Page 68 - Intro to Space Sciences Spacecraft Applications

Propulsion 55

chemical propellants through nozzles. Processes for imparting energy to
the propellant include chemical combustion, nuclear, electric, and others,
and the lists of available propellants is also long and varied. Before we can
look at these points, the principles of producing thrust via the expulsion
of mass must first be understood.

The Rocket Equation

Newton’s second law of motion was discussed in the previous chapter.
The law states that an applied force will result in a change in a body%
momentum. Stated mathematically:

where momentum is defined as the product of mass and velocity: p = mV.
The dot over the momentum term in equation 3-1 indicates the time rate
of change of that quantity, and the line over a term indicates that it is a
vector quantity having both magnitude and direction.
In a situation where the mass does not change, equation 3-1 reduces to
the familiar form F = mii, where ai represents the acceleration of the mass.
However, as a rocket ejects exhaust gases for propulsion, the mass term is
not constant. To determine the change in momentum, and thus the associ-
ated force, we must look at the situation at two different instances in time
as shown in Figure 3- 1.
The figure illustrates a rocket at time t having a velocity V, and the same
rocket at time t + At with a new velocity B + AV having exhausted an
amount of propellant Am, which now has its own velocity Vo. If we con-
sider a closed system consisting of both the rocket and the ejected pro-

m Am m- Am
+ d
....
- ..... -
V VO V+ A?
b
t t+ At time

Figure 3-1. Rocket momentum. A rocket trades momentum with its
exhausted propellant to produce thrust and increase velocity.