[Verse 1] Six elements dress an orbit like a skeleton in space — Semi-major axis stretches out the ellipse, sets the pace, Eccentricity decides how squashed or round the curve will lay, Inclination tilts the plane against the equatorial sway, RAAN swings the node around the equator's longitude, Argument of perigee — where closest approach is queued, True anomaly pins the craft exactly where it sits — Kepler proved the radius sweeps equal areas in equal bits [Chorus] Орбітальні елементи, шість ключів до небес, Ми летимо до Місяця крізь математичний ліс — Hohmann transfer, elliptical arc, tangential burn, Апогей і перигей — є що вивчати, є що знати, Every orbit has a story written in the parameters [Verse 2] A Hohmann transfer stitches two circular paths with one ellipse — Two tangential burns, delta-vee is sipped in careful drips, Plane changes bleed the most velocity, so time them late, Phasing orbits synchronize arrival — patience calibrates, Launch azimuth depends on where your launchpad sits by latitude, Cape Canaveral at twenty-eight degrees gives attitude — The window opens when the Moon sweeps through the outbound plane, Miss it by an hour and you wait another month again [Chorus] Орбітальні елементи, шість ключів до небес, Ми летимо до Місяця крізь математичний ліс — Hohmann transfer, elliptical arc, tangential burn, Апогей і перигей — є що вивчати, є що знати, Every orbit has a story written in the parameters [Bridge] Patch the conics where the spheres of influence divide — Inside sixty-six thousand kilometres, the Moon's the guide, Three bodies tangle where no closed solution can be found, But Lagrange blessed us five equilibrium points around, Trans-lunar injection fires you free from parking's hold, Mid-course corrections nudge the trajectory, controlled and cold, Lunar orbit insertion brakes you into selenoid embrace — Free-return trajectory — Apollo Thirteen's saving grace [Verse 3] Perturbations creep like whispers underneath the clean ideal — J-two oblateness makes the orbital node rotate and reel, Mascons buried in the lunar crust pull spacecraft off the arc, Solar radiation pressure — photons leave a drifting mark, Third-body gravity from the Sun tugs subtly on the thread, Navigation teams correct for every influence overhead, Stack the errors, miss the margin — Mare Tranquillitatis waits, Model every force precisely — that is how you thread the gates [Chorus] Орбітальні елементи, шість ключів до небес, Ми летимо до Місяця крізь математичний ліс — Hohmann transfer, elliptical arc, tangential burn, Апогей і перигей — є що вивчати, є що знати, Every orbit has a story written in the parameters [Outro] Кеплер, Ньютон, Лагранж — їх формули живуть, Six elements, three burns, one Moon — the mathematics bloom
← 1 The Rocket Equation and Propulsion Fundamentals | 3 Atmospheric Flight →