Space debris metrics that cannot be added up

The Challenge

ESA's MASTER-8 and NASA's ORDEM 3.1 are the two premier orbital debris engineering models. Both are authoritative. Both are carefully built. Both describe the same physical reality. On identical simulation cases they diverge sharply, and the joint ESA and NASA comparison study is explicit that this is not a matter of one being right: "each model provides its agency's best estimate of the orbital debris environment. One model may be more accurate in one regime while the other may be more accurate in another, and it is expected that the truth lies somewhere in between."

The structural cause is stated in the same paper, and it is the sentence that matters: "a direct comparison of the source models is not immediately possible from the model output." MASTER-8 divides the population by generative source, into fragments, solid rocket motor slag and dust, NaK droplets, paint flakes, ejecta and MLI fragments. ORDEM 3.1 divides it by material density, into low, medium, high, NaK and intacts. One population, orthogonal cuts, only the NaK component in common.

Why this is a safety problem, not a housekeeping problem

Every environmental indicator is computed over an underlying population model, and therefore silently inherits that model's partition. ECOB, the Criticality of Spacecraft Index and the Space Sustainability Rating mission index each carry an inheritance their outputs do not record. Combine two indicators built on different models and you have combined two incompatible partitions with no trace that it happened.

There is no error message. The composed indicator returns a number, and the number gets used. It is the same class of failure as a unit mismatch, and it has the same property: cheap to prevent by construction, effectively undetectable afterwards.

The third row is the one that shows the tool is doing real work. A checker that refuses everything is useless, and one that permits everything is dangerous. ECOB and the SSR mission index genuinely are structurally combinable, and the framework permits the combination while flagging that both derive from MASTER-8 and are therefore not independent estimates. Shared source-population error is common-mode, so a composed figure will understate its own uncertainty. That is a judgement a spreadsheet cannot make and a dashboard will not surface.

The gap this sits in

A decade of orbital debris ontology work exists in the literature. The Space Object Ontology, the Space Situational Awareness Ontology and an associated orbital event ontology are all formalised in OWL, and all are described by their authors as under development. None has been mapped to an operational data standard or to an engineering model.

Meanwhile the CCSDS orbit, conjunction and tracking message families are mature and operationally adopted, but they are syntactic: they standardise message structure, not the meaning of a derived quantity, not the population partition it was computed over, and not the assumptions under which it holds. Four layers, developed independently, none mapped to the next. This artifact is one small, concrete step across that gap.

Scope, stated plainly

The declarations capture the structural commitments of each metric: quantity kind, denominator, source model, inherited partition, regime of validity and stated assumptions. They do not reimplement the metrics' formulae and are not a substitute for the primary literature; parameter-level definitions should be confirmed with the metric authors before operational use. The ORDEM-derived indicator is constructed for demonstration and is not a published index. The orthogonality assertion between the two partitions is evidenced by the cited ESA and NASA study rather than asserted by us. This is a demonstrator built to show that the composition problem is mechanically checkable, and it is deliberately small.

Why we could build it quickly

Because the method was not invented here. This is the third domain in which we have applied the same pattern: formalise each authoritative representation's commitments machine-readably, compute where a mapping is sound, lossy or invalid, and emit a certificate a reviewer can check independently rather than having to trust us. Previously for defence and security information exchange, in the IES to HQDM crosswalk with its reasoner-certified 21-axiom bridge, and for UK government digital twin semantics through the National Digital Twin Programme.

The domains differ. The problem does not: two or more authoritative representations of the same reality, built on different assumptions, that somebody now needs to use together.