362(5): Convective Derivative of the General Vector, Application to Orbits

The convective derivative of any vector field V(t, r(t), theta(t)) is given by Eq. (7) and involves two Cartan derivatives as shown. The result is applied to the Coriolis velocity in Eq. (22) and the Coriolis accelerations in Eq. (23). The components of the orbital Coriolis velocity are changed to Eqs. (35) and (36) when the orbiting object of mass m is considered to move through a fluid spacetime or aether instead of as a point particle as in the usual orbital theory. The observable square of the orbital velocity is changed to Eq. (38), and the Newtonian result (39) is changed by the presence of the spin connection (26) of fluid dynamics and Cartan geometry. By suitable choice of spin connection components it should be possible to produce a precessing orbit, and also the hyperbolic spiral orbit of a whirlpool galaxy. The kinetic energy, hamiltonian and lagrangian are changed by the assumption of a fluid spacetime, aether or vacuum. Computer algebra could be used to model a precessing orbit and hyperbolic spiral orbit with choice of spin connection components. At this point I will write up Sections 1 and 2 of UFT362 and pencil in Section 3 for co author Horst Eckardt as usaul.


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