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*To*: stevev@efn.org*Subject*: (Re:)^3 Doppler effect*From*: DotarSojat@aol.com*Date*: Tue, 8 Oct 1996 18:11:16 -0400*cc*: T.L.G.vanderLinden@student.utwente.nl

Hi Steve I'm glad to hear that a second edition of "Spacetime Physics" has been published; I'll try to find a copy. All I have of the 1966 edition are Xerox copies of some pages that I found inter- esting in 1989. To quote selectively my Xeroxed page 97: "Exercise 51. Clock paradox III ... "(b) How much velocity does the spaceship have after a given time? (question in italics) This is the moment to object to the question and rephrase it. Velocity [beta] (the original has the greek letter) is not the simple quantity to analyze. The simple quantity is the velocity parameter [theta]. It is simple because it is additive in this sense: Let the velocity parameter of the spaceship in Figure 76 with respect to the imaginary instantaneously comoving inertial frame change from 0 to d[theta] in an astronaut time d[t']. (Let me use t' in place of the authors' [tau]). Then the velocity parameter of the spaceship with respect to the laboratory frame changes in the same astronaut time from the initial value [theta] to the subsequent value [theta] + d[theta]. Now relate d[theta] to the acceleration [g/c] in the instantaneously comoving inertial frame. In this frame [g/c] * d[t'] = d[beta] = tanh(d[theta]) ~ d[theta] " (Note: I never felt comfortable with this sequence.) "so that d[theta] = [g/c] * d[t'] (64)" I call a variant of this last equation (with g replaced by F/m), F = m * c * d[theta]/dt' the "velocity-parameter equation of motion." That is not the authors' term. I believe that my derivation of the VPEM (my term, abbreviated) on pp 12-13 of my paper is more straightfor- ward because it doesn't need the questionable approximations in the sequence above. (This would be a place for a correction in the second edition.) My paper "An Engineering Review of Relativity for Interstellar Flight" is in 4 files in MSWORD6.0a for Windows. If you have WORD6.0a to open them in, I can attach the files, one at a time, to email notes (I successfully did this to send a copy to Timothy, although I backed it up with snail mail). I don't know what TeX, troff, or Postscript are. Regards, Rex

**Follow-Ups**:**(Re:)^3 Doppler effect***From:*Steve VanDevender <stevev@efn.org>

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