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Re: starship-design: Motion of sail driven by constant-power beam
At 9/11 you wrote:
>For a power, Pe, sent out by an emitter, the power received by
>a sail (ignoring inverse-square effects) that is receding at an
>apparent velocity, beta lt-yr/yr, is
> Pr = Pe * sqrt[(1 - beta)/(1 + beta)]
> ....Doppler shift
> = Pe * gamma * (1 - beta)
> ....gamma = 1/sqrt(1 - beta^2)
> = Pe * [cosh(theta) - sinh(theta)]
> ....gamma = cosh(theta); beta = tanh(theta)
> (definition of velocity parameter, theta)
> = Pe * exp(-theta)
> ....using exp forms of hyp functions.
>(I believe this relation, with theta = a * t' for constant a, is
>the source of the logarithmic time dependence introduced by Steve
>in his email of 8/20 to the Group.)
But why do you believe that?
Steve's results are not related to the red-shift, they are based on the
signal travel time, which increases exponentially with the trip-time.
Am I right to say that during constant acceleration not only the energy of
the photons, but also the amount of photons decreases?
Steve's calculations pointed to the amount (density) of photons, while yours
seem to point only to their energy.