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What you will learn in Rocketry and Launch Systems
1. How a rocket works
A rocket does not push against the air. It pushes against what it throws — which is why the equation on the widget has no term for the atmosphere in it, and why the best engine on the panel cannot leave the ground.
2. The rocket equation
Δv grows as the logarithm of the mass ratio, so every doubling of the propellant buys the same 2.11 km/s — while the mass you must build and fuel grows with the ratio itself. Watch the payload sliver on the bar get thinner every time you ask for more.
3. Why rockets have stages
No stage can beat a mass ratio of one over its structural coefficient, however much money it has. Two stages of 8 are one stage of 64, and one stage of 64 does not exist.
4. Why they lean over
Drag the pitch rate to zero and fly the misconception yourself. The rocket reaches 4,686 km, comes down 0 km from the pad, and had 0 m/s sideways at the top against the 7,844 m/s an orbit needs.
5. Landing them again
The mass ratio a vehicle needs to reach orbit is exactly what it was before anybody landed a booster. The propellant reserved for the landing burn is mass that does not go to the payload — and the widget will let you watch an orbit be lost to it.