An orbital demonstration · Luke Steuber
Recording a finite-thrust flight…
LEO → GEO · finite thrust
A numerical flight through the Earth–Moon gravity model.
Jump to an integrated event and pause. Camera framing stays fixed.
Ports follow station-kept reference paths. Select one to change the view.
A deterministic numerical demonstration, not a real mission or an engineering ephemeris. The tug starts in a 420 km, 51.6° low Earth orbit. The planner solves two finite burns to meet the equatorial GEO port.
Three spatial dimensions in a fixed Earth-centred inertial frame. Body radii and distances share one scale: 1 scene unit = 1,000 km. Ship, port and burn markers are enlarged for visibility. The dashed line is the recorded flight; the bright trail is the part already flown. No gravity funnel is drawn.
Playback lasts 76 seconds. Coasts accelerate, each burn takes 18 seconds, and event buttons use exact recorded times. Positions between integrated samples use cubic Hermite interpolation. The arrow at the ship shows velocity direction; an amber exhaust appears only during a finite burn. The camera changes only when you select a focus or reset the view; it never follows an event.
An orbit is the path produced by position, velocity and gravity. Velocity is the direction and speed of motion, not a drawn orbit or a force. Coasting uses no fuel: gravity still changes velocity. Thrust changes the orbit over time, rather than jumping the ship to a new path.
The 12 t dry tug starts with 40 t propellant and no cargo. Thrust is 220 kN; specific impulse is 450 s. Mass flow is T / (Isp × g₀). Ideal engine Δv is Isp × g₀ × ln(m₀ / m₁); this is not the change in inertial speed during a burn, since gravity acts at the same time.
The ship uses the existing adaptive Dormand–Prince integrator, point-mass Earth and Moon gravity, and finite constant-thrust burns. J2 is off. Drag, the Sun’s tide, radiation pressure, detailed attitude and engine transients are omitted.
The Moon follows the Astronomical Almanac low-precision series, not a live ephemeris: errors may be roughly 2,000 km along-track and 1,000 km in distance. Lunar frame switching also introduces a force discontinuity; this demonstration stays near Earth. Ports follow ideal reference orbits with assumed station keeping; their nodes and phases are invented. Capture means within 2 km and 5 m/s, with the final metres abstracted. The recorded ship continues coasting after arrival without snapping to a dock.
Textures: Solar System Scope, CC BY 4.0. Imagery provenance · Three.js MIT license · Font license · Full physics notes · Demonstration notes