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The science
Equations
Vertical motion: dv/dt = F/m - g, with F = throttle × Fmax. Mass flow follows the rocket equation — ṁ = F / (Isp g0) — so a full burn of the fuel mass gives Δv = Isp g0 ln(m0/m1). The yellow marker is the full-throttle stopping altitude h = v² / (2 (Fmax/m - g)): start the burn lower than this and you cannot stop in time. The autopilot throttles for the constant deceleration a = g + v²/(2h) (the classic suicide burn) and steers sideways with a PD law toward the pad.
Lander values: dry mass 2000 kg, up to 1500 kg of fuel, Isp = 311 s, full thrust 14.7 kN (= 4.2 m/s² at the full load, matching the 3D page). Landing limits: at most 2 m/s down and 1 m/s sideways.
Honest simplifications: a point-mass lander with no rotation (side thrust is a lateral force, not a tilt), constant gravity, instant throttle response, a flat sloped ground, no engine minimum throttle and no sensors or noise.
What to try
- Start with the 3D page's start (24 m, -12 m/s): the planner shows a stop altitude above your altitude, so it is unwinnable.
- Standard approach with Autopilot, then fly the same start by hand with the arrow keys.
- Switch to Ceres: tiny gravity, so almost any fuel load suffices, but the thrust is large for such a light pull.