2.  You will know the Doppler effect as the falling note of a car or train horn as it approaches, passes, and then goes away from you.

3.  The importance of the Doppler effect is that it is seen with light waves and radio waves.

4.  For any object that is moving with a speed much less than that of light, it can be shown that the change in frequency is given by:  ∆f - change in frequency (Hz)  f - original frequency (Hz)  v - speed of object (m/s)  c - speed of light (m/s)

5.  The equation in terms of wavelength is:  ∆λ - change in wavelength (m)  λ - original wavelength (m)  v - speed of object (m/s)  c - speed of light (m/s)

6.  Objects moving towards the observer have a positive speed; moving away from the observer the speed is negative.  If the object is moving away, the frequency is lower so that ∆f is negative. The wavelength will be longer.  If the object is coming towards the observer, the frequency is higher, so ∆f will be positive. The wavelength will be shorter.

7.  The minus sign tells us that the star is receding from us. The longer wavelength is called red shift, i.e. it has been shifted towards the red end of the spectrum. This is shown below:

8.  In 1929, along with Milton Humason discovered a rough proportionality of the objects' distances with their redshifts.   the universe is, in fact, expanding.

9.  A relationship between the velocity of recession of a galaxy and its distance from the Earth.

10.  The equation from this graph is:  v is the recession velocity (km s -1 ),  d is the distance to the galaxy (Mpc).  H 0 is called Hubble's Constant (km s -1 Mpc -1 )  Currently accepted value = 65 km s -1 Mpc -1.

11.  If we were to plot a graph of recession speed against distance from Earth, we would get a graph like this one.  The gradient of which is H 0, the Hubble constant, 70 km s -1 Mpc -1 = 2.3 x 10 -18 s -1  This value is one that we are trying to gain more accuracy as we develop the technology to look deeper into space and determine recessional velocities.

12.  This also means that every point in the Universe is receding from every other point, therefore the Universe is expanding.  Since the speed of light caps the speed of recession of a galaxy, it means that the Universe is infinite in size, which then resolves Olbers’ paradox.