ORCAS

The problem

On 10 February 2009, at 16:56 UTC and an altitude of 788.6 km over Siberia, the active communications satellite Iridium 33 collided with the derelict Cosmos 2251 at a relative velocity of 11.7 km/s. Standard deterministic algorithms had predicted a safe miss distance of over 500 metres.

They were not wrong about the distance. They were wrong to treat it as a distance.

Radar telemetry carries positional uncertainty. That uncertainty is a covariance matrix — an ellipsoid around the predicted position, oriented along the orbit. When two ellipsoids overlap substantially, the centres can be half a kilometre apart and the objects can still hit. Deterministic screening throws that information away at the first step, and the 2009 event is the demonstration of what that costs: the first accidental hypervelocity collision between two intact satellites, and a debris cloud we are still cataloguing.

The system

ORCAS replaces the distance threshold with a probability of collision.

Broad phase

A Python/FastAPI backend ingests dynamic Two-Line Element sets from CelesTrak and propagates them with SGP4. Screening every object against every other object is O(n²) and does not survive a real catalogue, so the broad phase uses volumetric spatial hashing over a scipy.spatial.cKDTree to reduce it to roughly O(n log n) — enough to hold a constellation-wide sweep inside a frame budget.

Narrow phase

Surviving pairs go to the narrow phase, which is where the actual argument lives:

1. Propagate both objects’ state vectors to the time of closest approach in ECI.
2. Transform the covariance to ECEF through the Jacobian — C_ECEF = J · C_ECI · Jᵀ.
3. Project onto the B-plane, the plane perpendicular to relative velocity at TCA — C_B = P · C_c · Pᵀ. This collapses a three-dimensional encounter into the two-dimensional geometry that actually determines whether the objects intersect.
4. Integrate the 2D Gaussian over the combined hardbody cross-section to get P_c.

A Random Forest ensemble classifies the encounter from these kinematic features — principally the Mahalanobis distance, which measures separation in units of the uncertainty itself rather than in metres.

Rendering

A React-Three-Fiber frontend renders the result: dynamic Earth synced to GMST, selectable satellite meshes, orbit paths, and — for the Kessler case — a THREE.InstancedMesh swarm of ten thousand fragments with additive-blended volumetric density heatmaps, at a continuous 60 fps.

The validation

The method is only interesting if it changes an answer. So the system re-runs 2009, time-decoupled, using the historical elements:

Quantity	Value
Altitude at T₀	788.6 km
Velocity (Iridium 33 / Cosmos 2251)	7.46 / 7.42 km s⁻¹
Covariance determinant, primary	2.4 × 10⁴ km²
Covariance determinant, secondary	4.1 × 10⁴ km²
Mahalanobis distance D_M	1.84
Probability of collision P_c	4.2 × 10⁻³
Alert threshold	1.0 × 10⁻⁴

P_c comes out two orders of magnitude above the alert threshold. The deterministic models of the day flagged this encounter as a miss. The probabilistic pipeline flags it critical.

Status and scope

Done: SGP4 propagation engine, covariance/conjunction pipeline, Random Forest classifier, OMM ingestion with legacy TLE adapter, and a golden-file test of the 2009 Iridium 33 / Cosmos 2251 historical reconstruction.

Roadmap: Kessler swarm visualisation, density heatmaps, CSV export, J2 and atmospheric drag perturbations in the propagator, ML-driven orbital decay prediction, and full backend collision integration.

Honest scope note: the interactive simulation on this page is a deliberately small slice — two-body Keplerian propagation, no perturbations, representative elements rather than live TLEs. The real engine is a separate application.

Reproducibility

The repository isn’t public yet — full open-sourcing is planned once the simulation reaches parity (Phase P6). It will be a one-command docker compose up when it opens.