Chapter20 Flashcards
Why do we use different units of measurement for cosmology?
Bevause the distances are so far using it in standard form is pointless, and hard to compare
So what are the three distances?
1) the AU
- average distance from earth tk the sun
2) light hear
- distance covered by speed of light in one earth year
3) the PARSEC
Before defining the parsec, we must define the angles arcsecond and arc minutes!
In 1° there is 60 arc minutes
In 1 arc minute there is 60 arc seconds
Thus in 1\3600 degrees = 1 arc second
We use these as the angles measured are sooo small
So whats the definition of a parsec?
A parsec is the distance at which an angle of 1 arcsecond subtends a distance ( radius) 1 AU
This forms a triangle , with oppsite being AU, adjacent being parsec and angle being 1 arc second
As arcsecond is so small, what expression can we make
Therefore what can we say for the angles needed to subtend 1 AU at DIFFERENT parsecs?
Use small angle approximation
Therefore tan 1m arcsecond = roughly 1 AU/ 1 Parsec
So if we double distance away (from sun), and stil, want to subtended 1 AU, the only way this works is if the angle becomes 1/2 too (1/2 = 1/2)
Therefore theta is inversely proprtinsl to distance in parsecs! As an approximation
So what’s the formula relating theta and parsec distance ti subtend a radius of 1 au , and how
Theta inversely prop to parsec distance
Due to small angle approx. Derived from definition of parsec …
What is the stellar parallax technique used ti find?
What is stellar parallax
The distances of relatively close stars to earth , less than 100 pc
It is the APPARENT shift in positon kf a star against a FAR AWAY BACKDROP when observed fro, different places in the earths orbit
Explain how the stellar parallax works
So when we are in postion A, looking at a star we see it in a specific place relative to the backdrop
Come back to this on its OPPSITE point of orbit, we saw the star shifted to a new place relative to its back drop
In reality the star hadn’t moved at all, it’s just an illusion due ti the ANGLE WE SEE IT AT
This angle is the PARALLAX ANGLE
As the distance is always 1 AU from the sun from both OPPSITE points of orbit, if thr angle is in arc seconds then we know the distance to the sun measured in par secs is = 1 / angle !
So if we know thr paralled angle, we can roughly work out how far away
Why is the stellar parallax only used for stars less than 100pc away? Why not any more
Because the father awya you go, the less the stellar parallax is , and thus the harder it is to calculate the parallax angle
In fact it becomes impossible with current level of resolution of equipmemt on earth so far , thus we can’t
Stellar parallax summary
Used to find the distance of a nearby star to thr sun using the illusion of the apparent shift in postion of the star relative to a fixed background drop
Take two points of oppsite orbit on the earth and see the parallax angle. As the distance being subtended by this angle is 1 AU, we can use d = 1/p to find how far it is
But must be in parsecs and arcsecond, don’t lack
Parallax angle definition
This is the angle which subtends a raidus 1 au ar a certain distance away in parsecs from the sun
What is the Doppler effect
The apparent shifts in frequency / wavelength due to the relative motion between the object and the observer
Where the change in freuwney is prop to the velocity of thr object
Explain Doppler shift
As something moves further away, due to the wavelengths being more spread out from each other, the apparent wavkefnth observed at the observer is much bigger than what it was before, thus frewuency less too
As something moves closer to you, the wbakengghd catch up with each other, making the apparent wbskenght less and thus the freuwneyc increase
This effect is observed for any wave, so light as well as sound
In the context of planets?
If a planet is moving awya from us, the frequencies will be less, as a result all th spectral lines for absorption will be shifted to the red side = red shift
If comes to us then blue shift
As most of them are red shift, we can conclude in general u inverse is expanding
If you found the shifted frequency of one, how to find the shifted wl bery esislyl
Use speed of light
When doing Doppler shift for sound, or ultrasound or whatever what is the equation changed
Need to use speed of thing, so sound, ultrasound etc
That’d why when I run fast as I can I don’t become red, I do but very slightly because of speed of light fsctor
But when sound moved away we do hear it become low frequency because the speed of the object is comparable to the speed of sound .
IMPORTSNT POINT
Why within a spectral line, will the indicual lines not be the EXACT same shift?
What is the same ?
As the equation shows the change in wavelength is prop to wavlength and speed
If speed is the same fro each wavelength, then the change is only proprtinsl to its CURRENT WAVELENGTH
Therefore the absolute shifts are different but percentage is the same, with ratio v/c constsnt!
Thus if something red shifts, the red ones will red shift THE MOST and the blue ones thr lesdt
But in this case the PERCENAGGE SHIFT is the same for each one, as it must be
This is why you can’t straight compare the distances first, need to reverse the shift and then compare
If further away stars have a more red shift, what does this mean fully
This means Fully that rhe stars are travelling faster (not to do with further away) as change in wavelength is proptinal to speed
As a result, if the further away stars are travelling faster than closer ones
- this means universe expanding at an ACCELERATING RATE
What were the conclusions bubble made
1) that light coming from most GALAXIES (nit stars because too close ) confirmed were red shifted
2) that the further away thr galaxy was, the MORE red shifted (and thus faster speed ) it was travelling at
