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My son and I have been discussing the concept of a constant-acceleration rocket, as described here and here. We're willing to assume advanced technology such as a fusion rocket, which, according to some sources, could someday provide a specific impulse $I_{sp}$ in the neighborhood of 100,000 s. We're trying to figure out if constant-acceleration trips around the solar system are at all feasible with this sort of technology.

So our question is this: assuming such an $I_{sp}$, what's the ratio of fuel to payload we would need to keep up an acceleration of 1G for a few days? What if we settled for 0.5G?

(Note that the second reference provides some handy equations and examples for a rocket converting mass to radiation with 100% efficiency, but I don't understand how to generalize that to a more realistic exhaust velocity.)

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    $\begingroup$ This may be well answered by "Why are rockets so big?"/ $\endgroup$
    – dmckee --- ex-moderator kitten
    Sep 19, 2014 at 16:46
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    $\begingroup$ Are constant-acceleration trips around the solar system at all feasible - yes. You're on one right now. :P $\endgroup$
    – user121330
    Sep 19, 2014 at 18:12
  • $\begingroup$ @dmckee: not as far as I can see. I know how to calculate the delta-V for a rocket with a constant exhaust velocity and mass fraction. But I don't know the mass fraction or delta-V here, and I'm not even concerned with delta-V; I'm just trying to figure out if I can maintain a certain acceleration for a certain amount of time. $\endgroup$
    – Joe Strout
    Sep 19, 2014 at 19:49
  • $\begingroup$ In practice one would keep up acceleration on the order of 1e-3g for months and years (or decades for interstellar flights) with electric rocket propulsion. ISP of 100,000 is possible with nuclear fragment propulsion: en.wikipedia.org/wiki/Fission-fragment_rocket $\endgroup$
    – CuriousOne
    Sep 19, 2014 at 19:51

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Not a full answer, but too long for a comment. Maybe this can lead you the right way.

I'm going to ignore the changing mass for a moment and assume a ship with a fuel fraction of $0.5$. If we could get enough thrust from the engines to give a $1g$ thrust to the fuel, we could give a $0.5g$ thrust to the ship.

If you have an engine with $I_{sp} = x$, and a thrust $F$ can burn for $x$ time with a quantity of fuel that has a weight of $F$.

This means engines at that power would run for $100000s$, or just over a day.

Now the nice part is things get better from there. You'd either maintain thrust and increase acceleration to $1g$ as the fuel is exhausted in a day, or you'd throttle down to maintain $0.5g$ and the fuel would last longer. Given that, I assume there's a nice log equation to show the exact relationship between fuel fraction and burn time.

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Literal tons. Tons and Tons of fuel. Even with an antimatter reaction, constant acceleration would take literal tons of material.

http://nathangeffen.webfactional.com/spacetravel/spacetravel.php

This calculator should give you the exact maths dependent on fuel conversion. Hydrogen fusion for instance is, 0.007%, which is widely efficient compared to all our current forms of power generation, but still not enough for practical 1g acceleration.

For example, if you want to travel for 1 lightyear in 1 ton ship, using fusion, you'd need a minimum of 864 tons of fuel. Even with a anti-matter drive, you'd need 6 tons of fuel, 6 times the mass of the ship.

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