360(4): Force Law for a Precessing Elliptical Orbit in a Plane

From fluid gravitational theory this is the Lagrange or convective derivative of the orbital velocity, and is given by the inverse square law (19) with X and Y defined by Eqs. (17) and (18) respectively. The latter two equations define the moving frame of reference in which the convective derivative of v is taken. Therefore the Hooke / Newton inverse square law has been generalized to any orbit in two or three dimensions, a major advance in physics and cosmology. In general, an orbit is any function r = f(theta) in two dimensions and r = f(phi, theta) in three dimensions. The Einstein theory of orbital precession is riddled with errors, so the observed orbital precession factor is used. Experimentally, it is 1 + 3MG / (c squared alpha) to high precision, measured by many satellites and so on. X and Y of Eqs. (17) can each be plotted against r and theta in three dimensional graphics. These define the moving frame, the dynamics of spacetime itself (or aether or vacuum). In a sense, spacetime or the aether or the vacuum guides a particle of mass m in orbit around a particle of mass M. The spacetime is a fluid described by the ECE2 / Kambe field equations of fluid dynamics. These have the same strucure as the ECE2 gravitational field equations and electromagnetic field equations. The structure is based on Cartan geometry and the overall theory is a generally covariant unified field theory, the first unified field theory that is simple and easily comparable with experimental data.


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