Chapter 12

Question 0

Inverse square law

Answer 0

Intensity is proportional to 1/distance^2

Question 1

Time dialation equation

Answer 1

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

Question 2

Astronomical parallax

Answer 2

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

Question 3

Colour - luminosity relationship of stars

Answer 3

Using inverse square law to compare intensities of light from stars that are of equal brightness. Can get a ratio of distances

Question 4

How do we know the universe is expanding?

Answer 4

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

Question 5

Hubble constant

Answer 5

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)

Question 6

Estimating age of the universe

Answer 6

1/Hubble constant = distance/recession velocity

BUT is the Hubble constant really constant? Gravity will slow down expansion.

Question 7

Expanding universe and Doppler effect

Answer 7

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

Question 8

Evidence for universe evolving

Answer 8

• 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

Question 9

Evidence for hot Big Bang

Answer 9

Cosmic micro background radiation

Question 10

Cosmic micro background radiation

Answer 10

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

Question 11

Red shift of CMBR

Answer 11

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!!

Question 12

Problems with expansion theory

Answer 12

• 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….

Question 13

Radar ranging to measure distance

Answer 13

Send out radio pulse and measure time delay.
s=(delta)t/2 * c
REMEMBER OVER 2!!!!

Question 14

Radar ranging to measure velocity

Answer 14

Send 2 pulses, time t apart
Estimate of velocity given by
v= c(delta t2 - delta t1)/2t

Question 15

Limits of radar ranging

Answer 15

Can only do things that are close enough that return signal is visible

Question 16

Doppler effect

Answer 16

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

Question 17

Deriving Doppler shift equation

Answer 17

Change in wavelength = new wavelength - original wavelength
= (c-v)/f - c/f = -v/f
Ratio of wavelengths (change in wavelength / original wavelength) =
-v/c

Question 18

Normal one way Doppler shift equation

Answer 18

Delta(wavelength)/wavelength =(-)v/c
Valid with light provided v«c
Wavelength received/wavelength emitted = 1 + v/c
Negative for blue shifted

Question 19

2 way Doppler shift (e.g. Radar ranging)

Answer 19

Delta(wavelength)/wavelength = -2v/c

When wavelength is stretched when moving towards object and again on reflection

Question 20

Relativistic one way Doppler shift

Answer 20

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

Question 21

Relativistic 2 way Doppler shift

Answer 21

Wavelength received/wavelength emitted = (1+v/c)/(1-v/c)

Question 22

Einstein’s postulates

Answer 22

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

Question 23

Consequences of Einstein’s postulates

Answer 23

1) time is relative
2) space is relative
3) time and space are treated as separate entities: SPACETIME

Question 24

Space time diagrams

Answer 24

• 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.