Coaxial return on the Sirius segment

\(L\) and \(C\) from one geometry · period \(27.02\,\mathrm{yr}\) · printed \(11.004\,\mathrm{yr}\) stays the invert

Date: 2026-10-08 Status: RECORD · public page /cosmology/isorotation · no ledger row · no promote Parent: measey.com documents/a_geom_ft_stellar_condensation_cascade_chunk3.md

A coaxial return of length \(l=8.136\times 10^{16}\,\mathrm{m}\) (the scored \(8.6\,\mathrm{ly}\) Sirius segment), inner radius \(100\,\mathrm{AU}\), and \(b/a=2\), has \(L=1.13\times 10^{10}\,\mathrm{H}\) and \(C=6.53\times 10^{6}\,\mathrm{F}\). The period is the output: \(\pi\sqrt{LC}=\pi l/c=27.02\,\mathrm{yr}\), and the full ring is \(54.03\,\mathrm{yr}\). The printed \(11.004\,\mathrm{yr}\) remains the invert of \(1.35\times 10^{11}\,\mathrm{H}\) and \(9.05\times 10^{4}\,\mathrm{F}\).

The pair is

\[ L=\frac{\mu_0 l}{2\pi}\ln\frac{b}{a},\qquad C=\frac{2\pi\varepsilon_0 l}{\ln(b/a)}. \]

Their product cancels the radius ratio: \(\sqrt{LC}=l/c\). Any other \(b/a\) on this length returns the same period and a different split between \(L\) and \(C\). The partial inductance of the isolated segment remains \(1.350\times 10^{11}\,\mathrm{H}\). The sheath capacitance that produces \(11.004\,\mathrm{yr}\) remains the invert at \(3.76\times 10^{8}\,\mathrm{V}\).

The homopolar potential is axisymmetric. Joy’s tilt still needs a non-axisymmetric term. Hale polarity remains one dipole under the \(\Omega\)-effect. The dynamo-flow seat stays closed. The live line stays §0bn1188. No chip. No promote.

Figure: public/figures/isorotation/fig2_coaxial_period.png.