Physics Review - 1st term

• 1. objective (same for everyone)
• 2. falsifiable
• 3. common to all lines of scientific inquiry

• 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

- quantitative (amt)

• - value (15 today)
• - unit (15 degrees C today)
• - uncertainty (15 +/- 25 degrees C today)

1

magnitude of uncertainty

• 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

smaller

1 arcmin --> cant observe with naked eye

bigger


so 1/2 arcsec = 2pc, 1/10 arcsec = 10 pc, and 1/100" = 100 pc

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

• 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.

• 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

sun, magnetism

Edmund Halley (1716) - using observation that Venus occasionally moves across the sun

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

because venus is closer to earth and gives a larger parallax

1769 (5% accuracy - not much before that)

accelerating towards earth

life on earth --> no types of energy on earth can produce enough energy to form life

4.

light

• 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

spectrum, temp related to peak of wavelength

• 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)

lower

F_a / F_b = R_b² / R_a²

the ability to do work

• mass x distance² / time^{2 -->}
• Joule = kg x m² / sec²
• Erg = g x cm² / sec²
• Kinetic energy (in motion) = 1/2mv²

amount of energy extended per unit time

distance

we know the luminosity of the object

then can measure distance

R = √(L/4πF)

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)

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

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

a spectrum of many colors

spectrum: high energy photons - blue, low energy photons - red

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

wavelength and energy

higher

electric and magnetic

there are wavelengths (energies) of light above and below what the eye can see (can have any length)

electromagnetic radiation

frequency, measured in 1/s or Hz

constant

the distance light travels in a year

energy - the ability to do work

applying some force (F) to an object as it moves across a distance

motion of mass (m) due to its velocity

KE = 1/2mv²

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

V_rotation = √((GM_central)/r)

• ==> velocity decreases with increasing radius
• M_central = mass of sun
• Sun has all the mass, so GM_central is constant with radius

F_g = (GMm)/r² (rotating w/ constant velocity.

force pushing out (like being in the passenger side of a car when it rounds a corner)

F_c = mV² / r V = 2πr / P

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)

the motion of their atoms/molecules (heat)

a continuous spectrum or thermal spectrum

temperature of the object ONLY

infrared (night vision goggles detect infrared radiation)

relates wavelength at which maximum amount of radiation is emitted to the temperature of the object

Wavelength_max = .0029 (meters x Kelvin) / T

max wavelength is the wavelength of maximum radiation in meters

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 =

Wavelength_max = .0029 m x K / 300 K

Wavelength_max = 1 x 10-5 m

reflected light --> thermal radiation or emission/absorption lines

with some exceptions - burner on electric stove, filament in lightbulb --> emit visible thermal radiation

charges

F = Qq / R²

waves

1 wavelength, 2 wavelengths

discreet separate orbits for electrons around a nuclei

discreet, specific energies

drop to a lower orbit if there is space available

--> emits energy as a photon

the energy difference between the two orbits

only some will appear in a specific wavelength range --> some will have shorter wavelengths, but most at longer wavelengths

a photon producing an emission line spectrum

different sets of emission lines (fingerprints) when electrons drop orbital levels

• high energy = blue
• low = red
• bright colors = hot gas

BIG intensity

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)

composition, temperature, density

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)

frequency and wavelength

same in all directions (ripples on a pond)

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)

higher frequency (blue end of spectrum)

lower frequencies (red end)

wave travels through a medium

you wont hear waves --> sonic boom!

No and No

the velocity of the emitter along the line of sight (either towards or away from) --> cant measure velocity perpendicular to the line of sight

- 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)

broad emission lines - 10,000 km/s wide

the emitting material has a wide range of velocities

• - 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

• - 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)

reflectors

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

wave-like properties of light in quantum mechanics

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

Big crest

Big trough

cancel out

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

1 arcsec --> go above earth's atmosphere

bigger telescope --> more light, more sensitive

improves resolution

D (aperature) = 2.4 - smaller than many telescopes on the ground

b/c in space, can achieve diffraction limited resolution

excellent for imaging

spectroscopy - measuring spectra produced when matter interacts with / emits electromagnetic radiation

• Historically, the eye (not accurate)
• Then, photographic fil
• Today- CCD's (Charge Coupled Devices)

• - results unreliable
• - not very sensitive --> limited by the "memory" of photoneurons in our eye (refresh)
• - hard to quantify intensity

• - more sensitive than the eye - can integrate for arbitrarily long periods
• - can more accurately find intensity
• - can store results
• - can make copies

• - 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 where most energy comes out gives you temperature

• - shorter peak wavelength
• - lower temp

radians (unitless) --> arcsec

blurs to 1 arcsec, minimum we can see

same amount of time, smaller telescope aperature

no - doesnt tell you anything about luminosity, temperature, or distance

temperature

still has finite energy --> no maximum size, keeps expanding infinitely

light can pass through

10 mins x speed of light = size of object

all have nuclear fusion of hydrogen (hydrogen burning) as main energy source

almost all properties - where it will sit on main sequence, spectral type

• cool, faint
• hot, bright

the principle of hydrostatic equilibrium

red stars have a lower luminosity than blue stars (for same radius)

- 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

• - 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

total number of stars, concentration of stars at center, how big they are, ect.

different places

stay until their H is burned off, then they evolve off

how old they are

(typically a few hundred thousand yrs)

burn faster, higher luminosities, shorter lives

giants, supergiants

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

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

because of a proton proton chian (produces Helium - means all the hydrogen will eventually burn up --> about 10 billion years)

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)

the atmosphere is opaque to much of electromagnetic spectrum - absorbs most of the light

"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

angular positions in the sky

2

• 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

yes

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

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)

north celestial pole (north pole)

your latitude

• large magellanic cloud
• small magellanic cloud
• center of milky way

(southern declinations not visible in north)

23.5 degrees

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

sometime during the year

only half the sky is ever visible