The hard-body radius is the combined physical size of two objects in a conjunction — the radius of the circle that counts as a hit in the collision-probability integral. It is usually the sum of a sphere circumscribing each object, so it errs on the large side deliberately.
Understanding Hard-Body Radius
Why a sphere, when satellites are anything but
A real conjunction involves two tumbling or slewing shapes meeting at an unknown mutual orientation, at a relative speed that makes attitude prediction pointless. Rather than model that, practitioners collapse each object to its worst case: the circumscribing sphere, which guarantees the computed probability bounds the true one from above whatever the orientation. More refined treatments exist — projecting actual dimensions onto the encounter plane, or Monte Carlo sampling over attitudes — and fleet operators sometimes use them to trim false alarms for their own well-known vehicles. For the general catalogue, where many secondaries are debris of uncertain shape known mainly through their radar cross-section, the sphere remains the honest default.
Size from radar: estimating the unknown half
For the debris that makes up most conjunction secondaries, nobody has a datasheet. Trackers infer size from radar cross-section — how strongly the object reflects — which correlates loosely with physical dimensions but depends on material, shape and aspect. Screening pipelines bucket objects (small/medium/large) from RCS statistics and assign each bucket a standard radius contribution. The uncertainty this injects into Pc is real but bounded: because the assumed radii are conservative and the covariance usually dominates the calculation, an approximate HBR rarely changes a manoeuvre decision — though it is one more reason operators treat marginal Pc values as ranges, not verdicts.