Re: Okay, I give up ( well, not exactly ;)

[T.L.G.vanderLinden@student.utwente.nl (Timothy van der Linden)]

>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.