05 · Escape Needs Thermal Over Gravity — tested
Supplied working report; original verdicts not validated.
Review status: Needs review. This is an archival source note, not a passed proof.
report.md
# 05 · Escape Needs Thermal Over Gravity — tested **Source:** Incoprea Theory, Volume XXII, Theory 87 (escape-thermal-velocity). **Claim (verbatim):** "Whether an atmosphere escapes is set by the ratio of thermal velocity to escape velocity, so a warm light gas escapes from a planet that retains a cold heavy one." **Prediction:** "Escape should track the ratio by species." **Refutation:** "Escape tracking mass alone would remove temperature." ## Why probable This is the Jeans escape parameter λ = GMm/(kTr) — the textbook criterion for thermal atmospheric escape, standard in planetary science. ## Method Closed-form computation (code/jeans_test.py) of the escape velocity, Jeans parameter λ and the escape flux factor (1+λ)e^(−λ) for H₂, He, H₂O, N₂, O₂, CO₂ at Earth, Mars, Venus and Titan using published exobase radii and temperatures. ## Results | body | H₂ λ | He λ | N₂ λ | CO₂ λ | pattern | |---|---|---|---|---|---| | Earth | 14.1 | 27.9 | 195 | 307 | H₂/He escape; N₂, O₂, CO₂ retained | | Mars | 11.5 | 22.7 | 159 | 250 | H₂ escapes; CO₂ retained (thin) | | Venus | 50.0 | 99.3 | 695 | 1092 | heavy gases retained; H₂O lost | | Titan | 3.6 | 7.2 | 50.6 | 79.5 | H₂ escapes; N₂/CH₄ retained (cold) | - The computed λ ordering reproduces the observed pattern: **warm light gases escape where cold heavy ones are retained**, on the same body (Earth: H₂ λ≈14 escaped vs N₂ λ≈195 retained) and across bodies (Titan keeps N₂ at λ≈51 despite gravity 0.14 g thanks to its cold exobase). - Species ordering is set by the **ratio** of thermal to escape velocity — not by mass alone: on cold Titan, H₂ (lightest) still escapes (λ=3.6) while much heavier CO₂ would be retained; on hot-Venus-like conditions even moderately heavy gases would escape. ## Verdict **SUPPORTED.** Escape tracks λ (thermal velocity / escape velocity) by species exactly as claimed; the mass-only refutation fails because temperature changes the ranking across bodies. ## Limitations - Jeans (thermal) escape only; non-thermal escape (photochemical, sputtering, hydrodynamic) dominates for Mars O and early Earth H — noted, not modelled. - Exobase temperatures are literature values with real uncertainties. Working report — not peer reviewed. Educational information, not medical advice. AI-assisted test: DeepSeek.