Chapter 12 Flashcards
Inverse square law
Intensity is proportional to 1/distance^2
Time dialation equation
t=(gamma)(tor)
Where t is the actual time (if the moving frame was still)
tor is the time I observe
Moving clocks (tor) run slow
Astronomical parallax
tan(x)=A/d
If x = 1/3600 of a degree (1 sec of an angle), d= 1 parsec = 3.09x10^16
If x is too small, can’t observe change in angle, so becomes difficult to measure really big distances accurately
Colour - luminosity relationship of stars
Using inverse square law to compare intensities of light from stars that are of equal brightness. Can get a ratio of distances
How do we know the universe is expanding?
Light from most galaxies is red shifted, implying galaxies are moving away. The further they are away, the faster the recession velocity.
v=H(o)T
Where v is recession velocity, H is the Hubble constant and t is distance
Hubble constant
recession velocity = H(o) distance
H tells is how fast universe is expanding. The bigger H is, the younger the universe is (less long to reach present size)
Estimating age of the universe
1/Hubble constant = distance/recession velocity
BUT is the Hubble constant really constant? Gravity will slow down expansion.
Expanding universe and Doppler effect
For red shifted things that are really far away, red shift can be thought of as the waves stretching as space stretches
Red shift, z = change in wavelength/wavelength
Factor of universe stretching is 1 + z
Evidence for universe evolving
- can view the universe when was 1/10 of size through red shifts
- young stars contain heavy elements whilst old stars are 9:1 H and He
- if universe was smaller and hotter, would get 9:1 H and He proportions
Evidence for hot Big Bang
Cosmic micro background radiation
Cosmic micro background radiation
At Big Bang, elementary particles interact with photons, then atoms form as universe cools, and photons stop interacting. As temp is proportional to energy of photons which is proportional to frequency, as universe stretches lowering frequency (red shift) temp falls
Red shift of CMBR
From when universe was at 3000K when atoms formed - wavelength if 1 micro metre
Now universe is 3K and radiation is 1 mm: 1000 times greater due to red shift!!
Problems with expansion theory
- dark matter: galaxies surrounded by dark matter. 10x more of this
- smooth: few fluctuations in CMBR, but need fluctuations to form clustered matter. Gravity extends fluctuations
- age: universe has to be at critical density
- dark energy: expansion is increasing with time: dark energy used to explain this….
Radar ranging to measure distance
Send out radio pulse and measure time delay.
s=(delta)t/2 * c
REMEMBER OVER 2!!!!
Radar ranging to measure velocity
Send 2 pulses, time t apart
Estimate of velocity given by
v= c(delta t2 - delta t1)/2t
Limits of radar ranging
Can only do things that are close enough that return signal is visible
Doppler effect
When a source is moving towards you with velocity v, velocity if wave relative to source is c-v. Wavelength received is (c-v)/f
Deriving Doppler shift equation
Change in wavelength = new wavelength - original wavelength
= (c-v)/f - c/f = -v/f
Ratio of wavelengths (change in wavelength / original wavelength) =
-v/c
Normal one way Doppler shift equation
Delta(wavelength)/wavelength =(-)v/c
Valid with light provided v«c
Wavelength received/wavelength emitted = 1 + v/c
Negative for blue shifted
2 way Doppler shift (e.g. Radar ranging)
Delta(wavelength)/wavelength = -2v/c
When wavelength is stretched when moving towards object and again on reflection
Relativistic one way Doppler shift
Wavelength received/wavelength emitted = (gamma)(1 + v/c)
Where gamma = 1/root(1-v^2/c^2)
When v is small, gamma = 1. As v -> c, gamma -> infinity
Relativistic 2 way Doppler shift
Wavelength received/wavelength emitted = (1+v/c)/(1-v/c)
Einstein’s postulates
1) the laws of physics are the same in all inertial reference frames
2) the speed of light is the same in all inertial reference frames
Consequences of Einstein’s postulates
1) time is relative
2) space is relative
3) time and space are treated as separate entities: SPACETIME
Space time diagrams
- time is on y axis
- distance on x axis in units x/c
- drawn from point if view of a given platform: moves up y axis
- any object at rest to platform moves up a vertical line
- lines of objects are called world lines
- moving objects have a sloping world line
- light travels at 1 light second per second, so has a 45 degree world line. Nothing can be beyond this.
