Sensitivity of the Dominant Obliquity Forcing Period to Earth's Dynamical Ellipticity: A Reduced J2–Precession Model

In a reduced secular model, we quantify the sensitivity of Earth's dominant ~41-kyr obliquity forcing period to its dynamical oblateness J2. The axial precession rate p = k cosε has precession constant k proportional to the dynamical ellipticity E_d=(C−A)/C, itself proportional to J2; the dominant obliquity line sits at ν = p + s₃ with s₃ a J2-independent secular node frequency, giving period P = 1,296,000″/|ν|. Hence d(ln P)/d(ln J2) = −p/(p+s₃) ≈ −1.60: a larger dynamical ellipticity gives faster precession and a shorter dominant obliquity period. A direct RK4 integration of the averaged spin-precession equation reproduces the analytic line to four significant figures (slope −1.605). This corrects and rescopes a prior version that had the sign reversed and over-extended to a climate-feedback prediction; contemporary-J2 application is retained here only as an explicitly conditional illustration. Supplementary code included.--Author: James E. Dunn — Independent Researcher, Hydrogen Lifecycle Research ProgrammeORCID: https://orcid.org/0009-0005-2679-6574Corpus: https://zenodo.org/search?q=creators.orcid:0009-0005-2679-6574 · License: CC BY 4.0