Rocket Staging

A rocket burns fuel with an oxidiser to make hot gas, which shoots out of the nozzle at very high speed. Pushing the gas backward makes the gas push the rocket forward with an equal force, called thrust. Rockets carry their own oxygen, so they also work in space.

Newton's third law says every action has an equal and opposite reaction. The rocket pushes exhaust gas backward (action) and the gas pushes the rocket forward (reaction). It's the same reason a balloon zooms around when you let the air out.

A rocket must carry huge tanks that become empty as fuel burns. Staging drops each empty section and its engines, so the remaining rocket is lighter and the same fuel gives more speed. Without stages, reaching orbit is extremely hard.

Δv = vₑ ln(m₀/m_f), where Δv is the change in speed, vₑ the exhaust speed, m₀ the starting mass and m_f the mass after the fuel is burned. It shows that speed grows only with the logarithm of the mass ratio, which is why rockets are mostly fuel.

Thrust-to-weight ratio is the engine thrust divided by the rocket's weight. It must be greater than 1 for a rocket to lift off. Most rockets launch with a ratio of about 1.2 to 1.6, so they rise slowly at first and speed up as fuel burns away.

Orbit needs a huge sideways speed, about 7.8 km/s, not just height. Rockets go up through the thick air first, then gradually tilt over to fly sideways. This simulation launches straight up to keep things simple, so it shows height and escape rather than orbit.