## Discussion of notes 363(4), 363(5)

These are very interesting continuative or inductive remarks. I agree that the x theory is a first approximation, mathematically it is quite interesting because it gives the fractal conic sections, but in physics Eq. (22) of Note 363(5) must be integrated to give the orbit in terms of the spin connection and force. The work in 324 / 328 is the simplest and best explanation of orbital precession ever achieved, and could be improved by simultaneously solving Eqs. (3) and (4) of Note 363(5), incorporating the spin connections. Use of different spin connections will give different precessing orbits and if large spin connections are used the orbit could be changed completely, for example into an inverse cubed law, giving the characteristics of a whirlpool galaxy. For example, what spin connections change the inverse square law into the inverse cube law? I think that the force law in Eqs. (10), (11) and (18) is OK because Eq. (11) for example is the Leibnitz equation of 1689:

F = – partial U / partial r = -mMG / r squared

= right hand side of Eq. (11).

This assumes that the force between m and M is still only a function of r. More generally it would be a function of r(t) and theta(t) in this new theory.

To: Emyrone@aol.com

Sent: 16/12/2016 18:55:41 GMT Standard Time

Subj: notes 363(4), 363(5)The notes are correct. Only in eqs.(11) ff. of note 5 the term dU/dr has

been omitted.

A continuative consideration:

So far we have two explanations for precessing conical section orbits:

the x factor resp. the spin connection (this work) and the invariant

metric of general/special relativity (papers 324/328). I wonder if both

can be reduced to a common cause. This would mean that the invariance

known from special relativity must have something to do with the fluid

dynamics structure of spacetime. Eq.(43) of note 363(5) means that the

length function R(r) is changed by a constant rate depending on

distance. Similar is known from the length contraction of special

relativity in a linear approximation (we know that the x factor is a

very crude approximation). Perhaps these considerations could lead us to

a completely new foundation of the invariance property of special

realtivity.Horst

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