Change of Mass

Center of Mass

As a motor burns, it ejects mass out of its nozzle, and propels the rocket forward. The motor also has a limited amount of fuel, and it eventually burns this up. As it does this the rocket loses mass. After motor burn out, the rocket is lighter. This makes the drag force greater relative to the rockets forward motion, but it also causes gravitational forces to be smaller as well. For many cases the forces very nearly cancel each other, so, we can assume them to be negligible. NASA however uses a set of differential equations to simulate the burning of the propellant, and the overall change in mass as a function of flight time, and is able to determine the exact velocity at any point in the flight. Some rockets burn out after atmospheric drag has greatly decreased, so they are able to make use of the much lighter vehicle. Ballistic Missiles like the ones shown below make use of this fact:

Figure 1 Army and Navy Ballistic Missiles (also fall in the category of Sounding Rockets.)

For a sounding Rocket to be stable, the center of mass must be in front of the center of pressure. The center of pressure is the point where the rocket’s thrust originates from. Fins move the center of pressure rearward by providing drag. The center of mass moves forward as the propellant is burned (more and more mass is in the front of the rocket, because less and less mass is in the back (motor) section. Sometimes NASA rockets are made deliberately unstable (CP in front of CM) at burn out to make them flat spin on reentry to atmosphere and slow down the rocket without need for parachutes.