Orbital laboratory (2D)

What you see

Left: the orbit seen from above the North Pole (altitude exaggerated five times) with a Blender-rendered station sprite and Earth disc. Right: the laboratory frame, where free-flyers released near the station trace Hill-Clohessy-Wiltshire curves.

The 3D page shows the same simulation with a full Blender model.

A research station on a circular equatorial orbit. A Blender-modelled station (lab module, node with a cupola, habitat, truss, Sun-tracking solar arrays, radiators) flies nose-forward above a baked Earth. In the orbit view the station is enlarged about 400 times so you can see it; in the close-up it is at its real size relative to the free-flyers.

Orbit and period

Gravity g = μ/r² with μ = 3.986×10¹⁴ m³/s². A circular orbit has v = √(μ/r) and T = 2π√(a³/μ): 92.97 min at 420 km. The motion is integrated with a 4th-order Runge-Kutta scheme in the orbital plane (point-mass Earth: no J2 bulge, no inclination, no eclipses).

Why it is weightless

At 420 km gravity is still 88 % of the surface value. Crew and station are in continuous free fall: the centripetal term n²a equals μ/a². Weightlessness is not the absence of gravity.

Atmospheric drag and decay

a_drag = ½ ρ (CdA/m) v_rel² against the co-rotating air, with ρ(h) from an illustrative log-linear thermosphere table multiplied by the solar-activity factor. The orbit decays at da/dt = −(a²/μ) ρ B v_rel² v, which the page compares with the simulated decay. The real thermosphere changes with the solar cycle, day/night and geomagnetic storms by large factors; this table is a teaching model, not a forecast.

Station keeping

When the mean altitude drops below the trigger, a two-burn Hohmann reboost raises it back to the target: Δv₁ = √(μ(2/r₁ − 1/at)) − √(μ/r₁), circularise at apoapsis. The Δv spent is accumulated and compared with the analytic Hohmann cost.

Microgravity quality

A rack at height x above the centre of mass feels the gravity gradient 3n²x (radial) plus the drag deceleration. At 12 m this is about 4.7 µg (g₀ = 9.81 m/s²): it grows linearly with distance, which is why sensitive experiments sit near the centre of mass. Crew motion, thrusters, pumps and fans are not modelled.

Free-flyers

Objects released near the station follow the Hill-Clohessy-Wiltshire equations: ẍ = 3n²x + 2nẏ, ÿ = −2nẋ, z̈ = −n²z. A release above the centre of mass drifts backwards and away; the page checks the closed-form solution against two full two-body orbits.

Model limits

Planar circular reference orbit, point-mass gravity, illustrative atmosphere, instantaneous impulsive burns, no attitude dynamics. Independent educational model of a generic research station.