415(4): Final Orbit Equations for m Theory and Double Cross Check of its Angular Momentum
The final orbit equations are Eq. (23) and (30). The angular momentum was worked out from the fundamental L = r x p and is given by Eq. (21). The fundamental property dL / dt was double cross checked in Eqs. (24) and (37). The position vector in m space is given by Eq. (12) and is indeed different from the position vector in the space of UFT414. In m theory the position vector is r bold = (r/m(r) power half) e bold sub r. This result is shown to be consistent with the line element (1) of m space. If one uses r bold = r e sub r bold in m theory, the double cross check does not work. I decided not to use the Einstein Hilbert action because that, again, is based on a geometry without torsion. The m(r) function of ECE theory can be used in this note. That was given in Note 415(3). The m function of the so called Schwarzschild metric gives inconsistent results and has been refuted in many different ways in the UFT series. One can proceed by using m and the spin connection as input parameters or adjustables. It will be very interesting to find what kind of orbits emerge and to compare them with S star systems and the Hulse Taylor binary pulsar. The next note will incorporate frame rotation theory, so that the spin connection can be calculated. The double and triple cross checks in UFT414 and UFT415 give great confidence in the theory and of course all the calculations can be checked by computer algebra to eliminate human error from the Baconian method.