Many thanks, this was first derived in UFT141, but ECE2 provides a rigorous method of eliminating the tangent space indices, and bringing both torsion and curvature in to the theory. ECE and ECE2 make up a long chain of ideas and reasoning over more than thirteen years of development. My ancestral cousin John Aubrey attributed the discovery of the inverse square law to Robert Hooke as described in this blog (John Aubrey “Brief Lives”, a classic of literature consisting of short biographies, or brief lives). Hooke was Aubrey’s colleague at Oxford. According to Aubrey, Hooke gave the basic idea to Newton, but the latter used his powers of reasoning to develop the universal law of gravitation from 1665 to 1687. However it was Leibniz who first develop the correct orbital equation, in which Newtonian attraction is counter balanced by centrifugal repulsion. It is usually written in the textbooks that Newton inferred the inverse square law at his ancestral home of Woolsthorpe Manor in 1665, and spent the next twenty years developing the calculus needed to explain why the inverse square law gives an elliptical orbit. A recently discovered autograph manuscript by Robert Hooke has been evaluated at a million pounds. It is handwritten minutes of Royal Society meetings. First and second editions of the Principia by Newton are also very valuable. My Ph .D. supervisor Mansel Davies had a second edition which he showed me. It is written in Latin and does not use modern calculus at all. For non specialists it is exceedingly difficult to find where the Newton laws occur or how they are inferred. Similarly, Kepler is written in Latin and it is almost impossible to find where his three orbital laws occur. The best account is Koestler, “The Sleepwalkers” (online). The Hooke / Newton inverse square law explains the three orbital laws of Kepler but as is well known does nto explain light bending by gravitation and so on. This has been explained in the x sub theory of ECE (2014) without using Einstein’s ideas at all. The aim now is to explain it using ECE2.
Fundamentally important of course. Now students of all ages can understand Newton properly for the first time – with no assumptions.
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