The lander is a point mass under constant downward gravity g plus thrust from its own engine, integrated with semi-implicit Euler at a fixed 1/120 s sub-step:
ax = T·sin(θ) (lateral component of thrust)
ay = T·cos(θ) − g (vertical component minus gravity)
vx += ax·dt, vy += ay·dt
x += vx·dt, y += vy·dt
fuel -= burnRate·dt (only while thrusting)
Rotating left/right changes θ, the thrust vector's tilt from vertical, so a tilted burn also pushes you sideways — exactly like a real reaction-control lander. Touchdown is scored against real limits: land with |vertical speed| ≤ 3 m/s, |horizontal speed| ≤ 2 m/s and |tilt| ≤ 12° on the flat landing pad to land safely; exceed any limit, run out of fuel mid-air, or hit rough terrain and it's a crash.
- Gravity — slide from the Moon's 1.62 m/s² up toward Earth's 9.81 m/s² to feel how much harder a heavier world makes the landing.
- Thrust power — the engine's maximum acceleration; too little and you can't out-burn gravity, too much and small taps overcorrect.
- Fuel load — total burn-seconds available; every second of thrust consumes it, so wasted braking early can leave nothing for the final flare.