S.1 Spacecraft Propulsion Systems Chapter 1: Introduction to ...

S.5 Total Impulse
- 6-
From the Basic Rocket Equation follows with mf = mS/C – mP :
Propellant Quantity required for a spacecraft velocity change ∆v:
⎛
m ⎜
P = mS
C 1−
e
⎜
⎝
∆v
−
v
e
⎟ ⎟
⎞
⎠
/ [kg]
The Total Impulse delivered by a certain quantity of propellant is calculated by:
I
tot
τ
m p
= ∫ Fdt = ve
∫
0
0
dm = v m
e
p
[Ns]
This equation shows again the importance of the thruster exhaust velocity. For a given mass of
propellant, mP, the thruster exhaust velocity ve shall be high for obtaining a high (delivered) total
impulse, Itot.