Physics Review - 1st term
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The Scientific method
ideas expressed are
- 1. objective (same for everyone)
- 2. falsifiable
- 3. common to all lines of scientific inquiry
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
- 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)
When giving the uncertainty of a measurement give how many sig figs?
when giving the value of a measurement, use the number of sig figs to ...
magnitude of uncertainty
3 fundamental units
- mass (g)
- length (cm)
- time (sec)
- everything else is a combination of these
- - 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)
- everything (including earth) moves in circles around the sun
- but then why dont we see the stars shift in angle (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
more distant stars have _________ parallax angles
smallest angular resolution we can see is ...
1 arcmin --> cant observe with naked eye
the smaller the arcsec, the ________ the parsec
so 1/2 arcsec = 2pc, 1/10 arcsec = 10 pc, and 1/100" = 100 pc
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
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.
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
--> more distant planets orbit the sun at slower avg speeds, obeying a precise mathematical relationship P2
B/c distant planets move more slowly, Kepeler suggested that planetary motion might be a result of the ______ but he suggested _____________
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
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
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
Year of 1st distance to sun with some accuracy
1769 (5% accuracy - not much before that)
What does earths gravity do to the moon, which way is it always accelerating?
accelerating towards earth
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
Law of Gravity - if one planet increases its mass by a factor of 4, then the force increases by a factor of ___
Astronomy uses ________ to make measurements
Three types of Astronomical Data
- Images (intensity vs position)
- Light curve (intensity vs time)
- Spectrum (intensity vs photon energy / wavelength)
intensity vs position
- - pictures of sky
- - determines positions of stars
- - morphology: structure
- - ex: supernova remnant - x-ray
intensity vs time
- ex: cepheid variables
- - graph with dots
- - by looking at how bright, we can measure the distance
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
Temperature of an object determines its ________. Temp is related to ________
spectrum, temp related to peak of wavelength
Hottest stars are what color, temp. same with cooler stars
- hottest = blue (15000 - 20000 K)
- cooler = red (5000 - 4000 K)
the total amount of energy emitted by an object per unit time (energy/time) --> erg / sec
ie how bright the object actually is
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)
The further away an object is, the ________ its flux is.
What equation represents this?
Fa / Fb = Rb2 / Ra2
represented by three basic units. What are they?
the ability to do work
- mass x distance2 / time2 -->Joule = kg x m2 / sec2Erg = g x cm2 / sec2Kinetic energy (in motion) = 1/2mv2
amount of energy extended per unit time
We can measure flux, but we must also know ________ in order to determine luminosity
permits us to determine ___________, using what equation
we know the luminosity of the object
then can measure distance
R = √(L/4πF)
Types of standard candles
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)
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
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
Newton showed that white light is actually __________
a spectrum of many colors
spectrum: high energy photons - blue, low energy photons - red
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
each color has a specific __________ and _________
wavelength and energy
shorter wavelength = __________ energy
waves of what kinds of fields (2)
electric and magnetic
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)
light is also called
can also characterize the wave-nature of light by its ____________, measured in what?
frequency, measured in 1/s or Hz
C (speed of light) is __________ in a vacuum
the distance light travels in a year
Light carries ___________
energy - the ability to do work
applying some force (F) to an object as it moves across a distance
Kinetic Energy is associated with ...
motion of mass (m) due to its velocity
KE = 1/2mv2
Gravitational potential energy
energy associated with the gravitational field between a mass M and another mass m
PE = (-GMm)/r
G = (6.672 +/- .004) x 10-8 cm3 g-1 sec-2
Rotation curve of planets around the sun - "keplerian rotation"
- ==> velocity decreases with increasing radius
- Mcentral = mass of sun
- Sun has all the mass, so GMcentral is constant with radius
Newton's Law of Gravitation (second law of motion)
Fg = (GMm)/r2 (rotating w/ constant velocity.
force pushing out (like being in the passenger side of a car when it rounds a corner)
Fc = mV2 / r V = 2πr / P
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)
- all objects emit electromagnetic energy because of what?
the motion of their atoms/molecules (heat)
emission is called
a continuous spectrum or thermal spectrum
amount of radiation at each wavelength depends on what?
temperature of the object ONLY
room temp. objects produce thermal spectra at which wavelengths
infrared (night vision goggles detect infrared radiation)
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
We can calculate the temperature of astronomical bodies using Wien's law by observing what?
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 =
= .0029 m x K / 300 K
= 1 x 10-5 m
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
Atoms have nuclei of different what?
Force between two charges Q and q is represented by what formula?
F = Qq / R2
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?
1 wavelength, 2 wavelengths
discreet separate orbits for electrons around a nuclei
Electron orbits have _______
discreet, specific energies
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
The amount of energy a photon emits when it drops orbit levels = what?
the energy difference between the two orbits
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
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
different elements produce
different sets of emission lines (fingerprints) when electrons drop orbital levels
High energy emission = what color?
bright colors indicate what?
- high energy = blue
- low = red
- bright colors = hot gas
Short wavelength = what kind of intensity?
emission line spectrum
dropping multiple energy levels, get multiple emission lines
based on molecules (ex: H2O) --> get a different set of lines, which allows us to identify molecules
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)
Line strengths/shapes determine ...
composition, temperature, density
Kirchoff's Laws of Radiation
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)
Doppler shift: waves have a ________ and _________
frequency and wavelength
if object emitting wave is stationary, then frequency and wavelength are ....
same in all directions (ripples on a pond)
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)
emission line moving towards observer --> shifted to
vs moving away from
higher frequency (blue end of spectrum)
lower frequencies (red end)
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!
Does light travel through a medium?
Can you travel faster than the speed of light?
No and No
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
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)
Spectrum of a quasar
broad emission lines - 10,000 km/s wide
the emitting material has a wide range of velocities
- used in
- 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
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
different colors of light focuses at different places (never at same place)- bubbles in glass ruin image quality (more volume --> more chance of bubbles)
Modern telescopes are ...
use curved mirror to collect / focus light
- no chromatic abberration
- - lighter, can be supported from behind
- - very large, but very thin mirrors can be constructed
Interference of light is a consequence of what?
wave-like properties of light in quantum mechanics
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
When waves interfere
if 2 crests -->
2 Troughs -->
1 trough, 1 crest -->
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
Because earths atmosphere blurs stars, resolution cannot improve beyond --> solution?
1 arcsec --> go above earth's atmosphere
smaller diffraction angular resolution needs _____ telescope, which means ...
larger telescope aperture -->
bigger telescope --> more light, more sensitive
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
Larger ground based telescopes are better for _________
spectroscopy - measuring spectra produced when matter interacts with / emits electromagnetic radiation
Series of Optical Telescope Detectors
- Historically, the eye (not accurate)
- Then, photographic fil
- Today- CCD's (Charge Coupled Devices)
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
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
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
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
- 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
When you are measuring parallax distance you get an answer in "units" of ______. Have to convert to _______
radians (unitless) --> arcsec
blurs to 1 arcsec, minimum we can see
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
can you determine anything if you know only flux?
no - doesnt tell you anything about luminosity, temperature, or distance
Wiens law - if you have peak wavelength, you can figure out
If you have an open universe
still has finite energy --> no maximum size, keeps expanding infinitely
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
What is characteristic of main sequence stars
all have nuclear fusion of hydrogen (hydrogen burning) as main energy source
Main sequence star - mass determines what?
almost all properties - where it will sit on main sequence, spectral type
low mass stars are ____
high mass stars are _______
stellar radius is determined by what?
the principle of hydrostatic equilibrium
red stars have a lower luminosity than blue stars (for same radius)
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
- 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
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.
Stars of different masses are born onto main sequence in same or different places?
how long do they stay?
stay until their H is burned off, then they evolve off
Turn off from the main sequence in globular clusters tells us what about them
how old they are
(typically a few hundred thousand yrs)
more massive stars burn fuel _______, have _______ luminosities, and ______ lives
burn faster, higher luminosities, shorter lives
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
- stellar endpoints:
- black hole (after a supernova)
- neutron star (after a supernova)
- white dwarfs (after planetary nebulae)
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
- 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
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)
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)
why space based observing?
the atmosphere is opaque to much of electromagnetic spectrum - absorbs most of the light
William Herschel- what concept?
"island universe" galaxy
- - 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
Objects in the sky are indicated by their what?
angular positions in the sky
You can define any direction in the sky using ___ angular numbers:
- LOCAL CELESTIAL COORDINATES
- Altitude - from 0 to 90 degrees above the horizon
Azimuth - from 0 to 360 degrees east of north
from 0 to 90 degrees above the horizon
from 0 to 360 degrees east of north
point directly over the observers head
Do stars change their positions with time in local celestial coordinates?
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
based on analogy of earths latitude and longitude projected onto sky
any position on earth can be specified using ________ and _________
latitude and longitude
0 degrees latitude and longitude
- 0 lat = equator
- 0 long = Greenwich england
the circle through the zenith connecting the north and and south poles
sun rises east of meridian, sets west of meridian
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.
- exact direction of the sun as it passes through dec = 0 degrees in the spring (March 21) - the Zero point for R.A.
celestial latitude (measured in degrees n/s of celestial equator)
Polaris marks location of what
north celestial pole (north pole)
altitude of polaris =
From montreal you will never see
- large magellanic cloud
- small magellanic cloud
- center of milky way
(southern declinations not visible in north)
tilt of earths axis
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
when direction to the sun from earths center is furthest from the ecliptic plane (june 21, dec 21 - longest / shortest days)
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
the plane which contains the ellipses in which the earth travels around the sun
at equator, all constellations visible
at a pole (N or S)
sometime during the year
only half the sky is ever visible
What would you like to do?
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