The Elliptical Error.
Kepler was able to determine that the motion of celestial objects were elliptical around the sun. Newton was able to write down a force equation that demonstrated that an ellipse would still obey an inverse square law. Ever since we have persisted in the notion that an attraction exists between the symmetrical centres of 2 bodies. This mutual attraction was shown to combine into a motion around a common centre often said to be calculated by Archimedes lever principle. However this makes te assumption that the instantaneous velocities are accelerated constantly tangentially to a circular path, not an elliptical one.
Making these assumptions in the past allowed Newton to give highly accurate Approximations to the data, but as he pointed out, these were approximations everybody overlooked the error because of the accuracy and the elegance by which the approximations were obtained. Keplers cumbersome calculations which established the eccentricity of the paths were demonstrated to be complied with by the Newtonian "formulation". However this is not the case. The Newtonian formulation does not comply with the Keplerian one. However newtons rhetorical exposition demonstrated the very close approximation, and the process of adjustment that he applied to achieve any desired degree of accuracy.
Because Kepler and Newton could be reconciled in this way it has been ignored that Kepler has demonstrated that so called gravity actually acts from 2 centres of attraction not 1. By leaving out the 2 nd centre, theorists have proposed that gravity is mono polar in its field, whereas every other field is bipolar, having an attractive and a repulsive centre. This is in fact not Newtons misrepresentation, because Newton clearly demonstrates mutuality in attraction and mutuality in repulsion in the action of gravity. The centrifugal force that Newton always pointed out as necessary is in fact this second contra force within Newtons concept of the gravitational action.
When Faradays field notion was applied to electricity and magnetism, gravity which had the same formulation was deliberately excluded. Finally the field notion was applied but the corresponding "negative" mass was excluded, and the elliptical motion was subsumed under notions of circular orbits. This went uncorrected but not unchallenged, but the propaganda machinery always diverted from the clear implication that electro magnetic fields were typical of gravity and therefore gravitational fields may be incorrectly applied.
Einsteins reworking of the notion of aether into the concept of spacetime allowed these corrections to be made under cover of relativity. However it was only later thought necessary to apply relativistic conceptions to electromagnetism. When this is done it shows that gravity and electromagnetism are indistinguishable.
To convey these ideas using a better intuitive model than a ballistic one Einstein came up with the rubber sheet as a model of spacetime which is the renamed aether.. The rubber sheet works because it portrays the relationship between objects in space as being vorticular rather than attractive and repulsive. Attraction and repulsion arise as equilibrium forces as covered in the catch all 3rd law of motion.
The introduction of the field of influence by Faraday provided Einstein with a new way to portray he interactions and behaviours of matter, but it also provided a new model of matter. Matter is ultimately not a substance, it is a vorticular entity in a field. That this field concept has many analogous names is not surprising: aether,ether, space, spacetime, vacuum vacuum energy, energy, force, inertia, quantum foam, d Branes, strings, plasma, dark matter, dark energy….. It is not surprising because it is the fundamental tautological issue of ontology: given the experience of existence how do I proportion it? Everyone has to come up with their own answer. This makes consensus rather tricky to say the least! But as far as we assent to a consensus we have a shared experience, but because it is a consensual process, that shared reality is subject to change. As a symbiotic colonic entity change is resisted by the symbiotic arrangements within the colony. This is the inertia of a colonic structure. In a similar way change in the fields which are archiving instantaneous dynamic equilibrium , are resisted by that dynamic equilibrium. This is field inertia.
Matter as this fractal vorticular dynamic field is revealed by the elliptical orbit error.
Being indoctrinated with the traditionsl Mechanical view of the workings of motion makes it nigh impossible to spot the mechanical and dynamic MODEL that Newton presents. In addition, the confusion relating to geometry makes the mechanical dynamical geometrical model even harder to spot. Add to this the misinformation about the Astrological origins of Mechanics, and the complete Astrological(Celestial) Mechanical dynamical geometrical MODEL is completely obscured. In this regard , the Lagrangian Celestial Mechanics goes some way toward restoring a complete picture of the process. In such a picture the 2 centres of the ellipse are clearly positied as dynamical centres for the motion. The fact that on is inside the body of a planet, while the other is in "empty space" is not obscured. However it is ignored as the calculus of variation is proceeded with to give instantaneous "laws" for the dynamical or Lagrangian constraints.
This next video shows exactly how it is ignored and how a proportional derivation is turned into an exact solution!
What do these notions of a model and a dynamical centre mean? They mean that the Newtonian model is a Euclidean field model, in which the field is constructed from the Euclidean Mechanical principles of the day and appears as invisible and giving "action at a distance". The field concept was not delineated in the Form Faraday positied it in those days, nevertheless spheres of crystal were posited for each supposed layer in which the motions were embedded. Because terrestial mechanics involved bodies, the motions of terrestrial transmission of "force" involved these colliding bodies. In fact force itself was not a very secure mechanical notion being part biological and part theological/angelic. Thus the Lagrangian Mechanical system is the first to minimise force as a concept and to declare that only velocity or motion was necessary. What changed and indeed induced velocity was not his concern. He proposed principles sufficient to explain all observed mechanical behaviour dependent of velocity and avoided the debate.
Whereas Newton has established a completely quantifiable model, a model based on measurement of quantitiesand on definitions of these measures, he nevertheless couched these measures in tautological language to enhance the flow of intuition and the closeness of analogy to divine iteraction. That is to say that Newton had no conflict with his belief that God ordained and maintained the workings of His universe applying Mechanical and Geometrical procedures which he revealed to the devout believer.
The action at a distance therefore was an unsatisfactory mechanical explanation which collision could not explain, despite La Sages lifelong valiant attempt. The oly allowable principle was magnetism which Newton puts forward as a type. But what Newton had created was a dynamical equilibrium system which accounted for the movement by equilibrium reasoning/ Lagrange took this as sufficient and exploited it in terms of varying the equilibrium constraints. These models therfore used an Equilibrium field concept to explain orbital motion. This in turn defined a force field concept which in turn was the first field descritio of motion. However, these fields were tied to masses and therefore the dynamical centres that were in space and defined away as inertia were ignored leading to the strange imbalance in the so called gravitational field.
The equlibrium field is not tied to mass, but to the dynamical structure of the field. Thus a dynamical centre can exist in free space just as well as in the centre of a body. This was not at all obvious until Maxwell and later Einstein clarified the Field description of matter.
The nature of charge and mass therefore are field effects and this changes everything.