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Final Exam Study Notes

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McGill University
PHYS 183
Tracy Webb

CHAPTER 1: OUR PLACE IN THE UNIVERSE  planet  solar system  galaxy  local group  local supercluster  universe  local group: 2 galaxies (Milky Way & Andromeda) + 20 small galaxies  local supercluster: collection of galaxies in universe held together by gravity  the sun is our star o black spots on it are large magnetic fields  our solar system consists of the following planets in order moving farther from the sun: o Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus & Neptune  nebula: a cloud of interstellar gas and dust  new stars are born out of this material  Milky Way: our galaxy; collection of approximately 1 billion stars; colour & formation due to starlight  other galaxies: islands of stars, gas & dark matter held together by gravity; ie/ Andromeda  universe: sum total of all matter & energy  everything  brief history of the universe o universe expanded through the Big Bang  everything stays the same, just moves farther & farther away o occurred 14 billion years ago o galaxies first thing to form  very dense & were closer together in past o heavy elements condensed in stars & then formed planets  we can look back in time due to the speed of light (300 000 km/s)  telescopes act as time machines o light from sun takes 8 minutes to reach us o light from the closest star (Alpha Centauri) takes 4 years to reach us o light from the closest galaxy (Andromeda) takes 2.5 million years to reach us o this means that the pictures we have of Andromeda are 2.5 million years old  light year: distance light travels in one year; a unit of distance, not time; about 10 trillion km  planets vary in size & the solar system is quite empty  if the sun was the size of a grapefruit, the earth would be the size of a ball point on a pen o Mercury would be 5 m from the sun, Earth is 10 m, Jupiter is 100 m and Neptune is 320 m o nearest star would be in Vancouver (Alpha Centuri is about the same size as our sun) o we are in a very dense galaxy  most of the universe is empty space  there is 100 billion stars for each 100 billion galaxies  10 stars in the observable universe  life happened almost instantaneously on earth o January 1 : Big Bang o February: Milky Way forms o September 3 : Earth forms o September 22 : Early life on Earth o December 17 : Cambrian explosion o December 26 : Rise of the dinosaurs th o December 30 : Extinction of dinosaurs o December 31 st  9 pm: early hominids evolve  11:58: modern humans evolve  25 seconds ago: agriculture arises  11 seconds ago: pyramids built  1 second ago: Kepler & Galileo show that Earth orbits sun  we are never standing still o earth rotates around its axis once/day  faster at equator than poles o earth orbits the sun once/year  100 000 km/hour o solar system moves relative to nearby stars o Milky Way rotates o galaxy moves relative to others in local group o universe expands  the sun moves randomly throughout the galaxy with respect to near-by stars  70 000 km/hour o orbits centre of Milky Way once/230 million years  800 000 km/hour  galaxies move throughout space due to expansion of universe (raisin bun model)  Milky Way & Andromeda will merge in 3 billion years o further apart galaxies are, the faster they are receding from each other o Milky Way & Andromeda are moving away from everything else CHAPTER 3: ASTRONOMY AS A SCIENCE  scientific method is based on simple concepts of experiments, trial & error and evidence  astronomy as a science has roots in many ancient cultures since always used for navigation & marking seasons  240 BC measured circumference of earth using shadows  Greeks among first to make mathematical models of nature  attempted to explain patterns with supernatural o used geocentric model of the universe & believed the heavens must be perfect  driven by evidence & philosophy o evidence  sun, stars & planets appear to move around earth; no perceptible movement of earth o philosophy  insisted on mathematical perfection (whole numbers) which lead to stagnant models & refusal to change with new evidence  geocentric model of the universe: earth at the centre  Ptolemy’s model (150 AD) o complex motions of planets difficult to explain without geocentric model o each planet moves around earth on small circle that turns upon larger circle  explains apparent retrograde motion of planets o retrograde motion: planets usually appear to move E to W but occasionally reverse direction o didn’t understand why this happened back then but do now  periods of time when earth moving ahead of mars & other times that mars is moving ahead of earth o introduced epicycles to model of solar system  fixed model for 1500 years until measurements improved, but eventually models became too complicated  The Copernican Revolution: Copernicus changed the way we perceive our place in the universe which spurred development of virtually all modern science & technology  Nicholas Copernicus (Polish)  reintroduced heliocentric model (sun at centre of universe) by calculating each planet’s orbital period & relative distance to sun o insisted on spherical orbits o heliocentric model = crucial paradigm shift  Tycho Brahe (Danish)  compiled 30 years of precise observational data o built first astronomical observatory o convinced planets must orbit sun but inability to detect stellar parallax made him conclude earth stationary o stellar parallax: measuring distances through triangulation; position of specific star looks like it’s in different position depending on what month you look at it  Johannes Kepler (German)  3 laws demonstrating new mathematical descriptions for universe o worked for Tycho to explain motions of planets  discrepancies between his work and Tycho’s made him abandon idea of circular orbits o key discovery  planetary orbits not circle but special ovals called ellipse o 3 laws of motion:  planets move in ellipses, not circle  planet’s distance from sun varies during orbit  closest at perihelion & farthest at aphelion  planets move in elliptical orbits with Sun at one focus & nothing at other focus  sun-planet distance varies during orbit  eccentricity describes how much ellipse deviates  lead to departure of insistence on perfect spheres  planets sweep out equal areas in equal time  planets move faster when closer to sun & slower when farther away  force of gravity increases near sun  planets move slower in orbit when farther from the sun  P = a where p is the time it takes to complete 1 orbit in years and a is the distance to the sun  3 main objections to Copernican view continued to be: o earth couldn’t be moving because objects in air would be left behind o non-circular orbits not perfect as heavens should be o if earth really orbiting sun, we should detect stellar parallax  Galileo Galilei (Italian)  solidified results through careful experiment & observation o showed objects in motion stay in motion unless stopped by external force  objects that share earth’s motion through space will move with earth o first to observe sky with telescope and saw craters/spots/orbits/phases (full planet phase requires Copernican view)  heavens & heavenly bodies not perfect o didn’t observe stellar parallax but showed Milky Way made up of thousands of stars o forced to recant model & placed under house arrest by Catholic Church (believed geocentric model)  church vindicated him in 1992  the Copernican revolution was a revolution in astronomy & science o science seeks natural explanations for workings of the world based on evidence o a scientific theory/model must be testable and falsifiable o a model can never be proven, only disproved o science looks for the simplest explanation (Occam’s razor)  scientific theory: not a hypothesis; it must: o explain wide variety of observations with few simple principles o be supported by large & compelling body of evidence o not have failed any crucial test of its validity CHAPTER 4: UNDERSTANDING MOTION, ENERGY & GRAVITY  speed: rate at which an object moves  speed = distance/time (units m/s)  velocity: speed and direction  10 m/s, due East 2  acceleration: any change in velocity  acceleration = velocity / time (units m/s ) o positive acceleration  when velocity increasing o positive acceleration  when direction changes but speed constant o negative acceleration  when velocity decreasing  acceleration due to gravity, g: in the absence of friction/air resistance, all falling objects accelerate at the same rate  9.8 m/s o object increases its speed by 9.8 m/s each second, so after 2 seconds it is approx. 20 m/s o first shown by Galileo  momentum: product of the mass of an object and its velocity; momentum = mass x velocity o hard to get something moving if it has a lot of mass o easy to get something moving if it has little mass  angular momentum: rotational momentum of a spinning or orbiting object  force: anything that causes a change in an object’s momentum  usually a change in acceleration  torque: type of force that changes an object’s angular momentum  twisting force o amount depends on how much force is applied & where it is applied  mass: the amount of matter in an object  weight: the force that acts upon an object  elevator example o when the elevator moves at a constant velocity/is stationary your weight is normal o when the elevator accelerates upward you are heavier o when the elevator accelerates downward you are lighter o if the cable breaks so that you are in free fall you are weightless  there is gravity in space, that’s why the space station stays in orbit  weightlessness is due to a constant state of free fall  Newton changed view of the universe  realized same physical laws on earth also in heavens o discovered laws of motion & gravity  3 laws of motions o objects in motion stay in motion o amount of acceleration depends on object’s mass & force exerted  acceleration = force / mass  larger planets have greater effects on asteroids/comets since they exert stronger gravitational forces o for any force there is always an equal & opposite reaction force  don’t fall through objects when you touch them because of the force upon you  you fall to earth when you jump since you exert more acceleration (smaller mass)  conservation of momentum: total momentum of interacting objects can’t change unless net force acts upon them o momentum of rocket shooting forward = momentum of gases shooting back o transfer momentum, not speed  pool ball 1 has m = 0 and pool ball 2 has m = m x v; after collision 1 has m = m x v and 2 has m = 0  conservation of angular momentum: angular momentum of set of interacting objects can’t change unless torque acts upon it o explains why objects rotate faster as they shrink in radius  spinning faster when arms tucked in during figure skating o keeps a planet orbiting sun  rotation & orbit of earth around sun will continue indefinitely o angular momentum = mass x velocity x radius  conservation of energy: energy cannot be created nor destroyed  all actions involve exchanges of E o kinetic energy: energy of motion  earth has kinetic energy as it orbits around the sun o radiative energy: energy carried by light  energy from lamps, computers, the sun o potential energy: stored energy that can be converted later  gas, food o thermal energy: total kinetic energy of many individual particles  all objects contain this since particles always moving  particles move more in higher temperatures, less in lower temperatures  depends on temperature & density  air in oven at 400 F is hotter than boiling water at 212 F BUT the water has more thermal energy since it is at a higher density  temperature: the average kinetic energy of many particles in a substance  temperature scales  science uses Kelvin where 0 is absolute zero/absolute coldest o water boils at 373.15 K, 100 C & 212 F o water freezes at 273.15 K, 0 C & 32 F o absolute zero is at 0 K, -273.15 C & -459.67 F  gravitational potential energy: depends on object’s mass, strength of gravity & distance an object could fall o mgh where m = mass, g = acceleration of gravity, h = height above ground o when ball tossed up, at the peak it has more gravitational potential energy & less kinetic energy  as it continues towards ground, there is less gravitational potential energy & more kinetic energy o a collapsing cloud of gas (star formation)  mass stays constant, distances decrease, cloud heats up as it collapses & a star is born  as cloud contracts, gravitational potential energy converted to thermal energy  when in cloud, more GPE & less thermal energy, when converted less GPE & more thermal E  mass energy: mass is a form of potential energy through E = mc where E = amount of potential energy, m = mass of object and c = speed of light o a small amount of mass can be converted into a very large amount of energy o concentrated energy (light) can spontaneously turn into particles (mass) o happens in particle accelerators  the universal law of gravitation: Fg= G (M 1 2 d ) where F gs the force of gravitational attraction, 1 and M 2re masses of 2 objects, d is the distance between their centres & G is a constant called the gravitational constant (6.67 x 10m / (kg x s )) o every mass attracts every other mass through force called gravity o strength of attraction directly proportional to product of their masses o strength of attraction inversely proportional to the square of their separation distance  centre of mass: what objects orbit around o for 2 objects of equal mass, centre of mass halfway between them o for 2 objects of different masses, centre of mass closer to more massive one o if 1 object so much more massive than planet, centre of mass can lie inside star  Newton used Kepler’s Third Law to show that you can find total mass of a system by using orbital period & orbital distance o earth’s orbital period & distance from sun tells us the mass of the sun o satellite’s orbital period & distance from earth tells us the mass of the earth  energy + gravity = stable orbits o total orbital energy = gravitational potential energy + kinetic energy  it is conserved! o farther from sun  larger orbital distance so more GPE & less kinetic energy o closer to sun  smaller orbital distance so less GPE & more kinetic energy  to change an orbit there must be an external force/exchange of energy o gravitational encounter: when 2 objects pass near enough so that each can feel the effects of the other’s gravity o satellites in low earth orbit crash to earth because of friction with small amount of atmosphere o planets can capture moons o planets can alter orbits of comets around sun & used to change/boost orbit of space craft  escape velocity: when given enough orbital energy, spacecrafts end up in unbound orbit that allow it to escape earth completely o escape velocity for the surface of the earth is 11 km/s or 40 000 km/hour o a rocket stars in low orbit  firing the rocket gives a little extra orbital energy, raising it to a higher, more elliptical orbit  doing this long enough gives it enough extra orbital energy to escape earth  moon’s gravity pulls harder on near side of earth than far side  stretches earth & causes tidal bulges o size of tides depend on phase of the moon o spring tides: during new or full moon, sun & moon aligned so work together to cause large tide o neap tides: during quarter moons, sun & moon work against each other to cause small tide  tidal friction: since tidal forces stretch earth, friction is created o between earth & moon, earth’s rotation slowed & distance between them increased  synchronous rotation: moons always shows same face to earth due to tidal friction CHAPTER 5: LIGHT AND MATTER  light: form of energy that is always moving so carries energy o rate measured in power (1 joule/second = 1 watt) o everything we know about universe is due to light o comes in different colours  all colours together is called a spectrum  light interacts with matter in 4 basic ways which determines appearance of everything we see o emission: a light bulb emits visible light o absorption: when you place hand near incandescent light bulb, hand absorbs some of the light o transmission: some matter transmits light, which lets it pass through o reflection/scattering: light can bounce off matter leading to reflection (bouncing all in same general direction) or scattering (bouncing more random)  light is a wave & a particle o photon: a particle of light  each photon has a wavelength & frequency  each photon carries a certain amount of energy  energy = Planck’s constant x frequency  E = h x f -34  h = 6.626 x 10 joules/s o wave: pattern of motion which carries energy, but not matter  characterized by wavelength x frequency = speed  wavelength: peak to peak distance  unit of length  frequency: number of peaks passing a point per second; unit of Hz (per sec)  speed: how fast the peaks travel  units of distance/time  wavelength x frequency = speed of light = constant  λ x f = x  since speed of light constant, can figure out wavelength & frequency of light o high frequency = short wavelength = high energy o radio waves = light waves converted into sound waves  electromagnetic spectrum: the complete spectrum of light  gamma rays, x-rays, ultraviolet, visible, infrared, microwaves, radio waves o gamma rays = highest frequency, shortest wavelength o radio waves = lowest frequency, longest wavelength  atomic number: number of protons; defines an element  atomic mass number: number of protons and number of neutrons  isotope: elements with the same number of protons but different number of neutrons  molecule: two or more atoms bound together chemically by sharing electrons  different phases of matter have different chemical bonds but are made of the same thing  change with temperature & pressure o solid: low average kinetic energy; each molecule bound tightly to neighbour  ice o liquid: molecules move more freely but not entirely free from one another  water o gas: increasing kinetic energy breaks bond between neighbour molecules  water vapour  melting: breaking rigid chemical bonds between molecules  evaporation: breaking flexible chemical bonds between molecules  molecular dissociation: breaking of molecular bonds  ionization: stripping atoms of their electrons  energy is stored in atoms through electrons with potential energy o further from nucleus = more E since it takes energy to pull them apart (they are attracted to each other)  continuous spectrum: spectrum of light bulb spans all wavelengths of visible light without interruption o since rainbow spans a broad range of wavelengths without interruption, it is continuous  emission line spectrum: low density cloud emits light only at specific wavelengths that depend on composition & temperature o bright emission lines against black background o increased intensity  extra light  absorption line spectrum: cloud of gas absorbs light of specific wavelengths o spectrum shows dark absorption lines over background rainbow o decreased intensity  lacking light  increased intensity = increased light = increased energy  light provides chemical fingerprints  each kind of atom has a unique set of energy levels & each transition corresponds to a unique frequency, wavelength & energy o downward transition = emission lines  electrons lose energy as they fall closer to nucleus o upward transition = absorption lines o each element has a different spectrum so combining all of them tells composition of the gas  a continuous spectrum is produced in the core & the outer atmosphere absorbs photons according to its composition (absorption lines)  molecules have additional energy levels since they vibrate & rotate  objects change colour with changing temperature  thermal radiation: radiation emitted from any object with a temperature o hotter objects emit more energy  they are brighter o hotter objects emit photons with a higher average energy  they are bluer (hottest)  the Doppler effect: learn about motion of distance objects from changes in their spectra o blueshift: occurs when an object is coming towards us  wavelengths become shorter so blue o redshift: occurs when an object is moving away from us  wavelengths become longer so red o larger the shifter, faster the object is moving o measure the shift through the location of spectra lines o can only tell motion of object toward or away from us, not perpendicular CHAPTER 6: TELESCOPES  light collecting area: how much total light a telescope can collect at one time o larger light collecting area = gather more light in shorter time can see fainter objects o depends on the area of the dish  area of a circle = πr  angular resolution: smallest angle over which we can tell that two dots/stars are distinct o tells you the minimum angular separation that you can distinguish/smallest detail you can see o larger telescopes take images with greater detail  sharper image o depends on the radius of the dish, not the area o depends on wavelength of light o angular resolution = 1.22 x wavelength (ϴ) / telescope diameter o lower angular resolution = more you can see  telescope arrays: place many telescopes over large area of earth and they work together to increase angular resolution o Very Large Array (VLA) in New Mexico = 27 radio dishes over 36 km  acts like a 36 m single dish with an angular resolution of ~ 1 arcsecond o biggest telescope array is the size of the earth  atmospheric turbulence distorts images on very short timescales  this is why stars appear to twinkle o limits resolution to about 1 arcsec from the ground o hard to fix telescopes in space, so place ground telescopes at high and dry areas  decreases atmospheric turbulence since less moisture in the air  only radio & optical light pass through the atmosphere to the ground  space based astronomy key  gather 3 kinds of data with CCD images o images  photographs of astronomical objects  place colour filters to allow particular colours (wavelengths)  most images are combined images of different filters o spectroscopy  obtain & study spectra  pass light through prism to disperse it into different wavelengths o timing  tracks how objects change with time  light curve tells us how relative brightness of an object changes with time CHAPTER 14: OUR SUN  gravitational equilibrium: outward push of pressure in the sun’s core balances the inward pull of gravity o keeps the sun’s core hot & dense enough to maintain nuclear fusion reactions  the sun’s structure o corona: outermost layer of sun’s atmosphere  1 million K  emit’s most of the sun’s x rays  very low density o chromosphere: middle layer of the solar atmosphere & region that radiates most of the sun’s ultraviolet light  10 000 K o photosphere: lowest layer of the atmosphere; visible surface of sun  6000 K  where you find sunspots o convection zone: where energy generated in solar core travels upward, transported by rising of hot gas & falling of cool gas (convection)  cause of sun’s seething, churning appearance  lots of turbulence o radiation zone: energy moves outward primarily in form of photons o core: source of sun’s energy  15 million K  the sun is almost entirely hydrogen  nuclear fission: process of splitting a nucleus into two smaller nuclei  heavy to light  nuclear fusion: process of combining nuclei to make a nucleus with a greater number of protons or neutrons  light to heavy o requires high temperatures  at low speeds, electromagnetic repulsion prevents the collision of nuclei but at high speeds, nuclei come close enough for the strong force to bind them together o sun’s core = sea of nuclei & free electrons moving very fast (high temperature) so 4 H fuse into 1 He  releases energy through E = mc2 o source of all energy released by sun into space o generates gamma ray (very high energy) in the core  proton-proton chain: sequence of steps occurring in sun with collisions between individual protons (H) o step 1: 2 p fuse together to make deuterium (H isotope; 1 proton, 1 neutron)  occurs 2x o step 2: deuteritum + p fuse to make He-3 (He isotope; 2 protons, 1 neutron)  occurs 2x o step 3: 2 He-3 nuclei fuse to form He-4 (2 protons, 2 neutrons)  releases 2 excess protons o result: output = gamma rays + neutrinos  radiative diffusion: sun’s interior so dense photons continually bump into electrons on way out so takes a long time to leave (thousands of years) o with each collision, photon & electron share energy  by the time the photons reach outside of sun they mirror the temperature of the gas  solar neutrino: subatomic particles made by fusion reactions in core of sun o reach us within minutes by travelling nearly the speed of light o react very rarely with other matter so take very direct path out of core (not like photons)  the solar neutrino problem: early detection experiments consistently detected only 1/3 of predicted solar neutrinos o meant we didn’t understand the sun or subatomic particles  subatomic particles not okay o in Sudbury, Ontario it was found there are 3 kinds of neutrinos  electron, muon, tau o 1/3 of neutrinos found previously were electron neutrinos o sun produces electron neutrinos but 2/3 change into muon & tau neutrinos before reaching earth CHAPTER 15: STARS  the brightness of a star depends on distance & luminosity  apparent brightness: amount of starlight reaching earth  energy/second/metre 2  luminosity: total amount of power the star radiates into space  energy/second o not the same as brightness o if you know how luminous the star is then you can determine how far away it is since energy is spread over an area of a sphere (inverse square law)  brightness = luminosity / 4πr2 o most luminous stars = 10 L sun -4 o least luminous stars = 10 Lsun o use stellar parallax to measure luminosity  a star with a parallax of 1 arcsec is 1 parcsec away from the sun  p = parallax angle  d (in parsecs) = 1 / p (in arcsecs)  d (in light years) = 3.26 x (1 / p (in arsecs))  measure the temperature of stars through continuum or spectral lines (absorption) o continuum spectra 
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