Final Version of Note 419(5)

Final Version of Note 419(5)

This version repairs some algebraic errors found in the checking work by Horst Eckart of my preliminary hand calculations, and extends the calculation to give the generalized spiral orbit (54) of the stars in the arms of a whirlpool galaxy. It can be seen that many different kinds of spirals and galaxies emerge for different m(r). Some more remarks are given to explain the reasoning that underpins the approximation of the rigorous Eq. (32) by Eq. (40). The basic reason is that the most general orbit is sought that gives a constant v as r goes to infinity in m(r) theory. So the second term on the right hand side of Eq. (32) remains finite because 1 / r power four is counterbalanced by (dr / dphi) squared.

a419thpapernotes5.pdf

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Results of central mass variation for S2 orbit

Results of central mass variation for S2 orbit

Many thanks, these results show that the S2 orbit is described by m = 0.9877, a constant. The Schwarzschild function gives wildly incorrect results, and it seems that the orbit is nearly elliptical. The Einsteinian precession has not been observed experimentally. This is very good numerical work by Horst Eckardt and there is intense interest in the latest UFT papers.

Results of central mass variation for S2 orbit
To: Myron Evans <myronevans123>

I did a calculation with constant m=0.9877. Using the Newtonian "experimental" central mass, then more or less the results of the "best fit" are reproduced. This means, this m function reproduced the full set of orbit parameters:

M=8.3627*10^36 /* best fit */
T=16.07 eps=0.88323 rmin=1.79530e13 rmax=2.89596e14 dphi=5.7710e-4
M=8.572*10^36 /*exp. data used*/
T=9.65 eps=0.83724 rmin=1.79520e13 rmax=2.02688e14 dphi=6.0636e-4
M=8.572*10^36 /*exp. data with m=0.9877*/
T=16.07 eps=0.88332 rmin=1.79530e13 rmax=2.89596e14 dphi=5.9144e-4

Using the Einsteinian m=1-r0/r gives desastrous results, the orbit period shrinks by a factor 10 or so. Reducing the term r0/r by a factor 100:

m = 1 – 0.01*r0/r

still gives half the orbit period only, although the correction to unity is extremely small. The sign of the correction has to be changed to arrive at the experimental T=16.05 y.
Using the extended version

m = 1 – r0/r – alpha/r^2

with alpha>0 worsens the result as expected. With alpha=-2.25e23 m the experimental orbit period can roughly be reproduced, but there is a huge precession of about 1/3*2 pi.

Will try other m functions. The orbit seem to be very sensitive to dm/dr.

Horst

Am 16.11.2018 um 09:54 schrieb Myron Evans:

Results of central mass variation for S2 orbit

Many thanks. This is a clear and logical method of finding the optimal mass about which S2 orbits. The graphs show the dependence of T on M, the dependence of the eccentricity on M, and the dependence of rmax on M. They all show that the orbit is not Newtonian. I would suggest a computation of the orbit of S2 for the optimal mass M found with Horst’s method. This would be the rigorous computation from
dH / dt = 0

419(5): Velocity Curves of Galaxies in m Theory

419(5): Velocity Curves of Galaxies in m Theory

The general expression for the velocity curve is Eq. (18). If it is assumed that the orbit is the spiral, Eq. (19), then m(r) goes to Eq. (31) as r goes to infinity. This is a constant. Einstein and Newton produce v goes to zero as r goes to infinity, and fail completely. The general m(r) for the observed velocity curve is given by Eq. (38), giving m as a function of r. The most general orbit for a constant velocity at infinite r is given by Eq. (45), which is a generalized spiral. When m(r) = 1 Eq. (45) gives a spiral. In general any m(r) can be used to produce all kinds of whirlpool galaxies, which are described by the choice of m(r). The most general orbit is obtained by solving dH / dt = 0 and dL / dt = 0 numerically, with initial conditions. This is also true in any galaxy.

a419thpapernotes5.pdf

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

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

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.

Fwd: 419(4): The Three Kepler Laws in m Theory – effective mass of S2 star

419(4): The Three Kepler Laws in m Theory – effective mass of S2 star

This is very interesting, it means that the orbit is nearly that with m(r) = 1, i.e. m(r) = 0.9877. If so it is not Einsteinian. The Einstein theory produces a precession of 0.218 degrees per S2 orbit. However the astronomers have not observed any precession of S2. A few theoreticians have use R power n theory and Yukawa theory to produce enormous retrograde and forward precessions respectively, but the m theory shows that those precessions cannot be true. The claim that S2 verifies Einstein is a false claim. The orbit of S2 is not Einsteinian. This can be shown using m(r) = 0.9877 and computing the precession from dH / dt = 0, dL / dt = 0 with the initial conditions from the latest data on its closest approach of 18th May 2018.

419(4): The Three Kepler Laws in m Theory – effective mass of S2 star

It is revealing that the Newtonian mass (36) of the S2 star, using the experimental values T and a, is exactly

8.572 e36 kg,

this is given so in the experimental data, i.e. derived from Newtonian theory. Now we can be quite sure that the discrepancy between orbit period calculation and exp. value is from this assumption. To obtain the right orbit period, we have to use an effective mass which is 8.3627 e36 kg. As the calculations have been shown, the gamma factor is 1.0005 in maximum, i.e. the average m function must be

m ~ sqrt(M_eff / M_Newton) = sqrt (8.3627 / 8.572) = 0.9877.

Horst

Am 16.11.2018 um 06:28 schrieb Myron Evans:

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

Many thanks! The orbital parameters M, a, and r and v at closest approach completely violate Kepler’s third law for the S2 star, so the m theory applied to the Kepler laws is the only theory that could attempt to explain the orbit. The parameters M , a and epsilon given in Wikipedia should result in an Einsteinian precession of 0.218 degrees per S2 orbit, but this has not been observed, so the Einstein theory is also completely refuted. This leaves the m theory as the only theory of S2.
419(4): The Three Kepler Laws in m Theory

Great achievements again!

Sent from my Samsung Galaxy smartphone.

19(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.

Results of central mass variation for S2 orbit

Results of central mass variation for S2 orbit

Many thanks. This is a clear and logical method of finding the optimal mass about which S2 orbits. The graphs show the dependence of T on M, the dependence of the eccentricity on M, and the dependence of rmax on M. They all show that the orbit is not Newtonian. I would suggest a computation of the orbit of S2 for the optimal mass M found with Horst’s method. This would be the rigorous computation from
dH / dt = 0

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

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

Many thanks! The orbital parameters M, a, and r and v at closest approach completely violate Kepler’s third law for the S2 star, so the m theory applied to the Kepler laws is the only theory that could attempt to explain the orbit. The parameters M , a and epsilon given in Wikipedia should result in an Einsteinian precession of 0.218 degrees per S2 orbit, but this has not been observed, so the Einstein theory is also completely refuted. This leaves the m theory as the only theory of S2.
419(4): The Three Kepler Laws in m Theory

Great achievements again!

Sent from my Samsung Galaxy smartphone.

19(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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