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I have a simple question about how to calculate the total propellant mass used by a satellite in space. From Simulink, I have a graph of thrust VS time, so I could integrate this to calculate the total impulse. How can I compute the total propellant mass used by the satellite from this information?

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2 Answers 2

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Honestly, I'd ignore the total impulse and start with the thrust instead. Take the rocket thrust equation

Thrust$=\dot{m}V_e + (p_e-p_0)A_e$

Solve for $\dot{m}$, the mass flow rate through the nozzle, then integrate THAT in time for your total mass used in the burn.

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  • $\begingroup$ Thank you very much! $\endgroup$
    – Sato Yusei
    Commented Nov 18, 2022 at 12:04
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Consider the simplest case: constant thrust for a given time. Thrust is $\dot{m}c$ where the first is flow rate and $c$ is effective exhaust velocity. So, $total impulse= Ft=\dot{m}ct=M_pc$

where $M_p$ is the total propellant used. In SI units, $F$ in newtons, c in m/s, $M_p$ in kg and $\dot{m}$ in kg/s. If you use F in pounds-force and $M_p$ in pounds-mass, then use specific impulse for $c$.

Integration of F with time should give the same equation.

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  • $\begingroup$ Thank you very much! $\endgroup$
    – Sato Yusei
    Commented Nov 18, 2022 at 12:04

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