[net.physics] Doppler shift and relativity

trk@byucsc.UUCP (Tom Kimpton) (08/02/84)

I've got a question that popped into my mind the other day, that maybe
one of you physics types can answer:
	Suppose you have a spaceship flying towards you at such a speed
that a red light(638nm) shining from it is blue-shifted such that
it appears blue(475nm). To figure out the speed that it would have 
to travel for this doppler shift I used the equation:

		f' = f(1-v/c)/((1-v**2/c**2)**.5)

Which transforms to:

		v = ((f**2 - f'**2)/(f**2 + f'**2))*c

Plugging in appropriate values I obtained ~8.57*10**4 km/s.

	Let us say that an astronaut on this space ship shines this light
towards us for exactly 1 second.  During this time his light emits
~4.68*10**14 wave crests ( cycles = f*t ). 

	But because of his speed he has a time contraction which is:

		t' = t((1 - v**2/c**2)**.5)

or t' = .958t or 1.044t' = t.

	Then during his 1 second of time, 1.044 seconds would have elapsed
our time. During this time ~6.57*10**14 wave crests of blue light
would have been received.  Somehow these two figures 4.68 and 6.57
don't match.  What have I done wrong, or where have I misunderstood
things?  I'd appreciate any help on this. Please reply via Mail to:

		Tom Kimpton
harpo!utah-cs!beesvax!byucsa!byucsc!trk