CALC-080

Solar radiation pressure in the graveyard-orbit disposal relation

Feeds CLM-0751. Answers QST-011. Basis: minimum perigee increase in km; area-to-mass ratio in m2/kg; equivalent areal density in kg/m2. No SBSP design parameter is used anywhere.

Why it was needed. The IADC and ITU disposal relation is treated across the corpus as a fixed 235 km constant with a small correction. For a kilometre-scale, very light structure the correction is not small, and whether it dominates is decidable by arithmetic over the publishing source's own stated input range.

Inputs. Every numeric input is STATED, verbatim, by the source that publishes the relation.

The range inputs are not merely cited, they are quoted verbatim from the page that states them, so a checker can confirm the range without holding the document. And the one genuinely uncertain assumption - whether three standards bodies mean the same thing by A/m - is identified in the claim's own assumes field rather than left for a verifier to find. A definitional non-equivalence between sources is exactly the kind of assumption that silently invalidates a sensitivity analysis, and it is named.

Working, transcribed. Four corners of the stated ranges, then a break-even.

-- Four corners --
Cr = 1, A/m = 0.01   ->  1000 x 1 x 0.01 =  10   delta-H = 245 km
Cr = 2, A/m = 0.01   ->  1000 x 2 x 0.01 =  20   delta-H = 255 km
Cr = 1, A/m = 0.1    ->  1000 x 1 x 0.1  = 100   delta-H = 335 km
Cr = 2, A/m = 0.1    ->  1000 x 2 x 0.1  = 200   delta-H = 435 km

Ratio at the top of the source's own stated range:
     435 / 235 = 1.851

-- Break-even: where the radiation term equals the 235 km constant --
     1000 x Cr x A/m = 235      =>   Cr x A/m = 0.235

     at Cr = 1   A/m = 0.235   m2/kg   ->  1/0.235   = 4.255 kg/m2
     at Cr = 2   A/m = 0.1175  m2/kg   ->  1/0.1175  = 8.511 kg/m2

Result: the required perigee increase ranges from 245 km to 435 km across the source's own stated input ranges - at the top of that range, 1.85 times the 235 km constant. The radiation-pressure term equals the constant at a sun-facing areal density of about 4.26 kg/m2 at Cr = 1, or about 8.51 kg/m2 at Cr = 2.

State what the 8.5 kg/m2 is, because it is the number that will get quoted. It is a break-even areal density - the value at which the solar-radiation-pressure term alone equals the entire protected-region-plus-perturbation constant. Anything lighter per square metre of sun-facing area needs a radiation allowance larger than that whole constant. It is not a design limit, not a compliance threshold, and not a statement about any satellite.

Conclusion. It converts a regulatory constant into a design-dependent quantity, and thereby generates a checkable question for any SBSP proponent: what is your aspect-area-to-dry-mass ratio, and what perigee raise does it imply? That question has a propellant, and therefore a mass and a cost, consequence on VC04 and XC02 which this record does not carry through and which should be.

Where this fails, and the restriction is the claim's own and is absolute. - This is a sensitivity analysis of a published formula over the publishing source's own stated input range. It is NOT a finding about any SBSP design, and it may NOT be used to say that any proposed satellite fails, or would fail, the disposal requirement. - No source held gives an aspect-area-to-dry-mass ratio for any SBSP concept, so whether any design falls inside or outside the 0.01-0.1 range is not established and is recorded as unevidenced. - This arithmetic may not support the words validated, safe, achieved, proven or demonstrated. It bounds a quantity; it does not test a design. - The relation has an alternative compliance route in SRC-226 and SRC-228 - a perigee high enough that perturbations do not return the payload to the protected region within 100 years - which this calculation does not evaluate at all. - The A/m definitional non-equivalence above is unresolved. - VER-630 CONFIRMED 2026-09-04.

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