Physics Review - 1st term

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Physics Review - 1st term
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  1. The Scientific method

    ideas expressed are
    1.
    2.
    3.
    • 1. objective (same for everyone)
    • 2. falsifiable
    • 3. common to all lines of scientific inquiry
  2. Steps in the scientific process
    • 1. formulate hypothesis - must be consistent with existing evidence, if not this is speculation
    • 2. Test hypothesis (experiment can never have been performed before, has to be able to prove hypothesis false)
    • 3. if outcome agrees --> supporting evidence, if not --> discard whole hypothesis
  3. Measurements

    - qualitative or quantitative
    - what three do you need for a measurement
    - quantitative (amt)

    • - value (15 today)
    • - unit (15 degrees C today)
    • - uncertainty (15 +/- 25 degrees C today)
  4. When giving the uncertainty of a measurement give how many sig figs?
    1
  5. when giving the value of a measurement, use the number of sig figs to ...
    magnitude of uncertainty
  6. 3 fundamental units
    • mass (g)
    • length (cm)
    • time (sec)

    - everything else is a combination of these
  7. Ptolemaic Universe
    • - 1st view of the universe - 140 AD
    • - earth is center
    • - the planets and sun are in spheres that rotate around earth
    • - stars occupy different uniformly rotating spheres
    • - system is based on constant velocity (uniform motion) along perfect spheres (epicycles)
  8. Copernican Revolution
    - everything (including earth) moves in circles around the sun

    - but then why dont we see the stars shift in angle (parallax)
  9. Stellar parallax
    • - small annual shifts in a stars apparent position caused by earth's motion around the sun
    • - measure parallax of stars by comparing observations of a nearby star made 6 months apart.
    • - nearby star appears to shift agains background b/c observing from opposite points in earths orbit
    • - parallactic angle = half annual back and forth shift
  10. more distant stars have _________ parallax angles
    smaller
  11. smallest angular resolution we can see is ...
    1 arcmin --> cant observe with naked eye
  12. the smaller the arcsec, the ________ the parsec
    bigger


    so 1/2 arcsec = 2pc, 1/10 arcsec = 10 pc, and 1/100" = 100 pc
  13. Can also use parallax to calculate a star's _________ using which law?
    luminosity using the inverse square law (also FLUX)

    • We are located at distance D from star with Luminosity L. The apparent brightness of the star is the power per unit area (flux) that we receive at our distance d. We find this apparent brightness by imagining a giant sphere with radius D and surface area 4πD2 (the surface area of any sphere is 4π x radius2). As the star’s light passes through the imaginary sphere, so the apparent brightness at any point on this sphere is simply the star’s luminosity L divided by the sphere’s surface area
    • Apparent brightness = star’s luminosity / Surface area of imaginary sphere
    • = L / 4π x D2
  14. Tycho Brahe and Johannes Kepeler
    • Brahe - after Copernicul
    • Kepeler is his student, studied his observations and saw that planets move through ellipses with the sun as one of two foci.
  15. Kepelers 3 laws
    • 1. Planets move around the sun tracing ellipses, not circles (distance from the sun varies during orbit
    • (average of the farthest and closest distances on the ellipses = semi-major axis - avg distance from sun)

    2. the orbits sweep out equal area in equal amt of time --> travels faster when nearer to sun, slower when farther ==> Accelerating and Decelerating in their orbits.

    3. The Period of the orbit is related to the semi-major axis a (radius of the circle - distance between that planet and the sun as P2 = a3 --> more distant planets orbit the sun at slower avg speeds, obeying a precise mathematical relationship P2 = a3
  16. B/c distant planets move more slowly, Kepeler suggested that planetary motion might be a result of the ______ but he suggested _____________
    sun, magnetism
  17. First accurate measurement of 1 AU (Earth / sun distance) made by whom, using what observation
    Edmund Halley (1716) - using observation that Venus occasionally moves across the sun
  18. Explain the transit of venus
    During Planetary transit (planet appears to move across the face of the sun), observers in different locations would see it trace slightly different paths

    observations of transit from different places (S and N Hemispheres) allows precise measurement of the planets parallax, then use geometry to measure Venus' true distance, allows us to compute Sun's distance) - b/c we know the radius of the earth
  19. Why do we use venus for transit and not mercury if mercury passes more often
    because venus is closer to earth and gives a larger parallax
  20. Year of 1st distance to sun with some accuracy
    1769 (5% accuracy - not much before that)
  21. What does earths gravity do to the moon, which way is it always accelerating?
    accelerating towards earth
  22. What is the evidence of the sun's producing energy
    life on earth --> no types of energy on earth can produce enough energy to form life
  23. Law of Gravity - if one planet increases its mass by a factor of 4, then the force increases by a factor of ___
    4.
  24. Astronomy uses ________ to make measurements
    light
  25. Three types of Astronomical Data
    • Images (intensity vs position)
    • Light curve (intensity vs time)
    • Spectrum (intensity vs photon energy / wavelength)
  26. Images
    intensity vs position

    • - pictures of sky
    • - determines positions of stars
    • - morphology: structure
    • - ex: supernova remnant - x-ray
  27. light curve
    intensity vs time

    • ex: cepheid variables
    • - graph with dots
    • - by looking at how bright, we can measure the distance
  28. Spectrum
    intensity vs "color" - photon energy/wavelength)

    • - use spectrum to determine a stars temp, composition, and evolutionary state
    • - use an instrument to detect photons --> gives temp. Tempt determines spectrum: thermal spectrum. Photons hitting an instrument produce a thermal spectrum - rectangle of color with little black lines
  29. Temperature of an object determines its ________. Temp is related to ________
    spectrum, temp related to peak of wavelength
  30. Hottest stars are what color, temp. same with cooler stars
    • hottest = blue (15000 - 20000 K)
    • cooler = red (5000 - 4000 K)
  31. Luminosity
    the total amount of energy emitted by an object per unit time (energy/time) --> erg / sec

    ie how bright the object actually is
  32. Flux
    the amount of energy that passes through a unit area per unit time

    • flux = luminosity / area (erg / sec x cm2)
    • --> flux = L / 4πR2 (4πR2 = surface area of the sphere)
    • R is the radius of the sphere around the object emitting light (essentially distance to the observer)
  33. The further away an object is, the ________ its flux is.

    What equation represents this?
    lower

    Fa / Fb = Rb2 / Ra2
  34. Energy

    represented by three basic units. What are they?
    the ability to do work

    • mass x distance2 / time2 -->
    • Joule = kg x m2 / sec2
    • Erg = g x cm2 / sec2
    • Kinetic energy (in motion) = 1/2mv2
  35. Power
    amount of energy extended per unit time
  36. We can measure flux, but we must also know ________ in order to determine luminosity
    distance
  37. Standard candle

    permits us to determine ___________, using what equation
    we know the luminosity of the object

    then can measure distance

    R = √(L/4πF)
  38. Types of standard candles
    stars (standardizable)

    cepheid variables (supergiant stars with high luminosity - able to be viewed beyond our local group - Andromeda Galaxy, but many in our galaxy too)

    Supernovae type 1a - big distance

    Galaxies (standardizable through several techniques)
  39. How do you know if an object is good enough to be a standard candle
    depends on luminosity

    stars are not good (not bright enough) - can only use to find distances in our own galaxy

    but supernovae type 1a are - can be used for distance out to Gpcs
  40. Where do you find standard candles? How common

    supernovae type 1a vs stars
    supernovae are very rare --> use to map the universe, not in our galaxy

    stars all over our galaxy --> can use them to map our galaxy but not the universe
  41. Newton showed that white light is actually __________
    a spectrum of many colors

    spectrum: high energy photons - blue, low energy photons - red
  42. light has a dual nature
    can be described as a wave that wiggles through space

    or as a particle called a photon

    characterize wave nature by wavelength, characterize particle nature by energy
  43. each color has a specific __________ and _________
    wavelength and energy
  44. shorter wavelength = __________ energy
    higher
  45. waves of what kinds of fields (2)
    electric and magnetic
  46. Electromagnetic spectrum - anything above / below visible light?
    there are wavelengths (energies) of light above and below what the eye can see (can have any length)
  47. light is also called
    electromagnetic radiation
  48. can also characterize the wave-nature of light by its ____________, measured in what?
    frequency, measured in 1/s or Hz
  49. C (speed of light) is __________ in a vacuum
    constant
  50. light year
    the distance light travels in a year
  51. Light carries ___________
    energy - the ability to do work
  52. Work
    applying some force (F) to an object as it moves across a distance
  53. Kinetic Energy is associated with ...
    motion of mass (m) due to its velocity

    KE = 1/2mv2
  54. Gravitational potential energy
    energy associated with the gravitational field between a mass M and another mass m
  55. PE = (-GMm)/r
    G = (6.672 +/- .004) x 10-8 cm3 g-1 sec-2
  56. Rotation curve of planets around the sun - "keplerian rotation"
    Vrotation = √((GMcentral)/r)

    • ==> velocity decreases with increasing radius
    • Mcentral = mass of sun
    • Sun has all the mass, so GMcentral is constant with radius
  57. Newton's Law of Gravitation (second law of motion)
    Fg = (GMm)/r2 (rotating w/ constant velocity.
  58. Centripetal force
    force pushing out (like being in the passenger side of a car when it rounds a corner)

    Fc = mV2 / r V = 2πr / P
  59. Centripetal force and gravitational force are _________ and ___________

    what does this mean?
    opposite and equal --> we can set them equal to eachother



    Fg = Fc

    • GMm / r2 = m (2πr/p)2 / r
    • P2 = 1 / (GM) x 4π2r3
    • V = √(GM/r)
  60. Thermal Radiation

    - all objects emit electromagnetic energy because of what?
    the motion of their atoms/molecules (heat)
  61. emission is called
    a continuous spectrum or thermal spectrum
  62. amount of radiation at each wavelength depends on what?
    temperature of the object ONLY
  63. room temp. objects produce thermal spectra at which wavelengths
    infrared (night vision goggles detect infrared radiation)
  64. Wien's law
    relates wavelength at which maximum amount of radiation is emitted to the temperature of the object

    Wavelengthmax = .0029 (meters x Kelvin) / T

    max wavelength is the wavelength of maximum radiation in meters
  65. We can calculate the temperature of astronomical bodies using Wien's law by observing what?
    spectra!

    Ex:the sun’s wavelength of maximum radiation is 510 nm

    • 510 x 10-9m = .0029 (m x K) / T
    • Sun’s Temp = 5700 K

    Ex: Objects at Room Temp – T = 300K, so wavelength of maximum radiation =

    Wavelengthmax = .0029 m x K / 300 K

    Wavelengthmax = 1 x 10-5 m
  66. The light that we see is _________
    reflected light --> thermal radiation or emission/absorption lines

    with some exceptions - burner on electric stove, filament in lightbulb --> emit visible thermal radiation
  67. Atoms have nuclei of different what?
    charges
  68. Force between two charges Q and q is represented by what formula?
    F = Qq / R2
  69. Particles act like _____ so the smallest size orbit for an electron around a nucleus is enough to fit ___________. the second smallest is enough to fit ___________.

    This produces what?
    waves

    1 wavelength, 2 wavelengths

    discreet separate orbits for electrons around a nuclei
  70. Electron orbits have _______
    discreet, specific energies
  71. If an electron occupies an outer orbit, it will ....

    What happens when this occurs?
    drop to a lower orbit if there is space available

    --> emits energy as a photon
  72. The amount of energy a photon emits when it drops orbit levels = what?
    the energy difference between the two orbits
  73. In principle, an atom will have an infinite number of emission lines, BUT
    only some will appear in a specific wavelength range --> some will have shorter wavelengths, but most at longer wavelengths
  74. Electrons falling within an atom from a higher energy state to a lower energy state emit the energy difference as ...
    a photon producing an emission line spectrum
  75. different elements produce
    different sets of emission lines (fingerprints) when electrons drop orbital levels
  76. High energy emission = what color?
    low energy?
    bright colors indicate what?
    • high energy = blue
    • low = red
    • bright colors = hot gas
  77. Short wavelength = what kind of intensity?
    BIG intensity
  78. emission line spectrum
    dropping multiple energy levels, get multiple emission lines
  79. molecular lines
    based on molecules (ex: H2O) --> get a different set of lines, which allows us to identify molecules
  80. Absorption lines
    like emission lines except they have a lack of hot as rather than an over abundance (black lines not lines of color)

    But still continuous spectrum --> lack of photons. Elements (cool gas) absorb photons, but has to have some background matter --> continuous

    There is an opaque source of thermal radiation with cooler gas in front of it --> dark lines superimposed due to absorption by cooler gas surrounding hotter gas (one of Kirchoff's Laws of Radiation)
  81. Line strengths/shapes determine ...
    composition, temperature, density
  82. Kirchoff's Laws of Radiation

    (from what)
    1.
    2.
    3.
    from observations of flames in lab

    • 1. Gas or heated solid will glow with a continuous spectrum (continuum / thermal spectrum)
    • 2. Hot gas will produce certain bright wavelengths (emission lines - characteristic set for different elements)
    • 3. If cool gas is between observer and hot continuous spectrum source, gas will absorb the spectrum --> absorption lines (continuous)
  83. Doppler shift: waves have a ________ and _________
    frequency and wavelength
  84. if object emitting wave is stationary, then frequency and wavelength are ....
    same in all directions (ripples on a pond)
  85. If the emitter is moving (velocity V), then the frequency and wavelength is ...
    different in different directions (a bug moving to the right in the water - behind him sees longer wavelengths, smaller frequency (lower pitch), before him sees shorter wavelengths, higher frequency, higher pitch)
  86. emission line moving towards observer --> shifted to

    vs moving away from
    higher frequency (blue end of spectrum)

    lower frequencies (red end)
  87. Doppler shift for sound/water occurs because ...

    If the speed of emitter exceeds speed of sound ...
    wave travels through a medium

    you wont hear waves --> sonic boom!
  88. Does light travel through a medium?

    Can you travel faster than the speed of light?
    No and No
  89. the magnitude of doppler shift allows the observer to measure
    the velocity of the emitter along the line of sight (either towards or away from) --> cant measure velocity perpendicular to the line of sight
  90. Discovery of Quasi-Stellar Radio sources (Quasars)
    - before interferometry, radio angular resolution was so poor the positions of strong radio sources were not very good.

    - discovery of Quasars gave much better position (bright point source with something nebulous nearby)
  91. Spectrum of a quasar

    implies what
    broad emission lines - 10,000 km/s wide

    the emitting material has a wide range of velocities
  92. Optical Telelscopes

    - used in
    - uses
    - 1st telescopes were
    - light is doing what, shape of lens?
    • - traditional astronomy (based on newtons principles)
    • - use glass lens to magnify and focus light
    • - 1st telescopes were refractors
    • - light is bending --> refraction because of a curved lens
  93. Disadvantages of refractors
    • - big telescope - big lens, glass is heavy
    • - bigger telescope --> structure bends more
    • - chromatic abberation - different colors of light focuses at different places (never at same place)
    • - bubbles in glass ruin image quality (more volume --> more chance of bubbles)
    • - best image requires glass to be at one temp --> more glass takes longer to cool at night, so whole lens can never be at same temp.
    • - Glass expands with heat - cooling air causes air flow --> worsen quality
  94. chromatic abberration
    different colors of light focuses at different places (never at same place)- bubbles in glass ruin image quality (more volume --> more chance of bubbles)
  95. Modern telescopes are ...
    reflectors
  96. reflector telescopes

    advantages
    use curved mirror to collect / focus light
  97. - no chromatic abberration
    • - lighter, can be supported from behind
    • - very large, but very thin mirrors can be constructed
  98. Interference of light is a consequence of what?
    wave-like properties of light in quantum mechanics
  99. Photons travel from distant stars and are reflected by a mirror onto a focal plane, but photons are not what? what does this mean?
    not particles (dont bounce off mirror) - photons are not real until they are detected --> quantum mechanics

    *think of that ONE photon as bouncing off every single point on the mirror, towards the detector
  100. When waves interfere

    if 2 crests -->
    2 Troughs -->
    1 trough, 1 crest -->
    Big crest

    Big trough

    cancel out
  101. Diffraction limit of a telescope
    minimum angle it can resolve (the closest two point sources can be, to still be able to tell them apart

    angle size of smallest measurable feature
  102. Because earths atmosphere blurs stars, resolution cannot improve beyond --> solution?
    1 arcsec --> go above earth's atmosphere
  103. smaller diffraction angular resolution needs _____ telescope, which means ...

    larger telescope aperture -->
    bigger telescope --> more light, more sensitive

    improves resolution
  104. The Hubble Space Telescope
    D (aperature) = 2.4 - smaller than many telescopes on the ground

    b/c in space, can achieve diffraction limited resolution

    excellent for imaging
  105. Larger ground based telescopes are better for _________
    spectroscopy - measuring spectra produced when matter interacts with / emits electromagnetic radiation
  106. Series of Optical Telescope Detectors
    • Historically, the eye (not accurate)
    • Then, photographic fil
    • Today- CCD's (Charge Coupled Devices)
  107. The eye as Optical telescope detectors
    • - results unreliable
    • - not very sensitive --> limited by the "memory" of photoneurons in our eye (refresh)
    • - hard to quantify intensity
  108. Photographic Film as optical telescope detectors
    • - more sensitive than the eye - can integrate for arbitrarily long periods
    • - can more accurately find intensity
    • - can store results
    • - can make copies
  109. CCD's (Charge Coupled Devices) as optical telescope detectors
    • - convert photons to electrons - produces electrical currents
    • - very light, sensitive
    • - easy to digitize, store, manipulate
    • - easy to quantify intensity, sensitivity
    • - compare with others
  110. Interferometry
    the resolution of the radio band (lambda 3 cm) is set by the maximum separation (D) between two radio focusing elements

    • - cells in our eyes are activated by only optical wavelengths
    • - detectors in our eyes only respond to visible light
    • - because of the energy of the photon wavelength
    • - lens suited for focusing optical photons
  111. Wiens law

    - measuring peak wavelength gives you what
    - larger temp =
    - longer wavelength =
    - measuring peak wavelength where most energy comes out gives you temperature

    • - shorter peak wavelength
    • - lower temp
  112. When you are measuring parallax distance you get an answer in "units" of ______. Have to convert to _______
    radians (unitless) --> arcsec
  113. atmospheric blurring
    blurs to 1 arcsec, minimum we can see
  114. If you have an object with a certain distance, and another object with the same luminosity but closer then what kind of telescope (bigger/smaller) and how long
    same amount of time, smaller telescope aperature
  115. can you determine anything if you know only flux?
    no - doesnt tell you anything about luminosity, temperature, or distance
  116. Wiens law - if you have peak wavelength, you can figure out
    temperature
  117. If you have an open universe
    still has finite energy --> no maximum size, keeps expanding infinitely
  118. What does causally related mean?

    so if something brightens over 10 mins
    light can pass through

    10 mins x speed of light = size of object
  119. What is characteristic of main sequence stars
    all have nuclear fusion of hydrogen (hydrogen burning) as main energy source
  120. Main sequence star - mass determines what?
    almost all properties - where it will sit on main sequence, spectral type
  121. low mass stars are ____
    high mass stars are _______
    • cool, faint
    • hot, bright
  122. stellar radius is determined by what?
    the principle of hydrostatic equilibrium
  123. Stefan-Boltzmann Law:
    red stars have a lower luminosity than blue stars (for same radius)
  124. if you can measure a stars spectrum and distance
    - from the peak in continuous spectrum measure temp, from total luminosity measure R (angular size)

    - geometric measurements of R are very difficult bc stars are far away and they are not resolved by optical telescopes
  125. Globular Clusters

    - how many stars, bound by what?
    - how many in our galaxy
    - size in diameter
    - stars in each formed when --> what does this say about them
    • - about 105 - 106 in each, bound gravitationally
    • - about 150 globular clusters in our galaxy
    • - about 10 pc in diameter
    • - stars in each formed at the same time - all same age but different masses
  126. Even though globular clusters look similar, what are some important difference among them
    total number of stars, concentration of stars at center, how big they are, ect.
  127. Stars of different masses are born onto main sequence in same or different places?

    how long do they stay?
    different places

    stay until their H is burned off, then they evolve off
  128. Turn off from the main sequence in globular clusters tells us what about them
    how old they are

    (typically a few hundred thousand yrs)
  129. more massive stars burn fuel _______, have _______ luminosities, and ______ lives
    burn faster, higher luminosities, shorter lives
  130. after stars have burned off all their hydrogen, they turn off the main sequence and evolve to become _______, then _______, before completing cycle at one of three stellar endpoints
    giants, supergiants

    • stellar endpoints:
    • black hole (after a supernova)
    • neutron star (after a supernova)
    • white dwarfs (after planetary nebulae)
  131. Stellar endpoint

    what does "endpoint" imply
    type of body which an evolving main sequence star will eventually end up as

    implies that it is that objects destiny to remain as that type of endpoint
  132. Stellar Birth
    • 1. clumps of gas collapse by gravitational attraction
    • 2. clumps collapse into a disk and central proto-star
    • 3. star begins to burn H, the pressure from the light produces jets, and clears away the disk
    • 4. after most of the disk is cleared, the star shines in all directions, and a planetary disk is left

    usually takes a few million years
  133. Why does the sun shine
    because of a proton proton chian (produces Helium - means all the hydrogen will eventually burn up --> about 10 billion years)
  134. is main sequence equally populated?
    no - many more cool (reddish) stars than hot ones; but cool stars are fainter (lower T, lower L) --> most prominent stars in night sky are numerically rarer (bluer - most luminous ones)
  135. why space based observing?
    the atmosphere is opaque to much of electromagnetic spectrum - absorbs most of the light
  136. William Herschel- what concept?
    "island universe" galaxy
  137. Olbers Paradox
    • - assumes the universe is infinite in size, has a constant number of stars per unit volume within it
    • - conflicts with the observation that the sky is dark at night
  138. Objects in the sky are indicated by their what?
    angular positions in the sky
  139. You can define any direction in the sky using ___ angular numbers:
    2

    • LOCAL CELESTIAL COORDINATES
    • Altitude - from 0 to 90 degrees above the horizon

    Azimuth - from 0 to 360 degrees east of north
  140. Altitude
    from 0 to 90 degrees above the horizon
  141. azimuth
    from 0 to 360 degrees east of north
  142. Zenith
    point directly over the observers head
  143. Do stars change their positions with time in local celestial coordinates?
    yes
  144. Altitude and Azimuth are specific to ________
    location of the observer - different coordinates to the same object depending on position on earth

    altitude and azimuth change with time as earth rotates
  145. Celestial Sphere
    based on analogy of earths latitude and longitude projected onto sky
  146. any position on earth can be specified using ________ and _________
    latitude and longitude
  147. 0 degrees latitude and longitude
    • 0 lat = equator
    • 0 long = Greenwich england
  148. meridian
    the circle through the zenith connecting the north and and south poles

    sun rises east of meridian, sets west of meridian
  149. Right Ascension
    celestial longitude - stays the same as earth rotates (measured in hrs, minutes, secs east of Vernal Equinox - exact direction of the sun as it passes through dec = 0 degrees in the spring (March 21) - the Zero point for R.A.
  150. Vernal Equinox
    - exact direction of the sun as it passes through dec = 0 degrees in the spring (March 21) - the Zero point for R.A.
  151. Declination
    celestial latitude (measured in degrees n/s of celestial equator)
  152. Polaris marks location of what
    north celestial pole (north pole)
  153. altitude of polaris =
    your latitude
  154. From montreal you will never see
    • large magellanic cloud
    • small magellanic cloud
    • center of milky way

    (southern declinations not visible in north)
  155. tilt of earths axis
    23.5 degrees
  156. what is the maximum altitude of the sun during the day?
    sun reaches max altitude as it crosses your meridian

    march 21 and sept 21 are the only two days of the year that the sun lies in the celestial plane - max altitude is 90 deg- your latitude
  157. solstice
    when direction to the sun from earths center is furthest from the ecliptic plane (june 21, dec 21 - longest / shortest days)
  158. equinox
    when the direction to the sun from the earths center lies in the ecliptic plane

    march 21, sept 21 - night and day are 12 hrs
  159. Ecliptic Plane
    the plane which contains the ellipses in which the earth travels around the sun
  160. at equator, all constellations visible

    at a pole (N or S)
    sometime during the year

    only half the sky is ever visible

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