Level 7: Landing on Mars

Rockets and landing · level 7 of 8 · rough age 15-16 (a guide for parents; anyone can start anywhere)

This level works out the landing on Mars from the physics up. You derive the drag equation and the ballistic coefficient, model the thin Martian air with height, find a parachute's terminal speed, estimate the heating on a heat shield, see why heavy landers must fire their engines while still supersonic, and finish with the first powered flight on another world.

Lesson	You will be able to
The drag equation	Derive \(F = \tfrac12\rho v^2 C_d A\) from momentum, and use the ballistic coefficient
Thin air	Model Mars's air with \(\rho = \rho_0 e^{-h/H}\), find Mach numbers, and compare with Earth
Parachutes and terminal speed	Find terminal speeds under a parachute on Mars, and size a parachute for a given landing speed
Entry heating	Estimate heating with \(q \propto \sqrt{\rho/r_n}\,v^3\), and explain blunt shapes and ablation
Supersonic retropropulsion	Explain why heavy landers stay supersonic near the ground, and must brake with engines
Flying on Mars	Work out the lift and hover power of a helicopter in Mars air, from the numbers of Ingenuity

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