Enigmatic Gravity Effects Observed during Solar Eclipses. Their Analyse by Quantum Model of Inertia and Gravitation

Foucault long pendulums, with spherical suspended mass, show Earth rotation by the constant velocity drift of their oscillation plane. Maurice Allais used a short, 84 centimeters pendulum, with a suspended bronze disc mass. He recorded its oscillation plane drift velocity, during solar eclipses, in 1954 and 1959. Both times, he noticed an anomalous drift of the oscillation plane. Several authors confirmed the effect, during next solar eclipses, with other types of pendulums. Then a group of Geophysicists, from the Science Academy of China, used an accurate digital gravimeter to measure Earth Gravity acceleration during March 09, 1997 solar eclipse. Their gravimeter recorded two drops of Earth Gravity acceleration (respectively 5.02 and 7.7 μ Gals) before and during first and last contacts of the Moon disc. However there was no acceleration drop during eclipse totality. Same phenomena were confirmed later, during next solar eclipses, with the same gravimeter. No classical causes for these facts were found, since modern gravimeters take care of temperature and atmospheric pressure variations. We analyse the effect of Moon rotation, and of solar Corona mass, in the frame of our Quantum model of Inertia and of Gravitation. The model predicts that Moon / Earth Gravity acceleration changes, when the Moon direction is close to the Sun one, as observed from the gravimeter place. That phenomenon should be tied to Quantum fluctuations dispersion by matter. Recorded measurements confirm that interpretation.


Background
First known from Toricelli in 1647, then better from Huygens in 1659, small amplitude oscillations periods T of pendulums of length L are isochronous, and tied to Earth Gravity acceleration g: T = 2π (L/g) ½ . That was the first instrument used to measure Earth Gravity acceleration g.
Leon Foucault demonstrated that a pendulum, made of a spherical mass, suspended by a long length L wire, oscillates with a constant drift velocity of the pendulum oscillation plane. The plane rotates clockwise in the North Earth hemisphere. A full turn is observed in 23 hours, 56 minutes and 4 seconds at North Pole. No plane rotation is observed at Earth equator, and anti-clockwise rotation is seen in the South Earth hemisphere. Foucault installed a 64 meters long demonstration pendulum, into the Pantheon monument in Paris, (Foucault, 1851), where the oscillation plane rotates a full turn in about 1.4 days.  Research Vol. 13, No. 2;2021 Similar "pedagogical" pendulums were installed in Belgium, Burundi, Canada, Czechoslovakia, Germany, Italy, Japan, Liechtenstein, Luxembourg, Norway, Poland, Spain, Switzerland, Tunisia, United Kingdom, and USA.
Such long and slow pendulums were however not used for observations during solar eclipses.

Maurice ALLAIS Observations
Maurice Allais (1911Allais ( -2010, engineer and contemporary physicist, Nobel economy laureate in 1988, was interested by Gravitation during his career. He observed the behaviour of a "paraconical" pendulum during solar eclipses of 1954 and 1959.

Figure 2. Maurice Allais and his 84 cm long pendulum
Maurice Allais experiments consisted to leave the pendulum disc oscillating, while recording carefully its clockwise azimuth drift, versus time. Oscillations were damped by air drag, so the pendulum oscillation had to be reset every 20 minutes approximately. Allais took great care not to perturb the pendulum from wind or personal movements. During 1954 and 1959 solar eclipses, visible from France, Allais observed strong modifications of the pendulum oscillation plane drift velocity.
The anomalous effects were intense (10 Grads azimuth change during short time eclipses), so Allais informed the French Science Academy (Allais 1954(Allais & 1959.
Observations with pendulums had a too low time resolution, for being exploited with our quantum model.
There were similar attempts, with superconducting gravimeters, during the 1999 total solar eclipse, visible from the north of France, but with not enough gravity sensitivity, and too much noise, for our exploitation. See that angular thickness of solar corona was about 25 % the Moon angular diameter in 1999.

Observations with a High Resolution LaCoste-Romberg Gravimeter
Fortunately a group of Geophysicists from Sciences Academy of Beijing (China), used the best available digital gravimeter, to measure Earth Gravity acceleration during several solar eclipses, for example the one of March 09, 1997 (Wang & al, 2000(Wang & al, , 2002(Wang & al, , 2003. Their gravimeter had a sensitivity of about one µ Gal, and could record acceleration values at one sample per second rate. The gravimeter output signal was recorded on a portable computer and corrected automatically from Earth tidal effects. Random output noise of instrument = ± 0.5 µ Gal, Eclipse signal > -5 µGal.  Figure 11. The two gravity drops, during the 1997 solar eclipse. We added Moon shadow displacements onto Earth surface, during that eclipse. Acceleration drops observed before and after first and last contacts. Therefore only the vertical component of Gravity is measured this way.
LaCoste-Romberg gravimeters are based on the displacement of a mass suspended by a spring.
In order to avoid effects of temperature change and of atmospheric pressure change, LaCoste-Romberg gravimeters sensors are enclosed into a vacuum chamber, with accurately piloted temperature. Figure 13. Part of the patented internal diagram of a LaCoste-Romberg type gravimeter.
On the left side is the temperature controlled vacuum chamber with acceleration sensor. Such precautions are required, as atmospheric pressure and external temperature change during a solar eclipse.  "To further study the gravity effects related to solar eclipses, our scientific team took more observations during Zambia total solar eclipse of June 2001 and Australia total solar eclipse of December 2002. After data corrections, we found respectively two gravity anomalies, with 3 to 4 μ Gal for Zambia eclipse and 1.5 μ Gal for Australia eclipse".
The effect of external temperature change, onto gravimeter signal, is known from manufacturer calibration: Figure 16. Upper curve is the gravimeter vacuum chamber temperature change (right scale) when external air temperature varies from + 45 ° C to + 22 ° C. Time scale in hours, along a full day.
Lower curve is the gravimeter output signal, with tidal effect (left scale, with noise = ± 0.5 µGal).

There Was No Gravitation Absorption by the Moon Mass during the Solar Eclipse
Several authors expressed their intention to verify if there is Gravitation absorption by the Moon mass. For example, Wang et al., (2000) wrote: "The present work was thus motivated to test the possible effect of gravitational shielding during a total solar eclipse". Or Ruymbeke et al., (2003): "Search for the gravitational absorption effect". However, real gravimeter signal shows (Figures 10 & 11) that Earth Gravity acceleration value is the same, long before, during, and long after, the eclipse totality. The two Gravity acceleration drops are only momentary phenomena, occurring before first contact and after last contact, not during eclipse totality.

There Were No Instrumental or Environmental Artefacts
A physicist (Van Flanders, 2003), among others, suspected a Gravity drop caused by action, on the gravimeter, of local atmospheric pressure variation, or temperature variation, during solar eclipse. This hypothesis ignores the fact that LaCoste-Romberg gravimeters sensors are enclosed into a thermally controlled vacuum chamber. Therefore such instrumental or environmental causes are ruled out, particularly when looking at time scale of atmospheric pressure, and of local temperature, during an eclipse, versus the fast signal variation of Figure 11. The Wang group refutes such possible causes itself: "As many scientists have pointed out that pressure-gravity factor is lower than 0.3 μ Gal / hPa, it means that any gravity anomaly greater than 0.5 μ Gal could not be inferred as the results of atmospheric pressure change. The two more gravity anomalies recorded during the solar eclipses provided us strong evidence that some gravity anomalies could not simply be inferred as atmospheric pressure change." Therefore, clearly, there was not any artefact, into that enigmatic phenomenon. Figure 10 is particularly clear.

The Anomaly Amplitude Is Tied to the Moon Height Over the Horizon
According to Figure 11 time scale, in minutes, first contact of Moon disc occurred at time 483.7 minutes, and last contact occurred at time 622.9 minutes.
However, the two minima of Gravity acceleration drops occurred respectively at 458.33 minutes and 633.33 minutes, this means 25.37 minutes before first contact, and 10.43 minutes after last contact.
From the latitude, and from eclipse timing, we calculate the Moon height over the local horizon at different instants. It was 7.725 ° during the minimum of first acceleration drop, of 5.02 ± 1.64 µ Gal. And it was 30.251 ° during the minimum of second acceleration drop, of 7.7 ± 1.77 µ Gal.
Therefore the largest acceleration drop occurred while the Moon was much higher into the sky.
So we propose the hypothesis that the gravimeter measured the vertical component of an acceleration, tied to the Moon position in the sky. In this case, there should be more acceleration drop when the moon direction is closer to the zenith direction. This is effectively what was measured.
However, the gravimeter did not measured an acceleration drop proportional to a constant value, times the sinus of the Moon height, over the horizon. Effectively, Ratio [sin(30.251 °) / sin(7.725 )] = 0.267, and Ratio (5.02 µ Gal / 7.7 µ Gal) = 0.652, this means the acceleration drops were relatively smaller by a factor 2.44 times, than the Moon relative height change. This means that the acceleration drop real cause was not constant along the full eclipse. Nevertheless, there is apparently an effect of the acceleration drop projection along the vertical axis.

The Two Gravity Drop Durations Were Tied to the Moon Diameter
Onto Figure 11, we added the displacement of Moon shadow, on Earth surface, during the eclipse, from the eclipse timing and Astronomical movements. We see that the first Gravity acceleration drop corresponds to a Moon shadow displacement of 3517 km (from timing measured along the horizontal doted line, which is the average acceleration value before eclipse). And the second Gravity acceleration drop corresponds to a Moon shadow displacement of 3297 km. We know that the Moon diameter is 3476 km. Therefore the two Gravity drops durations corresponded respectively to 101.17 % and 94.85 % the Moon diameter displacement. So when taking into account errors margins, into evaluation of these durations, from noisy Figure 11 gravimeter signal, we can really consider that the two drops were exactly caused by Moon direction change, relative to the Sun direction.

There Are Three Accelerations Involved during a Solar Eclipse
Three astronomical masses are acting onto the gravimeter sensor mass: The Earth mass, the Moon mass, and the Sun mass. We can calculate the three Gravitational accelerations, according to Newton's Law: Where G = 6,6725985 . 10 -11 m 3 . kg -1 . s 2 , M * is the distant mass, and D is the distance expressed in meters. We need: Mass Here are the three gravitational accelerations "seen" from the gravimeter position: -Acceleration from Earth: 9.8 .10 8 μ Gals -Acceleration from Moon: 3.297 .10 3 μ Gals -Acceleration from Sun: 5.93 .10 5 μ Gals These accelerations are not oriented in the same space direction. Therefore at totality only the gravimeter "sees": -Vertical Acceleration from Earth: 9.8 .10 8 μ Gals.
-Vertical Acceleration from Sun: 2.125 .10 5 μ Gals. Therefore if we make the hypothesis of a variation of the Moon Gravity acceleration, we see that 5.02 µ Gal drop corresponds to 1.13 % of the Moon Gravity acceleration before first contact, and that 7.7 µ Gal drop corresponds to 0.46 % of the Moon Gravity acceleration after last contact.

What Is Gravitation Cause into Our Quantum Model?
In order to be able to analyse gravimeter observations during solar eclipses in the frame of our Quantum model of Gravitation , we must first recall what is Gravitation cause into that model.
The model predicts that Gravitation is an effect of Quantum Fluctuations of a general Quantum flux. This flux, (confirmed by laboratory experiments, Poher, 2011), is made of Quanta (Universons), propagating at light speed, and bearing each a same momentum (2.83 .10 -29 kg.m/s). That natural Universons flux is isotropic, with a tremendous intensity (6.3 .10 80 Universons / s . m 2 into the 4π steradians).
There is a permanent interaction of these Quanta with elementary matter particles. Each interaction develops during constant time (7.8 .10 -14 second), and is made without final energy exchange.
However, when the matter particle is accelerated, Universons quit the interaction with a trajectory direction change, proportional to the matter particle acceleration value. There is however no absorption of Universons by matter.
The main natural isotropic flux of these Quanta contains permanent random fluctuations, of its intensity and of its flow direction. These fluctuations have an average very large intensity (2.5 .10 40 Universons / s.m 2 into the 4π steradians). They are quite brief (average duration each of 4 .10 -41 second) and each of their own variable direction of propagation is fully random, but with a global average isotropy.
An isolated matter particle, situated far away, in Space, is not perturbed by these fluctuations for two reasons: -They are isotropically distributed on average, even if their occurrence is fully random.
-They are much too brief as compared to relatively slow interactions of matter with Universons. Effectively, the interaction duration is 2 .10 27 times longer than an average fluctuation duration. This means that matter is a kind of "filter" for fluctuations. The incident interacting flux contains fluctuations, but the emergent flux contains much less fluctuations (there remains only Universons from fluctuation that have not interacted). This is also true for macroscopic matter of course.
End of Neutron example.
This phenomenon of "partial transmission of fluctuations" occurs also of course for masses of matter of the Sun, of the Moon and of the Earth.
For the gravimeter, installed onto the Earth surface, there are incoming Universons (Gravitational Quanta) from all directions of Space. However, the Earth mass disperses a part of the Universons from fluctuations, coming from the NADIR direction. And there is no such dispersion from the Zenith direction.
This is the reason why the sensor mass of the gravimeter is accelerated towards the Nadir direction, as the Universons average flux intensity is larger from the Zenith than from the Nadir. This is Gravity acceleration from Earth mass.
The same phenomena apply for the Moon mass and for the Sun mass. There are LESS Universons, going towards the accelerometer, from the directions of the mass center of these astronomical bodies, exactly as it is the case for Earth mass.

Solar Eclipse Interpretation from Universons Model
During solar eclipse, the Sun mass and the Moon mass get progressively aligned, as seen from the gravimeter installed on Earth surface. So there are FIVE Universons fluxes to consider for the gravimeter sensor. The sensor reacts proportionally to the sum of these five fluxes. The main flux comes from deep space through the Sun mass. The secondary flux comes from deep space through But before the first contact, part of the secondary flux comes also through the sun Mass the Moon mass. . Flux #1 is coming from deep space, though Earth mass, in the nadir direction (really from 2π steradians under the gravimeter). This flux is "amputated" of a part of its fluctuations (proportionally to Earth mass). This flux is not illustrated onto Figure 17, it would come from the right side of Figure 17.
Flux #2 is coming from deep space, all around the Sun and Moon directions, (from 2 π steradians minus the Sun and Moon solid angles directions). This flux contains ALL fluctuations coming from these directions. This flux is not illustrated onto Figure 17.
Flux #3 is coming from deep space, through the SUN mass. This flux is "amputated" of a part of its fluctuations (proportionally to Sun mass). This flux is shown as deep grey onto Figure 17.
Flux # 4 is coming from deep space, through the MOON mass. This flux is "amputated" of a part of its apr.ccsenet.org Applied Physics Research Vol. 13, No. 2;2021 fluctuations (proportionally to MOON mass). This flux is not illustrated onto Figure 17.
Flux #5 is part of Flux #4, but is coming also through the surrounding SUN mass (Corona) before going through the MOON mass. This flux is illustrated in pale grey onto Figure 17. This flux is more "amputated" of a part of its fluctuations (proportionally to SOLAR CORONA plus MOON masses).
We should effectively not forget that there is a lot of matter mass, around the Sun disc, as seen from the gravimeter (see solar Corona on Figure 8 for example). Therefore Flux #5 "shape and thickness" are tied to solar Corona shape and dimension behind the Moon direction, as seen from the gravimeter position.
The Moon rotates (one turn in 29.53 days), so its matter particles are all accelerated. If they were not accelerated they would propagate in straight trajectories instead of following the Moon rotation.
Therefore according to Universons Inertia model, the moon particles deviate Universons trajectories interacting with them. The deviation angle is small, because matter Moon particles acceleration A is small: Nevertheless, finally, it appears that our Quantum model of Gravitation gives a plausible explanation, for this enigmatic behaviour of gravimeters, or of pendulums, during solar eclipses. To our knowledge, there is not any other pushing model considering Moon rotation and solar Corona effects.
And gravimeters bring, this way, a new experimental confirmation of our Quantum model.