Alpha Institute for Advanced Studies

Agreed about the fact that the apsidal method relates to the satellite orbit, but NASA / Stanford gave their results on Cornell arXiv (on the net) as milliarcseonds per year for some reason. I am glad that we have reached agreement and I will proceed to writing up and posting the final version of UFT404 using your data below. Eq. (18) seems to be OK, it is just the value of capital omega. This is a powerful new method which can be used with any precession to give the spin connection and vacuum fluctuation. So all precessions are due to vacuum fluctuations and we are making major progress in understanding. The net on the list are the de Sitter and Thomas precessions.

I have a problem with the relation of precession angles to one year. Isn’t Delta_phi the precessional difference angle between apogee and perigee? And doesn’t it relate to the satellite orbit? Then there is no relation to a terrestrial year. The units of eqs.(1) and (4) are radians. I guess that half the orbital period of the satellite has to be inserted for t in eq.(4).

In (18) obviously the factor omega_E is missing!
Inserting the satellite data for Omega in eq.(18) with

r = 7.02e6 m

gives from (18) in arc sec per year:

Omega =

which is identical with your result in the first three decimal numbers.
The result for <dr dr> is
m

and
<dr dr> / a^2 = ,

finally:
<dr> / a = .

The fluctuation radius is about 1% of the orbital radius of GPB. I think we have agreement now about the results. If you include the above numbers in the paper, I think there is no need for an extra section 3.

Horst

Am 06.04.2018 um 15:24 schrieb Myron Evans:

In this final version the apsidal and Larmor precessions are equated as in Eq. (8), and the vacuum fluctuation responsible for the Lense Thirring effect calculated as in Eqs. (23) ff., with the result (33). This is simpler and more incisive than previous versions. Once Horst has had a chance to look at this note, I will rewrite UFT404 and repost it. The problem posed in UFT345 remains unanswered – how did they separate the LT and de Sitter precessions? They are both always present. Also present is the orbital precession. Did they account for that? In the same way as a planet orbiting the sun precesses, GPB orbiting the earth precesses. This is once again a criticism of the standard model. There cannot be a precise fit of experiment and theory if the theory is totally wrong and the data ill defined and ill refined. However, I have always been an inductive scientist, as is co author Horst Eckardt and others of AIAS / UPITEC, so we are always looking for new ideas as well as new criticisms. So claims to the mysterious, very high precision of EGR are no longer taken seriously.

404(6).pdf

In this final version the apsidal and Larmor precessions are equated as in Eq. (8), and the vacuum fluctuation responsible for the Lense Thirring effect calculated as in Eqs. (23) ff., with the result (33). This is simpler and more incisive than previous versions. Once Horst has had a chance to look at this note, I will rewrite UFT404 and repost it. The problem posed in UFT345 remains unanswered – how did they separate the LT and de Sitter precessions? They are both always present. Also present is the orbital precession. Did they account for that? In the same way as a planet orbiting the sun precesses, GPB orbiting the earth precesses. This is once again a criticism of the standard model. There cannot be a precise fit of experiment and theory if the theory is totally wrong and the data ill defined and ill refined. However, I have always been an inductive scientist, as is co author Horst Eckardt and others of AIAS / UPITEC, so we are always looking for new ideas as well as new criticisms. So claims to the mysterious, very high precision of EGR are no longer taken seriously.

a404thpapernotes5.pdf

Agreed, the angular momentum of the satellite was used in the Newtonian approximation. Eq. (4) is OK because the angular part of the velocity squared is in the second term (Marion and Thornton chapter 7). The value of dr / dt is given by Eq. (30), which is the usual Newtonian expression. Then the spin connection and precession are calculated as in Note 404(2). The angular momentum is defined by Eq. (28), as in Marion and Thornton chapter seven, and the hamiltonian from Eq. (18), again as in Marion and Thornton chapter seven. So everything is standard Newton for the ellipse. The transformation (37) was used because wikipedia gives the orbital parameters with respect to the surface of the earth. They are needed with respect to the centre of the earth. The transformed alpha, b and a were used with the approximation (36).

In eq.(4) there should stand v^2 instead of (dr/dt)^2 but this has no relevance to the following.
The angular momentum (21) is that of the earth but I think it should be the orbital momentum of the satellite. This seems to be used in (26) ff.
How did you compute the values of dr/dt and Delta_phi? Did you compute a and b from (33) with the small value of alpha from (6) ? This does not give parameters of an ellipse. I changed

alpha –> alpha + r_E

and then computed a and b from (33) with this alpha. Inserting the results into (36) however gives

dr/dt=0.

Using (30) with r=a gives

dr/dt = 10 m/s.

Perhaps the perigee and apogee values should be used to computed a and b:

a = apogee + r[E]
b = perigee + r[E]

Horst

Am 04.04.2018 um 14:55 schrieb Myron Evans:

This derives dr / dt in the Newtonian approximation (30) and proceeds to the approximation (36). Eq. (37) is used to find the parameters with respect to the centre of the earth as required. The orbital parameters (6) to (10) given in a Wikipedia article seem to relate to the surface of the earth for some obscure reason. The result of this check for dr / dt is 751 metres per second. This compares with the initial guess made in Note 404(2) of 460 meters per second, the velocity of a point on the surface of the earth. Proceeding using eq. (40) it is found that the precession due to the rotation of the earth from the apsidal method is

delta phi (apsidal) = 0.86 ten power minus twelve radians per year

compared with the dubious experimental claim of

delta phi (Lense Thirring) = 1.02 ten power twelve radians per year

There is a typo in Eq (41) of the note, it should be ten power minus twelve. The key equation is the Newtonian Eq. (30) for the orbit of Gravity Probe B above the centre of the earth, as required by Newtonian dynamics, because the gravitational attraction of the earth regarded as a point mass M is at its centre, not its surface. So what is needed are a and b of Gravity Probe B with respect to the centre, and a point r such as the perihelion. The eccentricity of the Gravity Probe B orbit according to wikipedia is epsilon = 0.0014, so it is nearly circular. Therefore the apsidal method is an excellent approximation. This is an application of ECE2 gravitomagnetism.

This derives dr / dt in the Newtonian approximation (30) and proceeds to the approximation (36). Eq. (37) is used to find the parameters with respect to the centre of the earth as required. The orbital parameters (6) to (10) given in a Wikipedia article seem to relate to the surface of the earth for some obscure reason. The result of this check for dr / dt is 751 metres per second. This compares with the initial guess made in Note 404(2) of 460 meters per second, the velocity of a point on the surface of the earth. Proceeding using eq. (40) it is found that the precession due to the rotation of the earth from the apsidal method is

delta phi (apsidal) = 0.86 ten power minus twelve radians per year

compared with the dubious experimental claim of

delta phi (Lense Thirring) = 1.02 ten power twelve radians per year

There is a typo in Eq (41) of the note, it should be ten power minus twelve. The key equation is the Newtonian Eq. (30) for the orbit of Gravity Probe B above the centre of the earth, as required by Newtonian dynamics, because the gravitational attraction of the earth regarded as a point mass M is at its centre, not its surface. So what is needed are a and b of Gravity Probe B with respect to the centre, and a point r such as the perihelion. The eccentricity of the Gravity Probe B orbit according to wikipedia is epsilon = 0.0014, so it is nearly circular. Therefore the apsidal method is an excellent approximation. This is an application of ECE2 gravitomagnetism.

a404thpapernotes4.pdf

Many thanks indeed! These are useful calculations as usual. I will rewrite Note 404(2) in a final version because having thought about your comments, the meaning of dr / dt is the change in r as the Gravity Probe B satellite orbits the earth. Here r is the distance from the centre of the earth to the Gravity Probe B satellite. The precessions are very tiny, so the Newton theory is an excellent approximation. I will make this clear in the revised note. The satellite had a perigee and apogee, so its polar orbit around the earth was not quite circular. If it had been exactly circular then dr / dt = 0 and the vector potential Q(total) would not vary with time. This would mean no precession in the apsidal method. The eccentricity of the orbit was epsilon = 0.0014, so the near circular apsidal approximation is an excellent one. Using this Newtonian approximation, dr / dt can be calculated from the hamiltonian as usual, Eq. (7.15) of Marion and Thornton third edition. This gives dr / dt of the satellite with respect to the centre of the earth because the gravitational attraction of the earth of mass M resides at the centre, as shown by Newton. The constants of motion are H and L as usual (hamiltonian and total angular momentum). In the meantime v = dr / dt can simply be used as a parameter that can be adjusted to give exactly the the same Lense Thirring precession as claimed by NASA / Stanford. One can use the complete equations (26) or (29), or the approximation, Eq. (39). This is no problem, of course, for computer algebra. However as pointed out in UFT345 what they actually observed is inevitably a combination of the Lense Thirring precession and the de Sitter precession. The former originates in the rotation of the Earth and the latter from the mass of the Earth, even if it were not rotating. It is impossible to separate the effects experimentally. So the claim to have observed both Lense Thirring and de Sitter precession with incredible accuracy is just that: incredible in the literal sense of having no credibility. The classic UFT88 shows that the metrics used by de Sitter and by LT were totally wrong. They become wildly wrong, as you know, if torsion is correctly takeninto account. By now this has gone around the world many times over without any objection from rational scientists, and even from dogmatists. The latter have been silenced by rational argument and have been reduced to rolling out the dogma. Stuff that everyone knows to be obsolete, but which generates a lot of grant money.
Myron Evans <myronevans123>

I did extensive calculations. In eq. (2) an equality sign is missing before teh last term. Eq. (9) is ok. It is unclear what the velocity of Gravity Probe B was. When using eq. (37) for a free orbiting mass around the earth, it is about 7500 m/s while the tangential velocity of earth at the equator is 465 m/s. You seem to have used the latter value. I guess that in (40) the radius of Probe B has to be used for r, consequently also its orbital velocity of 7500 m/s. This gives different results than yours. The correct result for (42) with discerning both radii is
omega = .

The result for (48) is
Delta phi =

,

there is a minus sign in front of v/r. Wehn defining (46) with a plus sign, the result is
Delta phi =

,

we now have a factor of 3 before v. For eq.(51) we obtain either
Delta phi =
or
Delta phi =.
Using the second result, the value of Delta_phi is for the earth tangential velocity:

and for the Gravity Probe B orbital velocity:
.

Obviously the latter (although the more plausible one) is too large by an order of magnitude, compared to the experimental value.

Horst

404(2).pdf

OK agreed on all points. The apsidal method is described by Marion and Thornton chapter seven of the third edition, and by Fitzgeradl on the university of Texas farside site. I used a combination of both sources.
Note 404(1)
To: Myron Evans <myronevans123>

In eqs. (16-17) the factor m seems to be missing at the LHS due to

f(r) = F(r)/m

but this is not important since the calculation proceeds with f(r) from (21) onwards. I find it a bit audacious to replace a constant (r_c) by a variable (r) in (29) but this seems to be the procedure having done for the apsidal angle calculation. Eq. (26) is obviously taken from the solution of the diff. eq.

x dot dot + omega^2 x = 0

and comparing with (25). It follows that the negative of the expression in parentheses is a frequency. This is a bit difficult to guess for the reader.

Horst