<p><pre><code> >It’s also possible to land gently, you just need to end your 14th turn with a low altitude and velocity, and then use low thrust in your 15th turn, landing somewhere after 150 seconds. It’s just the theoretical full-thrust-on-landing suicide burn, that takes around 148 seconds, that eludes us.
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I expect the fuel-optimal <i>soft landing</i> strategy (ignored because it doesn't fit the exact form of a "suicide burn") would be to play 164.31426784 lbs/second at t=70 seconds, and then replace one of the subsequent 200 lbs/second inputs with 199.99999999 lbs/second.<p>The earlier you "play" 199.99999999 the better, so just use exhaustive search and select the earliest play that still achieve a soft landing.