About the Moon Landing Simulator
This simulator models the powered descent of an Apollo-style lunar module to a soft touch-down. It integrates Newton's second law under constant lunar gravity (g = 1.62 m/s²) with a variable-mass rocket: horizontal acceleration is T·sin(θ)/m and vertical acceleration is T·cos(θ)/m − g, where T is thrust, θ the tilt angle and m the current mass. Fuel burns by the Tsiolkovsky mass-flow relation dm/dt = −T/(Isp·g₀).
Two sliders give you control: a throttle (0–100% of the 16 kN engine) and a tilt angle (−30° to +30°) used to cancel sideways drift. Telemetry reports altitude, vertical and horizontal speed, fuel and engine state in real time. The exercise mirrors a genuine aerospace problem — managing limited propellant to arrive with |vᵧ| under 3 m/s and |vₓ| under 2 m/s, the regime real lunar landers must hit to avoid toppling.
Frequently Asked Questions
What does this simulator actually do?
It lets you pilot a descending lunar lander, starting at roughly 900 m altitude with sideways and downward velocity. You adjust throttle and tilt to slow the craft and reach the central landing pad gently. Touch down softly and you get a safe-landing message; come in too fast and the module crashes.
How is the motion calculated?
Each animation frame is split into four physics sub-steps using a small time step (DT = 1/240 s) and explicit Euler integration. Thrust resolved through the tilt angle gives the horizontal and vertical accelerations, gravity is subtracted from the vertical component, and the velocities and positions update step by step until the lander reaches the surface.
What do the throttle and tilt sliders do?
The throttle sets engine thrust from 0 to 100% of the 16 kN maximum, directly controlling how hard the engine pushes against gravity. The tilt slider rotates the thrust vector from −30° to +30°, letting you point part of the thrust sideways to cancel horizontal speed before landing.
What is the key equation behind the fuel burn?
Fuel is consumed according to the Tsiolkovsky mass-flow equation, dm/dt = −T/(Isp·g₀), where T is thrust, Isp is the specific impulse (311 s here) and g₀ is standard Earth gravity, 9.81 m/s². Higher thrust burns propellant faster, so the engine's efficiency is tied directly to its specific impulse.
Why is lunar gravity set to 1.62 m/s²?
That is the Moon's real surface gravitational acceleration, about one sixth of Earth's 9.81 m/s². It is the figure Apollo mission planners used, and it explains why a lander needs far less thrust to hover above the Moon than it would on Earth.
What were the real Apollo numbers this is based on?
The Apollo Descent Propulsion System (DPS) had a specific impulse of roughly 311 s and a rated thrust near 16 kN, and it could throttle deeply, between about 10% and 92.5%. The simulator uses these values, a 2,000 kg dry mass and 4,000 kg of initial fuel to give a representative descent.
Is the simulation physically accurate?
The core dynamics — variable mass, Tsiolkovsky fuel flow, vector thrust and constant lunar gravity — are faithful. It simplifies by treating the Moon as flat and airless near the pad, ignoring lander rotational dynamics, terrain slope and guidance computers, so it is an educational model rather than a flight-certified trajectory tool.
Why does my horizontal speed matter so much?
A lander that arrives with too much sideways velocity can tip over or shear a leg on touch-down. The success criterion requires |vₓ| under 2 m/s, so you must use the tilt control to angle the thrust and bleed off horizontal motion well before you reach the surface.
What happens when I run out of fuel?
Once the propellant tank empties the engine produces no more thrust, and gravity alone governs the descent. The model caps thrust to the fuel actually available each step, so an over-aggressive early burn can leave you with nothing to slow the final approach — a realistic constraint for any spacecraft.
How does the tilt angle change the trajectory?
Tilting rotates the thrust vector, splitting it into a vertical component T·cos(θ) that fights gravity and a horizontal component T·sin(θ) that pushes sideways. Leaning into your drift cancels horizontal speed, but it also reduces lift, so you usually need to add throttle to keep from descending too quickly.
What real-world skills does this illustrate?
It captures the trade-offs of real spacecraft landing guidance: balancing thrust against gravity, managing a finite propellant budget, and nulling lateral velocity before contact. The same principles underpin modern landers and reusable rockets that perform powered, propellant-limited descents to a target site.