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*To*: KellySt@aol.com, hous0042@maroon.tc.umn.edu, stevev@efn.org, rddesign@wolfenet.com, RUSSESS@cellpro.cellpro.com, jim@bogie2.bio.purdue.edu, zkulpa@zmit1.ippt.gov.pl*Subject*: Re: Okay, I give up ( well, not exactly ;)*From*: T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)*Date*: Sun, 26 Nov 1995 23:19:37 +0100

>if i turn down the Exhaust velocity, then the exhaust invarient mass must >increase. The original reason to increase the exhaust velocity was to >conserve RM. but if we can use a maser sail for the first half of the >trip, we might be able to accept a higher RM rate for the decell portion >of the trip. Going from 0.99996c to 0.85c means about 60 times more reaction mass... Plus since we can't use a maser beam for energy we have to bring the energy ourselves. >so here's what I need: > >a simple easy to use, relativisticlly correct formula that tells me how much >energy I need to accelerate a given exhaust mass to a given speed. > >I'll be using Me=G*(Ms+Mf) * gamma/(Ve *C) > >where >Ve is exhaust Velocity expressed as a fraction of C. >Me is Exhaust Mass. >Ms is ship's Mass. >Mf is Reaction Mass. >G is ship's acceleration. >gamma is SQRT(1 - Ve^2) I know Tim likes gamma= 1/sqrt(1-Ve^2), but then > he divides by it instead of multipling. In most formulas I use, I have to multiply by gamma. Your formula is one of few where I have to devide by it. >all mass is invarient or rest mass. >Ve is with respect to the ship, and I'm thinking it'll be in the .80-.9? >perecent of C range. To calculate the kinetic energy of a mass M use: K=M C^2 (1/gamma - 1) where gamma is according to your (unusual?) definition. You can substitute Me for M and simplify: K=G C (Ms+Mf) (1-gamma)/Ve (gamma is still according to your definition) Timothy P.S. If you are planning to calculate how much energy is needed to accelerate the Asimov and it's fuel&reaction mass for specific G, I've to tell you that these calculations have been done already.

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