# Astrophysics concepts study guide

Outline general structure of solar system
Order of planets: (including order in mass and radius; smallest to largest.)
Mercury; 1, 1
Venus; 3, 3
Earth;4, 4
Mars; 2, 2
Jupiter; 8,8
Saturn; 7,7
Uranus; 5, 6
Neptune; 6,
Distinguish between stellar cluster and a constellation
CONSTELLATIONS:
Stars that look like they are close together but do not have anything related physically except that they are all bright
STELLAR CLUSTER:
Group of stars that are physically close together rather than looking as they are, formed by the collapse of a gas cloud
define the light year
Distance light travels in a year, 9.46×10¹⁵
Compare relative distances between stars within a galaxy and between galaxies, in terms of order of magnitude
•Galaxy contain stars between 10³ and 10⁵ light years across
•each star aprox 1ly apart
•each galaxy 10⁶ ly apart
Describe the apparent motion of the stars/contellationss over a period of a year and explain these observations in terms of rotaion and revolutions of the Earth
Stars and constellations moving east to west, but the relative position of the constellations do not change. Earth rotates on its axis every 24 hours. Earth does full revolution of the sun every 365 days.
State the main energy source of stars
Fusion. Stars are composed of mainly hydrogen. Main reaction is that of nuclear fusion where hydrogen is fused into helium providing energy. Fusion process is called a proton-proton chain:
4¹₁H= ⁴₂He+2e⁺+2ve+2γ
Explain why stars are spheres
•When star is expending fuel it rises in temperature and therefore rises in pressure.
•required to keep a balance between the great force of gravity compress the star.
•Gravitation force can collapse the star
•radiation pressure which can make the star expand.
•equilibrium is gained through nuclear fusion which provides the energy the star needs to keep it hot so that the star’s radiation pressure is high enough to oppose gravitational contraction.
Explain the luminostiy of a star
Amount of energy radiated by the star per second (sun has luminosity of 3.8×10²⁶W)
Define apparent brightness and how it is measured
Amount of energy per second received per unit area. It is how bright a star seems to us depending on its luminosity and how far away it is.
b=L/(4πd² ) Wm⁻²
4πd² is surface area
(spectroscopic parallax)
explain how stefan-boltzmein law can compare luminosties of different stars
L=σAT4.
A=4πr²
The Stefan-Boltzmann constant: σ = 5.67 x 10⁻⁸Wm⁻²K⁻⁴ (given)
State Weins displacement law and apply it to explain the connection between color and temperatures of stars
the higher the temperature the lower the wavelength at which most of the energy is radiated.
Wein’s displacement law is stated as: λmax=(2.9×10⁻³)/T (given)
Explain how the atomic spectra may be used to deduce chemical and physical data for stars
•surface temperature of a star is determined by measuring the wavelength at which most of the radiation is emitted.
•Most stars essentially have the same chemical composition, yet show different absorption spectra as they have different temperatures.
•Absorption spectra gives information about the temperature of the star and its chemical composition.
•Doppler shift information of speed relative to earth (red shift→longer wavelength, blue shift→shorter wavelength)
Explain overall classification system of spectral classes
CLASS:
O 60 000K-30 000K Blue
B 30 000K-10 000K Blue-white
A 10 000K- 7 500K White
F 7 500K- 6 000K Yellow-white
G 6 000K- 5 000K Yellow
K 5 000K- 3 500K Orange
M 3 500K- 2 000K Red

Acronym: Oh Be A Fair God, Kill Me

Describe the different types of stars
MAIN SEQUENCE STARS: centre of HR diagram, 90% of the stars we see.
GIANTS: cool star that gives out a lot of energy, large mass, luminosity 100 times that of our sun
SUPERGIANT: very big cool star, luminosity 106 times greater than sun, radii up to 1000 times that of the sun
WHITE DWARFS: small hot star, hotter than sun but only size of earth, low luminosity
VARIABLE STAR: has changing luminosity so position on HR diagram is not constant.
Discuss the characteristsics of spectroscopic and eclipsing binary stars
BINARY STARS:
pairs of stars that orbit each other (or more accurately, around their common centre of mass)
VISUAL BINARY STARS:
•one that can be distinguished as two separate stars using a telescope
SPECTROSCOPIC BINARY STARS:
•can be identified from its spectrum.
•Over time the system shows a spectrum that oscillates, being doppler shifted towards the blue and red with a regular period.
ECLIPSING BINARY:
•Orientation of orbit causes them to periodically pass between the earth and eachother then they eclipse each other.
•Causes a reduction in the stars apparent brightness (diagram is light curve)
SEE NOTES FOR DIAGRAMS
Identify the general regions of star types on an HR diagram
Main sequence, red giant, red supergiant, white dwarf and Cepheid stars should be shown, with scales of luminosity and/or absolute magnitude, spectral class and/or surface temperature indicated. Students should be aware that the scale is not linear.
Students should know that the mass of main sequence stars is dependent on position on the HR diagram.
Define the parsec
Defined in terms of the angle subtended at the star.
If the distance to a star is 1pc then the angle will be 1 second. dparsec=1/(p(arcsec⁡θ))
Describe the stellar parallax method of determining the distance to a star
Distance found by measuring the angle the telescope is rotated through when moving it from 2 different positions. The distance is very large so the angle will be very small.
explain why the mthod of stellar parallax is limited to measuring stellar distances less than several hundred parsecs
If the distance is too big then the angle that will be measured will be too small to calculate a distance.
Needs to be less than 100 parsecs away
Solve problems using stellar parallax
idk look for sample problems
Describe the apparent magnitude scale
•Scale that determines how bright a star is measured from 1 to 6 where 1 is 100 times brighter than 6
•(therefore 2.512=100^⅕ times brighter than the previous)
•gives relative visual brightness from earth
Define absolute magnitude
Magnitude of a star viewed from a distance of 10pc
m-M=5 log⁡(d/10)
d=10×10^((m-M)/5) pc (given)
Compare and contrast involving apparent brightness and apparent magnitude
Apparent brightness:
A measure of how bright a star appears to be when you see it from Earth.

Absolute brightness: A measure of how bright the star really is, if all stars were the same distance from Earth.

State that the luminosity of a star may be estimated from its spectrum
The most intense wavelength of light emitted from a star is used to find its temperature (using Wien’s law λ_max=(2.9×10⁻³)/T). From the HR diagram we can then find its luminosity.
explain how stellar distance may be determined using apparent brightness, and luminosity
b=L/(4πd² ) Wm⁻²
state the limit spectroscopic parallax has (the numerical distance
only has a limit of about 10Mpc, as stellar distances increase, the uncertainty in luminosity becomes greater and so the uncertainty in distance is creater
ex outline the nature of a cepheid variable
Unstable star that undergoes periodic expansions and contractions, leading to a periodic change in the apparent brightness of the star as viewed from Earth.
state the relationship between period and absolute magnitude for cepheid variables
theres a picture you can look at on http://www.atnf.csiro.au/outreach/education/senior/astrophysics/variable_cepheids.html
explain how cepheid variables may be used as “standard candles”
•”Standard Candles,” objects with known luminosity, and comparing this with their apparent magnitude we can easily calculate their distance
•Period of variation in luminosity for cepheid variable is related to average absolute magnitude. The greater the period the greater the maximum luminosity.
•Used when measuring distances greater than 10Mpc
explain how to determine the distance to a cepheid variable using the luminosity period relationship
•locate cepheid in galaxy
•measure period
•use graph to find its absolute magnitude M
•measure how bright it appears (maximum)
•calculate how far away it is
describe newtons model of the universe
•Infinitely big implying that the gravitational force on each star was the same in each direction holding them in static equilibrium.
•If the universe is static, then the stars will be in the same place forever.
•He also concluded that the universe must be uniform.
1) (If there was an infinite number of stars, why is the sky dark?) There is a finite number of stars and each star has a finite lifetime.
2) The universe has a finite age and stars that are beyond the event horizon have not yet had time for their light to reach Earth.
Relative to the doppler effect, explain how it is known the universe is expanding
•Light from distant galaxies is red-shifted meaning the wavelength is getting longer suggesting that the universe is expanding.
•Also the further galaxies are moving faster than inwards ones suggesting there was an explosion (big bang).
Describe both space and time originating with the big bang
•Time and space grew out of the big bang.
•Universe is expanding really means that space is growing rather than spreading into the nothingness that surrounds it.
Calculating Red shift: ∆λ/λ=v/c (given)
Describe the discovery of cosmic microwave background (CMB) radiation by penzias and wilson
•detected by Penzias and Wilson in 1960’s.
•big bang theory predicts that CMB corresponds to the black body at 3K λmax=b/T
•Was thought to be uniform but satellite detected very small variations that were just enough to show that the early universe was not completely uniform enabling galaxies to form.
explain how cosmic radioation in the microwave region is consistent with the big bang model
•temperature of universe after big bang was very high but as it expanded it cooled down to about 3K
•wavelength of CMB corresponds to temperature consisten with this cooling down
•red shift due to expansion of universe
suggest how the big bang model provides a resoultion to Olber’s paradox
The matter and radiation of our present time was initially all packed together into an extremely hot and dense fireball, that exploded giving rise to the Big Bang.
•Within seconds, matter was accelerated through 3 dimensions, expanding and developing very rapidly.
•Time became a measure of the rate of that expansion, the necessary 4th dimension.
describe the conditions that initiate fusion in a star
•formed when huge clouds of gas and dust are compressed
•cannot form on their own as gravitational force not big enough to pull particles together
•as cloud comes together, GPE→KE→temperature
•temperature causes outward pressure that pushes against gravitational attraction, however as atoms get closer together, the gravitational attraction increases so gas continues to collapse
•eventually dense core formed surrounded by cloud of dust and gas
•heats up until fusion of hydrogen takes place
state the effect of a star’s mass on the end product of nuclear fusion
LOW MASS:
•helium synthesis
SUFFICIENT MASS:
•red giant continues to fuse higher and higher elements
•fusion ends with nucleosythesis of iron (iron has the highest binding energy per nucleon of all nuclei, will no longer shine)
outline the changes that take place in nucleosynthesis when a star leaves the main sequence and becomes a red giant
•Star fuses hydrogen→helium
•eventually hydrogen will run out so fusion reaction happens less causing star to not be in equilibrium →core collapses, increasing the temperature
•now fusion of helium possible→star increases massively in size→expansion means outer layers are cooler hence RED GIANT
explain the mass-luminosity relation
•relationship between luminosity and mass of main sequence star
L∝m^n where 3
explain how the chandrasker and oppenheimer volkoff limits are used to predict the fate of stars of different masses, reference their values
CHANDRASEKHAR LIMIT:
•’critical mass’ of the initial star which dictates its evolution
•value is 1.4 ⨉ solar mass(mass of sun M⦿)
•no white dwarf can be more massive than this limit
•any degenerate object more massive must collapse into a neutron star
OPPENHEIMER-VOLKOFF LIMIT:
•largest mass for a neutron star
•value is 3 solar masses (mass of sun M⦿)
•Neutron degeneracy pressure also has a mass limit, above which it cannot support the sta
compare the fate of a red giant and a red supergiant
RED GIANT:
•forms a planetary nebula and then becomes a white dwarf
•a white dwarf is stable due to electron degeneracy pressure
RED SUPERGIANT:
•experiences a supernova and becomes a neutron star or collapses to a black hole
•a neutron star is stable due to neutron degeneracy pressure.
draw evolutionary paths of stars on a HR diagram
look for diagram in book or powerpoints
outline the characteristics of pulsars
•cosmic sources of very weak radio wave energy
•pulsates at a very rapid and precise frequency
•believed to be rotating neutron stars
•a rotating neutron star expected to emit an intense beam of radio waves in a specific direction
•since rotating, signal received comes at regular pulses
describe the distribution of galaxies in the universe
Galaxies tend to be found clustered together.
explain the red shift of light from distant galaxies
explain how the red shift of galaxies is related to the recession speed of galaxies
state Hubble’s law
•Relationship between distance of galaxy and how fast it appears to be moving away from us.
recession velocity∝distance
H₀=recession velocity/separation distance
v=H₀d
discuss the limitations of Hubble’s law
•on graph of recession speed of galaxies against distance from earth data points are scattered around best fit line which indicates there are some random errors in experiment
•since there are gravitational attraction between galaxies, speed of recession should be decreasing
•assume recession velocity is constant
explain how the Hubble constant may be dtermined
When graphing recession speed of galaxies against their distance from earth, the gradient of this line is Hubbles constant as
H₀=recessional velocity/separation distance
explain how the Hubble constant may be used to estimate the age of the universe
age of universe=separation distance/recessional velocity
→This is the same as 1/H₀
So the age of the universe=1/H₀
•But first need to convert distance into km
•calculation assumes velocity is constant (since we know gravitational attraction slows down galaxies, recession velocity much smaller than it was.
explain how the expansion of the universe made possible the formation of light nuclei and atoms
•at first no atoms as temperature was too high (photons were able to ionize atoms, preventing formation of atoms)
•as universe expanded, it cooled down until it reached a temperature of 4000K (which is equivalent to particle energy 0.4eV which is not enough to ionize hydrogen)
•electrons then started combining with protons to form atoms.
Categories: Astrophysics