Calculating propellant mass from total impulse

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?

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.

• Thank you very much! Commented Nov 18, 2022 at 12:04

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.

• Thank you very much! Commented Nov 18, 2022 at 12:04