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*To*: stevev@efn.org, DotarSojat@aol.com*Subject*: Re: Mistake*From*: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)*Date*: Tue, 19 Sep 1995 12:21:15 +0100

Hello Steve, > > Sorry for the confusion > >Don't worry about it. I've certainly made my share of mathematical >errors. And not only are these fine points of relativistic physics >often counterintuitive, but they are also quite hard to talk about >without resorting to elaborate mathematics. Thanks >I am interested to know the equation you got that produces the same >results as mine without looking at all the same. The result of my best calculations was: a t0 (-2 c + a t) c ArcSinh[------------------] t1 = 2 c (-c + a t) ----------------------------- a where t is the emit-time in Earth's frame and t1 is the recieve-time in the ship's frame Note that in this formula I did not use your definition of c=1. This morning I tried to do the same with c=1 but it gave me even more elaborate formulas. te=Emit time in Earth's frame (your t) tr=Receive time in Earth's frame te'=Emit time in the ship's frame tr'=Receive time in the ship's frame (your t1) f[x]=Function f determined by variable x The main idea is that I solve: x[tr]=c(tr-te) I first try to get a formula for x that does have a t in it instead of a t': x[t]=1/a Cosh[ArcSinh[a t]] Then I try to solve te, which in this case gives me a formula that I don't want to write down. Having found te, I can easely find te', just by using: t'=1/a ArcSinh[a t] >Once good point you had in your last post was that you really don't have >only two years to send power for the boost and deceleration phases of a >1 g constant-acceleration mission. You do, however, have only one year >to send the power for the boost phase. The situation is actually the >worst for the so-called "Forward sail" design, involving the use of a >detachable reflecting sail that reflects the beamed power back to the >ship for deceleration -- in that case the power continues to accelerate >the reflecting sail and therefore more drastically limits how long you >have to send power to be used through the entire mission. I think that when one uses the "Forward sail" the time would even be shorter than 2 years. The reason for this is that the sail will (after it is detached) probably accelerate faster than the ship, since it has less mass. I cannot directly write down what the maximum power-emit time would be since it involves 2 different accelerations. Timothy

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