Level 6: The rocket equation

Rockets and landing · level 6 of 8 · rough age 13-14 (a guide for parents; anyone can start anywhere)

This level reaches the most important equation in spaceflight. You start from conservation of momentum, work out recoil, measure engines by specific impulse, define a rocket's mass ratio, and then derive Tsiolkovsky's rocket equation, \(\Delta v = v_e \ln(m_0/m_1)\). It explains why rockets are mostly propellant, why getting off Earth is so hard, and why rockets come in stages.

Lesson	You will be able to
Conservation of momentum	Use the conservation of momentum for collisions, pushes and dockings
Recoil	Work out recoil speeds, and see why a rocket's gain shrinks with each kilogram it throws
Specific impulse	Convert between specific impulse and exhaust speed, and compare propellants
Mass ratio	Find a rocket's mass ratio and propellant fraction, and say what limits them
Tsiolkovsky's rocket equation	Derive and use \(\Delta v = v_e \ln(m_0/m_1)\) for launches, landings and the trip to Mars
Staging, worked out	Compare one stage with two and three, and find the payload each can carry

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