No Subject

[A West <andrew@hmm.u-net.com>]

As a follow on from some work I recently did, I thought I would do a few
calulations on what someone would need if they wanted to fly to a nearby star.

I am not a mathematician, nor am I am physicist, so I have run into a few
problems, and I was wondering if anyone could point out the error of my
ways.  I visited the ftp server with the old postings to this list, and I
downloaded the whole thing, but I haven't read it all yet (due to it being
2000+ pages) so I expect that this has either already been covered or is
too simple to be discussed :)  There are quite a few things I don't
understand, such as specific impulse (I know what impulse is) and what
context Delta V is taken in - I would assume this is accleration (dv/dt)
but this is something I was never taught :)

But, on to the problem:

I am assuming that I want to get to 90% c, and I am trying to calculate
with: every action has an equal and opposite reaction.  I am throwing fuel
out the back of my ship in order to go forwards - this seems the only way
to get anywhere unless you pick up the fuel on the way.  I am assuming I
want an acceleration of 10m/s, which means an accleration period of about
310 days to get to 90% c, then another 10 months to slow down again.  I
spend the intervening time drifting to my destination.  I am also assuming
that I use a fixed amount of fuel per second, and the velocity of that fuel
is used to change the acceleration of the ship.
So, for the out-going journey (assuming I never want to slow down)

Force on the Ship = impulse due to fuel.
		    = Mass of fuel * velocity of fuel / time

F = ma, where m = Total mass of ship.
		  = Mass of ship + mass of fuel -mass of fuel burnt + reletavistic mass
increase
		  = Mass of ship + Fuel burnt per second * journey duration - Total fuel
burnt (I am ignoring reletavistic mass increases, as I don't know the
equation :)

if Mass of fuel burnt per second = Mf, Velocity of fuel = Vf, time so far =
t, total time for journey = T and MF = fuel burnt so far, then:

ma = (Mf * Vf)/t

I am fairly sure I have got the wrong assumption somewhere, as:

Mass of Ship  = M + Mf * T - Mf * t
so
a(M + Mf * T - Mf * t) = (Mf * Vf) / t

if 2.7*10^7 = T.
   Mf = 10 kilos
    a = 10 m/s,
and M = 1 million kilos

10(1*10^6 + 2.7*10^8 -10t) = 10Vf /t
1*10^6 + 2.7*10^8 -10t = Vf/t			1*10^6 + 2.7*10^8 is about 2.7*10^8, so

2.7*10^8 * t -10t^2 = Vf

The Velocity of the fuel would have to be greater than the speed of light
at t = 1, so I have made a mistake somewhere... touble being that I do not
know where :(
I have an idea that I am measuring the fuel speed relative to the wrong
point in space... that Vf should equal the speed of the ship - Vf, but I am
far from certain if this is correct...

I hope this doesn't sound like "hey, can you do my homework for me", and if
it does, feel free to tell me to go away :), but I don't really know who
could help me with this - if anyone has any ideas, or has any ideas where I
can find this stuff out, please tell :)
I was planning on running the equation on my ocmputers, but I would be able
to run it in a series of iterations, making the final equation a bit
easier, but seeing as how I can't actually get the first equation right, it
scuppers my plans straight away...

Thanks, 

Andrew West