Chapter 20 Cosmology Flashcards
Why are the three astronomical units of distance in increasing orders
Define the AU and the light year
1) the AU
- this is the average distance from centre of earth to centre of sun
2) Light year
- distance light can travel in one year (in a vacuum)
3) parsec
Before defining the parsec must define small units of angle
What is the arc minute and ar second
SO HOW MANY ARCSECONDS IN A DEGREE
There are 60 arc minute in 1° and 60 arc seconds in 1 arc minute
Therefore in 1 ° = 3600 arc seconds
1 arc second = 1°/3600
So what is a parsec definition
The distance made when a radius of 1 Au subtended an angle 1 arc second
So basically triangle with AU opposite, 1 parsec adjacent and theta being 1 arc second
The parsec forms 90° with the sun and the earth au
How ti find exact distance of parsec
If angle is 1 arc second, tan arc sec = 1AU/ 1 Parsec
Rearrange to find distance
What can we say about the angle subtended if the distance away from the sun increases in parsecs
As tan theta = theta when theta is SMALL
A distance of 1 parsec gives the formula tan (1 arcsecond) = 1AU/ 1 parsec
- thus 1 arcsecond = 1 au / 1 parsec using small angle
So if we increase 1 parsec to 2, the equation corrects when the angle is now 1/2 arcsecond etc
So the relationship is theta is inversely propritnsk to distance in parsecs
So in summary, What is relationship using small angle approx again for angle subtended and distance In parsecs
!!!
Theta in arcsecond = 1/d in parsec
What is the technique stellar parallax used for ( short answer)
Used to determine the DISTANCE of stars relatively close to the earth
What does the parallax part in the stellar parallax mean?
Why do the background stars not apparently shift ?
Parallax is the APPARENT shift in the position of a star when compared to BACKGROUND STARS, as the earth ORBITS THE Sun
This is because the background stars further back are through to be constant
So explain how we can use stellar parallax to work distance
Well, when earth at summer, looking at nearby star agsisnt backdrop will postion it somewhere
- 6 month later when earth is in anti part of the orbit in winter, looking at same star against backdrop will place it somewhere else against the fixed backdrop
(This is just an illusion)
- using clear measurements, the PARALLAX ANGLE can be determined . Once we have this, we use precious formula of angle =1/d to d = 1/angle to find distance in parsecs star is from the SUN
What is parallax angle then?
This is the angle that the planet subtends 1 AU from the sun , with a specific distance away from the sun which is in PARSECS
Finally summarise the equations for parallax, what’s all we need to find the distance it is away from sun
Just parallax angle, then do d = 1/p for distance in parsecs it is from the sun
Why can’t parallax be used for far stars?
Apparent shift isn’t so apparent anymore as the further away you look the less it shifts
What is the basic idea of the Doppler effect with sound waves and an ambulance AMBULANCE COMING TOWARDS YOU
Basically, when someone in an ambulance and moves, hears constsnt frequency
But when the ambulance moves TOWARDS a stationary observer, as the source emits waves, it CATCHES UP TO THESE WAVES BASED ON ITS SPEED, and so by the time these waves reach observer, he’s hearing MORE waves per second than he should, and so waves are MORE COMPRESSED, and more waves per second = frequency INCREASES.
- thus as observed comes close to you, frequency appears to shift HIGHER, and so neeeee pitch is heard
What about Doppler effect when ambulance passes you and moves AWAY?
As it moves away, it moves AWAY from waves produced, so the distance between waves coming to you INCREASED, wavelength increases, and as less waves reaching you per second, frequency decreases
So lower pitch heard as it moves away from you
What’s a good summary definition of the Doppler effec then
The apparent shift in OBSERVED frequency/ wavelength CAUSED BY the relative motion between a source and an observer
Is Doppler effect only for sound?
No, all wave related
Okay so how does Doppler effect work for LIGHT COMING FROM STARS?
If we look at the ABSORBTION SPECTRA of an element found in earth, and in a star, then if the position of the absorption lines are different, then it MUST BE DUE TO THE RELATIVE MOTION BETWEEN STAR AND EARTH
So if all the lines have moved towards one end of spectrum or other, we can tell if the star is thus moving closer or AWAY FROM US
Okay so what way are all the spectrum lines shifted if it’s moving away or towards us?
The star moving away from us, (assuming we are stationary) that means light we see will be of longer wavelength DUE to Doppler effect and the relative motion between the star and the earth , and so towards red spectrum thus RED SHIFT,
If light we see is towards blue spectrum, then IT MEANS MOVING TOWARDS US, light we see is of higher frequencies due to Doppler effect, and so star is moving towards us = BLUE SHIFT
What is the DOPPLER SHIFT FULL EQUATION
change in f/ f = change in wl/ WL = V/C
Where change in F and WL is the mod of actual wavelength and observer wavelength
And V is the RELATIVE VELOCITY between the star and the earth or whatever
c is the speed of light
Why does the shifted frequency and wavelength of a galaxy still give speed of light
Thus if you found the shifted f, how can easily find shifted wavelength without using Doppler equation
As shifting f up shifts wl down, the ratio is the same
So if you found one, YOU CAN USE THE SPEED OF LIGHT TO FIND SHIFTED OTHER
So why does sprinting towards a camera not make me more bluer
But velocity towards a microphone DOES CAUSE A CHANGE IN PITCH
As The apparent shift is DEPENDENT ON the ratio between the RELATIVE VELOCITY AND SPEED OF LIGHT, if I run 20 ms1 that’s nothing compared to speed of light. Shift happens, but not noticeable
2)HOWEVER as with sound as it’s over 340, there is a noticeable shift of like 10% which we pick up!
Why does Doppler effect equation show that there is a GREATER absolute shift for things going at HIGHER VELOCITIES
As the shift dependent on ratio, higher ratio = higher shift
IMPORTANT
Why will the ABSOLUTE SHIFTS of each spectral line for same element NOT BE THE SAME
2) BUT what about each shift IS THE SAME and why
3) so if you’re given a spectra from a star, how can you go about trying to identity each element step by step
When the Doppler shift happens, scale is in WAVLENGTH
- if we check the equation, a higher ORIGINAL wavelength = results in a higher Doppler shift
- thus as the spectral lines will be of different wavelength, they will all shift by a DIFFERENT AMOUNT.
Here the higher wavelengths shift more, and lower less
2) HOWEVER. As the amount they shift each time is a constant = V/C
The PERCENTAGE SHIFT must be the same EACH TIME
For example, the ratio v/c = 2
So 10 m will become 20, but 30 will become 60
THUS THE ABSOLUTE SHIFTS ARE DIFFERENT, but percentage shift is the same each time!
3)
there will probably have to be some guessing of the elements first, and then see if they MATCH THE TREND . So if I have absorbtion soec of a star, then think could it be hydrogen, if it is hydrogen what is the Doppler shift, if thr doppler shift moves the other spectral (original hydrogen ) lines by the same amount , then it is hydrogen. Now you know the Doppler shift for sure , move all the rest back by same Doppler shift and compare to find the other elements
MISCONCEPTION
the further away a galaxy is does that mean it will red shift greater simply because it’s further away?
(Only talking about distance here because that’s what you assumed)
NO
Distance has no effect on Doppler shift, only RELATIVE VELOCITY
Distance just affects how far ago the light came from
What were 2 CONCLUSIONS Hubble made when investigating Doppler shift with star
1) in general most stars and galaxies were red shifted
= this Indicates most galaxies etc are MOVING AWAY FROM US
2) that FURTHER AWAY GALAXIES were often RED SHIFTED MORE THAN NEARBY
- this indicates that further away galaxies have GREATER realtive velocity due to being more red shifted. This means they’re moving away from us FASTER
(Nothing to do with distance, it just is)
If further away stars are red shift more meaning they trialing away faster than the stars close by, what does this suggest about the motion of expansion of universe?
It’s expanding at an ACCELERATING RATE
After finding different recessional velocities using Doppler shift for different distances of objects form earth, what was the relationship Hubble made?
Suggested that the recessional velocity is proprtinal to the distance away from earth
V PROP TO D
V = KD
AS a result this constsnt became HUBBLES CONSTANT
HUBBLES law using a graph
Plot recessional v against d from earth , and the GRADIENT (best fit) will be = to the HUBBLES constant
Make sure to keep units proper, can be Km parsec
What is the assumption that is the COSMOLOGICAL PRINCIPLE (3 points)!
(Why is having same laws assumption mean making predictions could be horrible off)
1) that the laws of physics can be applied across the whole universe (same laws apply here on earth everywhere)
2) universe is homogenous
3) universe is isotopic
- can never be certain that same laws of physics in other part of universe, so everything with Hubble etc are just assumptions
What does universe being homogenous mean?
That matter AND DENSITY is uniformly distributed across the universe, thus for a large volume similar structures are seen everywhere
So galaxies, rocks etc. = OUR PART IS NOTHING SPECIAL basically
What does universe being ISOTROPIC MEAN
Isotopic just means that for any observer the universe looks the same in all directions
Basically no edges, no centre
What does cosmological principle summarised mean
Everywhere e you go it looks and acts the same
(Same laws apply everywhere + isotopic (looks the same everywhere)+ homogenous (uniform density and structures seen everywhere) )
What is the action of the expansion of universe, are the galaxies the thing that are only moving?
NO the entire space time fabric , space between it is expanding , and the galaxies are being CARRIED BY THE space time instead of moving
Why does Hubble assumption breakdown for
1) galaxies close to us
2) galaxies too far from us
1) galaxies and stuff close to us are low-key being blue shifted as the grvatiaonl pull of galaxies interact with each other , thus it doesn’t follow
2) too far away have been accelerated TOO MUCH, and so they don’t follow the correlation as they have ‘escwped’
Before move on
If a Doppler effect spectral line is examined and a BLUE AND RED SHIFT has occurred at the same time, what system does this suggest and why
Suggests a BINARY STAR SYSTEM. This is where two stars same type orbit around a common centre
Here as they orbit at fastest points, one is COMING TOWARDS EARTH in the orbit and one going away. Thus as the speed is the same the shifts are the same, but it’s one red and the other blue!
What are the two pieces of evidence for Big Bang
1) HUBBLES law
2) cosmic microwave background radiation
Why does HUBBLES law support the Big Bang
But why on its own is it no enough to give enough evidence?
HUBBLES law suggest that due ti red shifts of most galaxies universe is expanding, and that too at an accelerating rate
So if we go back in time, it means the whole universe started from a smaller, denser and hotter SINGLE POINT
This single point is thought to be the point where Big Bang happened
2)HOWEVER the expansion of universe could be explained by other theories, so by itself it wasn’t enough…
Part 1
How did Big Bang theory predict CBMR and why is it microwaves now
Big Bang theory predicted it
- originally when university young dense hot etc it was saturated with high energy gamma photons
- as whole universe expanded , thr wavlenetgh of these STRETCHED over time going through every end of EM SPECTRUM
- at the current state, it’s now MICROWAVES
These microwaves found in the background of universe by physicists by accident.
Part 2
How does the temp of universe link with idea of CMBR using wiens law
As temp of universe is currently 2.7k , how does this link
IMPORTANT
Iringally universe hot, but as expansion energy dispersed and it’s become colder
If you model universe as black body radiation, then based on temo it will emit a peak wavelength
- as temp is 2.7K, this temp emits would be in microwave region, which it DOES
2) basicallt as universe got colder, it follows wiens law
How can we estimate age of the universe?
1) what assumption
2) so using s=d/t , how do you do it
3) why is assumption bad
1) if we assume the universe expanded at a constant velocity (which we know ti doesn’t)
(This is what HUBBLES law shows to prove, that the expansion of universe was at a constsnt accelrwtion, therefore the graph looks straight . In reality graoh would be curved upwards
2) then time taken = D/V
- as you can see this ratio is roughly = 1/H0
THEREFORE TIME = 1/H0 in s
3) assumption bad because we lit prove through Hubble universe not expanding at constsnt rate
What is the Big Bang theory summarised
The idea that everything was concentrated into an infinitely dense and small singularly, which expanded and created space time and everything we have
Evolution of universe
2 main details
1) at start it expands rapidly and cools down as expands
2) first fundamental particles gain mass through unknown higgs boson
3) then protons neutrons made
4) ince temp is low, the mass stop being made. This happened in 1S!!!
5) BY 380000 years, cool down enough so that atoms can form, as electrons are captiered by nuclei
Main details
All the mass is made in 1s as cool enough, first fundamental then hadrons . They gian mass by higgs boson
By 380k years atoms start to form due to it being cold enough. At this point, the background rsdisiton is MICROWAVES because of temp
What is dark energy and what is it an explanation for
Who much is universe made up of
MISCONCEPTION DONT LACKKKKK
STUDIES SHOWED UNIVERSE IS EXPANDING AT AN ACCELERATING RATE
- this accelrwtion for the expansion of the universe is explained as propelled by dark energy
(not only is the expansion of universe accelerating speed, but the rate of expansion is accelerating too)
this is in all of space and makes up 68% of universe, not much known about it
When analysing a galaxy, how can Doppler effect allow us to see that different part of galaxies travelling at different speeds?
This is because say with rotation if a galaxy, you’ll see that the end rotating away from us show a more red shift then edge rotating closer to us, same for the stars
What was the original idea for how stars move in relation to the whole galaxy as distance from centre increases?
WHY?
Why do we think most of the mass is at centre and thus this effect seen everhwrre?
Oringally through that stars move slower as the distance from the centre of the galaxy increases
This is because most of the MASS is concentrated in the centre of the galaxy
2) we thing most of mass is at the centre bevause that’s what it is for our galaxy and others, and so in others the SAME EFFECT IF VELOCITY IF STARS decreasing from centre is also observed
So what is actually seen as distance from galaxy increases?
And what’s the expiation
Actually seen is the velocity DOESNT REALLT DECREASE from centre, it stays the same
2) the only way to explain this is that there is MORE MASS we are not accounting for which allows for the speeds to be higher e
This is dark matter
So what is dark matter
1PROPERTIES
(Why not any other properties?
Is though ti be matter concentrated at the extremities if galaxies that interacts with GRAVIY but that’s it, nothing else
2) no other properties bevause we don’t see it emit light etc interact with matter so it’s not anti …
What is dark matter
2) where is it in a galaxy and how does it explain the fact further away stars can move at similar velocities
Matter must be at the extremes of galaxies ti allow it to gravitate the extreme stars
With this matter, it explains why stars away from the centr if galaxy are able to rotate and move at similar speeds to those near the centre of the galaxy where most of the mass is supposed to be concentrated.
Graph for predicted vs actual velocity of stars with distance away from centre
Predicted = goes up and then down
Actual goes up and stays up
How can we use Doppler shift to calculate speed of rotation for galaxies
Might not have to know
Further away part rotating away from us gonna show higher red shift, compared to part rotating towards us
Difference in this = rotation speed?
Probably not needed but
If given spectra of stars, how to find red shift and thus all elements
1) finding the red shift
2) once found red shift what ti do?
3) final comparison to find elements
You’ll need something to compare it to, and for this you have ti guess
Assume it has hydorgen, and find the red shift for the first line
- now check if this red shift causes the same PERCENTAGE SHIFT for the other spectral lines of the hydorgen
- if it does, correct shift, if it doesn’t, need to try again with helium or something
- once you found red shift, apply the reverse shift to EVERY SPECTRAL LINE
- and thud will give you all the lines how it looks ON EARTH
From this point, you can match the elements to absorption spectra produced by the elements on earth and identify the elemtnd !
Why is the CMBR microwaves ? What’s explanation
This is because origannly universe was dense with higher energy photons, but as the universe expanded and cooled the photons redshifted all the way to microwaves which is what we see now
