262(3): Force Law for the Whirlpool Galaxy

In thsi note this is derived using Lagrangian dynamics and the fundamental kinematics of the plane polar coordinates, i.e. the fundamental geometry, an example of Cartan’s more general geometry. It has been shown in note 262(2) that any planar orbit must become a hyperbolic spiral if its orbital linear vlecity becomes constant as r goes to infinity. This is precisely what is observed in a whirlpool gaalxy. The force law for this hyperbolic spiral orbit is the inverse cube of Eq. (20), the potential is the inverse square of Eq. (25). These do not contain M , the mass thought to be at the centre of a galaxy. The orbit is independent of M, and this is the result of fundamental kinematics appearing in every textbook such as Marion and Thornton Classical Dynamics”. The kinematics also give Eq. (22) self consistently, indicating constant velocity again. A whirlpool galaxy is therefore totally non Newtonian, and totally non Einsteinian. Both Newton and Einstein contain M, and Einstein is only a tiny correction to Newton (Eqs. (27) and (28) of this note). Newton is non relativistic, and Einstein developed his theory without torsion, a fundamental blunder rectified by ECE theory. After all this is the Einstein Cartan Evans (ECE) theory named in honour of Einstein and Cartan. Elementary geometry is therefore necessary and sufficient to describe all the main features of a whirlpool galaxy. Cartan geometry reduces to the geometry of plane polar coordinates, in which the axes are rotating, generating a spin connection. So this is a triumph of simplicity and direct comparison with experimental data, William of Ockham and Francis Bacon. As Peter Debye write: “Complexity is lack of understanding”. This note is classic natural philosophy. The standard physics is not physics at all, it is a complete shambles made up of dogma and hyper complexity that leads nowhere at all.

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