Displacement of the Earth's inner core
What kind of danger is this that threatens all of humanity? Conventionally, the body of the Earth is divided into several various fields(layers). The upper sphere - the earth's crust extends from the surface of the Earth to a depth of approximately 30-70 km. Under the surface of the oceans it is much thinner than 3 - 5 km.
Next area to a depth of 2900 km is called the mantle, and consists of hard rocky rocks. The third sphere is the outer core, which consists of liquid substance and extends to a distance of 2900 to 5000 km from the surface of our planet. The viscosity of the liquid outer core (according to Bullen) is approximately equal to the density of water.
Finally, at a depth of 5000 to 6371 km there is an internal solid
iron-nickel core. The radius of the inner core is 1390 km, its mass is 1.49 1023 kg, which is two masses of the Moon, i.e. quite significant.
At the beginning of the first systematic observations behind geo magnetic field(1829), it was noted that the Earth’s magnetic dipole (and, accordingly, the inner core) is shifted relative to the planet’s rotation axis by 252 km towards the Pacific Ocean. According to 1965 data, this displacement increased to 451 km, and continues to increase! It was not possible to find out at what distance from the center of the Earth the magnetic dipole is currently located, since for some reason this information is in open sources are no longer published.
The earth is a kind of gyroscope with three degrees of freedom. If the movement of the inner core towards the earth's surface continues, then after a certain time the center of mass of the planet will shift so much that the Earth will simply somersault in space, like a spinning top with a displaced center of gravity, in order to take a more stable position of its axis of rotation. The displacement of the inner core of our planet can occur suddenly, under the influence of external factors, i.e. when adding lunar and solar tides.
The great Russian scientist M.V. Lomonosov studied the issue of the displacement of the Earth’s inner core. In his treatise “On the Layers of the Earth,” he wrote: “Nature reveals the depths of the earth in two ways: one by the intensification of bodies circulating outside it, and another by the movement of its very interiors. External actions are strong winds, rains, river flows, sea waves, ice, fires in forests, floods; there is only one internal thing - an earthquake...” In Lomonosov’s correspondence you can read the following: “... I made four newly invented pendulas (pendulums) ... to find out whether the center from the Earth, attracting heavy bodies to itself, always stands still or changes place.” Using this device, measurements were taken continuously from 1756 to 1764, but since the accuracy did not meet the requirements of the research, the scientist was forced to admit: “The fluctuations in gravity are so small that they could not be noticed by the mentioned device.”
IN late XIX century, based on temporary variations in latitude changes, astronomers discovered a global phenomenon - the movement of the axis of rotation in the Earth's body. This phenomenon was studied by the President of the Royal Society of Great Britain J.G. Darwin (son of Charles Darwin) and the Japanese astronomer Kimura.
J.G. Darwin writes: “The Japanese astronomer Kimura drew attention to the following strange conclusion that he received from observations: ... the latitudes of all six observatories of the Geodetic Association change simultaneously by the same amount, and they simultaneously decrease or increase, and this change has annual period. Now it turns out that we must add a small movement of all observation sites immediately to the north or immediately to the south, having a period of a year. Such a movement could be caused by an alternating movement of the Earth's center of gravity north and south along the polar axis...
It is so difficult to comprehend the idea of moving the Earth's center of gravity that many tried to explain Kimura's result solely as a fictitious consequence of various inaccuracies in astronomical observations. But if these were only fictitious results, then the observatories of the southern hemisphere could not give completely opposite changes. Both hemispheres, of course, must be diametrically opposed in this respect. Observations were specially organized at the southern observatories for two years and the result was that the southern observatories gave exactly the same readings as the northern ones. The reality of this strange kind of oscillation of latitude, therefore, seems to be well established... and hitherto we must accept this fact as an as yet unsolved mystery.”
In 1976, Academician N.I. Korovyakov, by modeling the conditions and processes occurring in the center of the Earth (hydrodynamic top), established a previously unknown pattern of eccentric displacement of the inner core in the shell of our planet. He writes: "Dense earth's core does not stick out regally in the middle globe, nailed there by the authorities of geophysics, it travels in the molten magma along a pentagonal trajectory.” In his opinion, the movement of the core and melt of magma along the perimeter of the pentagon affects the movement of continents, the growth of mountains, and the drift of the Earth’s magnetic poles. Movements cause earthquakes, tsunamis, volcanic eruptions, and affect climate and ocean currents.
International Association of Authors scientific discoveries And Russian Academy natural sciences confirmed the authenticity of the discovery of world significance and in 1997 issued the scientist a diploma No. 63. Many years of experiments and calculations of the scientist made it possible to establish that the inner core of the Earth, under the influence of the gravity of the Moon and the Sun, moves in the magma along a unique orbit - a pentagonal-shaped trajectory (pentagram).
Our ancestors undoubtedly had esoteric knowledge about the causes of cataclysms that occurred in the distant past. It is not for nothing that in the occult sciences they use the pentagram to protect against Satan, whose possessions are in the underworld. When he breaks free (leaves the confines of the pentagram), then the world will undergo terrible devastation.
The daily and annual displacement of the core depends on the position of the night and daylight relative to our planet. Korovyakov expresses fears that a moment will come when the planet’s center of mass may shift. And then the “bell effect” will arise - mutual collisions of the inner core and solid rocks of the mantle, during which the Earth’s poles may shift towards the equator, as well as the disappearance of the magnetic field for an indefinite period.
The reason for the displacement of the inner core is most likely our neighbor - the Moon. Its mass is only 81 times less than the mass of the Earth. The Earth-Moon system is unique in terms of its mass ratio, solar system. The gravitational influence of the Moon on our planet is quite significant. Under the influence of lunar tides, the soil rises by half a meter, the ocean level by a meter, and in some places - up to 18 meters (Bay of Fundy in the Atlantic). Since ancient times, people have unsuccessfully tried to solve the mystery of the origin sea tides. A mystery they called "the tomb of human curiosity." The founder of hydrography, the French scientist Fournier, said: “We will never unravel the mystery of the sea tides until we find the happiness of finding ourselves in the sky.” This problem was solved by: the ancient Greek philosopher and astronomer Posidonius, the Roman scientist Pliny, the Arab scientist al-Qazwini, Galileo, Kepler, Newton, Euler, D. Bernoulli, Laplace, who made a major contribution to the creation of the theory of sea tides.
Our night star, due to its significant mass, causes small floods and tides on Earth twice a day. The moon attracts more strongly the point on the earth's surface that is closest to it, and a tidal hump grows at the sublunar point. On the opposite side of the Earth, another hump appears, but half as high.
There is no intelligible explanation why a tidal wave occurs in the Earth's hemisphere far from the Moon. I. Newton explained the formation of tides by the difference in centrifugal forces and gravitational forces acting on water when the Earth-Moon system moves around general center wt. Newton did not hide the fact that the theory of tides he created did not provide a complete scientific analysis of the forces causing this phenomenon. He wrote that “the periodic repetition of tides must have another interacting cause, which is as yet unknown.”
Every year, at least 100 thousand earthquakes are recorded by seismographs all over the world, and if we count very weak ones, then their number is close to 1 million! Earthquakes are a terrible natural disaster that kills tens, even hundreds of thousands human lives. Why do they arise? When solar and lunar tidal waves coincide at one point, especially in a fault zone earth's crust or active tectonic zone, an earthquake or volcanic eruption is most likely. There is a definite connection between tidal forces and earthquakes. Astronomer N.A. Kozyrev traced the relationship between tectonic processes occurring on the Moon and Earth. It turned out that most often they occur when the Moon is at its closest distance from the Earth. Tidal waves have significant energy. They act as a trigger for earthquakes, releasing their own energy. The location of a future cataclysm can be calculated with an accuracy of several minutes, but this is a rather difficult task; too many factors must be taken into account when calculating the addition of tidal waves.
Perhaps the cause of tectonic cataclysms that periodically repeat on our planet is our night star. Under the influence of the Moon's gravity, the Earth's core is displaced from its axis of rotation and as a result of the impact on it centrifugal force gradually moves away from the center of the Earth, overcoming the resistance of the viscous outer liquid core. There are no forces that would return the inner core to its original state. There is only one possibility to return to a state of stable equilibrium - to shift the Earth's axis of rotation.
According to numerous prophecies, before the End Light will happen tectonic catastrophe caused by displacement of the Earth's inner core. The harbingers of this destructive earthquake are already reminding us of themselves. At the end of November 2004, earthquakes continued in Japan for a month. Thunder-like rumbles were heard in the Indonesian region. Locals explained them first terrorist acts or fall large meteorites, but these assumptions were not confirmed. A week later (December 26), a major earthquake with an amplitude of 8.9 points, which caused a movement of the earth's crust and a powerful tsunami up to 10 m high, causing the death of about 230 thousand people and significant destruction on the island of Sri Lanka, Indonesia, India, Malaysia, Thailand, Bangladesh, and the islands of Oceania and the east coast of Africa. According to media reports, as a result of this cataclysm, the Earth's rotation axis shifted (so far slightly, only 2.5 cm) and the Earth's rotation speed increased. The island of Sumatra has shifted almost 30 m from its original position.
To understand the true causes of such a destructive earthquake, it is necessary to imagine internal structure of our planet.
Conventionally, the body of the Earth is divided into several different spheres (layers). The upper sphere, or crust, extends from the Earth's surface to a depth of approximately 30–70 km. Below the surface of the oceans it is much thinner (3–5 km). The next sphere to a depth of 2900 km is called the mantle and consists of hard rocky rocks. The third sphere, or outer core, consists of liquid matter and is located at a distance of 2900 to 5000 km from the surface of the planet. Finally, at a depth of 5000 to 6371 km, there is an inner solid iron-nickel core. Its radius is 1390 km, the mass of the inner core is quite significant - 1.49 1023 kg, which is two times the mass of the Moon.
The core of our planet is inextricably linked with the Earth's magnetic field. Back in the 17th century, it was noticed that the dipole magnetic field of our planet is changing significantly. Over the past 100 years, the magnetic field strength has decreased by almost 5%. Currently, the rate of decrease in field strength has increased even more and is 1.7% over the past 22 years. At this rate of change, the Earth's dipole field should almost completely disappear within 2000 years. And then a stream of solar and cosmic radiation will inevitably fall on the Earth, and the level of radiation on the surface of our planet will increase. The consequences can be the most dire.
But this is not the worst thing. At the beginning of the first systematic observations of the geomagnetic field (1829), it was noted that the Earth’s magnetic dipole (and, accordingly, the inner core) was shifted relative to the planet’s rotation axis by 252 km towards the Pacific Ocean. According to 1965 data, this displacement increased to 451 km, and continues to increase. It is impossible to find out at what distance from the center of the Earth the magnetic dipole is currently located, since this information is no longer published in open sources.
The earth is a kind of gyroscope with three degrees of freedom. If the movement of the inner core towards the earth's surface continues, then through certain time the center of mass of the planet will shift so much that the Earth will simply somersault in space, like a spinning top with a displaced center of gravity, in order to take a more stable position of its axis of rotation. A shift in the rotation axis can occur suddenly, under the influence of external factors, i.e., during the addition of lunar and solar tides, under the influence of galactic magnetic fields on the magnetic moment of the core, etc.
In 1976, Academician N.I. Korovyakov, modeling the conditions and processes occurring in the center of the Earth (hydrodynamic top), established a previously unknown pattern of eccentric displacement of the inner core in the shell of our planet. The International Association of Authors of Scientific Discoveries and the Russian Academy of Natural Sciences confirmed the authenticity of the discovery of world significance. The scientist's many years of experiments and calculations made it possible to establish that the inner core of the Earth, under the influence of the gravity of the Moon and the Sun, moves in the magma along a unique orbit - a pentagonal-shaped trajectory (pentagram).
Our ancestors undoubtedly possessed esoteric knowledge about the causes of cataclysms that occurred in the distant past. It is not for nothing that the pentagram is used in occult sciences to protect against Satan, whose possessions are in the underworld. When he breaks free (leaves the confines of the pentagram), the world faces terrible devastation.
The daily and annual displacement of the core depends on the position of the night and daylight relative to the Earth. Korovyakov expresses fears that the planet’s center of mass may shift. And then, as a result of the “bell effect” (mutual collisions of the inner core and solid rocks of the mantle), the Earth’s poles can shift towards the equator, and the magnetic field can disappear for an indefinite period.
The reason for the displacement of the inner core is most likely the Moon. Its mass is only 81 times less than the mass of the Earth. The Earth–Moon system is unique in the solar system in terms of its mass ratio. Under the influence of the Moon's gravity, the core of our planet periodically shifts from the axis of rotation and, as a result of the influence of centrifugal force on it, gradually moves away from the center of the Earth, overcoming the resistance of the viscous outer liquid core. There are no forces that would return the inner core to its original state. There is only one possibility to return to a state of stable equilibrium - a displacement of the Earth’s rotation axis
We all know that the Earth rotates under our feet, but recent study reports that the center of our planet is out of sync with the rest of it, and often speeds up or slows down.
Professor Hrvoj Tkalczyk from the College of Physical and Mathematical Sciences of the Australian national university and his team used data from twin earthquakes over the past 50 years to measure the rotation speed of the planet's inner core.
They were able to establish that the core not only rotates at a different speed than the mantle, but also that its rotation speed is variable.
“We found that the inner core rotated faster than the mantle in the 1970s and 1990s, but slowed down in the 1980s. And the biggest acceleration may have happened five years ago, but we need more data to confirm this,” says Tkalchik.
“Interestingly, Edmund Halley, after whom Halley's Comet was named, believed that inner part The Earth was spinning at a different speed back in 1692,” he says.
Until this point, scientists assumed that the rotation of the Earth's inner core was a constant, since there were no adequate mathematical methods for interpreting the available data. The new method uses double earthquakes - pairs of almost identical earthquakes, between which there is a gap of several weeks to 30-40 years.
“It's amazing how these earthquakes that are 10, 20, even 30 years apart are so similar. But each pair has its differences, and this difference is related to the inner core of the planet. We were able to use these small differences to reconstruct the history of the core's rotation over the past 50 years,” says Professor Tkalchik.
According to him, new method measurements may help understand the role of the inner core in creating the planet's magnetic field, which allowed life on Earth to evolve by acting as a shield from cosmic radiation.
“The method we have developed is a very powerful tool for studying internal structure and the dynamics of our planet,” says the professor.
Earth's core for some unknown reason accelerates
Scientists from the Australian National University have discovered that the core of our planet often becomes out of sync with the rest of the Earth and begins to rotate at higher or lower speeds. In other words, the hot core inside the Earth, for reasons still unclear, begins to either gain or decrease speed and rotate faster or slower than the Earth. Moreover, the change in speed occurs extremely quickly.
We already know a lot about space, but our own planet, on which the life of human civilization depends, still presents surprises. The fact of desynchronization of the rotation of the Earth and its core for a long time could not be detected, cnews.ru cites the words of scientists. But Australian scientists have used a very labor-intensive technique for studying the so-called earthquake doublets over the past 50 years.
These are pairs of identical earthquakes that can occur with an interval of 2 weeks to 30-40 years. Comparing the seismic pattern of two events separated in time allows us to study changes in the deep layers of the Earth, including learning about changes in the rotation speed of the planet’s core.
It turns out that the Earth's core rotates at a variable speed. It is not yet clear what this is connected with and what consequences it may have for humanity
As a result, scientists discovered that the planet's core not only rotates with at different speeds compared to the mantle (the layer between the core and the crust), but the speed of this rotation also changes with time. Thus, compared to the mantle, the inner core rotated faster in the 1970s and 1990s and, correspondingly, more slowly in the 1980s. In the past few years, the inner core has accelerated greatly, and it is rotating faster than in the entire history of the 50-year period studied. However, scientists note that these are preliminary data and further research is needed to confirm them.
Until now, scientists believed that the rotation speed of the inner core was constant, but a study by Australian scientists refutes this point of view. Important discovery raises many questions. First of all, you need to make changes to existing models devices of the Earth. It is also necessary to find the possible periodicity of acceleration and deceleration of the core and correlate this information with the observed consequences for life on the surface of our planet. This work is extremely important because the core has a huge impact on the surface of the planet and the Earth's magnetic field.
It is possible that core acceleration observed in last years, may be dangerous. Unfortunately, even if this is true, we are not able to influence this process.
Reference
The core of the earth is a place of boiling lava under enormous pressure. The existence of the core itself is extremely important for the preservation of life on earth. Modern science It was discovered that the center of the earth is the engine that ensures the life of our planet.
The core is a giant, red-hot generator. In the center of the planet, below us, streams of hot, liquid metal are seething, which with its mass creates a huge amount of magnetic energy. Magnetic waves pass through the earth and envelop the planet in an invisible force field.
This field serves as the planet's invisible shield from deadly cosmic radiation. If the Earth loses its magnetic shield, it will become a desert, like Mars.
Hypotheses on the topic
Pole shift 
Catastrophic pole shift- the theory according to which certain conditions it is possible to change the position of the Earth's geographic poles (i.e., its axis) geologically a short time, for example, due to changes in the position of the planet’s crust relative to its internal layers under the influence of certain forces. The theory predicts the possibility of a catastrophically rapid shift of the poles (with linear speed, which can reach about 3500 km/h in some hypotheses), which should be accompanied by large-scale disasters covering the entire planet, such as floods, earthquakes, volcanic eruptions, rising seabeds and land submergence, and so on.
Prediction on the topic
Edgar Cayce
The American “sleeping” prophet Edgar Cayce (1877-1945) warned of an imminent cataclysm: “If it seems to you that something is moving and rumbling in the bowels of the Earth, then the displacement of the Earth’s inner core has begun.”
Many prophets predict that global tectonic cataclysms will begin in the near future. What are the reasons for the impending catastrophe? From the book Nostradamus. Sixens, almanacs and letters about the future of humanity: “If we imagine in a simplified way the structure of our planet, then inside the Earth there is an iron-nickel inner core, which, like the yolk in an egg, “floats” in the liquid outer core of our planet.
Many prophets predict that global tectonic cataclysms will begin in the near future. What are the reasons for the impending catastrophe? From the book Nostradamus. Sixens, almanacs and letters about the future of humanity: “If we imagine the structure of our planet in a simplified way, then inside the Earth there is an iron-nickel inner core, which, like the yolk in an egg, “floats” in the liquid outer core of our planet. At the beginning of the first systematic observations of the geomagnetic field (1829 g.) it was noted that the Earth's magnetic dipole (and, accordingly, the inner core) is displaced relative to the planet's rotation axis by 252 km towards the Pacific Ocean.According to 1965 data, this displacement increased to 451 km, and continues to increase!
The displacement of our planet's core should somehow manifest itself, but due to the enormous angular momentum of the Earth, compared to the inner core, these changes will be insignificant. First of all, this should affect the slowdown in the rotation speed of our planet. In 1991, the length of the day increased by 1 second, in July 1992 an amendment was made to the daily time by another 1 second, and in 1993 a full two seconds were added. Already now there is a slow shift of the northern geographic pole in the direction of Greenland, the amplitude of the movement of the instantaneous pole increases, the daily nutation of the rotation axis increases, significant fluctuations in the geographic polar latitude occur - due to a change in the position of the rotation axis in the body of our planet and a shift in the center of mass of the Earth-core system.
Currently, there is a significant shift in the Earth's magnetic poles, and the strength of the magnetic and electric fields of our planet is significantly decreasing. In the direction of the displacement of the inner core, between Australia and Antarctica, the magnetic field strength increases and already reaches 0.7 Oersted, almost like at the pole. On the opposite side of the Earth in the southern part Atlantic Ocean on the contrary, the magnetic field strength decreased by 10%. In the future, all of the above changes should increase even more.
Scientists from German research center geophysicists from Helmholtz in Potsdam and the National Space Institute in Denmark discovered significant changes in the distribution of mass of matter near the Earth's core. These redistributions cause significant changes in the magnetic field of our planet. Using German artificial satellite CHAMP and Danish Orstaed scientists managed to record magma flows on the outer boundaries of the core at a depth of 3500 km. Observations using these satellites and ground stations were carried out for nine years. During this time, European geophysicists created a model describing the behavior outer layers core and molten metals near it. During 2008, equipment recorded rapid redistribution of matter within the planet and significant deviations from the conventional norm. The equipment recorded changes in the magnetic field caused by the redistribution of the mass of the liquid core. Moreover, if ordinary magnetic field fluctuations are seasonal and depend on solar activity, positions of the Sun and Moon, then the recorded changes are preserved, since they are the result of a redistribution of masses inside the Earth. The discovery of European geophysicists is noteworthy in that the recorded changes in the liquid core, and therefore in the Earth’s magnetic field, occurred too quickly: it took less than a year. This suggests that unknown processes are occurring inside our planet, which are likely caused by the displacement of the Earth's inner core.
At the bottom of the Pacific Ocean, scientists from the California Institute of Oceanography discovered new type volcanic activity. Many mini-volcanoes (“spots of activity”) pour fire-breathing lava from cracks in the earth’s crust. This phenomenon had not been observed before. Perhaps the inner core of the Earth, when displaced from the center of the planet, squeezes magma onto its surface.
Scientists have recorded an increase in water temperature in the Pacific Ocean. It is impossible to heat such a huge volume of water in a relatively short period of time. Climate warming human factor can't explain. Maybe, Pacific Ocean is already heating up the hot inner core of our planet, which is shifting precisely to this region of the globe. An increase in water temperature in big ocean our planet will have the most unpleasant consequences. The directions of sea currents, air currents and monsoon rains will change. Accordingly, they will change significantly climatic zones all over the Earth. Temperature contrasts will increase in summer and winter time. Floods from heavy rains, drought, fires, hurricanes, tornadoes, hail, etc. - these are only the relatively harmless consequences of rising temperatures on our planet.
As the core approaches the Earth's mantle, the number of earthquakes, volcanic eruptions and tsunamis will increase, especially in the Mediterranean region, the Indian and Pacific faults of the earth's crust - Japan, Kamchatka, Indonesia, the Philippines, in southeast Asia - Pakistan, India, China, as well as west coast of South America.
Seismic stations constantly monitor the “trembling” of the Earth, recording even minor vibrations of the subsoil. Available statistics indicate that earthquakes on our planet are occurring more and more often. In the 20th century (1900 - 1930) only 2000 earthquakes were recorded, from 1940 to 1982 - about (!) 1000 earthquakes annually. In 1983, 300,000 tremors were recorded, that is, more than 800 per day. Since 1984, the number of recorded earthquakes has been 1000 every day! Since 1994, the number of long-focus earthquakes on the planet, that is, coming from the depths of the Earth, has doubled. The number of tectonic disasters with numerous human casualties is also increasing. In the first half of the 20th century, there were 33 of them, and in the second half there were already 95. Some of them claimed hundreds of thousands of lives!
PHYSICS OF THE EARTH, 2004, No. 4, p. 63-66
© 2004 V. A. Antonov1, B. P. Kondratyev2
1Main Astronomical Observatory of the Russian Academy of Sciences, St. Petersburg 2Udmurt State University, Izhevsk Received November 28, 2002
Using a new method, the equations of motion of the solid inner core of the Earth in the surrounding outer liquid core under the influence of tidal force from celestial bodies. Only the tidal force from the Moon is real, and the influence of other celestial bodies on the inner core of our planet can be neglected. It was found that the displacement of the solid core arises only from the third harmonics of the disturbing potential, and the tidal force depends on the oblateness of the core and has only a slight effect on it. It was specifically established that the amplitude of the core oscillations when taking into account the Moon as the main disturbing body turns out to be negligibly small: in the stationary case, the upper limit of the displacement of the solid core turns out to be equal to only 6.1 x 10-4 cm. This is an order of magnitude less than the result obtained earlier by N.N. Pariysky and almost seven orders of magnitude less than the nuclear displacement estimates obtained by other authors. Keywords: inner core of the Earth, tidal forces, hydrodynamics.
1. INTRODUCTION
Currently, there are no clear ideas about the dynamics of the inner solid core of the Earth, as well as about the flows in the liquid core. In particular, the question of the displacement of the inner core as a whole under the influence of tidal forces from external bodies (in practice, only the Moon must be taken into account) was considered in the monograph [Avsyuk, 1996], but, in our opinion, not fully enough and with errors. Avsyuk’s estimate of the core displacement is about ten meters (page 10 of his monograph).
In [Chuikova et al., 1997], an attempt was made to analyze the oscillations of the Earth's inner core under the influence of gravitational and magnetic fields. However, in specific calculations, all nonlinear terms in the equations of motion were discarded, that is, the problem was solved in a trivial linear approximation. The calculation data turned out to be incomplete; in addition to the oscillation frequency, only an estimate of the stationary displacement of the Earth’s core was given (it turned out to be on the order of several hundred meters; in terms of the order of magnitude, it can be estimated simply as a consequence of the pear-shaped shape of the Earth). This work, in particular, did not say anything about the displacement of the core under the influence of other celestial bodies. But it is the latter that will interest us further.
In assessing the displacement of the solid core N.N. Pariyskiy [Pariyskiy, 2000] gives a completely different result. Using the potential of the Moon's gravitational pull on Earth in the form of McCullo
V =--1-- (a)
(M1 is the mass of the Moon, r is the distance between the centers of gravity of the Earth and the Moon, A, B, C are the main moments of inertia of the Earth, J is the moment of inertia of the Earth relative to the direction r), he finds the magnitude of the radial tidal acceleration at the center of the solid core equal to (5 - declination of the Moon, v - true anomaly, a - equatorial radius of the Earth)
And ar (5, v) = 0.495 GM^CzA (^^ 5). ^
As a result, N.N. Pariysky obtained a maximum displacement of the solid core under the influence of the Moon equal to only 7 x 10-3 cm.
In view of the sharp differences in estimates of nuclear displacement among different authors, it is necessary to consider this issue anew, and preferably with a different method. Below we will consider the question of tidal effects and the displacement of the inner core using the expression for the tidal potential of the Moon on the Earth.
Our approach differs from the approach of N.N. Parisky (remember that he used McCulloh’s formula), since it allows averaging the influence of the third harmonic on the inner core of the Earth. Pariysky’s method does not provide for any averaging: indeed, Aag from formula (b) expresses the tidal influence of the Moon on only one center point kernels. It is precisely in the presence of averaging that we see the reason for some difference in our
result from the offset found by N.N. Pari-skim.
2. ABOUT THE FORCE ACTING ON THE INNER CORE OF THE EARTH
Let us accept the following notation: Ф - the total gravitational potential inside the core, consisting of two parts Ф1 + Ф2, where Ф1 is the potential of the Earth itself, and Ф2 - external body(Moon); pe and -densities, respectively, of the outer and inner core of the Earth, assumed here to be constant (the effects of heterogeneity and compressibility practically do not change the result); Rae and R are the average radii of the outer and inner core of the Earth; T and 5 - region of space and surface of the inner core; n is the vector of the outer unit normal at the interface between the inner and outer cores; p is the pressure inside the liquid core (we neglect viscosity and magnetic field); у(ух, vy, v.) - vector of current speed in the liquid core.
Due to the extreme smallness of the expected tidal currents, inertial terms can be neglected in the equations of hydrodynamics, so what remains
■-- =--grad р + grad Ф, divv = 0. (1)
We use a coordinate system associated with solid body Earth. In addition, in vector equation (1) the term representing centrifugal acceleration is omitted, since this acceleration is obviously small and amounts to only 1-2% of the external tidal gravitational force.
Formally, equations (1) are satisfied by the solution
V x = v y = v. = 0, p = Re F. (2)
This solution, however, does not completely satisfy the boundary conditions, since when the nucleus moves, the interface is, generally speaking, mobile. Denoting the displacement vector of the center of inertia of the inner core through I and the corresponding speed
growth through w = - , we find the solution to system (1)
with a zero right-hand side, but a shifting interface (φ - velocity potential)
V = grad f, p = -p
a + w - ^n(wg) 1n = 0, (g = Rae),
24 = 1, a-24 = 0.
Obviously,
The complete solution is obtained by summing both previous ones
V = grad f, p = reGf --. (6)
Thus, the velocity field and pressure in the liquid core have been found.
Let us study the balance of forces acting on the inner core. Firstly, this is the force of pressure on it from the liquid environment
RP-5 = -ReDf --f)P-5 =
R-1[f -<-;п)я, - Сп)я .
The bulk of the potential comes from the gravity of the Earth itself. Moreover, in the state of rest Ф1(x, y, z) is a symmetric function and therefore the integration of grad Ф1 gives zero. The asymmetrical term comes from the displacement of the inner core. This shift gives, as it were, additional density p; - re against the background of a symmetric distribution, so that the corresponding addition to the potential
8F1 = 2KO(R; - Re) -2pO(R; - Re)
i2-;- (g + I)2
PO(P; - Re)Ig.
The gravitational influence on the core from the Earth’s mantle can be neglected here [Kondratiev, 2003].
We are interested in the tidal force from the Moon. Let the position of its center of inertia in the reference system associated with the solid shell of the Earth be given by the vector r "(x", y", ¿). We expand the gravitational potential of the Moon, Ф2, into a series in powers of coordinates x, y, z (without primes!) interior point of the Earth. The first-order terms are unimportant, since they give an acceleration acting on the entire Earth, which we exclude by fixing the position of the Earth's rigid body. The effect of the second-order term (for brevity we do not write it out) is symmetrical about the origin and also does not apply to the point. Possible impact begins only with members of the third degree
5(g g") 3 - 3 G2 (g g") g2
where m is the mass of the Moon. Then
^ ^ .[ 15(gg")2-3g,2g2]g"-6g"2(gg")g
gradФ2 = From ------7-----. (13)
Obviously, the integral of this grad Ф2 over an exact ball would be equal to zero, since any spherical harmonic of order >1, averaged over the entire sphere, gives zero. Therefore, at this point we have to take into account the nonsphericity of the Earth’s inner core. According to modern data [Bullen, 1978], it has the shape of a slightly compressed spheroid with a squared eccentricity e2 ~ 5 x 103. Let us denote the semi-axes of this spheroid by a, c. The results of integration over the body of the kernel give
|Ts(yy")2 yxyyyz = |Ts(xX + yy" + zz")2 yxyyyz =
4pa4s,2,2H 4pa2s3,2 (X + y) + Z;
AND! r2 yxyyyz =
8 pa4 s 4 pa2 s +
!!!(yy")2 gyxyyyz =
= |C)
