08 · Stars Balance Fusion and 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
# 08 · Stars Balance Fusion and Gravity — tested **Source:** Incoprea Theory, Volume XIX, Theory 49 (stellar-fusion-collapse). **Claim (verbatim):** "A star's main-sequence lifetime is set by the ratio of its fuel mass to its fusion rate, which scales steeply with mass, so massive stars die young despite having more fuel." **Prediction:** "Lifetime should fall with mass despite larger fuel." **Refutation:** "Lifetime tracking fuel mass would remove the luminosity scaling." ## Why probable The mass–luminosity relation (L ∝ M^4 below ~2 M☉, L ∝ M^3.5 above, L ∝ M^3 for very massive stars) is standard stellar astrophysics; τ ∝ M/L is its direct consequence. ## Method Closed-form computation (code/stellar_test.py): τ = 10 Gyr·M/L with the piecewise empirical mass–luminosity relation, plus an independent check — the predicted main-sequence turnoff mass M_to = (10 Gyr/age)^(1/2.5) versus published cluster ages. ## Results | Mass (M☉) | L (L☉) | main-sequence lifetime | |---|---|---| | 0.3 | 0.06 | 47.8 Gyr | | 1.0 | 1.0 | 10.0 Gyr | | 2.0 | 16 | 1.25 Gyr | | 5.0 | 280 | 179 Myr | | 10 | 3,162 | 32 Myr | | 20 | 35,777 | 6 Myr | | 40 | 404,772 | 1 Myr (L∝M^3.5) / ~6 Myr (L∝M^3) | Fuel mass rises with mass while lifetime falls ~M^−2.5 — a 40 M☉ star carries 40× the fuel and lives ~5,000× shorter than the Sun. Cluster turnoff check: | cluster | age | predicted turnoff | literature | |---|---|---|---| | Pleiades | 125 Myr | 5.8 M☉ | ~5.5–6 M☉ | | Hyades | 625 Myr | 3.0 M☉ | ~2.3–3 M☉ | | M67 | 4.0 Gyr | 1.44 M☉ | ~1.2–1.3 M☉ | | NGC 188 | 6.5 Gyr | 1.19 M☉ | ~1.15 M☉ | Predicted turnoff masses track the literature values (within ~10%, or the cluster-age uncertainty). ## Verdict **SUPPORTED.** Lifetime falls steeply with mass despite more fuel, and the same scaling independently predicts observed cluster turnoff masses. ## Limitations - Piecewise empirical L(M); scatter in real L(M) at fixed mass. - Turnoff comparison uses published ages/turnoffs, not re-derived from observations. Working report — not peer reviewed. Educational information, not medical advice. AI-assisted test: DeepSeek.