IB Physics Topic Option E Astrophysics

Define a planet.

•Celestial body that orbits around the sun

•has sufficient mass for its self gravity

•has cleared the neighborhood around its orbit

Define astroids.

Between orbits of Mars and Jupiter, smaller orbiting bodies

Define comets.

•small orbiting body

•loose particles of ice and rock that are blown off by the solar wind forming a tail

Outline the general structure of the solar system.

ORDER OF PLANETS:Mass Radius

Mercury 1 1

Venus 3 3

Earth 4 4

Mars 2 2

Jupiter 8 8

Saturn 7 7

Uranus 5 6

Neptune 6 5

Distinguish between a 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 a star.

white dwarf, red giant, supernova. Massive balls of plasma.

Define astronomical unit AU

1AU = 1.5x10¹¹ m

Define the light year

Distance light travels in a year 1 light year = 9.46x10¹⁵

Define parsec.

1parsec= 3.26 ly

distance at which 1AU subtends an angle of 1 arc sec

p=distance of earth from sun/distance of star from sun

Compare the 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/constellations over a period of a night and over a period of a year, and explain these observations in terms of the rotation and revolution 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 that fusion is the main energy source of stars.

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 that, in a stable star (for

example, our Sun), there is an

equilibrium between radiation

pressure and gravitational pressure.

•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.

Define the luminosity of a star.

Amount of energy radiated by the star per second (sun has luminosity of 3.8x10²⁶W)

Define apparent brightness and state 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)

Apply the Stefan-Boltzmann law to compare the luminosities of different stars.

L=σAT4.

A=4πr²

The Stefan-Boltzmann constant: σ = 5.67 x 10⁻⁸Wm⁻²K⁻⁴ (given)

State Wien's (displacement) law and apply it to explain the connection between the colour and temperature 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 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)

Describe the 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

Describe the different types of star.

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.

Describe the different types of 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 a Hertzsprung-Russell (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.

SEE NOTES FOR 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 method 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

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)

Solve problems involving apparent magnitude, absolute magnitude and distance.

b₁/b₀ =1/2.512^(m₁ )

b₁/b₂ =[2.512^(-m₁ )]/[2.512^(-m₂)]

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 that the method of

spectroscopic parallax is limited to measuring stellar distances less than about 10 Mpc.

as stellar distances increase, the uncertainty in luminosity becomes greater and so the uncertainty in distance is creater

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.

SEE NOTES FOR DIAGRAMS

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

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 Newton's 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.

Explain Olbers' paradox

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.

3) The radiation received is redshifted and so contains less energy.

Relationship between number in shell and intensity of light.

As number of stars in shell increases by R², intensity decreases by 1/R²

Suggest that the red-shift of light from galaxies indicates that 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 as 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.

•CMB radiation same in all directions, characteristic of black body radiation

SEE NOTES FOR BLACK BODY RADIATION CURVE

Explain how cosmic radiation 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 resolution to Olbers' 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.

Distinguish between the terms open, flat and closed when used to describe the development of the universe.

OPEN: keeps expanding

FLAT: the rate of expansion tends to zero at infinite time

CLOSED: stops expanding and starts to contract

Define the term critical density by reference to a flat model of the development of the universe.

•The density at which the closed universe becomes open.

•It is very unlikely that this is the way the universe is, since just one extra electron would make it contract.

•density of universe for which expansion rate slow to zero but never rest (produce flat universe)

•less that ρc universe expand for evermore

•greater than ρc universe expand then contract (closed)

Discuss how the density of the

universe determines the development of the universe.

Whether the universe will expand forever or close back on itself is determined by the comparison of these values.

Discuss problems associated with determining the density of the universe.

•Density measured by measuring the mass of all the stars in a given volume.

•If all the stars and gas clouds in a galaxy were measured the total mass is not big enough to give the gravitational attraction to hold it together (its only 4%) the rest is called dark matter.

DARK MATTER:

MACHOS: massive astronomical compact halo objects

WIMPS: weakly interacting massive particles

State that current scientific evidence suggests that the universe is open.

There is a red shift in energy absorbed from different galaxies (moving away without signs of stopping)

Evaluate arguments related to

investing significant resources into researching the nature of the universe.

ARGUMENTS FOR:

•understanding the nature of the universe sheds light on fundamental philosophical questions

•one of most fundamental, interesting and important area for mankind

•gives rise to technology that may eventually improve quality of life

•travel to new planets if life on earth becomes impossible

ARGUMENTS AGAINST:

•money could be spend on more useful earth bound needs

•money better spent on other areas of research such as medical

•better to fund less expensive projects

•is information really worth the cost

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

Apply the mass-luminosity relation.

•relationship between luminosity and mass of main sequence star

L∝m^n where 3

Explain how the Chandrasekhar and Oppenheimer-Volkoff limits are used to predict the fate of stars of different masses.

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 star

Fate of a small star.

•up to 4 solar masses

•once used up all helium, core continues to contract, radiating energy as it shrinks

•reaches electron degeneracy

•radiation from core blows away outer layers of star, exposing core

•this cools, becoming WHITE DWARF

Fate of a big star (bigger than 4M⦿)

•core pressure and temperature great enough for carbon fusion

•eventually fuse to form iron which forms central core

•fusion stops (highest binding energy) and core compresses until electron degeneracy prevents further contraction

•reaches point where it contains only neutrons packed closely to the nucleus

•outer layers rush in, bouncing off core, flying back out producing an explosion

•becomes supernova

•all that remains is neutron core (neutron star)

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 an HR diagram.

SEE BOOK FOR DIAGRAM

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.

Describe a galactic cluster.

Collection of galaxies drawn together by mutual gravitational attraction

Describe a galactic supercluster.

Typically seen as long and thin strands of clusters and galaxies intra cluster gases and "dark matter"

Explain the red-shift of light from distant galaxies.

•red shift implies receding

•found light from all galaxies are red shift

•furthest galaxies shifted more than close ones (implies universe is expanding)

• astronomers know that dark energy is causing our universe to expand at an accelerating rate

Solve problems involving red-shift and the recession speed of galaxies.

Δλ/λ≅v/c (given)

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 determined.

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.