Doppler effect: Motion toward or away from us distorts the pitch of sound, and it also distorts the wavelength of light. This phenomenon is known as the Doppler effect. In the case of light, the...

Doppler effect: Motion toward or away from us distorts the pitch of sound, and it also distorts the wavelength of light. This phenomenon is known as the Doppler effect. In the case of light, the distortion is measurable only for objects moving at extremely high velocities. Motion of objects toward us produces a blue shift in the spectrum, whereas motion of objects away from us produces a red shift. Quantitatively, the red shift S is the change in wavelength divided by the unshifted wavelength, and thus red shift is a pure number that has no units associated with it. Cosmologists believe that the universe is expanding and that many stellar objects are moving away from Earth at radial velocities sufficient to produce a measurable red shift. Particularly notable among these are quasars, which have a number of important properties (some of which remain poorly understood).11 Quasars are moving rapidlyaway from us and thus produce a large red shift. The radial velocity V can be calculated from the red shift S using

where c is the speed of light.

a. Most known quasars have a red shift greater than 1. What would be the radial velocity of a quasar showing a red shift of 2? Report your answer as a multiple of the speed of light.

b. Make a graph of the radial velocity (as a multiple of the speed of light) versus the red shift. Include values of the red shift from 0 to 5.

c. The quasar 3C 48 shows a red shift of 0.37. How fast is 3C 48 moving away from us?

d. Find approximately the red shift that would indicate a radial velocity of half the speed of light.

e. What is the maximum theoretical radial velocity that a quasar could achieve?