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Re: Re: Doppler effect
On 10/6 you wrote
>...I only wonder why at 8/26 you mentioned and used both parts
>of the Doppler effect while at 9/11 (to SD) you used only one
>of both parts.
On 8/26 I erroneously squared the Doppler relation to cover two
effects, not realizing then that it already covered two effects
within the one relation.
All that is needed to cover both parts (per my 9/11 writeup) is
Pr = Pe * sqrt[(1 - beta)/(1 + beta)]
= Pe * exp(-theta) .
I contend that, because we can derive Steve's result solely
from consideration of the Doppler shift, you shouldn't have to
worry about what property his analysis was based upon. Beyond
saying the above, I don't know how to address your confusion.
(Incidentally, I don't recall ever seeing the exponential
relation for the Doppler shift before.)
I think your question about "theta = a * t' " would have been
quickly resolved if you had turned to my derivation of the
"velocity-parameter equation of motion" ("VPEM") on pp 12-13 of
your copy of my paper "An Engineering Review of Relativity for
Interstellar Flight." I discussed the VPEM at some length in my
letter of 3/26 to you, and I cited this portion of my paper to
you in my letter of 4/21. (I wouldn't have expected you to have
available a copy of the book "Spacetime Physics" by Taylor and
Wheeler, where you'd find the VPEM on p 97; the book was pub-
lished in 1966 and is probably long out of print.)