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A2 Unit G494

Chapter 12 - Our Place in the Universe

Content

Description

Drawing Minkowski diagrams This task guides you through drawing a minkowski (space-time) diagram.

Minkowski Problems This task (powerpoint presentation) requires you to plot minkowski diagrams in order to find the distance and velocity of some nearby objects.
Parallax measurements There are lots of units used to measure astronomical distances.  Your teacher will explain about measuring distances in light seconds, light years, and parallax seconds.  When you are happy you understand try the questions on this sheet.

Standard Candles Look at this powerpoint presentation which explains about some of the methods we can use to measure the distance to distant galaxies using "standard candles".

Comparing the brightness of lamps Lamps of different brightness can appear the same brightness if they are at different distances - rather like our "standard candles".  Answer these questions to develop your understanding of how to calculate the apparent brightness of lamps at different distances.  You should see how this is analogous to our "standard candles", such as Cepheid variable stars and type 1a supernovae.

Brighter stars are not always nearer... This exercise looks at how the luminosity and brightness of stars are related, by comparing the amount of light they emit and their apparent brightness.
Doppler shift - demonstrations Listen to the sound from this "whirly-tube".  What causes the apparent variation in pitch?  Note that the person swinging it hears a constant tone!

You may also want to watch this short video, which shows the doppler shift of a car horn for a moving vehicle:

   

Doppler shift II - Applets These applets will help to clarify what is happening to cause the change in the pitch.  This yenka applet shows the effect brilliantly, but note that you will need the yenka plug-in installed (see DP).

Otherwise, this applet ilustrates the principle reasonably well, or this one by Walter Fendt.

Redshift I - what is a spectral line? Light from distant galaxies undergoes a doppler shift.  To understand this properly, we will need to remind ourselves about the absorption lines observed in the solar spectrum.

This powerpoint presentation has some useful images to help you understand the significance of these spectral lines.

If you need a reminder of why the spectral lines appear at these specific wavelengths, then this simulation will help!

Teacher note: can be useful to demo the K and H lines for calcium, using the CLEA software.

Redshift - quantifying redshift Your teacher will explain how to calculate the redshift "Z" of a wave, and how this quantity is related to velocity.  When you are happy you understand, try these questions (Q55S).
Hubble investigation software The CLEA "red shift" software allows you to collect data for a wide range of galaxies, by measuring the apparent magnitude, and the red shift of the K and H calcium absorption lines.  Record your results in this spreadsheet.

The approximate distance to the galaxy can be deduced from the apparent magnitude, and recession velocity can be calculated from the red shift measurements.  Your teacher will explain how to do these calculations.  When you have collected the data, plot a graph of recession velocity (km/sec) against distance (Mpc) and find the gradient.

Teacher note: you will need to install the software on your computer (install file here - hublab.exe).  It should already be available on the pupil's computers.Pupils use the spreadsheet provided.  There is a copy pre-filled with some basic data and with the graph already plotted here.  Visit the CLEA homepage here for more awesome software!

Modelling a one dimensional expanding universe... Class activity - model expansion of the universe using a long piece of elastic (approx 4-5m), with a number of galaxies placed along it (sticky labels or post-it notes - 5 works well).  Measure positions of galaxies, then expand universe (student runs to other end of room!).  Measure time taken for expansion.  Consider distance each galaxy has receded from our galaxy (nominate any one of your choice!).  Find apparent velocity of each galaxy.  Find hubbles constant for elastic universe!

Repeat for an observer in any other galaxy.  Consider 1/Ho as approximation for age of universe.

There is a worksheet here in word format.  Should ideally be enlarged to A3 size.

Redshift of Quasars Try these questions  (Q95S), which look at the red-shifts observed for "Quasi Stellar Radio Sources" (usually abbreviated to QSR or "quasar"), and the associated scale of the universe.
Cosmic Microwave Background Radiation Cosmic Microwave Background Radiation can be seen all around us, and is in fact extremely red-shifted radiation from the early stages of the formation of the universe.  There is a powerpoint with a few useful slides here.

[Insert link to "COBE" images, insert link to formation of atoms "transparent universe", images on page 88 of text book useful].

Answer these questions (Q100S).

   

 

 

 

Relativity

Simulation

Description

The Michelson-Morley Experiment This little applet shows the famous experiment which disproved the concept of an "aether", and hence the constancy of the speed of light.
The Light Clock This little applet illustrates why time dilation is a necessary consequence of the constancy of the speed of light.
The The Light Clock (questions) This question sheet demonstrates a derivation of Einstein's famous relativity equation by analysis of the light clock
The Twins Paradox

 

Wikipedia Article and Hyperphysics Article about Einstein's famous thought paradox, arising from the application of ideas about time dilation from the theory of Special Relativity.  The paradox expands upon these ideas illustrating the need for the theory of General Relativity.
The relativistic time dilation equation These questions will give you some practice with the relativistic time dilation equation
Time dilation for muons These questions look at an interesting phenomenon related to the numbers of muons observed at the surface of the earth, due to relativistic effects.