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For various population systems discuss the relationship between specific Impulse vs Thrust
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Force, is given by the change in momentum with respect to time dP/dt. If the exhaust velocity is not near the speed of light then the momentum is given by:
P=m*v
P dot=m dot * v=v *dm/dt
dt=v*dm/ (P dot)
And the energy is given by
E=(1/2)m*v^2
Therefore:
dt=sqrt(2*dE/dm)*dm/ (P dot)
dt=sqrt(dE)*sqrt(2*dm)/(P dot)
That is the specific impulse is proportional to the square root of the
Energy per mass and inversely proportional to the momentum.
Also note
P=2*E/v
P dot=2*(E dot)/v
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