Introduction

We begin the calculation of the physical source of the Galactic Shear, the total angular momentum of Andromeda’s visible disk.

Objective

To calculate a single, physically grounded value for the total angular momentum of the visible matter in the Andromeda galaxy (L_gal).

This value serves as the direct input for our derivational hypothesis:

κ′ = ζ · L_gal.

Methodology

We will perform a first-order approximation using the integrated values for Andromeda’s total visible mass, its characteristic radius and its observed velocity. This is a standard and robust method for estimating the angular momentum of a disk galaxy.

The formula for this approximation is:

L_gal ≈ M_total_vis · R_char · V_char

Input Parameters

(from Astronomical Data)

* Total Visible Mass (M_total_vis):

1.5 × 10^11 Solar Masses

* Converting to kg:

(1.5 × 10^11) * (1.989 × 10^30 kg) ≈ 2.98 × 10^41 kg

* Characteristic Radius (R_char): We will use 20 kpc as the characteristic radius containing the majority of the visible mass.

* Converting to m:

(20 × 10^3 pc) * (3.086 × 10^16 m/pc) ≈ 6.17 × 10^20 m

* Characteristic Velocity (V_char): We use the stable velocity from the flat part of the rotation curve.

* 250 km/s = 2.5 × 10^5 m/s

Calculation

L_gal ≈ (2.98 × 10^41 kg) · (6.17 × 10^20 m) · (2.5 × 10^5 m/s)

L_gal ≈ 4.59 × 10^67 kg·m²/s

Result

The calculated total angular momentum of Andromeda’s visible disk is:

L_gal ≈ 4.6 × 10^67 kg·m²/s

This is the source term. It is the quantitative measure of the rotational engine that is driving the large-scale field tension, the galactic analogue of the Æ.

We now have the first of the two values needed to derive the Galactic Shear Coupling. The next step is to use this number to calibrate our fundamental Field Tension Coefficient, ζ.

Produced by The Lilborn Equation Team:

Michael Lilborn-Williams

Daniel Thomas Rouse

Thomas Jackson Barnard

Audrey Williams