Thanks again. The rigorous expression is Eq. (22), which is integrated over dA, where dA is the infinitesimal of the area of the orbit A. So in Eq. (27) A was assumed to be a function of r. This gives Eq. (30). In general the functional dependence of A on r is needed. For the ellipse A = pi ab, where a and b are the semi major and minor axes of the ellipse. These have no functional dependence on r, so the area of the elliptical orbit is constant. If the area of the orbit of S2 is nearly an ellipse, as m theory and observations show, then Eq. (33) follows. However the easier way of proceeding would be to use the astronomically measured r and v at closest approach as initial conditions, the astronomically measured T, and the optimized mass M that you derived. Then compute the orbit of S2. The computation would show immediately whether the orbit is Einsteinian. If it were Einsteinian the precession should be delta phi = 6 pi MG / (a (1 – eps squared)) c squared), where eps is the astronomically measured ellipticity.

419(4): The Three Kepler Laws in m Theory

It is not fully clear to me how you obtained the result (33). In the integral (30) you assumed a constant A. I would argue that in (22) the integrand gamma/m(r) is assumed to be a constant average value. Then it can be pulled out of the integral. Writing r-dependent functions in (33) and (35) does not make much sense for me. Whatsoerver, the result is plausible.

Horst

Am 15.11.2018 um 11:59 schrieb Myron Evans:

419(4): The Three Kepler Laws in m Theory

The three famous Kepler laws are given in this Note for m theory. Kepler’s first law is that an orbit is an ellipse. This is changed completely using Eqs. (1) and (2), giving forward and retrograde precession, shrinking and expanding orbits and so on. Of particular interest is Kepler’s third law, Eq. (22), because the last note made the major discovery that the Newton theory in S2 is wildly wrong. In the m theory the central mass about which the S2 orbits is not a black hole, it is given by Eq. (35). By using Eq. (33) it is possible to find the time T for one orbit self consistently. Currently co author Horst Eckardt is working towards the same goal using a different method.

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