# Local stellar stream — circumference, pinch, and two inductances

### Sun–Pleiades distance at the printed speed · rope current at 5 μG · no ledger row · no promote

**CPT Framework — local Galactic neighbourhood**
**Date:** 2026-10-08
**Status:** **RECORD** · public page `/cosmology/local-stream` · this file charters no §0bn row
**Parents:** measey.com `documents/a_geom_ft_stellar_condensation_cascade_chunk5.md` · Alves et al. 2020, Nature, 578, 237 · Konietzka et al. 2024, Nature, 628, 62 · galactic current drift · P-HS

Tags: **[E algebra]** of the named lengths and fields · **[E honesty]** on what stays free

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## 0. One-line

> **At \(135\,\mathrm{pc}\) and \(20\,\mathrm{km\,s^{-1}}\), \(2\pi R/v=41.47\,\mathrm{Myr}\).** That radius is the Sun–Pleiades distance. The pinch force density is zero where \(j_z=0\). On a \(1\,\mathrm{kpc}\) filament of radius \(50\,\mathrm{pc}\) the external inductance is \(1.66\times 10^{13}\,\mathrm{H}\). A surface field of \(5\,\mu\mathrm{G}\) at that radius is \(3.86\times 10^{15}\,\mathrm{A}\).

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## 1. Circumference

\(1\,\mathrm{pc}=3.0857\times 10^{16}\,\mathrm{m}\). \(R=4.166\times 10^{18}\,\mathrm{m}\).

\[
T=\frac{2\pi R}{20\times 10^{3}}=1.309\times 10^{15}\,\mathrm{s}=41.47\,\mathrm{Myr}.
\]

The printed Pleiades vector has magnitude \(27.0\,\mathrm{km\,s^{-1}}\) and gives \(30.7\,\mathrm{Myr}\) at the same \(R\). Sirius’s printed vector has magnitude \(12.4\,\mathrm{km\,s^{-1}}\).

\(v^{2}/R=9.60\times 10^{-11}\,\mathrm{m\,s^{-2}}\). The Newtonian point mass is \(1.26\times 10^{7}\,M_\odot\). Newtonian \(v^{2}=2G\lambda\) needs \(4.65\times 10^{4}\,M_\odot\,\mathrm{pc^{-1}}\).

The Radcliffe gas class, order \(3\times 10^{6}\,M_\odot\) over \(2.7\,\mathrm{kpc}\), is about \(1.1\times 10^{3}\,M_\odot\,\mathrm{pc^{-1}}\) and supports \(3.1\,\mathrm{km\,s^{-1}}\). Konietzka et al. (2024) report vertical oscillation in the Galactic potential. Their solar period is not copied.

A harmonic slab gives a full period \(83.6\,\mathrm{Myr}\) at \(0.10\,M_\odot\,\mathrm{pc^{-3}}\) and \(68.2\,\mathrm{Myr}\) at \(0.15\). The half-periods are \(41.8\,\mathrm{Myr}\) and \(34.1\,\mathrm{Myr}\). The slab uses \(\rho\). The circumference uses \(R\) and \(v\).

The factor between \(41.5\,\mathrm{Myr}\) and the Pleistocene \(41\,\mathrm{kyr}\) obliquity cycle is \(1.01\times 10^{3}\). At \(20\,\mathrm{km\,s^{-1}}\), \(70\,\mathrm{yr}\) is \(295\,\mathrm{AU}\).

## 2. Pinch and the rope current

\[
B_\theta=\frac{\mu_0 I_{\mathrm{enc}}}{2\pi r}.
\]

\(\mathbf{j}\times\mathbf{B}\) is the force density on the current that is present. Outside the rope, \(j_z=0\).

At \(B=5\,\mu\mathrm{G}\) and \(a=50\,\mathrm{pc}\),

\[
I=\frac{2\pi a B}{\mu_0}=3.86\times 10^{15}\,\mathrm{A}.
\]

\(R_{pg}=\mu_0 I^{2}/(4\pi G\lambda^{2})\) is \(4.35\) on the wave gas and \(2.48\times 10^{-3}\) on the \(4.65\times 10^{4}\,M_\odot\,\mathrm{pc^{-1}}\) line. \(R_{pg}=1\) on that orbit line would take \(7.74\times 10^{16}\,\mathrm{A}\).

The disk loop stays \(I=BR/\mu_0=1.044\times 10^{17}\,\mathrm{A}\) at \(8.5\,\mathrm{kpc}\). The heliospheric radial current stays \(I_r=3.01\times 10^{9}\,\mathrm{A}\).

## 3. Two inductances

\[
\pi\sqrt{(1.35\times 10^{11})(9.05\times 10^{4})}=11.004\,\mathrm{yr}.
\]

External partial inductance \(L=(\mu_0 l/2\pi)[\ln(2l/a)-1]\):

| Length | Radius | \(L\) |
|---|---|---|
| \(100\,\mathrm{pc}\) | \(50\,\mathrm{pc}\) | \(2.38\times 10^{11}\,\mathrm{H}\) |
| \(135\,\mathrm{pc}\) | \(50\,\mathrm{pc}\) | \(5.72\times 10^{11}\,\mathrm{H}\) |
| \(300\,\mathrm{pc}\) | \(50\,\mathrm{pc}\) | \(2.75\times 10^{12}\,\mathrm{H}\) |
| \(1\,\mathrm{kpc}\) | \(50\,\mathrm{pc}\) | \(1.66\times 10^{13}\,\mathrm{H}\) |
| \(2.7\,\mathrm{kpc}\) | \(50\,\mathrm{pc}\) | \(6.14\times 10^{13}\,\mathrm{H}\) |
| \(300\,\mathrm{pc}\) | \(100\,\mathrm{AU}\) | \(2.41\times 10^{13}\,\mathrm{H}\) |

The radius that returns \(2\times 10^{13}\,\mathrm{H}\) is \(28.8\,\mathrm{pc}\) at \(1\,\mathrm{kpc}\), and an AU-scale radius on the \(100\)–\(300\,\mathrm{pc}\) lengths. A coaxial return \(L=(\mu_0 l/2\pi)\ln(b/a)\) at \(1\,\mathrm{kpc}\), \(a=50\,\mathrm{pc}\), and \(b/a=2\) is \(4.28\times 10^{12}\,\mathrm{H}\).

No meso capacitance and no \(j(r,\theta)\) are supplied.

## 4. What stays free

The particle halo is retired as inventory (§0bn1190). This page's current is not that retirement. Do not write \(\Omega_{\mathrm{CDM}}=0\) from this page. Gate 5 stays unpaid: the galactic centre is not given a jet. The tachocline seat stays closed. The wind bank stays `PASS_FT_CH_CURRENT_FIRST`. Interior fusion stays held. The live line stays §0bn1188. No chip. No promote.

The figure on the public page is `public/figures/local-stream/fig1_named_links.png`.

At \(50\,\mathrm{pc}\) the Lorentz force on a neutral star is zero. The gas line gives \(6.13\times 10^{-12}\,\mathrm{m\,s^{-2}}\) and the orbit line gives \(2.59\times 10^{-10}\,\mathrm{m\,s^{-2}}\). The coupling term remains absent. See `a_geom_neutral_star_force.md`.