Probability of Collision (Pc)

Probability of collision is the number that turns a close approach into a decision. A predicted miss distance alone is nearly meaningless — 400 metres is terrifying or trivial depending on how well both orbits are known — so conjunction assessment instead computes Pc: the probability that, given each object's covariance, the true separation at the time of closest approach will be smaller than the combined size of the two objects (their hard-body radius). Mathematically it integrates the combined position uncertainty over a disc the size of the merged objects in the encounter plane. The resulting figures look tiny but carry real weight: common decision thresholds are around 10⁻⁴ (1-in-10,000) for planning a collision-avoidance manoeuvre, with operators tracking the trend across successive CDMs rather than any single value. Pc behaves counterintuitively: it usually rises as tracking improves and covariance shrinks around a genuinely close geometry, and in the opposite regime — very poor data — it can be misleadingly small because the probability mass is smeared over a huge volume, the well-known "dilution" effect. Read properly, Pc is less a verdict than a live conversation between geometry and data quality.