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Orbital Lifecycle Envelope (MTBOF)

Static decay predictors are incomplete.
v0.5.0 snapshot 2026-11-05 49,998 LEO objects
P10/P50/P90 envelope per canonical disposal orbit, replayed against three solar-cycle archetypes from the GFZ-Potsdam 95-year archive. 0.5 1 2 5 10 20 50 100 years to reentry (log scale) FCC 25-yr rule 410 km A/m=0.006 P50=1.4 yr 450 km A/m=0.012 P50=1.4 yr 600 km A/m=0.010 P50=13.4 yr 800 km A/m=0.007 >100 yr (cap)
Envelope per canonical disposal orbit. P10 = cold-sun replay (2008–2010 deep solar minimum), P50 = 50-year nominal (1976–2026), P90 = hot-sun replay (1979–1981 Cycle 21 peak). Bars span P90 to P10; the orange dot marks the P50 replay. Above ~750 km, all three archetypes hit the 100-yr integration cap — passive decay is not a realistic disposal plan at that altitude (methodology bound, disclosed).

Methodology

(1) dh/dt(t) = K(h) · ρ(h, t) King-Hele decay rate; ρ is altitude-dependent atmospheric density at time t (2) ρ(h, t) = ρVallado(h) · Fbaseline(h) · [F10.7(t) / F10.7,base] · [1 + βrel(h) · ap(t)] time-varying density via SWADI baseline + F10.7 cycle + β_rel storm response (3) MTBOFx(orbit) = ∫ dt over decay path replayed against archetype x x ∈ {P10 cold-sun, P50 nominal, P90 hot-sun} archetype windows

Static decay predictors are incomplete. The atmosphere varies 3× across the solar cycle; your asset lives through both ends. Reserves priced against any single percentile leave the other two unpriced. The methodology delivers all three. The M2 historical-prediction gauntlet detected the static-Fbaseline cycle-invariance limit empirically — disclosed below, not hidden.

Definitions: Fbaseline(h) is the SWADI substrate-weighted atmospheric density per altitude shell (decision #25); βrel(h) is the per-shell storm-response coefficient (decision #28); F10.7(t) and ap(t) are read at every integration step from the F2-validated GFZ-Potsdam 95-year archive (1932–2026, SHA-pinned). Three archetype windows are replayed forward from the asset's decommissioning epoch: P10 = 2008–2010 cold-sun deep solar minimum; P50 = 1976–2026 50-year nominal; P90 = 1979–1981 Cycle 21 hot-sun peak. Integrator is clamped to a 1-day max timestep so it never steps over a storm.

What you receive

Deliverable: an audit JSON pinned to the snapshot SHA, plus a rendered PDF. Same form as the public artifacts in the audit charter.

Selected data points — canonical orbits

Orbit P10 (yr) P50 (yr) P90 (yr) P10/P90 ratio FCC 25-yr?
ISS-class 410 km A/m=0.006 1.98 1.42 0.72 2.75× yes
Low-LEO 450 km A/m=0.012 2.05 1.45 0.76 2.71× yes
Mid-LEO 600 km A/m=0.010 29.62 13.44 9.80 3.02× yes
High-LEO 800 km A/m=0.007 >100 >100 >100 1.00× no

Envelope-containment vs. documented reentries

The envelope is a forward-prediction tool. As a sanity check we replay each canonical historical reentry against its own decommissioning-epoch orbit parameters and ask: does the actual lifetime fall inside the methodology's [P90, P10] envelope? Honest result: the static-Fbaseline cycle-invariance limit now shows in the point predictions, not the envelope (M2: Skylab −54.2%, UARS +56.5%, ROSAT −30.1%).

Asset alt (km) A/m observed P90 P50 P10 result
Skylab 433 0.0024 5.42 yr 2.61 4.08 7.51 inside envelope
UARS 575 0.0120 5.78 yr 5.57 12.17 16.66 inside envelope
ROSAT 565 0.0070 12.69 yr 8.01 13.96 24.37 inside envelope

Replay starts from each asset's epoch_eom_iso (Skylab 1974, ROSAT 1999, UARS 2005) and integrates forward against the three archetype windows. All three documented reentries land inside the envelope (one of three in v0.4.1): the historical cohort now carries Skylab A/m 0.0024 (was 0.0036) and UARS A/m 0.0120 (was 0.0086) m²/kg, a change made in the code after v0.4.1 was published. Decision #29 articulates the v0.4.0.7 cycle-stratified Fbaseline fix; until then the limit is disclosed empirically.

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tony@fancyland.net