IT IS NOT ROCKET SCIENCE, or, well, it is but we¡¯ll run you through it.

Wait, how does one begin to build a rocket?

Why not start by making a rough sketch on how to build the engine, and how our fuel for the rocket will work, in order to aid our dear escape. 

Karl *from a distance*: GOOD IDEA!

This engine will be a gas chamber with pure H₂  gas as illustrated in figure 1.1. 

Okay, okay, I know. You may be wondering why we¡¯re using H₂ as our fuel source? Well, you see our wish list for Santa Claus has these three things:

1. We want a uniform distribution, meaning the probability of finding a particle in any given position is the same. 

2. No particle-on-particle-collision. We want them to act as ghosts just sliding through each other. 

3. ELASTIC COLLISION. Meaning the particles maintain the same velocity after a wall bounce (with opposite direction), meaning the particles maintain their kinetic energy.

¡®This wish list looks oddly familiar¡¯ you say? It is a small checklist for an ideal gas, and H₂ is a good approximation of one!! (There is no such thing as a perfect ideal gas). Santa fulfilled our wishes with an ideal gas as rocket fuel!! Merry Chrysler!!

How will this ideal gas fuel help us escape?

Let us heat things up a little bit, literally. Imagine you are on vacation and it is 35 degrees celsius. You will soon start to panic and run (either to the shade, beach or whatever cools you down, so you won¡¯t end up on somebody¡¯s dinner plate!). The same happens to our gas particles. Heat things up to 3000K and they start going crazy bouncing everywhere with high velocity. The pressure will soon increase based on the equation of state of an ideal gas: P = nkT. Think of it like an extreme hot air balloon, you have the same amount of gas inside it, but the warmer it is the more energy it can push on the balloon walls with, or ram at the wall would be more accurate. We¡¯re just giving that gas a slight bit more oumph, in order for it to have enough energy to ignite, and you have the gist of our rocket!

Did you catch it yet?

.

.

.

.

No?

Wait, we forgot to make a hole in our fuel tank! 

Alright, now we are back on track. So far we have ideal gas particles, H₂ with high velocity, our rockets should be able to move through space. Yet, how does adding a hole in our box change anything?

Well we have two ideas, that effectively say the same thing in slightly different ways:

1. Newton¡¯s third law of motion:

Gas particles will bounce everywhere with a high velocity. When they bounce the top wall of the box a force is created so that our particles will be shot downward. However, with Newton¡¯s third law there should be a counterforce to every force (opposite directions obviously). The force from the rocket igniting our gass: F, will push our particles down and out of the box, whilst a counterfore F¡¯ will , as the name suggests counteract this, pushing the rocket upward. Get ready for take off!

2. Conservation of momentum:
In space there are no exterior forces acting upon our rocket ship. This means the momentum will be conserved. Henceforth, to counterbalance the ¡®loss¡¯ of momentum, caused by our gas being propelled downwards, the rocket will gain an equal momentum in the opposite direction. So the system conserves its netto momentum. Let me illustrate it for you.

Last but not least, HOW TO RETAIN THE PRESSURE?

Shhh, I will give you the answer. The velocity of our particles can be represented with a Gaussian distribution (short explained: vector components of the velocity can be described as a gaussian distribution₁. We will explain it more in depth in the future)

The particle velocities will distribute themselves mostly around the center of the curve, near the average velocity value, mu. Meanwhile the probability of our gas particles having a higher or lower velocity than the average will decrease symmetrically on both sides of the curve, hence the bell curve. The curve is useful for a lot of distributions in nature and science, such as how fast a jellyfish is able to swim from a sea turtle. The reason we have to use it here, is because determining the exact velocity of a single particle is near impossible, making the velocity of each particle approximately random. So instead we opt to approximate the probability of them having a certain velocity. This gives us a good enough idea of the momentum they¡¯ll provide, to determine the kinetic energy.

NOW¡­ let¡¯s start building the rocket¡­