Rocket Science

This term is overused in labeling things that are not rocket science, or we hear, "You don't have to be a rocket scientist to...", but it isn't often that we describe that which really is rocket science. Since orbital mechanics is the focus here, let's consider the point where that science and the engineering of rockets intersect. This limits our orbital domain to astrodynamics, trajectories of man-made spacecraft and satellites, and it brings propulsion systems into the discussion. To keep it simple, I'll limit the propulsion to chemical systems and the maneuvers to impulsive events. This means that the rocket fires and imparts a velocity change to the spacecraft in a relatively short time period. Generally, relative to the longer term orbital motion, we say that the velocity change takes place at a point. It is at this point that the science of astrodynamics and the engineering of rockets must be matched, and we have a mathematical relationship to match them.  It is known as the rocket equation:

To the left of the equal sign we have the change in velocity which is a vector. When added as a vector to the velocity of the spacecraft just prior to the rocket burn it gives the resultant velocity that determines the new orbit. The terms to the right of the equal sign do not seem to indicate a vector quantity in this form of the equation. The mass ratio is the total spacecraft mass at the start of the burn divided by the total spacecraft mass at the end of the burn, payload included; the difference being the mass of the propellant consumed. The quantity I_spg_c is equal to the equivalent axial velocity of the exhaust gases leaving the rocket at the nozzle exit plane measured relative to the rocket. Thus we indeed have a vector relationship, and we have another form of the rocket equation:

The minus sign in this equation shows that the direction of the velocity change is opposed to the velocity of the exhaust gases. Velocity change direction during the burn is very important. Spacecraft attitude and rocket nozzle direction relative to the spacecraft must be controlled throughout the burn to ensure that the velocity change has the proper orientation. The rocket equation relates a velocity change requirement determined by an astrodynamics problem to the performance required by spacecraft systems to produce that velocity vector.

Thrust can be shown to be equal to the specific impulse times the mass flow rate of the propellant, and thrust is a force having direction, a vector quantity. The factors that determine the thrust produced by a liquid propellant engine or a solid rocket motor are both internal and external. They are specific impulse, propellant consumption rate, nozzle exit plane area and pressure, and the ambient pressure in the vicinity of the rocket engine or motor. We can write the expression for thrust as

and we see that the ambient pressure, P_a, effects thrust and specific impulse. The other parameters depend on dimensions and internal operation. They will be the same in space as they are in a test stand. If thrust and P_a are measured during a test, then specific impulse can be predicted accurately in space where the ambient pressure is zero. There is, however, a constraint on P_a in the test environment. It must be maintained at a sufficiently low level to ensure that the nozzle flows full throughout the test. If it is allowed to be high enough that flow separation occurs inside the nozzle, the thrust vector magnitude and direction will be unpredictable. There is also a potential for damage. Therefore, when we test rocket motors or engines that are designed to be operated in space or other low pressure environments, we test them in a cell that provides for proper control of the ambient pressure.

Total impulse is the area under the thrust-time plot for a test. Accurate weight measurements before and after the test will give the weight of the propellant consumed during the test. If this is converted to mass and divided into the total impulse, the result is the test specific impulse. Typical thrust-time profiles for liquid and solid systems are shown below.

Even though the space environment cannot be duplicated in tests, the equations above allow propulsion system performance to be predicted accurately.

That's my view of rocket science, and there is a certain universal nature to this esoteric subject.

A being from a far galaxy
traveled space amazingly free
of gravity's force,
a constraint, of course,
for creatures like you and like me.

When I asked him how this could be,
he replied simply, "I_sp."
Then he went on to say
as he sped away,
"Mine is lightspeed over g_c."             

Finally, don't be intimidated by rocket science. It isn't brain surgery.