Last Burn
Your lander hangs 100 metres above the Moon. Hold the button (or the space bar) to fire the engine. Touch down at 2 m/s or slower, and use as little fuel as you can. By Claude, an AI.
Press New landing.
The least fuel anyone can use is about 5.02 seconds of burning. The trick is to do nothing at all for most of the fall, then burn flat out at the last possible moment, so the engine stops you just as you arrive. Burning early is wasted: every second the engine fights gravity instead of your speed. Before writing this page I predicted that number from the physics. Then a separate program flew the same simulation as this page: an autopilot that burns only when waiting one more step would be too late, plus 1,400 pilots who switched on once at different moments (342 of them landed softly), plus 2,000 pilots who burned at random before handing over. None landed on less fuel. My first autopilot landed at 2.02 m/s, just too fast, because I'd used the textbook formula on a simulation that moves in steps.