Space systemsAerospace & marine

Satellite constellation

A 24-satellite Walker constellation, designed end to end — orbit propagation with J2, ground tracks and coverage, ground-station contact windows, a fleet-sizing trade, and a verification gate, all over a 3D globe.

DjiniousLabModelling & simulation

A DjiniousLab notebook timeline of 24 satellite passes over Toulouse across a 24-hour window, each pass coloured by peak elevation

Walker constellation: 24 / 3 / 1Walker constellation
orbit · 53° inclination: 550 kmorbit · 53° inclination
band coverage (24 h): ~93%band coverage (24 h)
J2 nodal regression: −4.49°/dayJ2 nodal regression
design notebooks: 9design notebooks
requirements verified: 6 / 6requirements verified

A constellation, designed where it flies.

A Walker-delta 24/3/1 constellation at 550 km and 53° inclination — the shape of a modern low-Earth-orbit fleet — propagated with two-body dynamics and J2 nodal precession, its coverage and ground-station contacts worked out over a 3D globe. From a single orbit to a fleet-sizing trade and a verification sign-off, the whole mission-design loop in one program.

From one orbit to a verified fleet.

Each stage is its own runnable notebook, building from a single propagated orbit up to constellation-level coverage and a sizing trade.

Orbit propagation

Two-body motion plus the J2 oblateness perturbation, propagated from classical elements — the ground track drifts ~24° west each period as the Earth turns beneath it.

Walker constellation

The 24/3/1 recipe places every satellite's RAAN and mean anomaly from the i:T/P/F rule — all 24 orbits rendered at true altitude on the globe, coloured per plane.

Coverage & revisit

An elevation-mask footprint (~15° half-angle, ~1665 km) tiled across the constellation gives a 3D choropleth of how many satellites see each point — and a band coverage near 93%.

Contact windows

For a ground station at Toulouse, every pass above 10° elevation over 24 hours — about 140 passes a day, ~7 minutes mean — laid out as a timeline and an hourly histogram.

Sizing trade

A sweep over planes × satellites-per-plane plots fleet size against worst-case revisit, and lands the 24/3/1 baseline at the cost-versus-service knee.

J2 precession

The oblateness-driven node regression of −4.49°/day, separated from the Keplerian baseline and used to search for repeat ground tracks.

A timeline of 24 satellites' passes over a ground station across 24 hours, each pass a coloured tick keyed to peak elevation — Every satellite pass over Toulouse in a day, above a 10° mask: each row is a satellite, each tick a pass, coloured by peak elevation. The diagonal banding is the three orbital planes sweeping the station in turn — about 140 contacts a day.

A scatter plot of fleet size against worst-case 24-hour revisit time, with the 24/3/1 baseline starred at the knee of the trade — The sizing trade: more satellites buy shorter revisit, but with diminishing returns. The 24/3/1 baseline (starred) sits at the knee — enough fleet to hold the revisit requirement without paying for satellites the mission doesn't need.

Coverage you can see, not just tabulate.

The constellation, its ground tracks and its instantaneous coverage all render on a 3D globe through the same notebook outputs that drive the numbers — orbits at true altitude coloured per plane, footprints extruded by how many satellites are in view. The propagation honours the J2 perturbation, the dominant secular effect at 550 km, so the node regression and repeat-track geometry are physical, not Keplerian idealisations. The mission-design loop — propagate, cover, contact, size, verify — lives in one place instead of three.

A notebook plot of the ascending-node longitude drifting over 14 days under J2 versus a non-precessing Keplerian baseline — J2 in action: the ascending node walks westward at −4.49°/day, diverging steadily from the Keplerian baseline over two weeks. That secular drift is what sets a constellation's repeat-track period — and a sun-synchronous design exploits it deliberately.

Mission requirements, re-derived and checked.

The sign-off notebook re-derives each requirement from the propagated constellation rather than restating the design intent.

Result

Band coverage (24 h): ~93%
Worst-case revisit: ≤ 6 h
Passes per day (Toulouse): ~140
J2 node regression: −4.49°/day
Requirements verified: 6 / 6

Target

Band coverage (24 h): ≥ 90%
Worst-case revisit: ≤ 6 h
Passes per day (Toulouse): —
J2 node regression: physical
Requirements verified: PASS

Mission-design fidelity.

Propagation is two-body plus J2 — the dominant secular perturbation at this altitude — not a full force model with drag, higher-order gravity, solar radiation pressure or third-body effects. The coverage footprint is a spherical-Earth elevation-mask cap on coarse grids, and revisit is evaluated over a 24-hour window. That is exactly the fidelity constellation sizing needs first: choosing planes and phasing, checking coverage and revisit, and counting ground-station contacts — before a high-precision orbit-determination tool ever enters the picture.