Science in Ancient Artwork and Science Today
The Theoretical Interpretation of Spacetime/motion

Frame-Dragging, the Geodetic Effect
of Spacetime
and the Sothic Cycle Number

Charles William Johnson

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In the Earth/matriX Series of essays, we have shown how to derive the Sothic Cycle Number, 1649.457812, from the Sothic Calendar. This number, that is apparently encoded into the selected days of the Sothic Calendar may have distinct meanings yet to be fully comprehended. Let us review this Sothic number in relation to some more recent findings in today's astronomy and astrophysics.

Recently, scientists have been attempting to measure two specific phenomena: 1) frame-dragging of spacetime and 2) the geodetic effect of spacetime. Einstein described gravity as a disturbance in the curvature of space and time, which has been called general relativity. The examples of illustration that are often provided show the sphere of the Earth lying on a grid-like or mesh-like plane with a distortion of the grid lines near it, where these are somewhat curved according to the curvature of the Earth itself.

It is said that the gravitational field of each star, planet or any other body of mass causes such a depression on the grid or mesh, much like a ball lying on the mattress of a bed. The distortion of curvature in the grid is called the geodetic effect, which causes the distances in space to be somewhat different than what they would be were the Earth to be non-existent in that area.

Furthermore, Einstein is said to have predicted a frame-dragging effect, which is caused by rotating bodies. This also creates a further disturbance in the measurements of spacetime. In order to perceive this effect, it is shown that as the Earth rotates, the theoretical posit of the grid-plane or mesh of spacetime is twisted and dragged along by the rotating Earth, thereby creating a kind of whirlpool effect. This also causes a further distortion and disturbs the measurement of space and time, as observed in the disturbance of radio transmissions from satellites passing near a massive body.

Measuring the frame-dragging effect and the geodetic effect is extremely difficult due to the fact that the measurements must be made in an environment of microgravity. The theoretically predicted values offered for each one of these phenomena, however, may be considered in relation to other reckoning events, such as the Sothic Cycle Number coming out of the Sothic Calendar as proposed in a previous Earth/matriX study.

Most sources attribute the concept of frame-dragging to Albert Einstein and his postulates about general relativity. However, it has also be said that W Lense and H. Thirring, in 1918, two years after Einstein proposed his general relativity, proposed that according to the theoretical propositions a rotating massive body should slowly drag space and time around it. Nothing further developed regarding such an idea until 1959. It was then that Leonard Schiff (Stanford University) and George Pugh (the Defense Department, separately considered orbiting gyroscopes. According to Schiff's computations, a gyroscope in polar orbit at 400 miles would turn with the Earth through an angle of 42 milliarc-seconds per year.

The measurement of the frame-dragging effect is being carried out by the Gravity Probe B satellite project.

Again, according to Einstein's general relativity, the Earth warps space-time. Accordingly, there is a greater change in spin direction, which is now called the geodetic effect, and also obeys the gyroscope's motion through the spacetime curvature. W. de Sitter, in 1916, predicted an ever so slight correction to the complex movements of the Earth-Moon barycenter system around the Sun. This effect was finally detected in 1988 through lunar ranging and radio interferometry data gathering. The measurement for a gyroscope consists of a rotation in the orbit-plane of 6,600 milliarc-seconds per year.

The Gravity Probe B is carrying out the measurement of the geodetic effect. In polar orbit, the measuring gyroscopes of the Gravity Probe B satellite allow the frame-dragging and the geodetic effects to be at right angles, with each of the four gyroscopes on board measuring both phenomena. The findings of these measurements are far-reaching, as they examine the relativistic effects on massive bodies and the conservation laws for massive spinning bodies. Further, the findings may shed light on the gravitational action of moving matter and the concept of gravitomagnetism, which may or may not exist. These findings shall also be significant for considering Mach's Principle, and even further, they may be relevant to the theory of grand unification of the strong and weak forces.

Any comments regarding spacetime are difficult to illustrate in today's physics and astrophysics, given the fact that most examples of spacetime are generally based on the mechanical illustrations of Newtonian physics. In spite of everything that has been written about Einstein's concept of spacetime, invariably the illustrated examples depend on existing clocks, railways, elevators, spinning tops for the wobble of the Earth, a planar mesh or grid-like sheet for showing spacetime's curvature, and so on.

In our mind, before analyzing any relationships of spacetime, it would be necessary to comment the shortcomings of the commonly-held illustrations of spacetime today. The visualization of the Earth's sphere lying on a blanket-like planar of a curved spacetime grid is unfortunate in our mind. Possibly with the graphics of computers today, we may come closer to showing illustrations that better reflect the infinite dimensions of spacetime existence. For now, however, we are left with the summarized views of spacetime that, at times, hinder the perception of spacetime itself.

In our analysis, we shall limit our comments for now about the numbers involved in the frame-dragging effect and the geodetic effect of the curvature of spacetime. Let us accept the numbers (42 milliarc seconds and 6,600 milliarc seconds per year) relating respectively to the frame-dragging effect and the geodetic effect of curved spacetime as cited above. Let us consider these numbers in relation to the Sothic Cycle Number, 1649.457812, which we have identified in earlier writings.

A few considerations are in order first. A relevant time-cycle in astronomy considers the precession of the Earth. Precession has been cited to be distinct values throughout the ages. The theoretical value for the Precession of Earth is considered to be 26000 years. The Platonic Great Cycle was considered to be 25920 years. The ancient Maya considered this time-cycle to consist of 25956 years. Today, the measurement that is most frequently offered consists of 25800 years, give or take a few years of more precise measurements.

It is valid to consider these values of time-cycles in relation to the precess values of the frame-dragging (42 milliarc-seconds/year) and the geodetic effects (6,600 milliarc-seconds/year) as given above.

Consider the following relational number series:

And, further, consider three distinct ancient reckoning numbers:

One cannot help but consider the 81c of the Earth-Moon system as affirmed by many astronomers.

And, consider the reciprocal of the 81c number:

Now, let us consider the perceived ancient Sothic Cycle Number, 1649.457812c, in relation to the frame-dragging effect (42c) and the geodetic effect (6600c).

1649.457812 x 6600 = 10886421.56

1649.457812 x 42 = 69277.2281

From the previous computations we may see that there is a coincidence of values for the Sothic Cycle Number (1649.457812c) and the value given today for the Geodetic Effect (6600 milliarc-seconds per year), with regard to the 108864c fractal value. Such a coincidence of terms causes one to question whether the ancient Sothic Cycle may have been taking into consideration the geodetic effect of spacetime. But, then, one views the value for frame-dragging (6277.2281c), and the previous coincidence of number appears to be only that a coincidence. Or is it?

There is another number in the ancient reckoning system that is historically significant coming out of the ancient Maya system. The Maya had two companion numbers for day-counts: the 1366560c and the 1385540c day-counts. We have been discussing the computational possibilities of these two companion numbers throughout the Earth/matriX series. In this regard, we were not surprised to find the presence of one of the companion numbers in the frame-dragging effect.

Consider again the frame-dragging computation with the Sothic Cycle Number:

1649.457812 x 42 = 69277.2281

Now, double the 69277.2281 value:

69277.2281 x 2 = 138554.4562 [= 1385540c Maya Companion]

It may be worthwhile to view these values once again in their final expressions:

In this manner, we see two ancient reckoning numbers (108864c; 138554c) make their appearance in relation to another ancient reckoning number (1649.457812c) and the two theoretical values given today for the frame-dragging (42c) and the geodetic (6600c) effects. The coincidence of having these five numbers appear in such elementary computations suggests a significance for the Sothic Cycle Number heretofore undetected.

Now, another coincidence that would appear to be significant concerns the difference between the two previously cited values:

1088640.0 minus 69277.0 = 1019363

The 1019c [GeV] count is employed today as the particle mass value in computations of the equation of relativity [E = mc² ]

Further, the 108864c relates to the Nineveh count of 2268c.

The 108864c relates further to the Kemi count employed in the measurements of the Great Pyramid of Giza, whose baseline perimeter has been cited as being 3024c feet [ 4 x 756c side measurement = 3024c].

1088640 / 42 = 25920c Platonic Great Cycle of Precession

This last example reveals a direct relationship among the Sothic Cycle Number, the geodetic effect fractal number and the baseline of the Great Pyramid of Giza to a fractional decimal expression. And so on. Please, examine some of our previous essays for further computations of this nature in relating the distinct ancient reckoning counts among themselves and to other physical and chemical constants.

Now, remember the 5184c number series cited at the beginning of our analysis:

3024 / 66 = 4581.8181

5184 / 42 = 123.4285714

5184 / 1649.457812 = 3.142850919 [ = pi-like reciprocal of seven series]

We invite the reader to examine this particular series (1458c) with respect to the Boguer constant (4185c) cited in the study of gravity, that appears in the Earth/matriX series of essays. We also examine this count in relation to the projected height of the Great Pyramid of Giza which has been cited as 481.5 feet.

The numbers of the ancient reckoning system relate to the Frame-Dragging Effect (42 milliarc-seconds per year) and to the Geodetic Effect (6600 milliarc seconds per year) in relation to the Sothic Cycle Number (1649.457812) as identified by us in previous Earth/matriX essays. The relationships are expressed nearly in whole numbers. The encoded Sothic Cycle Number may enjoy various meanings, one of which may be its relevancy to the concepts of frame-dragging and the geodetic effect of spacetime.

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