What you’ll explore
Land it softly: motion, forces and energy at once. In this lab you land a spacecraft softly and test your intuition against a real physics simulation.
Challenge levels
- Engine off. The lander hangs still 100 m above the Moon (g = 1.62 m/s²) and the engine never fires. How fast does it hit the ground, in m/s?
- Hover. The full-power engine gives 8,100 N. The fuelled lander has a mass of 2,000 kg. What throttle, in %, makes it hover on the Moon?
- When to light it. Falling from 100 m with the engine off, choose the altitude where full power switches on so you touch down at 2 m/s or less.
- One steady throttle. You are at 100 m, already falling at 15 m/s, engine on now. Pick one throttle setting that touches down at 2 m/s or less.
- What if: Earth. Same lander, same full-power engine, but on Earth (g = 9.81 m/s²), engine on from 100 m. How fast does it hit the ground, in m/s?
Key ideas
Show the explanations (spoilers: try the levels first)
- With no thrust the only force is gravity: v = √(2gh) = √(2 × 1.62 × 100) ≈ 18.0 m/s. That is about 65 km/h into the ground: the legs are built for 2 m/s.
- To hover, thrust must equal the weight: m·g = 2,000 kg × 1.62 m/s² = 3,240 N, which is 40% of 8,100 N. As fuel burns the lander gets lighter, so at a fixed 40% it slowly starts to climb.
- Gravity speeds you up over (100 − h); full thrust (2.5× the weight, so a net 1.5 g upward) must remove that speed in h: g(100 − h) = 1.5g·h gives h = 40 m. Too early and you stop in mid-air and drop; too late and you hit hard.
- To lose 15 m/s over 100 m you need a net upward acceleration of 15² ÷ (2 × 100) = 1.125 m/s², so thrust = m(g + 1.125) ≈ 5,490 N ≈ 68%. The lander gets lighter as it burns, so the exact answer is slightly lower.
- On Earth the lander weighs 19,620 N, far more than the 8,100 N engine: net acceleration ≈ −5.8 m/s² downward, so it still hits at about 34 m/s. Lunar landers only work because the Moon’s gravity is weak.
About the model
- Straight-down (1D) landing; constant gravity (Moon 1.62 m/s², Earth 9.81 m/s²); no atmosphere on the Moon, and air drag is also ignored for the Earth what-if.
- Lander: 1,500 kg dry + up to 800 kg fuel (500 kg default). Engine: 8,100 N full thrust (2.5× the fuelled lander’s lunar weight), exhaust speed 3,000 m/s, so fuel burns at thrust ÷ 3,000 kg/s.
- Mass loss is included exactly (rocket equation): v = v₁ + u·ln(m₁/m) − g·t. The level explanations use the constant-mass shortcut (h = 40 m, 68 %); the simulation shows the small correction.
- The engine fires once, at a fixed throttle, from the chosen altitude until the tank is empty, the lander touches down, or it stops descending (automatic cut-off, as a real lander would do instead of climbing away). It never re-lights.
- A touchdown at 2 m/s or less counts as soft. Legs, bounce and tipping are not modeled. The lander is drawn about twice its true size (≈ 7 m tall) so it reads on a phone; altitudes and speeds are true.
- The steady-throttle level starts already falling at 15 m/s (a lander on its approach), so it is moving at t = 0 by design.
Every number on screen comes from the simulation, and each lab passes automated checks against the physics formulas. Spotted a mistake? Tell us.