Page 69 - Intro to Space Sciences Spacecraft Applications

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Zntroduction to Space Sciences and Spacecraft Applications
pellants at all times, momentum must be conserved from one time instant
to the next. At time t the momentum is:

and at time At:

The change in momentum is:
-
Ap = ir,t + At) - P(t)
= mV + mAT - AmV - AmAv + AmVo - mV

which, if we ignore the product of two differential terms, reduces to:

Ap = mAV + (50 - V)Am

Dividing through by At and taking the limit as At approaches zero:

dp
- dm
dT
- m- + (8, - v) -
=
dt dt dt
or, rewriting:
d8 dj5 dm
m- = -+(8-T0)- (3 - 2)
dt dt dt

Looking at each term of equation 3-2, we see that the term on the left-hand
side of the equation represents the instantaneous ucceZerution of the rock-
et mass m.
The first term on the right-hand side of the equation represents the
change of momentum for the entire system. Since we are considering a
closed system consisting of the rocket and exhaust gases at all times, a
change in the overall system momentum can only be caused by forces
external to the described system. This term represents external forces
(Fat) such as gravity, drag, solar pressure, and others. The vector nomen-
clature shows that force direction must be understood. Some of these