Thrust
The center of thrust, also known as the center of pressure, is the intermediate point on the surface area of an object like an airplane. It is described as the average location of the pressure. Calculating the center of pressure requires the use of calculus. It is a difficult calculation due to the variation of pressure at different points on the aircraft.
Mass
Center of mass, also known as the center of gravity, is the point of an object where there is equilibrium. It represents the point where the weight is equal in either direction. Maintaining the center of mass is crucial for aircraft. It requires calculating the weight of the fuel, baggage and passengers. Too much weight on one-half of an aircraft is dangerous. This explains why, especially on smaller commercial aircraft, passengers are sometimes moved to redistribute weight.
Location
For a rocket to fly the center of mass has to be ahead of the center of thrust. The distance must be sufficient for air currents to produce a stabilizing effect. A distance equal to the diameter of the rocket is a good rule of thumb. A rocket rotates around its center of mass during flight. When the center of thrust is behind the center of mass the air exerts greater force on the tail, thus keeping the rocket stable. If the center of thrust is ahead of the center of mass the air hits towards the nose of the rocket causing it to flip over and out of control.
Alterations
One method to alter the relationship between the center of thrust and the center of mass is to move them. Shifting weight in a rocket changes the center of mass. Put more weight in the nose of the rocket and the center of mass shifts towards the nose. Make the fins larger and the center of thrust moves towards the bottom. Change the design until the proper relationship is met that ensures a stable flight.