323(5): Explanation of the Perihelion Precession with the Lorentz Transform

This note uses the general Lorentz transform of the acceleration due to gravity to deduce the general orbital equation in ECE2 theory, Eq. (6). This equation applies to three dimensional orbits in general, and to the whole of dynamics. In general it is highly non trivial to solve. The Lorentz transform is that of the generally covariant ECE2 field equations, which have a structure that is also Lorentz covariant. Eq. (6) is simplified to the case of planar orbits, giving the orbital equation (39). In this development the primed frame is considered to be the frame in which the axes are not moving, (the Newtonian or inertial frame), and the unprimed frame is the frame in which the axes are moving in general with a velocity v with respect to the unprimed frame. The plane polar coordinates are defined by the unprimed frame rotating in a circle with respect to the unprimed frame. So in this case v = omega x r and the gravitomagnetic field is – omega, where omega is the angular velocity perpendicular to the frame. In this case the Lorentz transform defines an effective potential eq. (59), giving the orbital equation (60) which could be integrated numerically. However, even in this simplified case, the numerical integration is a non trivial task, and it is easer to use the experimentally observed precessing orbit (63) defined by the x factor of previous work. At the perihelion this is related to the Lorentz factor by the simple Eq. (68). Therefore the precession of a planar orbit is due to the general Lorentz transform of the ECE2 field tensor of gravitomagnetism and general dynamics. This is a new kind of dynamics in which the concept of the Lorentz transform is applied to frames, and not particles.

a323rdpapernotes5.pdf

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