- #1
ileacus
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I'm trying to solve a rocket problem and have found no clear answer on how to do this. If I have a rocket in space (no significant gravitational forces, no drag, etc.) with a known constant thrust (T), mass flow rate (mdot), exhaust velocity (Ve), total initial mass including propellant (Mi), and propellant mass (Mp), I know that I can easily find delta-V with the rocket equation and amount of burn time is simple enough, but what I can't seem to figure out is how to calculate how far it travels.
My initial naive attempt at this was to derive an equation for instantaneous acceleration as a function of time: a(t) = T / (Mi - mdot * t), and then integrate to get an equation for velocity, and then again for position. I'm guessing the fact that it's not a closed system is why this is wrong?
In any case, is there a reasonably straightforward solution to this problem? I know that for computing orbital trajectories and accounting for all the different forces during launch, like gravity, drag, etc., the real rocket scientists use numerical integration to solve the problem. But I'm hoping that for a such a simplified system, that won't be necessary.
My initial naive attempt at this was to derive an equation for instantaneous acceleration as a function of time: a(t) = T / (Mi - mdot * t), and then integrate to get an equation for velocity, and then again for position. I'm guessing the fact that it's not a closed system is why this is wrong?
In any case, is there a reasonably straightforward solution to this problem? I know that for computing orbital trajectories and accounting for all the different forces during launch, like gravity, drag, etc., the real rocket scientists use numerical integration to solve the problem. But I'm hoping that for a such a simplified system, that won't be necessary.
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