RU2251662C2 - Method and device for simulating western drift of solid core of planet (versions) - Google Patents

Abstract

FIELD: astrophysics.

SUBSTANCE: method and device can be used for investigation of deep dynamics of planets. Weight in form of body of rotation is suspended by means of thread on the support mounted for rotation around vertical axis. Weight is submerged into fluid disposed inside vessel which is capable of rotating around the other vertical axis and distance between vertical axes of rotation of support and vessel is preset. Vessel is driven into rotation at permanent angular velocity and supported is rotated synchronously with rotation of the weight. While changing distance between axes of rotation, maximal angular velocity of weight is measured relatively the distance. Influence of solid core's tidal shift is evaluated on velocity of its western drift is evaluated on the base of the dependence found before. The relation of (Ω-ω)/Ω=s/r is used, where r is radius of sphere taken as model of solid core, s is distance between axes of rotation of vessel and core taken as an analog of tidal shift of solid core, Ω is permanent angular velocity of vessel, (Ω-ω)is analog of angular velocity of western drift. According to the other version of the method, vessel and sphere suspended on the thread are both put into rotation with different permanent velocities and distances between their axes of rotation are found at which distances angle of thread twist equals to zero. Device has two pulleys having vertical axes of rotation. Vessel containing fluid is mounted onto lower pulley and sphere is suspended by means of thread on top pulley admitting horizontal movement. Simulation represents western drift of geomagnetic field from where follows that the source of the field has to be solid magnetized envelope of internal core subjected to periodical heating till melting and changing polarity at repeated hardening. Thickness of the envelope is limited by change of phase in FeH at sharp drop of pressure of melting lower than 3000GPa. Raise in frequency of field inversions is caused by deposition of thorium dioxide on the envelope which interrupts once every 100 million years due to convective collapse in external liquid core. Pressure of 300GPa splits d-zone of electrons of envelope to form filled subzone being spin-noncompensated and isolated from Fermi level by energy gap which allows excluding influence of temperature on magnetic order. The phenomenon is called as baromagnetism.

EFFECT: improved comfort at exploitation.

23 cl, 55 dwg

Description

The invention relates to the field of astrophysics and can be used to study the deep dynamics of the planets, as well as a visual aid when setting out the internal structure of the Earth in educational institutions.

A known method of measuring viscosity using a fluid flow between coaxial cylinders (G. Schlichting, Theory of the boundary layer, M .: Nauka, 1969, p. 86). Known methods for fixing the direction in space, based on the inertia of rotating bodies immersed in a fluid (patent of the Russian Federation 2116623, meter class G 01 C 19/20, 1998), navigation devices with float gyroscopes (copyright certificate of the Russian Federation 1779129, meter class G 01 C 19/20, 1996, European patent EP 0226084 B1, M.C. G 01 C 19/20, 1992). Float gyroscopes contain a housing, a rotor driven into rotation by an external motor and having a spherical cavity partially filled with liquid, inside of which a float is located with a gap. The parameters of the float and liquid satisfy the condition of zero buoyancy. The rotation of the rotor leads to the rotation of the float, which, due to the absence of bonds, is centered inside the spherical cavity.

The centering effect is the opposite of the conditions of the western drift of the solid core of the planet. Three physical factors are essential in the formation of a drift:

1) centrifugal displacement of the core in the cavity of the mantle of the planet,

2) the motion of the center of mass of the core relative to the mantle in orbit with a radius equal to centrifugal displacement,

3) rotational separation of the flow from the surface of the core.

The gravitation of the core toward the center of mass of the planet is proportional to the square of the displacement, while the centrifugal force is proportional to the first degree of displacement and therefore prevails at displacements small compared to the radius of the nucleus. As a result, the distance of the center of mass of the nucleus from the axis of rotation of the planet is 1.31 km near the Earth and approximately 100 km at Jupiter with the radii of the nuclei 1670 km (with a shell) and 9000 km, respectively.

Lagging of the core from the mantle in a centrifugal orbit is the result of a loss of speed due to mass transfer during cyclic melting of the surface layer of the core. Rotational separation of the flow of molten medium creates a region with a reverse flow at the surface of the displaced core, which inhibits the rotation of the core.

These features of the simulated phenomenon are not provided in the known methods and devices, which therefore cannot be applied to solve the problem posed in the present invention. The literature analysis allows us to conclude that the methods for modeling the western drift of the solid core of the planet and the devices for their implementation are not known.

According to indirect signs in the literature, the opposite opinion has been put forward and widely disseminated - that the solid core of the Earth rotates eastward relative to the mantle and lithosphere, i.e. ahead of them, having a higher angular velocity, and thus makes an eastern drift (X.Song, PGRichards, Nature, July 18, 1996, Vol.382, No.6588, p. 212-224; a drawing of the Earth with the eastern drift of the solid core is shown in close-up on the cover of this issue of the journal).

The experiments underlying the proposed method lead to a physically sound and completely reliable conclusion about the western drift of the Earth’s solid core, that is, about the lag of the solid core from the mantle and lithosphere during rotation.

The purpose of the proposed method and device is to provide direct experimental means for the quantitative study of this phenomenon and for its inclusion in educational programs in view of the cognitive and aesthetic significance of the issues associated with it.

The essence of the proposed method for modeling the western drift of the solid core of the planet consists in a combination of two (seemingly laboratory incompatible) conditions: 1) the displacement of the center of the core model relative to the axis of rotation of the mantle model, 2) the complete elimination of the influence of bonds on the rotation of the core model as if the model were in zero gravity. Such a combination makes it possible to create experimentally characteristic for a solid core conditions of free rotation with an eccentric arrangement in a rotating liquid medium.

In view of this, the research method based on the proposed method can be called the axial zero gravity method.

The model of the solid core in this method is a ball suspended on a thread, which provides a given radial displacement of the model. To eliminate the resistance of elastic twisting of the thread, it is rotated synchronously with the ball. The tangential drift of the ball by the flow of a rotating fluid is quite small and practically does not affect the magnitude of the radial displacement.

The main modeling process is the steady synchronous rotation of the ball and the untwisted thread. The approach to this state is ensured in the method in that the spinning of the thread is also excluded at the initial stage of rotation of the ball, which follows the turning on of the engine and the beginning of rotation of the vessel. At the indicated initial stage of rotation, the angular velocities of the ball and thread equally increase in time.

A ball-shaped load is suspended using a thread on a support having the ability to rotate around a vertical axis and made in the form of a pulley. The load is immersed in a liquid located in a vessel that can rotate around another vertical axis, the distance between the vertical axes of rotation of the support and the vessel is set, the vessel is rotated at a constant angular velocity. Carried away by the liquid, the load also begins to rotate, the angular velocity of which gradually increases to a certain limit, after which it becomes constant.

Controlling the rotation of the load, for example, by a mark on its surface, synchronously with the rotation of the load rotate the support of the thread. Quantitatively, this is expressed in the fact that the number of revolutions of the support is maintained equal to the number of revolutions of the cargo from the moment the vessel begins to rotate - in the initial period of the angular acceleration of the cargo and after reaching the stationary mode when the angular velocity of the cargo becomes constant. In the stationary mode of rotation, the limiting angular velocity of the load is estimated, which coincides with the actually achieved speed.

The distance between the axes of rotation is varied and the dependence of the maximum speed of the load on the specified distance is found. The initial portion of the found dependence is represented by an asymptotic equation showing a linear relationship between the angular velocity of the western drift of the solid core of the planet and the displacement of the center of the core from the axis of rotation of the mantle:

(Ω -ω) / Ω = s / r, (1)

Where

r is the radius of the ball as a model of a solid core,

s is the distance between the axis of rotation of the vessel and the ball as an analogue of the displacement of the solid core,

Ω is the constant angular velocity of the vessel,

ω is the limiting angular velocity of the ball,

Ω -ω is the value corresponding to the angular velocity of the western drift.

In the conditions of simulating the drift of a solid core, the distance between the axes of rotation of the vessel and the support of the thread practically coincides with the distance between the axes of rotation of the vessel and the ball. Adjusting the device and limiting the speed of rotation make it possible to achieve this coincidence with any necessary accuracy.

The equality of the speed numbers of the support and the load is supported with an accuracy of one revolution, which is controlled by the degree of twisting of the thread. This accuracy is acceptable with a thread diameter of 0.1 mm or less. The design of the proposed device allows, if necessary, to improve the accuracy of synchronous rotation up to 0.01 revolution (up to 3 angular degrees).

The rotation of the vessel continues until the monotonous increase in the angular velocity of the load with time ceases, which is a sign of establishing a stationary rotation mode and the practical achievement of the maximum speed of the load with relatively small fluctuations. Use a vessel in the shape of a truncated sphere, for example a round glass flask. As a thread, nylon monofilament is used.

Another variant of the proposed method for modeling the western drift of the solid core of the planet is also useful, which has the feature that both the vessel and the support are brought into rotation with constant angular velocities from the very beginning of the simulation. With a fixed ratio of the angular velocities of the vessel and the support, the distance between the axes of their rotation is varied and the angle of twisting of the thread is controlled. The distances corresponding to the absence of twisting are found, which are used to judge the effect of the tidal displacement of the solid core on the angular velocity of the backlog of the core from the mantle during planet rotation.

In the general case, to each ratio of angular velocities there correspond two values of the indicated center distance at which the thread does not twist, that is, does not affect the rotation of the ball.

The second variant of the method provides the ability to automatically simulate at any one distance between the axes of the vessel and support. Automatism lies in the fact that stationary rotation without twisting the thread does not require the participation of an experimenter. This makes the second variant of the method useful, in particular, for demonstrating the drift of the planetary core in the classroom at educational institutions.

Along with the independent application of the second variant of the method, this variant can be used immediately after the first variant of the method. In this case, the simulation is carried out in two stages: first, the vessel is brought into rotation with a constant angular velocity, and the support is rotated with an acceleration equal to the acceleration of rotation of the ball until the ball reaches the maximum rotation speed (first version of the method), after which the rotation speed of the support is fixed at a constant level (second variant of the method). Fixing the speed of the support, achieved, for example, by starting a belt drive, eliminates its visual coordination with the speed of rotation of the ball and puts the device into automatic operation.

The fixed speed of the support is determined by the gear ratio of the pulleys and wheels of the device. If it is installed approximately, then after fixing the speed of the support, a difference in the speeds of the support and the ball is possible, which must be eliminated in the process of applying the second variant of the method. With this combination, the first and second variants of the method serve, respectively, as the first and second approximations, which increases the accuracy of the measurements during simulation.

The proposed device for modeling the western drift of the solid core of the planet contains a frame, two pulleys mounted one below the other on the vertical axes with the possibility of changing the distance between the axes and with the possibility of transmitting rotation from one pulley to another through a vertical shaft.

A vessel with a liquid is located on the lower pulley, a load immersed in the liquid is suspended using a thread on the upper pulley, the lower pulley is connected to the engine, the upper pulley is equipped with means for controlling the twisting of the thread and means for limiting the specified twist, the vessel and cargo have marks for counting the speed.

The axis of the lower pulley is fixed to the base of the frame and carries a rolling bearing, the outer ring of which is located in the cylindrical socket of the lower pulley. The lower and upper drive wheels are attached to the vertical shaft, connected by belt drives, respectively, to the lower and upper pulleys, which have grooves for belts, and the lower pulley is connected to the engine by means of a friction gear that overlaps the groove with the belt.

The axis of the upper pulley is made in the form of a cylindrical tube, fastened to the pulley and inserted into the bearing. The thread centering unit is dressed on top of the tube, from which the thread descends to the ball and is freely, that is, with a gap, placed inside the tube.

The thread centering unit includes a cylindrical cap with an end hole for the thread, the cap is dressed with a gap on the tube, and its axis is offset from the tube axis by a screw by a distance equal to the difference between the radii of the thread and the end hole. The tube bearing is connected by a support plate to a horizontal micrometer screw, and the belt drive of the upper pulley has a tension roller. An annular scale of rotation angles is applied to the surface of the upper pulley, and a rotation angle indicator is mounted on the base plate.

The lower end of the thread is enclosed in a flexible sleeve having an extension and inserted into the axial channel of the screw, and the load has a threaded hole for the specified screw. The vessel has a lid with a central hole and radial ribs, the lower parts of which are immersed in liquid. Such ribs rotate the surface layer of liquid in the vessel, which eliminates the error introduced by the inhibition of the surface of the liquid by the load.

The load is made in the shape of a ball. When the distance between the axes exceeds the diameter of the ball, it is more efficient to rotate the liquid with a cover in the form of an umbrella, the barrel of which is fixed in the bottom of the vessel.

The means for controlling the spin of the thread includes an auxiliary thread fastened with a load and stretched by means of counterweights. If there is no twist of the main thread, the specified auxiliary thread does not affect the rotation of the load.

Counterweights allow you to set the tension of the auxiliary thread, regardless of the tension of the main thread, which is determined by the difference in the weight of the cargo and the liquid displaced by it. Spin control can also be done using one or more sticky flags attached to the thread above the liquid level in the vessel.

A means of limiting the spin of the thread is a handle mounted above the upper pulley, which makes it possible to rotate the support by hand in time with the rotation of the ball. Under conditions of rotation of the vessel at a speed of less than one revolution per second, the rotation of the support by hand, averaged over 10 revolutions of the ball, gives results when measuring the maximum angular velocity of the ball, reproducible to the nearest tenth of a percent. The handle is loosely mounted on the axis of the upper pulley and fixed with a screw. This embodiment of the handle allows you to coordinate its initial orientation with the mark on the ball and maintain this correspondence during rotation.

At the bottom of the vessel there is a shock absorber in the form of a plate that protects the vessel from damage in the event of an accidental drop in cargo. The plate is composed of individual sheets of rubber, which increases its damping ability.

The upper part of the device frame includes two parallel rods separated by a gap lying on the shelves supported by the uprights, and the base of the frame rests on the crossbars having level adjustment screws.

On the middle line of the belt drive, the upper and lower pulleys have the same diameters, and the ratio of the diameters of the upper and lower drive wheels satisfies the condition

D ₁₂ / D ₁₁ = 1- (s / r) for s / r≤ 0.1, (2)

where D ₁₂ is the diameter of the upper drive wheel,

D ₁₁ - the diameter of the lower drive wheel,

s is the distance between the axis of rotation of the vessel and the ball, coinciding with the distance between the axis of rotation of the upper and lower pulleys,

r is the radius of the ball.

The invention and its applications are illustrated by drawings having the following contents.

Figure 1 - A device that implements the method of modeling the western drift of the solid core of the planet (a general view with an imitation of the transparency of a glass vessel, through the wall of which you can see a ball simulating the solid core of the Earth immersed in a liquid melt). Figure 2 - View A in figure 1. Figure 3 - Block of the upper pulley. Figure 4 - Section bB in figure 3. Figure 5 - Block of the lower pulley. 6 - Block centering the thread. Fig.7 - Section bb in Fig.6. Fig - Block mounting thread. Fig.9 - The node connecting the thread and the ball. Figure 10 - Kinematic diagram of the device explaining its operation. 11 - A vessel with radial ribs used to rotate the free surface of the liquid at a ball position close to central. Fig - Vessel with a centered lid, used when the displacement of the ball in excess of its radius.

Fig - Means of control of the twist of the thread, including folded in half an additional thread. Fig. 14 - An additional thread in the form of a loop with counterweights at the ends. Fig - Washer for coupling an additional thread with a ball. Fig. 16 is a view of D in Fig. 15. Fig - Crossed ends of the additional thread when twisting the main thread half a turn. Fig. 18 illustrates an additional thread suspension unit. Fig.19 - View D in Fig.18.

Figure 20 is an embodiment of the device. Fig.21 - View E in Fig.20; Fig.22 - Section FJ in Fig.20. Fig - Scheme of measuring the bias of the thread with a suspended ball; when considering the diameter of the thread, such a measurement is equivalent to measuring the distance between the axis of rotation of the vessel and the load.

Fig - Scheme for determining the central position of the ball in the vessel according to the fracture on the dependence of the angular velocity ω of the ball on the distance s between the axes of rotation of the vessel and the ball. The possible trajectories of the rotation axis P of the rotation of the upper pulley relative to the axis Q of rotation of the lower pulley are shown when adjusting the displacement: 1) the axis P is compatible with the axis Q (solid horizontal line, reading along which gives the true value s), 2) the axis P moves past the axis Q with the minimum distance between the axes s _min (a dashed horizontal line, counting along which gives the apparent value of s). The indicated trajectories correspond to the solid and dashed lines in the coordinates ω / Ω, s / r.

Fig - Graph of rotation of the ball “angle φ - time t” under the influence of the spin φ _{0 of the} thread per revolution (φ ₀ = 2π) and half a revolution (φ ₀ = π); the twist was made at time t = 0 and then kept constant by synchronously rotating the pulley on which the thread is fixed, at the same speed as the ball.

Fig. 26 is a graph of the damped oscillations of a ball after eliminating a twist of one revolution in magnitude (the graphs of Figs. 25 and 26 are obtained for a ball with a diameter of 68 mm and a mass of 285 g suspended on a nylon fiber with a diameter of 0.07 mm and a length of 220 mm in the center of a spherical vessel, the cavity of which with a diameter of 230 mm filled with water).

Fig - Measured by the proposed method, the ratio of the angular velocity ω of the ball to the angular Speed Ω of the vessel as a function of the ratio of the displacement s of the ball to the radius r of the ball, ω / Ω = f (s / r). The function found here has a universal character: it does not depend on the size of the ball and the liquid rotation speed for Reynolds numbers Re> 30 (measurements were carried out in the Re range from 50 to 2000; the displacement s is equal to the distance between the axis of rotation of the ball and the vessel).

The initial linear portion of this dependence, expressed by the asymptote (Ω -ω) / Ω = s / r, can be applied to the solid core of the planet. Together with the magnetic shell covering it, the solid core of the Earth currently has a radius r = 1.67 · 10 ⁶ m.

Fig. 28 is a diagram of a solid core of the Earth making a western drift with an angular velocity δ = Ω -ω. The straight line NS is the axis of its own rotation passing through the center of mass of the core, parallel to the axis of rotation of the Earth's mantle and offset from the last axis by a distance s. G = Ks ² is the gravity of the core to the axis of rotation of the mantle, K is a coefficient independent of s. The dotted circle is a non-magnetic subnucleus under the magnetic shell. The orientation of the north pole of the central magnetic dipole (towards the geographical north) is shown by a solid conical arrow and corresponds to the state until the last inversion of the magnetic field (780 thousand years ago). Currently, the dipole is in the opposite direction.

Fig.29, 30, 31 - Successive states of the variable baromagnetic shell of the solid subunit of the Earth during the last inversion of the field. The direction of the magnetic field induction vector is indicated schematically by hollow arrows (by definition, the lines of force surrounding a magnetic dipole come from its north pole). Fig.29 - The shell of the subnucleus is formed by a hard magnetic substance, and the induction vectors inside the shell and inside the subnucleus are directed to geographic north. Fig. 30 - After melting, the shell becomes magnetically soft and shunts the magnetic field accumulated in the subnucleus, which is accompanied by a rotation of the induction vector in the shell towards the geographical south. Fig - Solidification of the melt in the form of a new baromagnetic shell with fixation and amplification of the inverted field, which gradually, under the influence of the shell, penetrates into the subnucleus. The hatched arrow characterizes the direction and magnitude of the magnetic moment of the equivalent central dipole.

Fig, 33 - Intermediate state of the baromagnetic shell. Fig - Peeling the outer part of the shell during the melting process. Fig - The initial stage of hardening of the shell - the formation of a magnetized ring around the equatorial region of the subnucleus.

Fig. 34 - Repulsion of a magnetized solid core by its images in a moving melt of a liquid core. Images I _w , I _e in the equatorial region of the liquid core are due to the western drift of the solid core and tend to combine the magnetic axis of the solid core with the axis of rotation of the Earth. Images I _n , I _s arise due to vortex movements of the melt in the polar regions of the liquid core and prevent the alignment of these axes. The repulsive forces (arrows) are shown schematically as if they acted between the magnetic poles of a solid core and its images (circles with + and - signs).

Fig. 35-38 - Stages of penetration of the refractory thorium oxide into the liquid core of the Earth. Fig - Surrounded by a hydrogen atmosphere and covered with a crust core of the Earth at the stage of accretion. Fig - Deposition of a layer of particles (circles) of thorium dioxide on the core of the core due to the explosion of a supernova in the vicinity of the solar system. Fig. 37 - Formation of a mantle above a layer of thorium dioxide and melting of the outer part of the core. Fig. 38 - Melting of the core crust under thorium dioxide, immersion of solid thorium dioxide particles in a liquid core, raising a relatively small fraction of thorium dioxide to the Earth's surface with magma.

Fig.39-42 - Radial movement of a cloud of refractory particles of thorium dioxide in the liquid core of the Earth. Fig. 39 - Upper position of a heated cloud, heat exchange with the mantle, and enhanced magmatism. Fig - Gradual sedimentation of particles of thorium dioxide in a lighter melt of the liquid core. Fig. 41 - Cloud thickening in the vicinity of the subnucleus, acceleration of the melting and solidification cycles of the baromagnetic shell. Fig. 42 shows the convective collapse of the liquid core due to an increase in the radial temperature gradient, displacing an overheated cloud of thorium dioxide with cooler melt flows from the periphery (then returning to the upper position of the cloud under the mantle, according to Fig. 39).

43, 44 illustrate the state of the substance of the baromagnetic shell.

Fig - Comparison of the relative densities σ of iron (Fe) and atomic hydrogen (H) absorbed in the metal as functions of pressure under adiabatic compression. Dash-dotted line - extrapolation of known data on the compression of pure hydrogen by combining the initial density with the effective density of hydrogen in metals at atmospheric pressure (0.6 g cm ^-3 ). The intersection of the curves indicates the coordinate of a possible phase transition. In constructing the graph of FIG. 43, literature data on adiabatic compression of elements were used (in the book “Shock waves and extreme conditions of matter”, as amended by V.E. Fortov, L.V. Altshuler, R.F. Trunin, A.I. Funtikov , M: Nauka, 2000, p. 15, 298).

Fig. 44 - The formation of a bidipole in an iron atom as a result of concentration of an electric field by ultrahigh pressure. The paired electrons of the unfilled inner shell of the atom go into a state with parallel spins and with a violation of the symmetry of their orbits relative to the nucleus, resulting in conjugate magnetic and electric dipole moments with a fixed relative orientation, in which the direction from the negative charge (-) to positive in the corresponding dipoles (+) coincides with the direction from the south magnetic pole (S) to the north (N). The elliptical orbit of two electrons (circles with arrows indicating spin magnetic moments) around the nucleus (double circle) is shown schematically. Inside the orbit is the symbol of the bidipole, the electric part of which is oriented against the external field, emanating (as an example) from the plates of the double electric layer (the upper plate is positive, the lower one is negative).

Fig. 45 is a schematic representation of the relationship of baromagnetism with a bi-dipole state of a substance.

Fig - Location of the d-electron zone of a ferromagnetic substance such as iron on the dependence of the density of states η _d on the energy ε at a relatively low pressure p << 300 GPa, f _e - Fermi distribution (highlighted by oblique hatching).

Fig. 47 - Deformation of the zone of d-electrons by pressure p = 300 GPa (in the coordinates of Fig. 46); the decrease in the symmetry of the crystal field intensified by compression leads to the splitting of the d-zone Z ₀ of the iron hydride into fully occupied and almost free parts, Z ₁ and Z ₂ , respectively (the filled parts of the d-zone are highlighted by cross-hatching, the arrows show the preferred orientation of the spins). The increase in the Fermi level ε _F caused by compression weakens the effect of temperature.

Under these conditions characteristic of baromagnetism, thermal energy cannot be fully transferred to electrons with uncompensated spins and therefore cannot violate the magnetic order.

,t) жидкого ядра вдоль радиуса

Земли в последовательные моменты времени t до (t=t_e) и после (t=t_a) конвективного коллапса (вытеснение нагретого расплава от границы с субъядром,

=r_s, на границу с мантией,

=r_m); r_a и r_e – радиусы баромагнитной оболочки при t=t_a и t=t_e, соответственно; Т_m(

) - кривая ABCDEFG плавления гидрида железа FeH с температурным скачком BD, ограничивающим толщину баромагнитной оболочки; T_s(

, t_e) - адиабатическое распределение температуры в пределах от Tα до Тβ ; Тμ и Тσ - температуры плавления и переохлаждения баромагнитной оболочки при

=r_s; Тρ - максимальная температура на границе с мантией после коллапса.Fig. 48 - Temperature distribution T = T (

, t) of the liquid core along the radius

Earth at successive times t before (t = t _e ) and after (t = t _a ) convective collapse (displacement of the heated melt from the boundary with the subnucleus,

= r _s , to the boundary with the mantle,

= r _m ); r _a and r _e are the radii of the baromagnetic shell at t = t _a and t = t _e , respectively; T _m (

) is the ABCDEFG curve for the melting of iron hydride FeH with a temperature jump BD that limits the thickness of the baromagnetic shell; T _s (

, t _e ) is the adiabatic temperature distribution ranging from Tα to Tβ; Тμ and Тσ are the melting and supercooling temperatures of the baromagnetic shell at

= r _s ; Тρ is the maximum temperature at the boundary with the mantle after the collapse.

The stepped shape of the melting curve of the liquid core is the result of the intersection of the isentropic with the phase transition boundary between the normal (α - [FeH]) and densified (β - [FeH]) forms of iron hydride. The phase boundary is represented by a steep section of the BD melting curve, the gentle sections AB and DG are close to isentropes.

The jump-like increase in BD of the hydride melting temperature is due to a decrease in the size of the hydrogen atom in the hydride and occurs in the same pressure range (p ≈ 300 GPa) that the transition of molecular hydrogen into an atomic metal form (see Fig. 43).

, t) частиц диоксида тория вдоль радиуса

жидкого ядра в различные моменты времени t: после вытеснения облака диоксида тория на периферию жидкого ядра (t=t_a) и после сгущения облака во внутренней части жидкого ядра (t=t_e); с_i - остаточная концентрация радиоактивных элементов как начало отсчета с_th.Fig. 49 - Distribution of concentration c _th (

, t) thorium dioxide particles along the radius

a liquid core at different points in time t: after displacement of a cloud of thorium dioxide to the periphery of the liquid core (t = t _a ) and after thickening of the cloud in the inner part of the liquid core (t = t _e ); with _i - residual concentration of radioactive elements as a reference from _th .

Fig. 50 — Cycle of the frequency ν _{i of the} inversions of the geomagnetic field with time t: frequency increase during the thickening of the thorium dioxide cloud (time interval from t _a to t _e ), frequency decrease as a result of displacement of the cloud to the periphery of the liquid core (time interval from t _e to t _c ; the difference t _c -t _a is the period of the frequency cycle, the difference t _b -t _a is the largest interval of constant polarity before the first inversion of the cycle).

Fig.51, 52 - Comparison of regular intervals and episodes between inversions of the geomagnetic field. Fig - Regular form of changes in the field strength H _e at the equator of the Earth with time t, characteristic of a single-layer baromagnetic shell; τ _a1 and τ _a2 are successive lifetimes of shells with a constant magnetic orientation, arrows indicate the field direction in the shell cross section (the cross section diagram is enclosed in a circle).

Fig - Episode in the change in tension, characteristic of a two-layer baromagnetic shell and due to the difference in lifetimes τ _b1 and τ _{b2 of} individual layers; Δ τ = τ _b1 -τ _b2 is the duration of the episode. The remaining designations are as in Fig. 51.

Fig.53, 54 - Two types of relative motion of the ball and the medium with an angular velocity of ± Ω. Fig - Ball system: the center of the ball is stationary in a fluid rotating together with the vessel.

54 - Vessel system: the center of the ball makes a circular motion in a fluid that is stationary at the walls of the vessel. Both types of movement lead to western drift. The radius of the vessel can be infinite.

Fig - Waveform of the speed of a rotating fluid in the vicinity of a displaced freely rotating ball. Obtained by registering the current on the electrode immersed in the vessel of the device of figure 1. The electrode rotates with the vessel at the equatorial level of the ball with a period of Tν. The path of the electrode is shown by a dashed circle around the contour of the ball. Ball radius r = 34 mm, offset s = 3 mm. Two current maxima for the period correspond to the deceleration of the liquid at the points of closest approach and removal of the electrode from the ball (marked by arrows).

A device that implements a method for modeling the western drift of the Earth’s solid core contains a frame 1, a lower pulley 2 with a fixed axis 3, and an upper pulley 4, whose axis 5 can be moved in the horizontal direction. On the lower pulley there is a spherical glass vessel 6 with liquid 7. On the upper pulley with the help of thread 8, a load 9 suspended in liquid is suspended.

The thread is aligned with the geometric axis 10 of rotation of the upper pulley using the centering unit 11. The load is made in the form of a ball 12. The vessel has a lid 13 with radial ribs 14, which touch the free surface 15 of the liquid. The axis of symmetry of the vessel is combined with the geometric axis 16 of rotation of the lower pulley. Marks 17, 18 are applied to the ball and the lid of the vessel, allowing control of the rotation process.

The modeling method has two options, in one of which the pulleys are disconnected, and in the other kinematically connected through a vertical shaft 19, freely inserted into bearings 20, 21. Lower and upper drive wheels 22, 23 of the lower and upper belt drives 24, 25 are fixed to the shaft connecting these wheels, respectively, with the lower and upper pulleys.

The upper gear has a roller 26 for keeping the belt in tension when the upper pulley is shifted horizontally. In addition, an essential function of the roller is the ability to turn on the belt drive in the simulation process itself, for example, to move from one simulation option to another without stopping the rotation of the ball. To move the roller, use the slider 27.

The axis of the upper pulley is located on the support plate 28, which is located in the gap 29 between the two guide rods 30, 31 with the possibility of sliding along this gap. The position of the base plate is fixed with a micrometer screw 32 inserted into the fixed nut 33.

A vertical shaft 35 is attached to the lever 34 located above the upper pulley, which acts as a handle for rotating the upper pulley in the case when the pulleys are disconnected. An arrow 36 is installed on the base plate, which is used as a start when counting the angle of rotation of the upper pulley. A flag 37 is glued to the thread to determine the degree of twist of the thread. The axis 3 of the lower pulley is stationary and secured by a bolt 38 on the lower crossbar 39 of the frame. On the axis is a ball bearing 40, the outer ring 41 of which is included in the cylindrical socket 42 of the lower pulley. A rubber roller 44 is pressed against the working cylindrical surface 43 of the lower pulley, mounted on the shaft 45 of the engine 46, which is fastened to the lower beam of the frame with the help of the bracket 47. On the same working surface of the lower pulley, a groove 48 is made for the belt 49, which is recessed into the groove and does not touch the roller 44 of the engine.

On the lower crossbeam of the frame, cylindrical racks 50, 51 are fixed. On top of the racks are equipped with shelves 52, 53, on which the guide rods of the support plate of the upper pulley lie. Using nuts 54 and plates 55, the guide rods are pressed against the shelves. The frame rests on the corners 56, 57, fastened to the lower bar and equipped with four level 58 screws.

The axis 5 of the upper pulley is made in the form of a tube 59, which is inserted into the teflon bearing 60, mounted in the support plate 28, along the slide fit. The tube is pressed into the hole 61 of the pulley. The lever 34 of the handle is freely dressed on the tube and fixed on it by a screw 62. An annular scale of 64 angles is applied to the end face 63 of the upper pulley. The upper pulley has a groove 65 for a belt 66 of circular cross section 67, the center of which is located on the middle line 68 of the belt drive.

The yarn centering unit 11 includes a cylindrical cap 69 with an end opening 70 for the yarn 8. The cap is dressed with a gap 71 on the tube 59. An elastic gasket 72 is inserted into the gap. The axis 73 of the cap with the screw 74 is offset from the tube axis 75 by a distance equal to the radius difference end hole and thread radius,

W _s = R _s -R _c , (3)

where W _s is the distance between the axes of the cap and tube,

R _s is the radius of the end hole of the cap,

R _c is the radius of the thread.

Inside the tube 59, the thread 8 is located with a gap of 76. Nylon monofilament was used as the thread. The thread is passed through the side hole 77 of the cap, fixed with a screw 78 and a lining 79.

The lower end 80 of the thread 8 is enclosed in a flexible sleeve 81 having an extension 82 and inserted into the axial channel 83 of the screw 84, and the load in the form of a ball 12 has an opening 85 with a thread 86 for the specified screw.

The gear ratio of the pulleys of the device is

ω / Ω = D ₀₁ D ₁₂ / D ₀₂ D ₁₁ , (4)

where ω is the angular velocity of rotation of the ball 12,

Ω is the angular velocity of rotation of the vessel 6,

D ₀₁ - the diameter of the lower pulley 2,

D ₀₂ - the diameter of the upper pulley 4,

D ₁₁ - the diameter of the lower drive wheel 22,

D ₁₂ - the diameter of the upper drive wheel 23,

and the diameters are indicated on the midline of the belt drive.

There are options for the proposed device, expanding the range of simulation conditions. Along with the radial ribs 14, made as a whole with the cover 13, can be used removable L-shaped ribs 87, partially overlapping the Central hole 88 of the cover. This is advisable when conducting simulation with a displacement of the ball, which is less than the radius of the ball. At the bottom 89 of the vessel, a shock absorber 90 can be placed in the form of a packet of rubber sheets 91, 92 fastened at the edges 93.

When conducting simulation with a displacement of the ball, which is greater than the radius of the ball, it is advisable to use the cover 94 in the form of an umbrella 95, the barrel 96 of which is supported by a spider 97 installed in the bottom part 98 of the vessel. The means for controlling the twist of the thread may include an auxiliary thread 99 fastened through a washer 100 with a ball 101 and stretched by means of counterweights 102, 103. The auxiliary thread is bent in the form of a U-shaped loop 104. The lower part of the loop is hooked to the side grooves 105 of the washer, which has hole 106 for screw 84.

The ends of the auxiliary thread with counterweights bend around the protrusions 107 of the strap 108, which is worn on the bottom of the tube 59 and is fixed on it by a screw 109.

When the main thread is twisted in excess of half a turn, the ends of the auxiliary thread cross and it takes an X-shape 110. The auxiliary thread can also be used to automatically indicate the twist. To do this, it is necessary to pass alternating current through the loop and register electromagnetic radiation. Twisting the loop reduces its area as a loop and reduces the amplitude of the radiation.

The vessel can be made in the form of a spherical bulb 111 with a wide neck 112, on which ribs 113 are attached, touching the fluid 114. A removable bar 115 is located on the neck, which serves to measure the displacement s of the ball by the displacement of the thread (Fig. 23). The motor 116 is connected directly to the vertical shaft 117, which transmits rotation to the lower and upper pulleys 120, 121 through belt drives 118, 119.

The design of the device allows you to vary the distance s between the axes of the upper and lower pulleys from the value s = 0, when both axes coincide. The ability to give the displacement s arbitrarily small values is important for modeling the linear dependence of the drift on the displacement. Improving the accuracy of setting the zero bias is achieved by adjusting the device before modeling. A thread with a suspended ball serves as a guide when setting the vertical position of the axles of the pulleys using level 58 screws.

The accuracy of setting the zero bias can be verified as follows. A micrometer screw 32 moves the ball 12 through the central region of the vessel 6 in one direction so that the distance s between the axes 10 and 16 first decreases and then increases (Figs. 1, 10, 24). For different fixed screw positions, the rotation speeds of the vessel (Ω) and the ball (ω) are compared. A sign of zero displacement is the equality of the angular velocities of the ball and the vessel. In Fig.24, the desired value of ω / Ω = 1 corresponds to a kink in the curve of the graph. In this case, the path 122 of the axis 10 of the upper pulley intersects the axis 16 of the upper pulley.

The error in adjusting the device is expressed in the fact that the actual trajectory 123 of the axis 10 of the upper pulley passes at a certain distance s _min from the axis 16 of the lower pulley, and the corresponding curve of the graph (dashed line) has a gentle maximum that does not reach the value ω / Ω = 1. The controlled parameters of the device also include the acceleration of the ball under the influence of a constant twist of the thread (Fig.25) and the decay time of free oscillations of the ball (Fig.26).

When modeling the proposed method used balls and vessels of various sizes, in particular: balls with diameters of 68, 57, 38 mm made of plastic, 20 mm made of steel, a glass vessel in the form of a truncated sphere with an inner diameter of 230 mm, a height of 200 mm (figure 1) , a glass flask with internal diameters of 155 mm at the equator and 70 mm in the neck (Fig. 20), the thread is a nylon monofilament with a diameter of 0.07 mm, centered with an accuracy of 0.03 mm, the liquid in the vessel is distilled water (without emitting gas bubbles on the balls), temperature 20 ± 2 ° C.

The experiments were preceded by setting the vertical position of the thread, combining its axis with the axes of rotation of the lower and upper pulleys in the initial position of the device, which ensures equality of the distance between the axes of rotation of the pulleys to the distance s between the axes of rotation of the vessel and the ball.

Example 1. Modeling is performed on the device shown in figure 1. The radius of the ball is r = 3.40 cm, the inner diameter of the vessel is 23.0 cm. Using the micrometer screw, the center of the ball is offset from the axis of the lower pulley s = 3.80 ± 0.03 mm (coinciding with the distance between the axis of rotation of the vessel and the ball). The belt drive is turned off (the tension roller is retracted). The orientation of the handle of the upper pulley is brought into line with the position of the mark of the stationary ball so that this correspondence is visually preserved during the simulation.

Register the initial angular position of the flag on the thread relative to the orientation of the handle. By turning on the engine, the lower pulley is driven into rotation. For a minute and a half, the movement of fluid from the walls of the vessel reaches the ball, and it begins to rotate, gradually gaining speed. Using the handle, the upper pulley is rotated with the same increasing speed as the ball, controlling the synchronization of rotation along the mark on the ball.

In 5 minutes the ball reaches its maximum speed and a stationary rotation mode is established, which continues to be maintained by synchronous rotation of the handle. After 10 minutes from the moment the engine is turned on, the time of 10 revolutions of the ball is counted on the stopwatch: 68.6 s. Repeat the measurement three times and obtain a sequence of values: 68.5 s, 68.4 s, 68.6 s. The ball rotation period is defined as the average of the measured values divided by 10: T _c = 6.85 s.

The label measures the period Tν of rotation of the vessel. For this, a time of 10 revolutions is counted by the stopwatch: 60.7 s, whence Tν = 6.07 s.

The angular velocities are related to the periods found by expressions

Ω = 2π / Tν, ω = 2π / T _c . (5)

The ratio ω / Ω = Tν / T _c = 0.885 and the ratio s / r = 0.38 cm / 3.40 cm = 0.112 are calculated.

The latter value is compared with the difference 1-ω / Ω = 0.115. The proximity of both quantities shows that the asymptotic equation s / r = 1-ω / Ω, or

(Ω -ω) / Ω = s / r, (6)

performed under the conditions of this experiment with an accuracy of 1- (0.112 / 0.115) = 0.026 for the initial portion of the dependence of ω on s, which is characterized by a region s / r≤ 0.1 (Fig. 27).

Earth conditions correspond to the ratio

s / r = 1.31 km / 1670 km = 0.79 · 10 ^-3 , (7)

which falls into the indicated region, which allows using the asymptotic equation found by modeling. It shows a linear relationship between the angular velocity of the western drift of the solid core of the planet and the displacement of the center of mass of the core from the axis of rotation of the mantle.

The found asymptotic equation is of practical importance. It allows for the first time to calculate the angular velocity of the western drift of the Earth’s solid core. The relative angular velocity Ω of the orbital motion of the center of mass of the nucleus against the rotation of the planet (an analogue of the motion of the center of the ball relative to the vessel during modeling) can be found from the period of swings of the Earth’s pole, measured by S. Chandler (1891), T _ch = 430 days,

Ω = 2π / T _ch = 1.69 · 10 ^-7 s ^-1 . (8)

Hence, for the angular velocity δ of the westward drift of the nucleus,

δ = Ω -ω = Ω s / r = 1.69 · 10 ^-7 s ^-1 · 0.79 · 10 ^-3 = 1.34 · 10 ^-10 s ^-1 ,

δ = 1.34 · 10 ^-10 s ^-1 · (360 ° / 2π) · (3.15 · 10 ⁷ s / year) = 0.24 deg / year. (9)

More than 300 years ago, E. Halley discovered a systematic western drift of the Earth’s magnetic field. Its angular velocity is

δ _m = 1.66 · 10 ^-10 s ^-1 = 0.30 deg / year. (10)

The practical coincidence of the two numbers obtained independently and from the first principles confirms the applicability of the found asymptotic equation to the Earth's conditions and, in addition, reveals the hitherto unknown origin of the geomagnetic field. From the result it follows that the source of the geomagnetic field is the solid core of the Earth.

Under simulation conditions, the Reynolds number is determined by the formula

Re = 2Ω sr / μ _s , (11)

where μ _s is the kinematic viscosity. The condition Re> 100 fulfilled in this example corresponds to the estimate μ _s <10 m ² s ^-1 for the upper boundary of the kinematic viscosity of the melt in the vicinity of the solid core.

Example 2. Modeling to demonstrate the backlog of a solid core is performed with the same diameters of the lower and upper pulleys (120 mm). Set the gear ratio of the wheels of the vertical shaft D ₁₂ / D ₁₁ = 0.89, which corresponds to the conditions of example 1. When the radius of the ball r = 3.40 cm with a micrometer, the displacement of the ball to the value s = 0.38 cm

Disengage the clutch of the belt drive by pulling the tension roller. Turn on the engine and simultaneously with the rotation of the ball rotate the handle of the upper pulley. Upon reaching the maximum speed of the ball, the clutch is engaged and the handle is released, allowing the belt drive to rotate the upper pulley. Preservation of the initial orientation of the flag relative to the handle indicates the lag of the ball without twisting the thread. If the flag is rejected, it is returned to its original orientation (with an accuracy of ± 10 °), adjusting the displacement of the rotating ball with a micrometer screw.

The wheels of the vertical shaft are changed, the gear ratio is set to D ₁₂ / D ₁₁ = 0.70, and when the ball radius r = 3.40 cm, the distance s between the axes of rotation of the vessel and the ball is varied. In the stationary rotation of the ball control the angle of rotation of the thread. They find that with stationary rotation of the ball, the twist angle is zero for two values of the distance s: s ₁ = 1.33 cm, s ₂ = 4.90 cm. From the values found, it is determined that the ratio of the angular velocities of the ball and the vessel ω / Ω = 0.70 corresponds to two displacement ratios ball to its radius: (s / r) ₁ = 0.39 and (s / r) ₂ = 1.44.

Varying the ratio ω / Ω in the range from 0.6 to 1, we obtain two branches of the function ω / Ω = f (s / r) located on both sides of its minimum at s / r = 0.75 (Fig. 27). The result allows us to draw the conclusions described in the previous example.

Example 3. Use balls of various diameters. In particular, with a displacement of the ball s = 3.05 cm, a radius of the ball r = 1.90 cm and a period of rotation of the vessel Tν = 6.06 s, the simulation gives a period of steady rotation of the ball T _c = 8.37 s, which implies that the ratio of distances s / r = 1.605 corresponds to angular velocities ω / Ω = 6.06 s / 8.37 s = 0.724.

As a result, we obtain the function ω / Ω = f (s / r) with characteristic points that are independent of the radius of the ball:

initial slope

∂ (ω / Ω) / ∂ (s / r) = - 1.00 ± 0.05 with s / r = 0, (12)

minimum

min (ω / Ω) = 0.61 ± 0.01 for s / r = 0.75 ± 0.05. (thirteen)

The mechanism of rotational separation of the flow consists in the fact that at the surface of a solid core displaced from the axis of rotation of the liquid medium, a reverse flow region forms, which slows down the rotation of the core and thus creates an angular drift of the core relative to the planet. The size of the reverse flow region increases with increasing displacement.

In contrast to the usual separation of the flow, this phenomenon is expressed in the difference in the angular velocities of the vessel and the freely rotating ball. At small displacements, s / r <0.2, modeling experiments reveal two types of dependence of the ball drift on displacement: quadratic and linear. The transition from a quadratic change in the drift velocity to a linear one as the viscosity of the medium decreases is made in the vicinity of the Reynolds number Re≈ 30.

Allowing to detect rotational separation of the flow in stationary conditions, the proposed method also provides information about the stability of the fluid flow around the displaced core of the planet. With its help, a special type of regular self-oscillations of the linear velocity of the current is revealed, which is characteristic in that the extremes of velocity circulate around the nucleus.

In the process of circulation, the maximum and minimum speeds alternately pass through fixed places on the equator of the nucleus, which is expressed in local velocity fluctuations whose phases are opposite at diametrically opposite points of the equator. The extremum circulation frequency is close to the frequency of the relative orbital motion of the nucleus or coincides with it as a result of spontaneous synchronization. When modeling, the indicated frequency is equal to the frequency of rotation of the vessel relative to the fixed center of the freely rotating ball. The amplitude of the oscillations reaches 20% of the average speed in the same place.

The type of symmetry of the oscillating flow was found using two identical electrodes located on one vertical (along the axis of rotation of the vessel) so that one was at the equatorial level of the ball and the other at the pole level. The phases and amplitudes of the current at the electrodes practically coincide when the distance to the ball is less than its radius. This shows that self-oscillations have cylindrical symmetry.

From model experiments it follows that these self-oscillations are caused by deceleration in the central region of the rotating fluid and have common properties for various reasons of deceleration. The stationary flow is slowed down by any object that disrupts the solid-state rotation of the liquid along with the vessel. Such an object can be a fixed ball in the center of a rotating vessel or a freely rotating ball offset from the center of the same vessel. The latter is typical of the core of the planet.

If the ball is in the center and free in its rotation, then the deceleration can be caused even by a thin motionless probe immersed in any place of the rotating vessel. Due to energy dissipation on the probe, the ball will not be able to acquire the angular velocity of the vessel and will lag behind it. The lag rate of the ball — its drift relative to the vessel — is available for accurate measurement thanks to the proposed method and allows us to estimate the magnitude of losses.

In an unsteady process of spinning a spherical vessel with a liquid, the rotation of the central region of the liquid is slowed down due to inertia. Moreover, these self-oscillations occur in the absence of immersed objects.

In the stationary mode, in the presence of a displaced core, the relative amplitude of the self-oscillations of the velocity of the liquid medium decreases to zero with a decrease in the displacement, so that the oscillation process does not distort the described proportionality between the displacement and the angular velocity of the drift, which, according to the simulation conditions, is the average over the period of rotation of the vessel.

Based on the data obtained by the proposed method, the following patterns are established that underlie the deep dynamics of the planet:

1) the square-root gravity of the planet’s core

G = (32/9) π ² γ ρ Δ ρ r ² s ² , (14)

2) centrifugal displacement of the core

s = 3ν ² r / Sπ ρ γ (1 + ϑ _c ), (15)

s _c = s / (1 + ϑ _c ) = 3ν ² r / 8π ρ γ (1 + ϑ _c ) ² , (16)

3) rotational flow separation

δ = Ω s / r, (17)

where (for planetary conditions)

ϑ _c = {[m _e / (4/3) π r ³ Δ ρ] -1} ^-1 , (18)

γ = 6.672 · 10 ^-14 m ³ g ^-1 s ^-2 - gravitational constant,

m _e is the mass of the planet,

ρ is the density of the liquid medium around the core,

Δ ρ = ρ _s -ρ,

ρ _c is the average density of the nucleus,

r is the radius of the nucleus,

s is the distance between the centers of mass of the core and the rest of the planet with the replacement of the core by its environment (melt),

s _c is the distance of the center of mass of the nucleus from the center of mass of the entire planet,

ν is the angular velocity of the daily rotation of the planet,

δ is the angular velocity of the western rotational drift of the core relative to the planet,

Ω is the angular velocity of the western orbital drift of the core relative to the planet,

The above formulas are valid for the nuclei of various space objects, in particular pulsars. Under Earth conditions, their use is not limited only to the inner core floating in the mantle cavity.

The core in relation to the planet is also the mantle itself, which floats in a fluid medium - the asthenosphere, filling the gap of 300 km between the mantle and the lithosphere.

In the case of the inner core of the planet r << R, Δ ρ << ρ and ϑ _c << 0.01, which makes the formula quite accurate

s = 3ν ² r / 8π ρ γ. (19)

At the Earth, ν = 0.7272 · 10 ^-4 s ^-1 , R = 6370 km, m _e = 5.97 · 10 ²⁷ g; for the inner core with a shell: r = 1670 km, ρ = 12 g cm ^-3 , Δ ρ = 1 g cm ^-3 ,

ϑ _c = 3.28 · 10 ^-3 , (20)

whence for the displacement of the inner core (additional index o) relative to the axis of rotation of the planet follows

s _co≈ s = 1.31 km. (21)

For the Earth’s mantle, ϑ _{c is} significant: r = 5970 km, ρ = 3.8 g cm ^-3 , Δ ρ = 1.7 g cm ^-3 , ϑ _c = 0.368. It follows that in the role of the core, the mantle (additional index m) is shifted from the axis of rotation of the planet by a distance

s _cm = 8 km. (22)

In addition to its own displacement, the mantle reacts to the displacement of the inner core and must balance it to preserve the moment of momentum of the planet. Such a forced displacement of the mantle is

s _om = ϑ _c s _co = 3.28 · 10 ⁻³ · 1310 m = 4.3 m. (23)

The displacements of the core _sco and the mantle s _cm are the radii of the orbits along which the core and mantle move translationally, that is, without rotation, up to a relatively small angular drift. The periods of revolution in these orbits, respectively, T _co and T _cm , are significantly different. As a result, the center of mass of the mantle moves relative to the axis of rotation of the planet in two orbits with radii s _cm , s _om and periods T _cm , T _om = T _co .

Both movements of the mantle are accompanied by a counterflow of the asthenosphere, which prevents the displacement of the center of mass of the lithosphere - the outer layer of the planet with an average thickness of 100 km. However, under Antarctica, the mantle is linked to the lithosphere by a hill of sunken plates. Following the mantle, the lithosphere sways on this hill so that the orbits of the poles are close in radius to the orbit of the mantle. The precession of the lithosphere around the mantle is perceived as a swing of the globe and is recorded by the oscillations of the latitudes of the observatories as one of the components of the observed movement.

Systematic measurements of the coordinates of the North Pole over the past 100 years reveal spiraling trajectories around the middle pole with periods of 1 and 1.2 years, within a site with a radius of 10 m, in the direction from west to east.

In this case, the middle pole is shifted approximately in a straight line. Over 112 years (from 1890 to 2002), the shift was 14.5 m.

The period of 1 year has a seasonal origin associated with the movement of masses along the Earth's surface. A period of 1.2 years was identified by S. Chandler in 1891. After the seasonal component is separated, the rotation of the pole with a period of 1.2 years reveals beats with a period of 40 years and a change in the radius of the trajectory from 1 to 6 m. The beats indicate the addition of two rotations of the pole with close periods.

One of the rotations is identified in the literature with the Euler predicted precession of the Earth. The nature of the second rotation is not known. The data obtained by the proposed method clearly indicate the relationship of the second rotation of the pole with the western drift of the Earth's core.

The second rotation of the pole occurs in the westerly direction, but is somewhat inferior in radius to the Euler precession in the easterly direction. Hence T _co = 1.2 years.

The reason for the shift of the middle pole also becomes clear. He describes a circle with a radius R _p = 8 km, which is equal to the intrinsic displacement of the mantle. The shift Δ L _p = 14.5 m of the middle pole during the time Δ t _p is part of a circle of length L _p = 2π R _p = 50.3 km. The period T _{cm of} revolution of the middle pole is

T _cm = L _p Δ t _p / Δ L _p = 388 thousand years. (24)

Using the proposed method, the main phenomena associated with the geomagnetic field are explained — the western drift of the magnetic dipole and periodic polarities reversed.

The source of the field is an alternately solidifying and melting baromagnetic shell of a solid core, including iron hydride. At the present stage, during seismic sounding, the shell manifests itself as a transition layer F 470 km thick above the iron-nickel subnucleus, whose radius is 1200 km. The thickness of the shell and, accordingly, of the F layer is determined by the phase transition occurring in iron hydride at a pressure of p ≈ 300 GPa, which is reached at a depth of 4700 km (radius 1670 km from the center of the Earth).

Under a pressure of 300 GPa, the temperature of the magnetic ordering of the shell material (Curie temperature) exceeds the temperature of the structural ordering (melting temperature). Regardless of the state of aggregation - solid or liquid - the shell is magnetized.

The conditions of thermal convection in the liquid core are determined by the adiabatic temperature gradient. It is proportional to the acceleration of gravity, which doubles from the inner boundary of the liquid core to the outer.

In the series of inversions of the geomagnetic field, cycles are distinguished, including dozens of inversions each. During one cycle, a gradual heating of the inner region of the liquid core occurs. A critical temperature gradient is achieved at which the convective stability of the liquid core as a whole is violated. Convective collapse occurs: the melt of the periphery of the liquid core, cooled due to prolonged contact with the mantle, falls with its entire mass onto the sub-core and displaces the heated melt from the inner region of the liquid core.

During the inversion, located at the beginning or in the middle of the cycle, the melting of the shell is accompanied by convective mixing of the melt in the inner region of the liquid core. On the surface of the subnucleus, the melt is supercooled to a temperature lower than the solidification temperature. After solidification of the baromagnetic shell, the time of its reheating to the melting temperature depends on the degree of supercooling of the liquid core before the shell solidifies and on the rate of heat generation in its volume. The power of the internal heat source of the shell is determined by its composition, which is updated after each melting.

The main variable component of the shell is radioactive thorium dioxide, ThO ₂ , which at atmospheric pressure has a density of 10.0 g cm ^-3 and a melting point of 3660 K (pressure increases both parameters). Thorium dioxide is distributed over the volume of the liquid core in the form of refractory sand and gradually settles on the surface of the shell. During melting of the shell, the precipitate mixes with its melt, which leads to an increase in the concentration of thorium dioxide in the shell after it re-hardens. The rate of heat generation in the shell increases, the time interval until the next inversion is reduced. Within the cycle, the frequency of inversions increases with time. In the Phanerozoic for 520 million years, six such cycles are distinguished with sharp frequency drops between them. The last cycle of inversions began 100 million years ago.

The increase in the frequency of inversions in the cycle is limited by the accumulation of heat in the inner region of the liquid core and the violation of the convective stability of the liquid core as a whole. The cycle ends with the development of convective collapse in the liquid core, heating and softening of the mantle, and increased convection in it. The content of thorium oxide in the shell decreases sharply. The rate of heat generation in it and the frequency of inversions fall to a level corresponding to the residual concentration of radioactive elements.

After the completion of convective collapse, thorium dioxide pushed to the periphery begins to re-precipitate, which leads to a new cycle of an increase in the frequency of inversions.

The observed relationship between the intensity of magmatism and the frequency of magnetic field inversions is in agreement with the described inversion mechanism. During the Cretaceous, 120 million years ago, the rate of formation of the oceanic crust sharply increased 10 times, reflecting the speed of convective flows in the mantle. At the same time, there was an equally sharp decline in the frequency of inversions. After the recession, the first interval between inversions lasted 35 million years (from 118 to 83 million years ago), which is equivalent to a frequency of 0.03 inversions per 1 million years; the magnetic field had a constant polarity (direct).

After that, a wave-like, but on average gradual increase in frequency to the present level began (approximately one inversion per 1 million years). Magmatism retained an intensity close to maximum for 10 million years.

The anomalous duration of the first interval is due to two parameters of the melt that has descended from the boundary with the mantle:

1) a relatively low content of radioactive fuel, 2) a relatively low temperature. The wave-like nature of the increase in the frequency of inversions is caused by moderate convection, which violates the monotonic concentration profile of the deposited thorium dioxide.

These processes determine the evolution of the geomagnetic field (Fig.29-33). The solid core 124 of the Earth contains a sub core 125 and a baromagnetic shell 126 immersed in the melt 127 of the liquid core. The shell is formed by hard magnetic matter and is a permanent magnet, the lines of force 128 of which pass through the subnucleus, liquid core, mantle and lithosphere. In magnitude and direction of the field on the Earth's surface, the baromagnetic shell with induction 129 is equivalent to the central dipole with a moment 130 (Fig. 29).

The inversion process begins by melting the original shell. The resulting melt loses the properties of hard magnetic matter and the ability to independently create a field in the surrounding space.

Convection transfers the initial field from the shell to the volume of the liquid core, while maintaining the direction of induction 131 (see Fig. 30). A solid subnucleus, not subject to convection, retains the magnetic field accumulated in it longer than the molten shell. Due to the pressure of 300 GPa, the melt of the shell behaves as a magnetically soft substance and shunts the subnuclear field. Its lines of force 128 are closed by lines of force 132 in the region 133 of the molten shell, creating a field in the shell that is opposite to the original in the direction.

Replacing the heated melt in the vicinity of the subnucleus with a cooled one does not change the function of the magnetic melt as a shunt. It hardens in the form of a new baromagnetic shell 134, reinforcing a field 135 of the opposite direction (see Fig. 31).

The liquid core contains impurities that contribute to the formation of structural defects during solidification and create significant coercivity, fixing the field of the specified opposite direction.

The described field inversion process includes intermediate steps. In the simplest case, which is more likely at the beginning of the cycle, the baromagnetic shell consists of one layer. Sinking inside the shell at the stage of its melting, thorium dioxide accumulates at its bottom. After solidification of the melt, the power of the heat source in the inner part of the shell becomes higher than on its periphery. Therefore, the next melting of this shell begins at its border with the iron-nickel subnucleus. An inner layer 136 of liquid melt is formed. Then, the outer part of the shell 137 melts (and simultaneously peels off), which is accompanied by the formation of liquid melt along the entire length from the subnucleus to the mantle.

The near convection following the melting of the outer layer of the shell differs from the convective collapse by a relatively low intensity and does not stop the deposition of thorium sand from the liquid core. Along the surface of the subnucleus, the temperature is minimal at the equator due to cold currents descending from the mantle. Therefore, hardening of the shell begins in the equatorial region 138 of the subnucleus by the formation of a solid ring 139 at first and extends to the poles. Shell melting, on the contrary, begins at the poles.

The magnetic orientation is reproduced at the solidification front due to the interaction between the magnetoelectric bi-fields of the solidified and liquid phases, which is possible without applying an external field. Preservation of the opposite field orientation is ensured by the single-domain magnetic structure of the shell, which is stable under conditions of relatively large shell sizes.

The shell thickness is limited by a threshold pressure below which a phase transition occurs in iron hydride with a sharp decrease in the melting temperature. In contrast to the melting of the entire shell that occurs during inversions, the surface layer a few centimeters thick melts and hardens with a period of revolution of the core in its internal orbit with a radius equal to centrifugal displacement. The melting zone of the surface moves along the core, inhibiting its movement in the mantle cavity. Solid fragments of the shell that separated from it for any reason gradually melt, going beyond the critical radius (1670 km).

Until the growth of the new shell is completed, its hardened part in the form of a ring 139 and the melt 140 of the liquid core surrounding the shell have oppositely directed inductions 141, 142 and form a double magnetic layer. Mutual compensation of the fields of the double layer is expressed in the passage of the magnetic moment of the central dipole through zero. When a new baromagnetic shell is heated up, the described cycle repeats and ends with the next reorientation of the Earth’s magnetic dipole.

A solid magnet placed in a cavity of a rotating electrically conductive sphere is oriented along the axis of rotation, starting from its images in the cavity walls. The Earth’s relative rotation of the liquid core as an electrically conductive sphere is due to the drift of the solid core. Another effect is superimposed on the polar orientation effect - the deviation of the Earth’s axis 143 of the Earth’s magnetic dipole from the planet’s axis of rotation 144 (at an angle of 11 °). The reason for the deviation is the additional repulsion that the magnetic shell 145 experiences from its images in the polar regions 146, 147 of the liquid core, which are the site of intense vortex movements of the melt (Fig. 34). Polar vortices of the Earth’s liquid core are described in the literature (P. Olson, J. Aurnou, Nature, vol. 420, 1999, p. 170-173). The mechanism of deflection of the magnetic axis of Jupiter is similar (by an angle of 10 °).

According to space chronology, during the formation of the solar system in its vicinity, a supernova burst with the release of neutronization products - heavy elements, including uranium and thorium, which are the main components of the star’s core at the final stage of its compression before the explosion.

The mechanism of variations of the geomagnetic field, found from the simulation results, allows one to reconstruct some details of this event. The products of a supernova explosion entered the solar system shortly after the formation of planetary nuclei. Due to their small size, meteorites and asteroids could not compete with planets in the attraction of ejected supernova matter. This explains the relatively low content of thorium and uranium in meteorites.

Under the influence of gravity, a cloud of particles from heavy elements created by the explosion was distributed between the nuclei of large planets, as well as the Sun, and began to fall on them, ahead of the light components of the protoplanetary medium.

Under Earth conditions, the time of thorium intake corresponded to the initial stage of accretion of substance 148 of the mantle (see Figs. 35, 36). By that time, the primary inner core 149 of iron and nickel, the outer core 150 containing iron hydride, core core 151 with a predominance of silicate rocks and a powerful atmosphere 152 of hydrogen, deuterium and helium were formed.

Particles of thorium oxide 153 fell to the Earth with the formation of an active layer 154 above the core crust. In the process of accretion, products of galactic nucleosynthesis also came to Earth. The lower mantle 155, the upper mantle 156 with the asthenosphere 157 (part of the upper mantle from a depth of 300 km) and the lithosphere 158 were successively formed. The loss of heat by radiation and then high pressure contributed to the hardening of the inner and outer nuclei, as well as the layers of the growing mantle.

After a considerable time, the gradual release of heat by nuclides melted the outer core 160, softened the mantle. A baromagnetic shell 161 was formed, the periodic melting of which contributed to the formation and inversions of the geomagnetic field (see Fig. 37, 38).

With hot plumes 162, part of thorium oxide was lifted into the upper mantle, formed fusible thorium silicate, and in the form of magma was ejected by volcanoes 163 onto the Earth's surface, where it is now present in the form of thick deposits 164.

The heating of the active layer of thorium oxide led to the fusion of the core cortex. The heavy sand 165 of thorium oxide sank into the expanded liquid core 166 and, after weakening convection, began to precipitate in the region 167 of the baromagnetic shell, which led to a gradual increase in the frequency of inversions of the geomagnetic field.

Comparison with the well-known chronology of inversions shows that the fusion of the active layer of thorium oxide with a liquid core occurred 600 million years ago. Prior to this, for a billion years, the frequency of inversions remained low (on average about 1 inversion per 10 million years) due to the initial deficiency of radioactive elements in the liquid core.

The 100-millionth cycles of increase in the frequency of inversions of the geomagnetic field that followed this event are directly related to the periodic movement of a cloud of solid particles of thorium oxide in the liquid core. The gradual accumulation of heavy thorium oxide in the inner region of the liquid core is accompanied by overheating of this region, a violation of convective stability and the development of collapse with the displacement of the heated melt containing thorium oxide to the mantle boundary, from which the deposition of thorium oxide resumes.

Such a cycle is repeated once every 100 million years. As thorium oxide is deposited, the rate of heat generation in the baromagnetic shell increases, its melting is faster, and the time interval between inversions decreases.

The cycle phase has the greatest influence on tectonic processes, when a heated melt with a cloud of thorium oxide 168 occupies an upper position on the periphery 169 of the liquid core at its boundary 170 with the mantle (see Fig. 39). The temperature of the transition layer 171 (layer D ₂ ) increases by several hundred degrees, the adjacent areas 172 of the mantle convection cells 173 melt. A silicate melt in the form of plumes 174 rises with the formation of hot spots 175 of the upper mantle and enhances convective motion in the asthenosphere. The main place for the removal of excess heat to the Earth's surface is the mid-ocean ridges and their surroundings. Oceanic crust spreading and subduction are accelerated. Volcanism is increasing on the continents.

The cooled melt layer 176, which has descended to the subnuclear surface 177, hardens to form an enlarged baromagnetic shell 178, which contains the base 179 and coating 180, which differ in the phase state of iron hydride.

A gradual increase in the temperature of the inner part of the liquid core contributes to a decrease in the shell thickness from inversion to inversion. By the end of the inversion cycle, the shell base remains uncoated.

The cooled melt entering the subnucleus as a result of convective collapse is practically devoid of thorium oxide. Since the material of the baromagnetic shell during its next solidification is this depleted melt, the power of the heat source in it drops sharply. The first interval of the new cycle turns out to be anomalously long if the arrival of the depleted melt found the shell in the molten state (35 Ma in the last cycle).

In the meantime, the cloud of thorium oxide particles raised by the collapse is gradually dropping and at an average position of 181 comes into contact with the baromagnum casing region 182 (see FIG. 40, the casing melting stage is shown). From this time, enrichment of the shell with thorium oxide and an increase in the frequency of inversions begin.

The maximum value of the inversion frequency reaches at the lower position 183 of the cloud (see Fig. 41). Almost all thorium oxide from the liquid core is concentrated in the shell, and a large fraction of particles predominates, which settles faster and at the same time includes the bulk of this nuclide. On the other hand, the upper melt layer 184, located under the mantle, loses not only the heat reserves, but also its source itself - thorium oxide.

A thermal crisis sets in in the liquid core. Threads 185 of the depleted melt fall onto subunit 125, displacing the heated melt and thorium oxide scattered therein (see FIG. 42), after which the heated melt with thorium oxide spreads around the periphery of the liquid core (returning to the position shown in FIG. 39).

The principal feature of the described magnetic transformations is the high temperature (at the level of 5000 K), which under ordinary conditions destroys the long-range magnetic order in all known substances. However, there are physical phenomena due to which the solid core of the Earth becomes a permanent magnet.

Like the large planets of the solar system, Jupiter, Saturn and Uranus also had a powerful hydrogen atmosphere. Under the influence of solar radiation, the Earth’s hydrogen atmosphere dissipated, after which the degradation of the upper mantle occurred. Due to the slowness of diffusion processes, hydrogen remained in the liquid core, where it is present in the form of iron hydride, stable at high pressures and not subject to gravitational separation. Iron hydride has metallic conductivity.

According to experimental data known from the literature, obtained at pressures up to 3 GPa, 3d metals with a significant hydrogen content exhibit magnetic properties (B. Baranovsky in the book “Hydrogen in Metals”, ed. G. Alefeld, I. Felkl, Moscow, Mir, 1981, vol. 2, p. 232).

When the pressure rises above 300 GPa, an abrupt increase in the melting temperature is likely. A comparison of this phenomenon with the known hydrogen phase transition at the same pressures (Fig. 43) allows us to relate the jump in the hydride melting curve to the decrease in the volume of the absorbed hydrogen atom. To maintain the magnetic order in iron hydride, the possibility of a bidipole state in it (Figs. 44, 45) and a rather high location of the Fermi level above the energy of electrons with uncompensated spins (Figs. 46, 47) are essential.

The most compact hydride structure is a densely packed face-centered cubic lattice of iron atoms, in the octahedral cavities of which there are hydrogen atoms with a 1: 1 ratio (similar to the NaCl lattice). Each iron atom is located in the center of the octahedron formed by six hydrogen atoms.

The decrease in the symmetry of the iron crystal lattice, associated with the presence of hydrogen in the octahedral interstitial sites, promotes the splitting of the d-electron zone into two subbands separated by an energy gap. First of all, the subband is filled, which is at a lower level relative to the Fermi energy. Compression increases the concentration of valence electrons, which leads to an additional increase in the Fermi level relative to the filled d-electron subband.

As a result of compression, the filled d-subband (Z ₁ in Fig. 47) is located deep below the Fermi level ε _F , outside its vicinity with the boundaries ε _F ± 2kT, where k = 8.617 · 10 ^-5 eV K ^-1 is the Boltzmann constant , 2kT = 0.86 eV at T = 5000 K. This position of the subband protects it from the influence of temperature.

For diamagnetic substances in fully occupied zones only electrons with paired spins can be. In the case of paramagnetic substances, the theory of metals allows the existence of fully occupied zones with uncompensated spins (I.M. Lifshits, M.Ya. Azbel, M.I. Kaganov, Electronic Theory of Metals, Moscow, Nauka, 1971, p.133).

Spin compensation is disturbed, in particular, by the transition of a substance to a bidipole state. Ultrahigh pressure leads to a significant increase in the intra-atomic electric field due to an increase in the bulk density of the electron charge - 1.5 times at the Earth (300 GPa, 5000 K) and 2 times at Jupiter (4500 GPa, 20,000 K). The concentration of the electric field is favorable for the stabilization of the bidipole state, which is confirmed by independent experiments.

Under laboratory conditions, a sufficiently strong electric field can be obtained in a double electric layer at the phase boundary, to which a potential difference is applied. Volumetric dielectric strength of crystals does not exceed 10 ⁸ Vm ^-1 . For a double layer, a field with a strength of 10 ¹⁰ Vm ^-1 is common and can be changed over a wide range when the potential difference changes in the range of 3 V.

Non-magnetic metals - titanium, copper, silver, platinum and several others - were immersed in an aqueous solution of sulfuric acid. Using a reference electrode, a negative potential was imposed on them. The adsorption of hydrogen taking place in this case was accompanied by the appearance and growth of a magnetic flux through the metal surface.

), на меди и серебре - от раствора к металлу (

). На платине по мере адсорбции ориентация диполя меняется: при малых покрытиях - от металла к раствору (

), при покрытиях, близких к полному (1:1) - от раствора к металлу (

) с вкладом одного атома водорода в магнитный момент поверхностиOn titanium, the adsorption of a hydrogen atom creates a dipole oriented by the north magnetic pole from metal to solution (

), on copper and silver - from solution to metal (

) In the case of adsorption on platinum, the dipole orientation changes: for small coatings, from metal to solution (

), with coatings close to full (1: 1) - from solution to metal (

) with the contribution of one hydrogen atom to the magnetic moment of the surface

μ _m (Н-Рt) = 2.2 · 10 ^-23 Am ² , (25)

which is close to the two magnetons of Bohr. For small platinum coatings, hydrogen is negatively charged, (-) H-Pt (+), and for large coatings it is positively charged, (+) H-Pt (-), which is associated with the gradual charging of platinum through an external circuit. Hydrogen performs the function of lining a double electric layer.

A change in magnetic polarity occurs simultaneously with a change in the sign of the potential jump in the double layer, which indicates a fixed relationship between the directions of the electric and magnetic fields. Spontaneous magnetic polarization of the surface occurs under the influence of an electric field, is uniquely associated with its magnitude and polarity. An external magnetic field with an induction of 0.1 T does not have a noticeable effect on it.

The surface properties significantly differs from the volume. Its openness makes it possible to observe the direct response of the condensed matter to the electric field of the intra-atomic force. The role of the nearest environment in this case is secondary, since there is obviously no magnetic order in the volume of the metal, and contact between the adsorbed atoms on the surface occurs only at the end of filling.

The presence or formation of an unfilled d-shell at surface metal atoms is significant. Platinum has it from the very beginning. In copper and silver, it forms when part of the d electrons is consumed to form the free charge of the double layer.

The experiments revealed the following causes of the magnetic order, corresponding to the described model of baromagnetism:

1) the property of paired electrons with parallel spins in a partially filled inner shell of an atom to occupy an orbit asymmetric relative to the nucleus with the formation of a bidipole — particles with conjugate magnetic and electric dipole moments,

,2) the uniqueness of the mutual orientation of the conjugated dipole moments so that in the corresponding dipoles the direction from negative to positive coincides with the direction from the south magnetic pole to the north, | S (-) (+) N

,

3) the transition of electrons to the bidipole state under the influence of the electric field of the intra-atomic level (above 10 ⁸ Vm ^-1 ),

4) the interaction of the electric component of the bidipole with an external electric field, entailing a coordinated orientation of the conjugated magnetic moment.

The listed factors act under conditions of d-, f-, g-shells with an elongated wave function, mainly without nodes, 3d, 4f, 5g. The sequential exclusion of two nodes of the 5d function with the formation of the 5g function was detected during hydrogen adsorption on platinum (A.Ya. Gokhshtein, Uspekhi Fizicheskikh Nauk, 2000, Volume 170, No. 7, pp. 797-804). In rare-earth atoms, a bidipole arises due to the proximity of the 4f shell to its own nucleus as an electric field source. The essential role of the own nucleus is also in the magnetism of 3d elements.

The significant dimensions of the baromagnetic shell provide it with a single-domain structure, which can retain magnetization until the next melting. The magnitude of the magnetization is determined by the competition between the bidipole interaction and heating.

The induction B _{c of the} material of the baromagnetic shell can be estimated by induction B _t on the Earth’s surface near the magnetic pole, B _t = 0.6 G = 0.06 mT, taking into account the radius of the shell r = 1.67 · 10 ⁶ m and the Earth R = 6.3 · 10 ⁶ m:

B _c = B _t (R / r) ³ = 3.33 mT. (26)

It is hundreds of times less than the saturation induction (of the order of 1 T). It follows that the effect of heating is significant. Local fluctuations in temperature and pressure lead to fluctuations in the geomagnetic field. The magnetic permeability of the molten shell increases when it is cooled by convection.

A simultaneous increase in temperature and pressure occurs while maintaining a magnetic order. Significant reserve gain of the magnetic field of the planet. At the equator of Jupiter, the field is 4 Gs, which is 10 times stronger than the field at the equator of the Earth. The source of the magnetic field of Jupiter’s field is located in the vicinity of its core, which has a radius of 15,000 km and is located under a layer 55,000 km thick, consisting mainly of hydrogen. The pressure on the surface of the core reaches 4500 GPa, the temperature - 20,000 K. The central region of the planet contains iron. It follows that the substance that creates the field is iron hydride.

The tenfold superiority of the Jovian field over the Earth's field has no direct relationship with the amount of magnetic substance. If it were possible to increase the diameter of the Earth and its constituent layers by 10 times without changing their magnetic properties, then the field on the surface of the Earth would retain its previous value. It would be determined by the previous induction in the core and the cube of the previous ratio of the radii of the core and surface.

For this reason, a comparison of the fields of the Earth and Jupiter indicates a tenfold increase in the induction in the magnetically active region of Jupiter, which is possible with an increase in the bidipole interaction as a result of the predominance of pressure increase over temperature increase. The pressure on the core of Jupiter is 10 times higher, and the temperature is only 5 times higher than on the core of the Earth.

According to the above mechanism, the inversion of the geomagnetic field is a self-oscillating process of a relaxation type. Long-term accumulation of heat in the hardened region of the liquid core is interrupted by wave-like melting of this region and convective heat removal, which occupies a relatively small part of the self-oscillation period, after which wave-like solidification takes place to a state similar to the initial one. Due to the alternation of field orientation, one cycle of magnetic vibrations includes two cycles of thermal vibrations.

Thermal vibrations in the Earth’s core are independent in their origin from magnetic vibrations and could have occurred without them. Magnetic vibrations, on the contrary, are caused by thermal vibrations. This circumstance is essential when solving the question of how the “first” orientation of the magnetic field arose, which then changed many times.

An analysis of the described phenomena leads to the conclusion that the global orientation of the magnetic field was formed gradually as a result of the combined action of two factors: 1) thermal fluctuations, 2) image forces between the solid magnetized core and the electrically conductive melt of the liquid core rotating around it.

At the initial stage of planetary field formation, the baromagnetic shell is composed of randomly oriented magnetized fragments. After melting of the shell, the field induced in the melt is filtered. Smaller spatial fluctuations dissipate faster, and the average field average over the shell is longer. This field, initially small, creates a preferential orientation when the new shell hardens. Subsequent melting and solidification cycles reinforce this orientation and make it the only one.

Changing the state of aggregation of the baromagnetic shell requires significant energy. In the case of the crystalline structure of the shell material, the bulk of this energy is the latent heat of fusion. With increasing pressure, the entropy Δ S _{m of} melting varies slightly, Δ S _m ≈ const. Under these conditions, the latent heat of fusion L _{m is} proportional to the temperature T _m at which melting occurs, L _m = T _m Δ S _m . To simplify the calculations, these parameters are considered below as average over the thickness of the shell (local values of the parameters are indicated in Fig. 48 by Greek indices).

The time interval τ _c between regular sequential inversions is

τ _c = [c _p (T _m −T _u ) + L _m ] / W _b . (27)

where L _m = T _m Δ S _m is the latent heat of fusion of the substance of the baromagnetic shell (iron hydride),

T _m is the melting point of the shell substance,

Δ S _m = θ _m R is the entropy of melting,

R is the gas constant

θ _m is a coefficient depending on pressure p; θ _m = ln2 = 0.693 at p≥ 300 GPa, when the hydride approaches the iron in terms of the melting temperature,

c _p is the heat capacity of the shell material at constant pressure,

c _p = 6R = 0.877 · 10 ³ J K ^-1 kg ^-1 for FeH,

T _u - the initial temperature of the shell material,

W _b is the power of the heat source inside the shell.

The regularity condition excludes knowingly random episodes. The melting temperature is constant, while the initial temperature increases within the cycle from the minimum temperature T _a to the melting temperature

T _a ≤ T _u ≤ T _m . (28)

The first interval τ _{c1 of the} cycle corresponds to the initial temperature T _u ≈ T _a . In the second interval τ _c2 and subsequent intervals Т _u ≈ Т _m . From (19) it follows

τ _c1 / τ _c2 = 1 + (c _p / L _m ) (T _m -T _a ) (29)

Substitution of values with _p = 6R and L _m = θ RT _m in (21) gives the relation

T _a / T _m = 1- (θ / 6) [(τ _c1 / τ _c2 ) -1], (30)

which can be used to estimate the melting point of iron hydride.

The minimum temperature T _a (in particular, Tα) at the boundary with the subnucleus (at r = r _s ) differs from the temperature T _b (in particular, Tβ) at the boundary with the mantle (at r = r _m ) by the adiabatic drop

T _a -T _b = T _b (r $\genfrac{}{}{0ex}{}{\text{2}}{\text{m}}$ -r $\genfrac{}{}{0ex}{}{\text{2}}{\text{s}}$ ) α b / 2c _p , (31)

where α is the linear coefficient of thermal expansion, b = 4.0 · 10 ^-6 s ^-2 is the known gradient of gravity in the region of the liquid core.

In accordance with published data, T _b ≈ 3000 K and α ≈ 1 · 10 ^-5 K ^-1 . Then T _a = 3720 K.

The durations of the first two regular intervals of the last cycle are τ _c1 = 35 million years and τ _c2 = 10 million years (4 + 6 million years, since the interval of 4 million years reveals signs of an episode). At θ = ln2, the calculation according to equation (22) gives the melting point of iron hydride T _m = 5232 K. The amplitude of the temperature self-oscillations in the inner part of the liquid core is Δ T _a = T _m -T _a = 1512 K.

In a first approximation, to estimate the power of a heat source, the value Δ S _m ≈ Rln2 = 5.76 J mol ^-1 K ^-1 can be used, where R is the gas constant. It corresponds to a change in positional entropy during melting of a monatomic substance - iron and does not take into account the contribution of hydrogen. The latter is permissible at a pressure p≥ 300 GPa due to the lack of a strong chemical bond between iron and hydrogen after a phase transition to a more compact structure.

Under these conditions, the melting temperature T _m = 5000 K (value rounded) corresponds to the heat L _m = 2.9 · 10 ⁴ J mol ^-1 . Under compression of 1.6 (300 GPa), the specific volume of FeH is 5.33–10 ^–6 m ³ mol ^–1 , L _m = 5.4 · 10 ⁹ J m ^–3 . In the case of an amorphous state of a substance, melting is stretched over a certain temperature range, but requires approximately the same energy L _m . The abundance of defects stabilized by high pressure leads to the fact that the state of the baromagnetic shell is intermediate between crystalline and amorphous. By the end of the inversion cycle, the source power approaches the limit value,

W _b → maxW _b . (32)

This implies the equality for the minimum interval per cycle between regular inversions min τ _c = L _m / max W _b .

According to the above, the maximum power of the heat source in the baromagnetic layer can be estimated by the formula

max W _b = L _m / min τ _c . (33)

The last cycle of inversions, which began 100 million years ago, is close to completion. In the current period of 5 million years, 4 large intervals were recorded between magnetic field inversions (as they recede into the past): Brunes (+), Matuyama (-), Gauss (+), Gilbert (-), where the signs (+) and (-) denote normal and reverse polarity. The Brunes interval began 780 thousand years ago and continues without interruption to the present.

Short breaks (episodes) in previous intervals are associated (as shown below) with secondary effects. Thus, the minimum interval between inversions min τ _c = 1 million years was practically reached. It corresponds to the modern power of the heat source inside the baromagnetic shell

maxW _b = 1.71 · 10 ^-4 Wm ^-3 . (34)

With a baromagnetic layer thickness of 470 km, its volume is V _b = 1.23 · 10 ¹⁹ m ³ , V _b / V _e = 0.0114, where V _e = 1.08 · 10 ²¹ m ³ is the volume of the Earth. The total power of the source Q _b = maxW _b V _b = 2.10 · 10 ¹⁵ W.

If it were constant, then on the surface of the Earth S _e = 0.51 · 10 ¹⁵ m ² it would correspond to a stationary heat flux q _b = 4.12 W m ^-2 , which is 59 times higher than the average flux q _e = 0.07 W m ^-2 , currently observed. Since the bulk of thorium oxide from the liquid core accumulates in the shell at the end of the cycle, the value of Q _b with a sufficient approximation also characterizes the power of heat generation in the entire volume of the liquid core.

The temperature on the surface of the earth is determined mainly by the energy received from the sun. From the solar energy flux 1367 W m ^{-2, the} Earth absorbs and then radiates q _sα = 237 W m ^-2 . The specified stream q _b from the core is able to increase this value to q _sβ = 241 W m ^-2 . The relative increase in temperature is

, (35)

, (35)

- температура поверхности, освещаемой Солнцем,Where

- the temperature of the surface illuminated by the Sun,

- температура, создаваемая на поверхности Земли совместным действием Солнца и глубинного источника. В данных условиях

/

=1.0042. При

=293 К этому соответствует

=294.2 К, то есть потепление на 1 К.

- the temperature created on the surface of the Earth by the combined action of the Sun and a deep source. In these conditions

/

= 1.0042. At

= 293 To this corresponds

= 294.2 K, i.e. warming by 1 K.

The heat flux calculated according to the modern frequency of inversions cannot reach the surface of the Earth without hindrance. On its way there are several layers performing thermal self-oscillations - the lower mantle, the upper mantle, including the asthenosphere. At depths of 670 and 400 km, there are regions of phase transitions detected by jumps in the speed of seismic waves. A layer of the asthenosphere about 300 km thick is partially melted.

Self-oscillatory heat transfer through the asthenosphere consists of two stages: 1) thickening of the molten layer without significant convection, 2) the development of annular convection. The critical Rayleigh number at which convective stability is violated is proportional to the temperature drop and the third degree of the layer thickness. At the thickening stage, the temperature of the molten layer is stable, since the input energy is stored in the form of latent heat of fusion. In this case, the temperature difference is insignificant, and an increase in thickness increases the stability of the asthenosphere against mixing, making it an insulator of heat coming from the mantle cavity for a long time.

The Rayleigh number is derived for a homogeneous layer and can be applied to the asthenosphere only qualitatively due to the significant increase in pressure with depth, which affects the composition of the substance and increases its melting temperature. The molten layer can thicken in two directions - up and down. From above, the thickening is stopped by the relatively low temperature of the lithosphere and is currently occurring in depth. This is the origin of the low heat flux currently observed.

The second stage will begin after stopping the thickening in depth and reaching a critical temperature gradient. The development of convection will lead to the removal of accumulated heat, mainly through the thin oceanic crust.

Since the formation of the Earth, the temperature of its surface gradually decreases. About a billion years ago, frequent glaciations began to occur, the maximums of which recur after 100-200 million years and extend to tropical latitudes. The average temperature drop across the Earth by 10-30 K corresponds to icing, which is much more than a warming of 1 K, which could be created by a stationary heat flux with a power of 4 W m ^-2 .

Paleomagnetism data show that the Earth’s magnetic field periodically changes polarity for more than two billion years, with more than a billion years the frequency of inversions being two orders of magnitude lower than in the modern era, and began to rise wavyly 600 million years ago (DMPechersky, Rusian Journal of Earth Sciences, vol. 1, No.2, 1998, p. 103-135). An increase in the frequency of field inversions as a whole in Phanerozoic indicates an increase in the power of the thermal source of the Earth’s core during its history, associated with the rapid development of life.

The question of the source of energy in the Earth’s core has remained unresolved until recently due to a lack of necessary information. The coincidence of the drift of the solid core with the known drift of the geomagnetic field found during the simulation provides additional material to overcome this difficulty.

Due to the inaccessibility of the Earth's core, meteorites with an age of 4.5 billion years are usually considered as its probable components. Radioactive nuclides are present in them, but their concentrations are very low. The most common is potassium ⁴⁰ K with a half-life of 1.28 · 10 ⁹ years and with an energy of 1.314 MeV along the main channel. At its meteorite concentration of 3 · 10 ^-3 mol m ^{-3, the} specific power of the heat source created by β-decay is

W _K = 0.5 · 10 ^-8 W m ^-3 , (36)

which is 4 orders of magnitude lower than the power required for the described magnetic field inversion mechanism.

The average contents of thorium ²³² Th and ²³⁸ U uranium in meteorites are, respectively, 2 · 10 ^-3 mol m ^-3 and 3 · 10 ^-4 mol m ^-3 . The half-period of α -decay and the energy of the main channel (77% of the total number of decays) in these nuclides are 1.41 · 10 ¹⁰ years, 4.016 MeV and 4.468 · 10 ⁹ years, 4.196 MeV. In the indicated amounts, they emit less energy than potassium. The average content of thorium and uranium in the earth's crust is two orders of magnitude higher than in meteorites: 1.3 · 10 ^-3 % and 2 · 10 ^-4 % by mass, or 0.18 mol m ^-3 and 0.028 mol m ^-3 , however, it does not enough. The simulation results allow us to conclude that the main source of thermal energy in the Earth’s liquid core is thorium dioxide ThO ₂ in the amount of 1.1% of the mass of the baromagnetic shell, or 0.08% of the mass of the liquid core and 0.03% of the mass of the Earth. The latter is an order of magnitude greater than the known thorium content in the earth's crust, but is consistent with a cyclical increase in the frequency of inversions with a multiplicity of 35 (for the last cycle).

If the nuclide is uniformly dissolved in the liquid core (for example, ⁴⁰ K with a sufficient amount of it), the multiplicity j _c of frequency increase in the cycle is limited to

j _c = 1 + (T _m -T _a ) (c _p / L _m ), (37)

which under the considered conditions is j _c = 4, i.e., 10 times less than the observed one.

An additional confirmation of the excess of thorium in the Earth's core is the thermal radiation of Jupiter (30 W m ² ). Related to the core of Jupiter (4% of the mass of the planet), it leads to a thorium dioxide content of 1% in the core. Thorium dioxide could not be conserved in the Sun in significant quantities due to the fission of ²³² Th by neutrons with energies above 1 MeV. The neutron fluxes generated by protons during solar flares reach energies of 1000 MeV.

The described cycle corresponds to changes in the temperature of the melt, the concentration of thorium dioxide, the frequency and period of inversions (Fig.48-52).

An important physical factor is the stepwise shape of the curve of melting of iron hydride 186 in the region from the boundary 187 of the liquid core with the subnucleus to the boundary 188 with the mantle. The jump 189 of the melting temperature occurs along the line 190 of the phase transition in iron hydride. The temperature distribution in the liquid core oscillates around this jump. When heated by an internal source, the temperature of the shell rises to the upper portion 191 of the curve, which leads to melting of the shell. Local convection gradually lowers the temperature of the melt of the shell to the level of 192 critical supercooling, after which the shell hardens again. The next interval between inversions is associated with a rise in temperature from subcooling level 192 to melting level 191. In view of the proximity of these levels in temperature (tens of degrees), the duration of heat evolution (the interval between field inversions) is determined, mainly, not by a rise in temperature, but by absorption of the latent heat of fusion.

During the inversion cycle, heat is generated in the inner region of the liquid core (inside the shell and beyond), which is partially removed and transferred to the mantle under conditions of an adiabatic temperature distribution 193. Despite the removal of heat, the temperature of the inner region of the liquid core at the interface with the baromagnetic shell gradually rises.

<r_e) и устремляется к границе с мантией, что находит выражение в конвективном коллапсе. Возникает распределение 194 температуры с максимумом 195 вблизи границы с мантией. Импульсный перегрев дна мантии достигает 300-500 К и активизирует цикл мантийной конвекции.There comes a time when the heated vicinity of the shell cannot cool it quickly enough until it hardens. The lighter heated melt of the shell manages to go beyond the solidification region (r _s <

<r _e ) and rushes to the boundary with the mantle, which finds expression in convective collapse. A temperature distribution 194 arises with a maximum of 195 near the boundary with the mantle. Pulse overheating of the bottom of the mantle reaches 300-500 K and activates the cycle of mantle convection.

The precipitation of a cloud of thorium dioxide begins with a concentration distribution 196, separated by a gap 197 from the boundary of the baromagnetic shell, and gradually turns into a distribution 198, in which the inner part 199 of the cloud is absorbed by the solid baromagnetic shell, and the outer part 200 remains in the molten liquid core.

Fluctuations 201 of the concentration of thorium dioxide caused by local convection entail fluctuations 202 of the inversion frequency (Fig. 50). With the uniform deposition of thorium dioxide, the shell solidifies on the subnucleus 203 in the form of a single layer 204, sufficiently uniform in composition, which is expressed in a regular alternation of polarity at comparable time intervals τ _a1 and τ _a2 (Fig. 51).

<r_e.If the uniform deposition is disturbed, layers 205, 206 are formed in the shell, which differ greatly in the nuclide content and, correspondingly, in the intervals τ _b1 and τ _b2 before melting (Fig. 52). Initially, the field inversion occurs in the outer thicker layer 206, which leads to a flip of the total field, since the contribution of the thin inner layer to the field is relatively small. However, when the melting time of the thin inner layer 205 occurs over the interval Δ τ = τ _b1 -τ _b2 , then the outer layer is also torn away from the shell, which melts, leaving the critical pressure range

<r _e .

In this way, the next inversion of the field occurs after a short period of time Δ τ, which is not a regular interval of inversions. A short burst of 207 reverse polarity is formed. Numerous episodes overlap with the main sequence of inversions and complicate the interpretation of paleomagnetism data.

Up to fluctuations, the process of deposition of ThO ₂ on a baromagnetic shell and an increase in the frequency of inversions with time are described by the following equations:

,t)=c₀[1+(ut/

)]² пpи r_h-ut≤

≤ r_m-ut, (38)c _th (

, t) = c ₀ [1+ (ut /

)] ^{2 for} r _h -ut≤

≤ r _m -ut, (38)

η _r (t) = 1 + (utc ₀ / h ₀ c _i ) [1+ (ut / r _e ) + (1/3) (ut / r _e ) ² ], (39)

ϑ _r (t) = [1+ (ut / r _e )] ² , (40)

max ϑ _r (t) = {1 + [(r _m -r _e ) / r _e )} ² , (41)

Where:

t is the deposition time (after the mixing stage with a uniform distribution of thorium dioxide in the liquid core),

- расстояние от центра Земли,

- distance from the center of the earth,

r _e is the outer radius of the baromagnetic shell,

r _m is the outer radius of the liquid core,

r _h is the initial lower boundary of the cloud of thorium dioxide (see Fig. 49),

h ₀ - the thickness of the baromagnetic shell,

u is the average velocity of thorium dioxide particles during their deposition in a molten liquid core,

в момент времени t),with _th is the concentration of thorium dioxide (at a distance

at time t),

,0)≈ constc ₀ - initial concentration of thorium oxide, с ₀ = с _th (

, 0) ≈ const

>r_h,at

> r _h

c _i is the effective background concentration of the nuclide in the liquid core (traces of soluble nuclides, as well as a fine fraction of ThO ₂ , the deposition rate of which is negligible),

η _r is the ratio of the inversion frequency v _i (t) to the initial level v _i (0),

η _r (t) = ν _i (t) / ν _i (0).

ϑ _r is the ratio of the growth rate of the inversion frequency ∂ ν _i / ∂ _t (t) to the initial level ∂ ν _i / ∂ t (0), ϑ _r = [∂ ν _i / ∂ t (t)] / [∂ ν _i / ∂ t (0)].

According to the Stokes equation for viscous fluid flowing around a sphere, the speed of thorium oxide particles is

₀)/

₀]g₀ a $\genfrac{}{}{0ex}{}{\text{2}}{\text{0}}$ /

₀, (42)u = (2/9) [(ρ _s -

₀ ) /

₀ ] g ₀ a $\genfrac{}{}{0ex}{}{\text{2}}{\text{0}}$ /

₀ , (42)

which includes the average values of the parameters depending on the coordinate:

₀ - средняя плотность расплава жидкого ядра по его объему,

₀ is the average density of the melt of the liquid core in its volume,

_s - плотность диоксида тория,

_s is the density of thorium dioxide,

₀ - средняя кинематическая вязкость расплава жидкого ядра,

₀ is the average kinematic viscosity of the molten liquid core,

g ₀ - acceleration of gravity in the region of the liquid core,

a ₀ is the effective radius of the thorium dioxide particle.

₀=10.6 г см^-3, ρ _s=16.0 г см^-3 (учтена сжимаемость, при атмосферном давлении соответствующие плотности равны 6.6 и 10.0 г см^-3),The following values are close to the conditions of the Earth’s liquid core:

₀ = 10.6 g cm ^-3 , ρ _s = 16.0 g cm ^-3 (compressibility is taken into account, at atmospheric pressure the corresponding densities are 6.6 and 10.0 g cm ^-3 ),

₀=1 м² с, a₀=20 мкм = 2· 10^-5 м. Отсюда u=3.71· 10^-10 м с^-1.g ₀ = 8.2 ms ^-2 ,

₀ = 1 m ² s, a ₀ = 20 μm = 2 · 10 ^-5 m. Hence, u = 3.71 · 10 ^-10 m s ^-1 .

The maximum path length of a thorium oxide particle during its deposition in a liquid core is r _m -r _e = (3.47-1.67) · 10 ⁶ m = 1.80 · 10 ⁶ m.

The maximum deposition time, which coincides with the maximum accumulation time of thorium oxide in the baromagnetic shell, is (r _m -r _e ) /u=1.54· 10 ⁸ years. This value (154 million years) somewhat exceeds, as it should be, the observed duration of one cycle of growth in the frequency of inversions (90-100 million years).

The effect of increasing the frequency growth rate within the inversion cycle is also consistent with observations. Since (r _m -r _e ) / r _e = 1.08, then max ϑ _r = 4.3. Known experimental results give max ϑ _r > 2.

The decay of thorium can initiate a thermonuclear reaction if cavities containing both hydrogen and deuterium are located on the path of the α particle. Due to the small amount of deuterium (1.56 · 10 ^-4 by mass relative to hydrogen), this heat source does not play a significant role in the mechanism of inversions of the geomagnetic field.

ThO ₂ is the most stable thorium compound in a liquid core environment. The bond of thorium with oxygen is stronger than that of other oxides present in the nucleus. Thorium dioxide cannot be reduced with hydrogen. The formation of silicate is associated with expansion, the value of which can be estimated from the data for atmospheric pressure: the molar volume of thorite ThSiO ₄ , 60 cm ³ mol ^-1 , is significantly larger than the sum of the molar volumes of ThO ₂ , 26.4 cm ³ mol ^-1 , and SiO ₂ , 25.9 cm ³ mol ^-1 . Pressure in the liquid core inhibits expansion.

The simulation results are of particular interest for hydrodynamics. In the vicinity of the zero displacement of the solid core, drift modeling can be carried out by reversing the movements of the ball and the vessel (Figs. 53, 54). A rotating vessel 208 and a ball 209 suspended on a support 210 with a fixed axis 211 are equivalent to a fixed vessel 212 with a ball 213 suspended on a support 214, the axis 215 of which performs translational motion along a circle 216. In the absence of twisting of the thread, the angular velocity of rotation of the ball in the second case coincides with the angular velocity of the drift, whereas in the first case, the angular velocity of the drift is equal to the difference in the angular velocities of the vessel and the ball.

Free rotation of the displaced ball in a rotating fluid, provided by the described device (Fig. 1), creates unique conditions for the experimental study of flows, in particular, using electrodes when filling the vessel with an electrolyte solution. Two current maximums for one period of vessel revolution (Fig. 55) indicate the presence of two diametrically located places of fluid deceleration, which is not trivial, since the ball is displaced in one direction.

In this experiment, we used an aqueous solution of potassium ferri- and ferrocyanide with a concentration of 0.2 mol per liter. The measuring and auxiliary electrodes are 0.2 mm thick nickel plates with dimensions of 7 × 7 mm, 30 × 30 mm, respectively. The voltage at the electrodes is 0.8 V. The electrodes are fastened to a rotating vessel and are stationary relative to the liquid in the case of its solid-state rotation.

The presence of a displaced ball creates fluctuations in the relative speed of the measuring electrode. It increases with deceleration of the liquid, which leads to an increase in current from its stationary value.

Claims (22)

1. The method of modeling the western drift of the solid core of the planet, characterized in that on a support that can rotate around a vertical axis, a ball-shaped load is suspended using a thread, the load is immersed in a liquid located in a vessel that can rotate around another vertical axis , set the distance between the vertical axes of rotation of the support and the vessel, bring the vessel into rotation with a constant angular velocity, and support support rotate synchronously with the rotation of the load, estimate the limiting angular velocity of the load, vary standing between the rotation axes, find the dependence of the limiting angular velocity of the load on this distance, and the initial section of the found dependence is represented by an asymptotic equation showing a linear relationship of the angular velocity of the western drift of the solid core of the planet with the displacement of the center of the core from the axis of rotation of the mantle: (Ω-ω) / Ω = s / r, where r is the radius of the ball as a model of a solid core, s is the distance between the axis of rotation of the vessel and the ball as an analogue of the displacement of the solid core, Ω is the constant angular velocity of the vessel, ω is the limiting angular velocity of the ball, Ω - ω is the value corresponding to the angular velocity of the western drift. 2. The method according to claim 1, characterized in that in the process of synchronous rotation the number of revolutions of the support is maintained equal to the number of revolutions of the load from the moment the vessel begins to rotate, moreover, the equality of the numbers of revolutions of the support and the load is controlled by the degree of twisting of the thread and stored to within one revolution. 3. The method according to claim 1, characterized in that the rotation of the vessel continues until the monotonous growth of the angular velocity of the load ceases with time. 4. The method of modeling the western drift of the solid core of the planet, characterized in that on a support that can rotate around a vertical axis, a ball-shaped load is suspended using a thread, the load is immersed in a liquid located in a vessel that has the ability to rotate around another vertical axis , the vessel and the support are brought into rotation with constant angular velocities, with a fixed ratio of these angular velocities, the distance between the indicated axes of rotation is varied and the values of this distance are found at which the angle the twisting of the thread is zero, and the difference in the angular velocities of the vessel and the ball in the absence of twisting of the thread is considered equal to the angular velocity of the drift. 5. The method according to claim 4, characterized in that the vessel is first brought into rotation with a constant angular velocity, and the support is rotated with an acceleration equal to the acceleration of rotation of the ball until the ball reaches the maximum rotation speed, after which the rotation speed of the support is fixed equal to the maximum speed of the ball. 6. Device for modeling the western drift of the solid core of the planet, characterized in that it contains a frame, two pulleys mounted one below the other on the vertical axes with the possibility of horizontal displacement of one of the axes and with the possibility of transmitting rotation from one pulley to another through a vertical shaft, on a vessel with liquid is located on the lower pulley, a load immersed in liquid is suspended on the upper pulley using a thread, the lower pulley is connected to the engine, the upper pulley is equipped with means for controlling the twisting of the thread and means for restricting azannoy twist, vessel and cargo are tagged. 7. The device according to claim 6, characterized in that the load is made in the form of a ball into which a screw having an axial hole is screwed. 8. The device according to claim 6, characterized in that the axis of the lower pulley is fixed to the base of the frame and carries a rolling bearing, the outer ring of which is located in the cylindrical socket of the lower pulley. 9. The device according to claim 6, characterized in that the lower and upper drive wheels are attached to the vertical shaft, connected by belt drives to the lower and upper pulleys, respectively, which have grooves for belts, and the lower pulley is connected to the engine by means of a friction gear. 10. The device according to claim 6, characterized in that the axis of the upper pulley is made in the form of a cylindrical tube, fastened with a pulley and inserted into the bearing, a thread centering unit is placed on top of the tube, which is placed with a gap inside the tube. 11. The device according to claim 10, characterized in that the thread centering unit includes a cylindrical cap with an end hole for the thread, the cap is dressed with a gap on the tube, and its axis is offset from the tube axis by a distance equal to the difference between the radii of the thread and the end holes. 12. The device according to claim 10, characterized in that the tube bearing is connected by a support plate with a horizontal micrometer screw, the belt drive of the upper pulley has a tension roller, an annular angle scale is applied to the end of the upper pulley, and the angle indicator is mounted on the support plate. 13. The device according to claim 7, characterized in that the lower end of the thread is enclosed in a flexible sleeve having an extension and inserted into the axial channel of the screw. 14. The device according to claim 6, characterized in that the vessel has a lid with a Central hole and radial ribs, the lower parts of which are immersed in liquid. 15. The device according to claim 6, characterized in that the vessel has a lid in the form of an umbrella, the trunk of which is fixed in the bottom of the vessel. 16. The device according to claim 6, characterized in that the means for controlling the spin of the thread includes an auxiliary thread fastened with a load and stretched by means of counterweights. 17. The device according to claim 6, characterized in that the means for controlling the twist of the thread is made in the form of a flag fastened to the thread. 18. The device according to claim 6, characterized in that the means of limiting the twist of the thread is a handle, dressed on the axis of the upper pulley with the possibility of rotation about the specified axis and with the possibility of fixing on this axis. 19. The device according to claim 6, characterized in that the upper and lower pulleys have the same diameters along the midline of the belt drive, and the ratio of the diameters of the upper and lower drive wheels satisfies the condition D ₁₂ / D ₁₁ = 1- (s / r), with s / r≤0.1, where D ₁₂ is the diameter of the upper drive wheel, D ₁₁ - the diameter of the lower drive wheel, s is the distance between the axis of rotation of the vessel and the ball, r is the radius of the ball. 20. The device according to claim 6, characterized in that the vessel has the shape of a truncated sphere, and a nylon monofilament is used as a thread. 21. The device according to claim 6, characterized in that at the bottom of the vessel there is a shock absorber in the form of a package of rubber sheets. 22. The device according to claim 6, characterized in that the upper part of the frame includes two parallel-separated by a gap gap, mounted on shelves supported by racks, and the base of the frame is supported by rungs having level adjustment screws.

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