Recombination Energy as a Fraction of Binding Energy in a One-Solar-Mass Red Giant Envelope

This paper examines the hydrogen-rich envelope of a one-solar-mass red giant, mass 0.55 solar masses, hydrogen mass fraction 0.70 and helium mass fraction 0.28, bound to a 0.45 solar-mass core at a radius of 120 solar radii. Using published input values and the standard energy comparison between envelope binding and orbital release, the calculation addresses the specific budget that decides the outcome for this pairing. The headline results are: recombination_fraction_of_binding = 0.454; recombination_energy_erg = 1.580e+46; binding_energy_erg = 3.477e+46. The method, inputs and limitations are stated in full so that any reader can reproduce or rescale every number from the deposited calculation script. Recombination is the most frequently invoked supplement to orbital energy, and the low-mass red giant is where its case is strongest: the envelope is cool, much of it sits near the hydrogen ionisation temperature, and the binding energy is comparatively modest. Agreement and disagreement with published values for this class are reported at their actual size, and the conclusions are limited to what the budget arithmetic supports.