Separate a star’s fuel inventory from its mass defect

1. Define the stellar inference

Net hydrogen fusion produces helium with less rest mass than the initial reactants; the difference appears in released energy and escaping particles. The proton–proton chain and the CNO catalytic cycle provide different reaction routes, with different temperature dependence, to a similar net conversion. Fusion is not chemical combustion and does not consume every kilogram of a star at once.

2. Connect mechanism and assumptions

The original budget supplies reference mass 2×10³⁰ kg, accessible hydrogen fraction f and ideal conversion efficiency 0.007 of that accessible mass. Released energy is E=0.007fMc². The factor f represents a declared accessible fuel inventory; the efficiency is the fraction of that fuel’s rest mass converted, not the fraction of the whole star immediately destroyed.

At a fixed luminosity 3.8×10²⁶ W, the ideal timescale is E/L. The model treats all released energy as available to that stated output and omits neutrino partition, evolving luminosity and changing fuel accessibility. It deliberately holds luminosity fixed when mass changes, so it must not be combined silently with a separate mass–luminosity law.

Fusion rates respond to temperature and density, and structural feedback can regulate a star: expansion can cool burning regions, while contraction can heat them. Actual burning histories and mixing determine accessible fuel. This simple conservation calculation explains a scale of available energy, not an exact stellar age or an operational nuclear process.

3. Work the supplied case

For one reference mass and accessible fraction 0.1, fuel mass is 2×10²⁹ kg and converted rest mass 1.4×10²⁷ kg. Ideal released energy is≈1.25826×10⁴⁴ J. Dividing by the supplied fixed luminosity and a 365.25-day year gives about 1.0493×10¹⁰ years.

4. Predict and investigate

Is 0.007 a fraction of the accessible fuel or automatically the fraction of the entire star?

Retain total mass, accessible fuel, converted mass, energy and power as separate ledger stages. Change accessible fraction and explain why a luminosity evolution would change the timescale.

Source and boundaries

Primary source. Checked 31 October 2026. All numerical records and diagrams here are original supplied models, not measured stellar populations or a full stellar-evolution solver. No direct observing or physical experiment is requested.