About Apoapsis

Apoapsis is a 3D rocket-flight simulation. Plan an ascent profile, manage staging, and reach a stable orbit around Earth — or beyond. Real Newtonian gravity (no patched conics simplification), realistic engine specifications, and atmospheric drag matter to your trajectory.

How to play

Configure your rocket: payload, stages, fuel mass. Throttle up, gravity-turn during ascent, stage at appropriate altitudes, circularize at apoapsis to lock in orbit. Three.js renders the trajectory in 3D; orbit parameters update live.

Frequently asked questions

How the model works — the real physics

Apoapsis integrates the equations of motion numerically every tick rather than drawing an analytic conic — the trajectory you see emerges from the forces, so a badly timed burn distorts the orbit exactly as it should. Units are SI throughout (metres, kilograms, seconds, newtons). Here is the actual math the code runs.

Gravity

Gravity is inverse-square about the current primary body. Earth's gravitational parameter is built from surface gravity and radius:

• GM = g₀·R², with g₀ = 9.80665 m/s² and R = 6 371 000 m.
• Acceleration magnitude at radius r is g = GM / r², directed along −r̂ (toward the body centre). Equivalently g(alt) = g₀·(R/(R+alt))².

Integration — semi-implicit (symplectic) Euler

Each step advances velocity first, then position with the updated velocity:

• v ← v + a·dt, then x ← x + v·dt, with a fixed step dt = 0.01 s.

This ordering is what makes the method symplectic: unlike plain (explicit) Euler it conserves orbital energy over many revolutions, so a circular orbit stays circular instead of spiralling out from integration error.

Thrust, mass flow & the rocket equation

Engines are defined by thrust F and specific impulse Isp. Propellant burns at the mass-flow rate

• ṁ = F / (Isp · g₀) — mass is drained from the active stage each step, so the vehicle accelerates harder as tanks empty (a = F/m with m falling).

Stage and total Δv budgets come straight from the Tsiolkovsky rocket equation:

• Δv = Isp · g₀ · ln(m_wet / m_dry), where Isp is thrust-weighted-averaged across the engines firing in that stage and m_wet/m_dry include all mass carried above the stage.

Atmosphere & drag

Air density follows the International Standard Atmosphere in the troposphere and an exponential fall-off above it:

• Below 11 km: T = T₀ − L·alt, then P = P₀·(T/T₀)^(g₀·M/(R·L)) and ρ = P·M/(R·T), with T₀ = 288.15 K, P₀ = 101 325 Pa, lapse L = 0.0065 K/m, molar mass M = 0.029 kg/mol, gas constant R = 8.314.
• Above 11 km: ρ = ρ₁₁·exp(−(alt−11000)/6500) — a 6.5 km scale height — cut to zero above 140 km.
• Drag force F_d = ½·ρ·v²·C_d·A, opposing the velocity vector.

Orbital elements — vis-viva & the eccentricity vector

Live orbit readouts are derived every tick from the state vectors (position r, velocity v):

• Specific orbital energy (the vis-viva relation) ε = v²/2 − μ/r.
• Specific angular momentum h = r × v.
• Eccentricity vector e = (v × h)/μ − r̂; eccentricity is its magnitude.
• Semi-major axis a = −μ/(2ε), giving periapsis a(1−e) and apoapsis a(1+e), each minus the body radius to report altitude. When ε ≥ 0 the orbit is unbound (hyperbolic/parabolic) and apoapsis is infinite.

What's simplified

Within the active body's sphere of influence gravity is integrated numerically from the single primary — genuine Newtonian motion, not a precomputed two-body conic. Transitions between bodies use the standard patched-conic / SOI hand-off (only one gravitating body at a time; no n-body perturbations). The Mun and Minmus and their SOI radii are KSP-scaled toy bodies (Mun radius 300 km, SOI 1500 km, etc.), deliberately shrunk so a transfer fits in a short play session rather than matching the real Earth-Moon system.

Related games

• BiosphereBlue — planet-scale geosim.
• BonnevilleSpillwayOperator — dam operator sim.
• Doctrine — geopolitical sim.
• Floodline — flood defense sim.