Lunar landing game madness

[EdS2]

Nice! This is a problem I've often thought about, in a shallow way, but never tried to program or simulate.

> A landing is a time-reversed takeoff.

That's a crucial insight! It's true if the simulation doesn't model the effect of fuel mass. A time-reversed landing would start with a light vehicle that rapidly becomes heavier.

> perfect landing sequence 3, 6, 0, 0, 0, 9, 9, 9, 9, 9, 9, 9, 9

Excellent to find one which works. But if 3, 6, 0 is a good start, then (I think) 0, 9, 0 should be slightly more effective at slowing the vehicle down. It should be too much. With luck, 0, 8, 0 would do the job - but of course that might be too little.

In my understanding, the ideal burn will have a partial burn followed by full burns until touchdown. (I think this is called a suicide burn - a searchable term.) Because the granularity of control is poor, you might need to fade in your burn, by having two or three partial burns before the long final full burn. But I think all the non-zero numbers should move to the right, and the sequence should be ascending.

Having said that, you've done the work, and I'm only pondering. What happens in your case if you start one round earlier, so your table of 5 preliminary burns becomes a table of four burns?

Maybe the problem is in the lack of fine control. If one or more of the final burns is not a 9 but an 8, there would be a need for more thrust in the early stage. That's a degree of freedom for fine-tuning, I think?