram [m, cm, km] [sec, msec] [g, kg] Based on: Wavelength of light of Kr Frequency of Cs atoms Mass of C atoms atom (Original kg in Paris) (Original m in Paris) Derived Units Area = Length * Length [1 m2 ] Density = Mass/Volume [1 kg/m3 ] Volume = Length * Length * Length[1 m3 ] Velocity = Length/Time [1 m/sec] Force = Mass * Acceleration [Newton] 1 N =1 kg m /sec2 Acceleration = Velocity/Time [1 m/sec2 ] 6 2) What we measure Getting information over large distances in astronomy: in Chapter V A) Electromagnetic radiation: Contains key information on what is happening out there radio, microwave, IR, light, UV, X, gamma rays B) Particles: Cosmic rays (sample of Milky Way Galaxy material) Meteors (sample of early solar system material) Comets (sample of early solar system material) Solar wind (sample of sun material) C) Forces: Gravity (the key to deducing masses) 3) Deduction We use Deduction, i.e. we measure something to deduce something else: We measure Make use of Deduce A) angle fi size or distance skinny triangle B) orbits fi masses in Chapter IV knowledge of gravity C) color fi temperature in Chapter VII blackbody (red:cool; yellow:hot; blue:very hot) D) change in frequency fi velocities in Chapter VII Doppler shift (frequency increases -> moves toward us; frequency decreases = moves away). 7 4) Scientific Reasoning We use Scientific Reasoning to test our view of the world and to develop new measurement methods. Scientific Reasoning consists of: i. Hypothesis ii. Prediction iii. Test A) i Earth goes around sun. ii. Prediction Aberration of starlight in Chapter V (analogy: raindrops seen from moving car) iii. Test Bradley (1726 - 1728): first proof that earth goes around sun ii. Prediction Stellar parallax in Chapter VII iii. Bessel 1838 -> first determination of distance to a star B) i. Earth rotates on its axis. ii. Prediction Coriolis force - apparent force as earth rotates iii. Test Foucault pendulum (1851): first proof of earth's rotation. (Coriolis also gives circulation of weather systems.) (Jupiter's red spot and Neptune's dark spot have circulation of high pressure systems.) C) i. Mercury & Venus orbit sun. in Chapter III ii. Prediction Phases full to crescent (like moon) iii. Test Galileo 1610 (observed with telescope) 8 5) Scientific Models To understand the universe and its contents we build models of what is going on.