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*To*: starship-design@lists.uoregon.edu*From*: A West <andrew@hmm.u-net.com>*Date*: Tue, 17 Feb 1998 16:13:10 +0000*Reply-To*: A West <andrew@hmm.u-net.com>*Sender*: owner-starship-design@lists.uoregon.edu

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

**Follow-Ups**:**starship-design: Calculations involving self-powered spaceflight***From:*Timothy van der Linden <TLG.van.der.Linden@tip.nl>

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