FYKOS Year 32 Series 2 Problem 4 — lunar lander · FYKOS 32 #32.2.4
Physics · mechanics · electromagnetism
Problem
How can the electronics of the Apollo landing module control an engine thrust T (and so regulate the consumption of fuel), so the rocket floats onto the surface of the Moon at a steady linear motion? The effective velocity of exhaust gases is u. The rocket has already slowed down its motion on an orbit and goes straight down in a homogeneous gravitational field with an acceleration g. The initial weight of the module is m0.
Bonus: How can the electronics of Apollo landing module control the engine thrust during landing from a height h and initial velocity v0, so the landing is so-called fall from null height and the consumption of the fuel minimalizes? Maximum engine thrust is T_max.