Orbital Lifecycle Envelope (MTBOF)

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) = ρ_Vallado(h) · F_baseline(h) · [F_10.7(t) / F_10.7,base] · [1 + β_rel(h) · ap(t)] time-varying density via SWADI baseline + F10.7 cycle + β_rel storm response (3) MTBOF_x(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-F_baseline cycle-invariance limit empirically — disclosed below, not hidden.

Definitions: F_baseline(h) is the SWADI substrate-weighted atmospheric density per altitude shell (decision #25); β_rel(h) is the per-shell storm-response coefficient (decision #28); F_10.7(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

P10/P50/P90 envelope for any orbit you specify (initial altitude + A/m + decommissioning epoch).
Solar-window-timed deorbit advisory (decision #22): "decommission today vs. maintain altitude until next solar maximum" — propellant cost vs. compliance horizon, surfaced numerically.
Calibration receipts: M2 historical-prediction errors per asset class + envelope-containment results against documented reentries.

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	2.05	1.67	0.65	3.17×	yes
Low-LEO 450 km A/m=0.012	2.14	1.73	0.67	3.18×	yes
Mid-LEO 600 km A/m=0.010	29.65	13.80	9.71	3.05×	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, with the static-F_baseline cycle-invariance limit visible.

Asset	alt (km)	A/m	observed	P90	P50	P10	result
Skylab	433	0.0036	5.42 yr	1.71	2.06	5.01	above P10 by 0.41 yr
UARS	575	0.0086	5.78 yr	7.75	17.38	23.19	below P90 by 1.97 yr
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. Skylab's actual atmosphere was quieter than even the cold-sun archetype's; UARS reentered during a hot-sun phase that exceeded the methodology's hot-sun replay. ROSAT, mid-cycle, lands inside the envelope. Decision #29 articulates the v0.4.0.7 cycle-stratified F_baseline fix; until then the limit is disclosed empirically.

Engagements are direct. Email with the asset, fleet, or jurisdiction you want assessed and a sample lands in your inbox within one day.

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tony@fancyland.net