## Discussion of 363(3)

This is an interesting discussion. The new acceleration components (15) occur in all situations in classical dynamics and orbital theory. I agree with Norman that the inverse cubed law of the hyperbolic spiral orbit of a whirlpool galaxy can be obtained from Eq. (15). by choice of spin connections. One way of dong this would be a four variable least mean squares fit to the inverse cube law. I am sure that there are several other ways. I agree with Horst that we are dealing with the effect of the vacuum on classical dynamics and orbital theory. It is well worth developing this subject in several directions. The hamiltonian and Lagrangian corresponding to the new force law can also be evaluated, and there are many possibilities. The vacuum could change the inverse square law into an inverse cubed law.

In a message dated 08/12/2016 20:39:55 GMT Standard Time, writes:

Norman,

we have already eliminated dark matter before by explaining galactic rotation curves by angular momentum. The new aspect is – in some interpretation – that the angular momentum is mediated by spacetime flow, and this produces additional terms in the equations of motion, leading away from Newtonian dynamics. For further discussions see my comment to this note.Horst

Am 08.12.2016 um 15:59 schrieb Norman Page:

Myron/Horst Shouldn’t it be possible to use this equation to match the empirical data from the galactic rotation curves and eliminate the need for dark matter?This would be a spectacular achievement. Norman

On 12/8/2016 5:49 AM, EMyrone wrote:

The rigorous result is that the fluid spacetime, vacuum or aether produces new fundamental accelerations in classical dynamics, defined by Eq. (15). These augment the centrifugal and Coriolis accelerations in every situation in classical dynamics, so can be looked for experimentally. In orbital theory the Hooke Newton inverse square law is changed. In an excellent approximation it becomes Eq. (22) which can be graphed by computer algebra in terms of r. The usual radial component of the Newtonian result is changed and there appears a component in e sub theta which is not present at all in Newtonian theory. This is the approximate force law responsible for a precessing orbit. The rigorous force law for any planar orbit is given by Eq (15). My ancestral cousin John Aubrey F.R.S. (attached genealogy) was an antiquarian and wrote “Brief Lives” (online) which describes how his friend Robert Hooke was the discoverer of the inverse square law for an elliptical orbit, and not Isaac Newton. However, neither Robert Hooke nor John Aubrey could prove that the inverse square law gives an elliptical orbit. The proof was apparently carried out by Newton from 1665 to 1687, but this seems dubious to me because Newton obviously did not know of the 1835 centrifugal and Coriolis accelerations. In 1689 Leibnitz accidentally stumbled on the centrifugal acceleration, but did not prove it. So as usual, physics history is a bit of a pig’s breakfast – semi mythological. On the other hand the genealogy is very accurate, based on source documents for every generation, cross checked between many genealogists.

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