Lunar flight planner
Flight simulation
The calculations continue below the simulation: scroll down the page.
Δv budget by phase
Each manoeuvre uses propellant from the stage that is burning. When a stage burns out, it is jettisoned and the next one takes over. Spacecraft manoeuvres include a margin in the required Δv.
Rocket to scale
Stage heights come from tank volume and diameter, engine bells from thrust, the payload from the spacecraft mass. You see the same shape in the launch simulation.
Launch site and Earth rotation
The surface rotation speed falls with the cosine of latitude. When launching east, the rocket gets it for free.
Launch window and body motion
Mission speeds
Launch vehicle stages
Ideal Δv from the Tsiolkovsky equation Δv = Isp·g₀·ln(m₀/m₁). The first stage uses an effective Isp between sea level and vacuum.
Mass over the mission
Logarithmic scale. It shows how many tonnes on the pad are needed for every kilogram that reaches the destination.
Mission profile comparison
Same rocket and spacecraft, only a different profile. On a flyby or orbit mission the lander is not carried.
Parameters worth knowing
Parameters that change the result. Those marked “in model” can be changed on the left; the model only describes the others.
Method and simplifications
Earth rotation. v_rot = ω·R·cos φ, ω = 7,2921·10⁻⁵ rad/s. 465 m/s at the equator, 310 m/s in Bratislava. The required Δv is the vector difference √(v² + v_rot² − 2·v·v_rot·sin Az), with azimuth from sin Az = cos i / cos φ. Centrifugal acceleration ω²R·cos²φ reduces the effective weight on the pad.
Ascent to orbit. Gravity losses k·g·t_burn (k = 0,62 / 0,17 / 0,06 for the 1st/2nd/3rd stage), aerodynamic losses proportional to Cd·A/m₀. For Saturn V about 1,7 km/s in total. The ascent animation uses the same accelerations and losses; altitude and flight path angle are a smoothed profile.
Moon. Vis-viva v_p = √(μ(2/r_p − 1/a)), arrival at the Moon from Kepler's equation, v∞ relative to the Moon (orbital speed 1,022 km/s). The Moon moves in the animation at its real angular rate of 13,18°/day, so the spacecraft is aimed at where the Moon will be a few days later.
Planets. Hohmann transfer between circular orbits in the ecliptic plane. Departure √(v∞² + 2μ⊕/r) − v_circ, capture √(v∞² + 2μ/r_p) − √(μ(2/r_p − 2/(r_p+r_a))). Planet positions from mean longitudes at J2000, which give both the launch window and the wait for the return.
Landing. Without an atmosphere: DOI to 15 km, powered descent + gravity losses 0,3·g·t + hover. Mars: the atmosphere and parachutes remove most of the speed and the engine handles the rest. Venus: one-way landing only (92 bar, 465 °C).
Drag and heating. Exponential atmosphere density ρ = ρ₀·e^(−h/H) (Earth 1,225 kg/m³, H 7,6 km; Mars 0,020 / 11,1 km; Venus 65 / 15,9 km). Dynamic pressure q = ½ρv², drag q·Cd·A. Heat flux from Sutton–Graves q̇ = k·√(ρ/r_n)·v³, shield temperature from radiative equilibrium T = (q̇/εσ)^¼, capped at the stagnation temperature. Atmospheric entry is integrated numerically with capsule lift (L/D 0,3, Apollo: ~7 g, ~2 200 °C).
Parking orbit. The spacecraft coasts around it with engines off at constant speed until it reaches the point from which the burn aims the trajectory at the future position of the target. The number of orbits is set by the “Coast in parking orbit” parameter (Apollo 11: 2,7 h ≈ 1,5 orbits).
What the model leaves out. Precise trajectory integration, three-body gravity, planetary orbit inclinations, gravity assists, aerobraking, heat shield mass, RCS propellant and profile optimisation. The results are an engineering estimate within ±5–15 %.
Constants: μ⊕ = 398 600,44 km³/s², μ☉ = 1,327·10¹¹ km³/s², 1 AU = 149 597 871 km, g₀ = 9,80665 m/s². Presets are based on public data on Saturn V/Apollo, Falcon 9 and MRO, rounded.