Conjunction Assessment
How Close-Approach Screening Predicts Collision Risk
Every conjunction assessment run begins with an orbital catalog. Each tracked object is represented by a state vector (position and velocity) and an associated error covariance that describes how uncertain that state is in the radial, in-track, and cross-track directions. Screening software propagates these states forward in time, typically over a seven-day horizon, and searches for any pair whose predicted separation falls inside a screening volume. A common volume is an ellipsoid roughly 1 km in the radial axis by 25 km in-track by 25 km cross-track, because in-track uncertainty grows fastest as a propagated orbit ages. Pairs that breach the volume become candidate conjunctions and advance to risk computation.
The headline risk metric is the probability of collision, Pc. It integrates the combined position covariance of the primary and secondary objects across the plane perpendicular to the relative velocity vector at the time of closest approach (the conjunction or B-plane). A counterintuitive consequence is probability dilution: when a secondary object is poorly tracked and its covariance is very large, the integrated Pc can fall well below the maneuver threshold even though the objects pass close, because the collision footprint is smeared across a wide uncertainty region. For this reason operators never read Pc in isolation; they weigh it against the hard-body miss distance and the freshness and quality of the covariance.
When a conjunction crosses an operator's risk threshold, the response is a collision-avoidance maneuver, usually a small posigrade or retrograde burn a few hours to a day before the time of closest approach. Even a 0.1 m/s burn applied a full orbit ahead shifts the in-track position by hundreds of meters, which is normally enough to push the miss distance and Pc back into the safe region. The cost is propellant and a temporary departure from the operational orbit, so the threshold policy balances safety against mission life.
Probability of Collision and Miss Distance
Pc = ∫∫ (1 / (2πσxσz)) × exp(−½[(x/σx)2 + (z/σz)2]) dA, over the combined hard-body radius
Combined hard-body radius:
RHB = rprimary + rsecondary
Miss distance at closest approach:
dmiss = | rprimary(TCA) − rsecondary(TCA) |
Where σx, σz are the combined covariance standard deviations projected onto the B-plane, RHB is the combined object radius, and TCA is the time of closest approach. Typical relative velocities at LEO conjunctions are 7 to 15 km/s, so the encounter is effectively instantaneous and a 2D static integral applies.
Conjunction Risk Decision Bands
| Probability of collision (Pc) | Risk band | Typical miss distance | Operator action | Tracking cadence |
|---|---|---|---|---|
| < 1×10-7 | Green | > 5 km | No action, archive | Routine |
| 1×10-7 to 1×10-5 | Low | 1 to 5 km | Monitor updated CDMs | Daily |
| 1×10-5 to 1×10-4 | Yellow / watch | 200 m to 1 km | Request added tracking | Multiple per day |
| > 1×10-4 | Red | < 500 m | Plan avoidance maneuver | Near-continuous |
| > 1×10-3 | Critical | < 200 m | Execute maneuver | Near-continuous |
Frequently Asked Questions
What probability of collision threshold triggers an avoidance maneuver?
Operators use tiered policies. A screening ellipsoid of roughly 1 km radial by 25 km in-track by 25 km cross-track flags candidate conjunctions, then probability of collision (Pc) drives the decision. Pc > 1×10-4 is the common red threshold that prompts a maneuver; 1×10-5 to 1×10-4 is a yellow watch band. Because Pc dilutes when covariance is large, analysts also weigh miss distance and covariance quality, not Pc alone.
What is a Conjunction Data Message and what does it contain?
A Conjunction Data Message (CDM) is the CCSDS 508.0-B-1 format used to deliver warnings from a screening provider, such as the U.S. Space Force, to operators. Each CDM lists the time of closest approach, miss distance split into radial, in-track, and cross-track components, relative velocity, the position and velocity covariance of both objects, and the computed Pc. CDMs typically arrive three to seven days before TCA and are reissued as fresh tracking shrinks the covariance.
How does radar tracking accuracy affect conjunction assessment?
The assessment is only as good as the orbital state and its covariance, which come from sensor tracking. Space-surveillance radars (for example the S-band Space Fence near 3.5 GHz) measure range to a few meters and angle to a fraction of a milliradian per pass. More passes and diverse geometry shrink the covariance ellipsoid and sharpen Pc. A stale two-line element set may carry several kilometers of in-track error, yielding unreliable Pc. Higher radar power-aperture product detects debris down to about 2 cm at LEO.