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I don't need an exact number, also it can be to travel to the ISS or the moon, it's not important. I just want to get an idea of how much fuel is used in a «recursive» sort of way.

Edit: I am asking how much of the initial total amount of fuel at takeoff is used to lift fuel. I know fuel is consumed on the go, but that does not render the question unanswerable.

Edit2: By saying it was not important that the travel was to the ISS or the moon, I meant that any example could be taken, and not that it was irrelevant to the calculation.

Winston
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1 Answers1

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I think the answer to your question lies in the rocket equation, which says

$$\Delta v = v_e\log M_i/M_f,$$

where $\Delta v$ is the total magnitude of changes in velocity during either a single manoeuvre or a whole voyage, $M_i$ is the initial mass, ie. sum total of payload and fuel, $M_f$ is the final mass, which would be your payload, and $v_e$ is the velocity of the exhaust, assumed constant.

So let $p$ be the proportion which is fuel, so $M_f = (1-p)M_i$. Then we have

$$\Delta v = v_e\log \left(\frac{1}{1-p} \right),$$

So you see why it's hard to answer you question as a percent. As $\Delta v$ increases, that is for farther or more complicated voyages, the proportion of fuel $p$ must increase as well.

If you'd like a differential relation between velocity and mass we can take $\Delta v \to dv$, $M_i \to M_f + dM$ in the rocket equation to obtain

$$dv = v_e dM/M.$$

(This is usually the formula which is derived first, by considering conservation of momentum.)

Ryan Thorngren
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