12 OUR PLACE IN THE UNIVERSE The parallax method Review knowledge and understanding of cosmology Learn how to use the parallax method to determine distances to stars Appreciate its limitations

The distance-brightness method Explain why observed stellar intensity follows an inverse-square law Explain how Cepheid variable stars can be used to determine absolute/intrinsic brightness (luminosity) Use the relation between apparent brightness and luminosity to determine distances to stars

The Doppler effect Explain the pulse-echo method of radar ranging of near-Earth objects, appreciating its limitations Explain the origin of the Doppler effect, and how it may be used when analysing spectra of astronomical objects to determine velocities

Special relativity Describe experimental evidence for the constancy of the speed of light in all reference frames State the Einstein postulates Use space-time diagrams to derive the relativistic Doppler relations

Special relativity Describe experimental evidence for the constancy of the speed of light in all reference frames State the Einstein postulates Use space-time diagrams to derive the relativistic Doppler relations

Postulate 1: Physical behaviour cannot depend on any ‘absolute velocity’. Physical laws must take the same form for all observers, no matter what their state of uniform motion in a straight line. Postulate 2: The speed of light c is a universal constant. It has the same value, regardless of the motion of the platform from which it is observed. In effect, the translation between distance and time units is the same for everybody. Einstein’s postulates

If the Earth was travelling in the direction of the beam the travel time for the light would change By slowly rotating the apparatus they ensured that the beams at some point would point along/across the Earth’s direction of travel. The fringes were expected to change as the apparatus turned They stayed put – either the Earth wasn’t moving in space or light wasn’t affected by the movement Michelson-Morley experiment

What are the limitations of this method? Reminder

Space time diagrams

Two-way radar speed measurement

Space time diagrams Construct a space-time diagram for the following situation. A spacecraft, initially 4 light-seconds distant from the Earth, travels towards the Earth at a speed 0.5c. After 1 second, a radar pulse from the Earth is sent out towards the spacecraft. Use the space-time diagram to determine: (a) At what time and where the radar pulse hits the spacecraft, (b) At what time the reflected radar pulse is received back on Earth, (c) Where the spacecraft is located when the reflected pulse is received back on Earth, (d) At what time the spacecraft reaches Earth.

Time dilation

Use the concept of the light clock to explain time dilation Resolve the Twins Paradox Use experimental data on muon lifetimes to illustrate time dilation effects

Twins Paradox

Time dilation The half life of a sub-atomic particle in the laboratory rest frame is 1 microsecond. Q1. What fraction of these particles would be expected to survive to a detector located 6 km away from the experiment? Assume the particles are travelling effectively at 3 x 10 8 ms -1. In fact, 25 % of the particles produced in the experiment survive out to the detector located at 6 km from the experiment. Q2. Use this information to calculate the relativistic factor γ (gamma) for the sub-atomic particle. Q3. At what speed are they actually travelling?

The expanding Universe Review evidence for expansion Use Hubble’s law to estimate an age for the Universe Explain the origin of red shifts > 1 in terms of relativistic Doppler effect and the expansion of space itself

The expanding Universe Review evidence for expansion Use Hubble’s law to estimate an age for the Universe Explain the origin of red shifts > 1 in terms of relativistic Doppler effect and the expansion of space itself

Hubble’s Law Recession velocity = constant x distance v = H 0 r

The bigger the Hubble constant the faster the universe expands, and the younger it must be to have got to its present size. Hubble constant – time scale for the universe This time is its reciprocal – the Hubble time: t = 1/H 0

Optical telescopes can see out to about 1000 million light-years, What red shift does this correspond to? (by Hubble’s Law) Radio and infrared telescopes can detect red-shifts (z =  / ) up to 3 or 4 At large distances, the red shift is best thought of not as a velocity of recession, but simply as the waves stretching as the space stretches z = 3-4, (with z =v/c) would imply a recession velocity of more than c.

List the difficulties associated with measuring the distance to the furthest and faintest galaxies

The history of the Universe Explain the origin of the cosmic microwave background Review evidence for the generally accepted model of the history of the Universe Appreciate that there are many unsolved problems in cosmology

R observed /R emitted = observed / emitted R observed /R emitted = ( observed +  / emitted R observed /R emitted =  z