RU2263974C2 - Device for modelling precession of lithosphere around planetary mantle - Google Patents

Abstract

FIELD: astronomy.

SUBSTANCE: device has spherical cover, geometric center of which is held fixed in space and which can rotate. Cover has an opening, through which passes a vertical rod, carrying a ball, positioned inside the cover. Opening of cover and cross-section of rod are of elongated shape. End of rod protruding from the cover is equipped with rotation limiter and enters a vertical channel at periphery of wheel, which is mounted with possible rotation around vertical axis, passing through geometric center of cover. The wheel is connected to engine. Cover is filled with liquid and is mounted on three rollers with horizontally directed cylindrical spikes. Spike holders are held on upper side of round platform. Lower side of platform has ring-shaped groove and is supported by balls, positioned in circular groove of base. Opening for rod is made in rubber bushing, positioned in the wall of cover. Rotation limiter is made in form of crankshaft, one end of which is connected to the rod, and other end has groove, holding a fixed cylindrical pin. During modeling, cover reproduces movement of planet lithosphere, the ball inside cover - movement of mantle, caused by centrifugal movement of solid core. The rod stands for link, connecting lithosphere to mantle at south-pole area of subject planet. Movement of mantle along circular orbit is transformed by link to swaying of lithosphere. Period of lithosphere sway equals to time of turn of solid core around orbit inside the mantle. Western drift of solid core, calculated on basis of this parameter, matches observed drift of geomagnetic field. This coincidence shows reason of inversions of geomagnetic field. These are provided for by melting of magnetized cover of solid core and closing of magnetic field, accumulated at inner portion of solid core, on melted down cover. Western drift of solid core is accompanied by rotary auto-oscillations of melted down substance in mantle hollow with period, equal to time of turn of solid core around orbit. Parameters of lithosphere precession provide estimate of asthenosphere viscosity of 10¹⁴ Pa order.

EFFECT: higher efficiency, broader functional capabilities.

1 cl, 35 dwg

Description

The invention relates to the field of astronomy and can be used to study periodic motions of the Earth's surface.

The lithosphere consists of plates forming a solid solid coating of the globe with thickenings in the form of continents. Plates are based on the asthenosphere - a layer with increased fluidity. Thermal convection in it gradually, over millions of years, deforms the lithosphere and changes the relative position of the continents (V.P. Trubitsyn, V.V. Rykov, Russian Journal of Earth Sciences, 1999, vol. 1, p. 87).

On average once a million years, inversions of the geomagnetic field occur. The search for the origin of the Earth’s magnetic field has been the subject of many works, in particular, on the hydrodynamics of rotating liquids (W. Parkinson. Introduction to geomagnetism, Moscow, 1986; FHBusse, CRCarrigan, J. Fluid Mech., 1974, vol. 62, p.379 ; K.Zhang, P.Earnshow, X. Liao, FHBusse, J. Fluid Mech., 2001, vol. 437, p. 103).

With periods of the order of one year, a complex displacement of the Earth’s poles takes place, among which the influence of the Sun and Moon is discussed (Yu.N. Avsyuk, V.V. Adushkin, V. M. Ovchinnikov. Physics of the Earth, 2001, No. 8, p. 64 ; N.S. Sidorenkov, Atmospheric processes and the rotation of the Earth, St. Petersburg, 2002).

The objective of the present invention is to create a model that reveals the mechanism of regular precession of the lithosphere as a whole around the mantle of the planet in the absence of the influence of other celestial bodies. The solution to this problem is essential for assessing the viscosity of the asthenosphere, searching for patterns that govern the motion of the nuclei of space objects, and also for determining the source of the geomagnetic field. The precession of the lithosphere around the mantle of the planet is not described in literature. Models of this phenomenon have not been previously proposed.

Known devices for testing rotating bodies (for example, RF patent No. 2131610, 1999, mcl G 01 P 3/16) and for their use as regulators (for example, copyright certificate of the Russian Federation No. 1358605, 1996, m incl. G 05 D 13/10). These and other known devices cannot be used to solve this problem.

The problem posed in the present invention is solved due to the fact that the proposed device contains a spherical shell, the geometric center of which is fixed in space and which can be rotated relative to this center, a hole is made in the shell through which a vertical rod passes, carrying a ball located inside the shell , the shell opening and the cross section of the rod are elongated.

The rod end protruding from the shell is equipped with a rotation limiter and is inserted into the vertical channel on the periphery of the wheel, which is mounted on the base with the possibility of rotation around a vertical axis passing through the geometric center of the shell, the wheel is connected to the engine.

The shell is supported by three rollers with horizontally oriented cylindrical spikes. The spikes of the rollers are located in the grooves of the holders mounted on the upper side of the round platform. The bottom side of the platform has an annular groove and rests on balls located in the annular groove of the base.

There is liquid in the shell. For its filling, a neck closed by a cork serves. The hole for the rod is made in a rubber sleeve integrated in the wall of the shell. The rubber sleeve is fastened around the perimeter with an elastic cap stretched over the annular protrusion of the rod, which ensures the sealing of the device.

Possible device options that differ in the position of the wheel: under the shell (the main version) or above the shell. In the main embodiment of the device, the wheel has a shaft on which a ball bearing and a pulley are mounted, connected by a belt rod to the engine pulley. The rotation limiter is made in the form of a connecting rod, one end of which is fastened to the rod, and the other end has a groove, which includes a fixed cylindrical pin. The shell is made detachable from two hemispheres. Its wall is made of transparent material.

Thanks to the indicated embodiment of the device, the relative movement of its elements reliably conveys the features of the motion of planetary elements - the mantle (in the model is represented by a ball) and the lithosphere (in the model is represented by a shell). In particular, the elongated cross-sectional shape of the rod and the hole through which the rod passes prevents the shell from rolling relative to the rod. The combination of the rolling elements of two types - balls and rollers - ensures the fixation of the geometric center of the spherical shell, which corresponds to maintaining the position of the center of mass of the planet with the relative movement of its parts. The connecting rod provides a ball movement close to translational, which is characteristic of the mantle in the coordinate system associated with the planet. The vertical axis passing through the geometric center of the shell corresponds to the axis of daily rotation of the planet. In the indicated coordinate system, the axis of daily rotation is fixed.

The invention and conclusions based on its application are illustrated by the following drawings.

Figure 1 - device for modeling the precession of the lithosphere around the mantle, General view. Figure 2 - view a in figure 1. Figure 3 is a view of B in figure 1. Figure 4 is a section bb in figure 1. 5 is a rod. 6 is a sleeve. Fig.7 is a view of G in Fig.6. Fig. 8 shows a shaft. Fig.9 - the position of the separator and the ball on the base. Figure 10 - roller. 11 is a view D in figure 10. 12 is a roller holder. Fig.13 is a cross-section EE in Fig.12. Fig.14 - connecting rod. Fig - section FJ in Fig. 14. Fig - a variant of the device with the location of the wheel above the shell.

17 and 18 are diagrams of successive positions of the lithosphere, mantle, and solid core with an interval of half a precession (meridional section of the planet). Fig. 19 is a diagram of the asthenosphere flow in the gap between the mantle and lithosphere (equatorial section of the planet; the flow is shown by a white arrow, the orbit of the solid core around the center of mass of the planet is shown by a black arrow).

Figure 20 is a diagram of the formation of an autonomous central region in the mantle cavity of a planet during a spontaneous shift of a solid core, leading to a precession of the lithosphere. Fig - scheme of creating equal pressure on the core when replacing the free surface of the autonomous region with a solid wall of the vessel (radial strokes - plot of the pressure of the liquid medium on the surface of the solid core).

Fig. 22 is a diagram of linear compensation of gravitation and pressure acting on a solid core in an autonomous region having a free surface (as in Fig. 21, a pressure plot is shown). 23 is a diagram of compensating gravitation and pressure for a ball floating in a liquid with a density close to the density of the ball, as an illustration of the suspended state of the solid core of the planet.

24 is a diagram of a one-sided tide for estimating from above the force of attraction of the core to a liquid medium. Fig - registration scheme of the attractive force of the nucleus, proportional to the square of its displacement. Fig. 26 is a diagram of the growth of the force of attraction when the nucleus is enclosed in a fixed vessel.

Fig.27 - 32 - successive stages of the inversion of the geomagnetic field generated by the solid core; the core consists of an iron-nickel subnucleus and a baromagnetic shell containing iron and nickel hydrides with an admixture of thorium dioxide, which gradually heats the baromagnetic shell as a result of radioactive decay. Fig - confirmed by the parameters of the precession of the lithosphere, the scheme of the inversion of the geomagnetic field: the melting of the outer part of the solid core and the closure of the internal magnetic field to the molten outer part.

Fig, 35 - phase of the flow of the melt in the mantle cavity around the solid core during its spontaneous shift from the axis of rotation of the planet, found by modeling.

A device for modeling the precession of the lithosphere around the mantle of the planet contains a spherical shell 1, the geometric center 2 of which is fixed in space. The shell has the ability to rotate around its geometric center. An opening 4 is made in the wall 3 of the shell, through which a vertical rod 5 passes, bearing a ball 6 located inside the shell. The hole of the shell and the cross section of the middle part 7 of the rod are elongated. The lower end 8 of the rod is equipped with a limiter 9 rotation and inserted into the vertical channel 10 on the periphery of the wheel 11.

The wheel is mounted on the base 12 with the possibility of rotation around a vertical axis 13 passing through the geometric center of the shell. The shell 1 is supported by three rollers 14, the spikes 15 of which are oriented horizontally and inserted into the grooves 16 of the holders 17. The holders are mounted on a round platform 18, which has an annular groove 19 at the bottom and is supported by six balls 20 located in the annular groove 21 of the base. Below the base has a cavity 22.

The hole 4 is made in a rubber sleeve 23, built into the wall of the shell. Along the perimeter of the sleeve it is fastened with an elastic cap 24, stretched over the annular protrusion 25 of the rod. In the upper part of the shell there is a neck 26 closed by a plug 27. The shell is made detachable from two hemispheres 28, 29, which are closed by flanges 30 and have a symmetry axis 31 common to the shell, passing through the neck and hole of the rubber sleeve, as well as through the geometric center of the shell. A mark 32 in the form of a protrusion is applied to the outer surface of the shell to record changes in latitude. The shell is filled with a fluid 33, for example water or glycerin.

The wheel has a shaft 34 on which a ball bearing 35 and a pulley 36 are located in the base cavity. A thread 37 is made at the lower end of the shaft, onto which a nut 38 is screwed, pressing the pulley 36 to the wheel. The wheel pulley is connected by a belt rod 39 to the pulley 40 of the engine 41. The rotation limiter is made in the form of a connecting rod 42, one end of which is fastened to the shaft with a screw 43, and the other end has a groove 44, which includes a fixed cylindrical pin 45.

The base and the engine are fastened by side plates 46, 47. The balls 20 are enclosed in a separator 48 made up of an outer ring 49 and an inner ring 50. A groove 51 is formed on the side surface of the rubber sleeve.

In another embodiment of the device (Fig. 16), the shell 52 is mounted on rollers 53. The difference is that the rubber sleeve 54 and the shaft 55 passing through its hole 56 are located in the upper part of the shell, which simplifies sealing when filling the shell with liquid.

The device operates as follows. Through a belt drive 35, the engine 41 drives the wheel 11 with the shaft 5, the angular orientation of which is fixed by the connecting rod 42. The rubber sleeve 23 coupled to the shaft describes the circle, which causes the shell axis of symmetry 31 to oscillate relative to the fixed vertical axis 13 in accordance with the axis of symmetry lithosphere relative to the axis of rotation of the planet. In this case, the mark 32 is shifted by an angle Δθ, corresponding to a change in latitude, which is the same for all places of the lithosphere. A ball fixed on the rod moves inside the shell in a circular orbit and reports the circular motion of the fluid enclosed in the gap between the ball and the shell, which corresponds to the flow of the asthenosphere. Rollers run around the outer surface of the shell. A round platform rotates on balls rolling in an annular groove of the base.

Near the Earth, the thickness of the lithosphere is on average 100 km, the asthenosphere - 300 km. The mantle in the present description refers to a relatively solid layer located under the asthenosphere with a thickness of about 2000 km (lower mantle); between this layer and the solid core is a melt layer of the same thickness (liquid core). In a simplified form, the mechanism of the precession of the lithosphere is shown in the diagrams of Fig.17-19.

The axis of symmetry 57 of the lithosphere 58 oscillates relative to the axis of rotation of the planet 59 passing through the center of mass 60 of planet 61. The oscillation is caused by circular translational movements of two bodies - a solid core 62 with a center of mass 63 in orbit 64 and a mantle 65 with a center of mass 66 in orbit 67 with a constant cohesion of the mantle with the inner protrusion of 68 lithosphere in the south polar region. The centers of both orbits coincide with the center of mass of the planet.

The radii of the orbits are denoted by s _c and s _m, respectively. The sum of the radii is equal to the centrifugal displacement s of the center of mass of the core from the center of mass of the mantle, in which the core is replaced by the displaced melt, s = s _c + s _m , with s _m ≪ _{s c} .

The solid core moves in the cavity 69 of the mantle filled with the melt 70. Between the mantle and the lithosphere is located the asthenosphere 71 — a layer of relatively fusible compounds in a viscoelastic state. The movement of the mantle creates a current of 72 in the asthenosphere.

Located on the lithosphere, the southern geographic pole 73, indicated by point S (Fig. 18), repeats the motion of the center of mass of the mantle and moves around circle 74 relative to the axis of rotation of the planet 59. The same circle, but in antiphase, is described by the north geographic pole 75, indicated by point N. The radius s _{m of} this circle is determined by the centrifugal displacement of the solid core.

Moving in this way in the coordinate system associated with the planet, the mantle and lithosphere maintain an azimuthal orientation, that is, do not rotate around their own axes. For this reason, the swing of the lithosphere is accompanied by a periodic change in the latitude of the objects located on it, which corresponds to a change in the latitude of the mark 32 in the device.

The relative difference between the polar and equatorial radii of the Earth is 1/298, which, with a sufficient approximation, allows us to consider the surfaces of the lithosphere and mantle spherical. The spontaneous shift of the solid core 62 lowers the symmetry of the mantle cavity (Fig. 20) and the planet as a whole. There are other disturbances in the symmetry of the planet, in particular, the spontaneous shift of the mantle relative to the lithosphere, estimated further. However, in size they are several orders of magnitude smaller than the radius of the Earth and practically do not affect the movement of the core inside the mantle.

Therefore, a spontaneous core shift is calculated here under the conditions of spherical symmetry of the upper layers of the planet attached to the mantle.

A mantle concentric with a mantle 76, containing a displaced core, limits the gravitationally autonomous region 77, in which the core interacts with the sickle-shaped melt layer 78. The nature of the interaction is determined by the conditions at the border 79 of the autonomous region.

If the autonomous region were enclosed in a solid vessel 80 capable of withstanding the load (Fig. 21), the melt pressure 81 would be the same at all points on the surface 82 of the core and would not contribute to the attractive force of 83 acting on the core (Fig. 21, radial strokes show the pressure diagram 84). Under these conditions, a solid vessel is similar to a hydraulic press, since it distributes maximum pressure to the entire surface of the core. At the same time, such pressure is created only in one place of the core - where the column of liquid reaches a maximum height of 2s (in the deepest place of the sickle-shaped layer).

In accordance with Hooke's law, the attractive force 83 would be proportional to the displacement s of the center of mass of the nucleus from the center of mass of the mantle, as well as the acceleration of gravity. The gravitational force found in this way, linear in s, is 634 times greater than the centrifugal force created by the daily rotation of the Earth, whence the conclusion about a stable central position of the core inside the planet follows.

In reality, however, there is no hydraulic press above the solid core. The boundary 79 of the autonomous region is similar to a free surface and, in particular, does not perform work in the transverse movement accompanying the motion of the nucleus. In any place on the surface of a solid core, the pressure of the sickle-shaped layer is determined by the height of the liquid column above this place. Under these conditions, the sickle-shaped melt layer 78 creates an uneven pressure 85 on the surface 82 of the displaced solid core, the resultant 86 of which is nonzero and compensates for the gravitational force 87 of the core to the center of the mantle (Fig. 22, the length of the strokes of the shown diagram 88 is proportional to the pressure).

A physical illustration of this phenomenon can be buoyancy - compensation of the force 89 of the gravity of the object by the resultant force 90 of the hydrostatic pressure 91 of the liquid on it from below. If a ball 93 with a density close to the density of water is immersed in water 92, then the hydrostatic pressure 91 is distributed along its surface 94 as well as along the surface of the core (Fig. 23). Diagram 95 of hydrostatic pressure on a floating ball coincides in shape with diagram 88 of pressure on a displaced planetary core - in both cases the pressure is proportional to the "depth", that is, the coordinate measured in the direction of gravity.

In this sense, the core is capable of floating on a melt drawn to it. However, in contrast to the usual buoyancy, the gravity of the core consists of two components: linear and quadratic in distance between the centers of mass of the core and mantle. The melt pressure completely compensates for the linear component. The relatively small quadratic component, the active gravitational force that can balance the centrifugal force, remains uncompensated.

The active gravitational force of the solid core 62 to the sickle-shaped layer 78 of the melt can be estimated using a mental experiment (Fig.24-26). A solid core 62, having a radius r and initially covered with a uniform melt layer 96 of thickness s≪r, is secured with a rod 97 containing an arrow dynamometer 98. At a sufficient distance from the solid core, a massive auxiliary ball 99 is installed, the gravitational field of which causes redistribution of the melt and the formation of a tidal hump 100, reproducing the shape of the sickle-shaped layer 78.

In the meridional section (shown in Fig. 24), the melt surface satisfies the equation

where x (abscissa) and y (ordinate) are rectangular coordinates with the origin in the center of 63 masses of the nucleus,

a is the acceleration created by attraction to the auxiliary ball along the x axis and acting on the melt particles,

g is the acceleration created by attraction to the effective mass of the core (total mass of the core minus the mass of the melt displaced by it),

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

Δρ = ρ _with -ρ is the difference between the average density ρ _{c of the} core and the density ρ of the melt at its surface,

s is the initial thickness of the melt layer, which coincides with the displacement of the center of mass of the solid core from the center of mass of the spherical mantle (in the cavity of which the core is replaced by the displaced melt).

векторов соответствующих ускорений a и g направлена по нормали к поверхности расплава. Использование эффективной массы ядра соответствует вектору

, проходящему через центр 63 масс ядра, что упрощает расчет, не снижая его точности. Использование полной массы ядра и, соответственно, ускорения силы тяжести, проходящего через общий центр масс ядра и слоя расплава, приводит к тому же результату, куда та же самая величина Δρ входит как параметр координаты общего центра масс.The above equation means that the sum

the vectors of the corresponding accelerations a and g are directed normal to the surface of the melt. Using the effective mass of the nucleus corresponds to the vector

passing through the center of mass of the nucleus 63, which simplifies the calculation without reducing its accuracy. Using the total mass of the core and, accordingly, the acceleration of gravity passing through the common center of mass of the core and the melt layer, leads to the same result, where the same value Δρ is included as a parameter of the coordinate of the common center of mass.

The solution to this equation is the circle of the initial radius r + s,

whose center is displaced from the center of the nucleus by the distance (r + s) a / g. In the case of the autonomous region, the displacement is s, the acceleration a is determined by the equation s = (r + s) a / g. Hence, a = (s / r) g up to a negligible quantity (s / r) ² g. With the same relative accuracy, the mass of the density melt layer ρ is m _s = 4πr ² sρ.

The force am _s created by the auxiliary ball reproduces the geometry of the sickle-shaped layer 78 (Figs. 20, 24) and, therefore, overcomes the driving force G of the mutual attraction of the core and the melt in the conditions of the autonomous region of the planet. Such a calculation gives an estimate of the driving force G from above

If the auxiliary ball 99 is removed quickly enough, the hump 100 of the melt will retain its shape for some time due to inertia (Fig.25). In this case, the same motive force of attraction is balanced by the inertia forces acting on the melt along the core surface (the normal component of the inertia forces is negligible).

Elimination of external influences makes it possible to determine the magnitude of the driving force of attraction of the nucleus with greater accuracy. The corresponding acceleration can be found by the slope of the free surface of the melt immediately after removal of the auxiliary ball 99 or, which is equivalent, as the tangential component a _{τ of} acceleration a in the presence of the auxiliary ball

where θ is the angle measured from the equatorial plane 101 of the solid core.

направлен по нормали к поверхности расплава, как и

Отсюда следует избыточность нормальной составляющей силы а m_s притяжения расплава к вспомогательному шару и возможность применения величины am_s именно в качестве оценки сверху для движущей силы G взаимного притяжения расплава и ядра.It is significant that, at s≪r, for the formation of a hump 100 (of the same height 2s and the same shape), the action of only the tangential component a _{τ of} acceleration a is sufficient. Total vector

directed normal to the surface of the melt, as

This implies the redundancy of the normal component of the force a m _{s of} attraction of the melt to the auxiliary ball and the possibility of using the value of am _s just as an upper estimate for the driving force G of the mutual attraction of the melt and the core.

At the same time, in the case of a sufficiently small displacement s, the force G arises only due to the tangential motion of the melt along the surface of the core. Since the tangential component a _{τ is} completely spent on stopping this movement, the total melt braking force calculated from it must be exactly equal to the active force of attraction of the core to the melt.

The melt layer has a thickness h = s (1 + cosθ) and can be divided into ring elements with a volume

One element experiences an attractive force dF _τ = a _τ ρdν ₀ . Its projection on the x axis (the direction of gravity of the nucleus) is sinθdF _τ . In this case, the force acts on the core

Integration over θ from 0 to π gives the desired active core gravity:

Go (s) = (32/9) π ² γρΔρr ² s ² , (8)

where the index “o” indicates that this result is valid for s≪r.

The value of G _O (s) is 1.5 times lower than the upper estimate obtained by introducing the auxiliary ball 99. On the other hand, the conclusion of the core with the surrounding melt into a fixed solid vessel 102, acting as a hydraulic press, should significantly increase the attractive force (in accordance with the circuit of Fig. 26). The difference in the forces tested by the core is schematically reflected in the change in the readings of dynamometer 98 (Figs. 24-26).

The addition of a spherical shell 103 (solid or liquid) by itself - if it is not fixed, is not attracted to the auxiliary ball and is able to move together with the melt layer, which retains its spherical surface during the formation of the hump - does not change the force perceived by the solid core in this experiment. The used inequality s≪r is usually satisfied under planetary conditions.

For arbitrary displacement s, the driving force of gravity of the nucleus can be found from the general equation of hydrodynamics. When the fluid velocity is zero, which corresponds to the beginning of the flow around the core, nonlinear terms are absent:

- вектор скорости жидкости, t - время,

- вектор ускорения жидкости,

- вектор ускорения избыточной силы тяжести (создается ядром за вычетом массы вытесненной жидкости), ρ - постоянная плотность жидкости, p - избыточное давление. Постоянство плотности упрощает расчет и вместе с тем не вносит, как показано далее, существенной погрешности.Where

is the fluid velocity vector, t is time,

is the fluid acceleration vector,

is the acceleration vector of excess gravity (created by the nucleus minus the mass of the displaced fluid), ρ is the constant density of the fluid, p is the excess pressure. The constancy of density simplifies the calculation and at the same time does not introduce, as shown below, a significant error.

In spherical coordinates with a start at the center of mass of the nucleus, a distance to the start of λ, and an angle θ from the axis of symmetry (defined above)

where the indices λ and θ denote the radial and tangential components of the vector. Consequently,

- the height of the liquid column above the surface of the core as a function of the angle θ.

On a fluid mass element in the form of a ring with radius λ sin θ

the force (dV / dt) _θ dm acts at an angle π / 2-θ to the axis of symmetry. The kernel perceives its projection onto the axis of symmetry (with the opposite sign)

The liquid occupies the region r <λ <λ _b , 0 <θ <π. Integration of dG over λ and θ within the specified limits gives the nucleus gravity at any of its shifts s in a liquid medium with constant density:

In the case of a variable density, ρ = ρ (λ), this result is valid up to a relative change in ρ in the region r <λ <λ _b .

For example, a mantle cavity of the Earth with a radius of 3400 km allows a displacement of a solid core with a radius r = 1670 km by a distance s = 1730 km ≈ r, while G (s) / G _O (s) = 1/3, i.e., accurate and approximate formulas give a 3 times difference in gravity. At the same time, a change in the density of the melt in the cavity is limited to 10 g cm ⁻³ <ρ <13 g cm ⁻³ , i.e., it is 1 / 1.3 and relatively little affects the nature of the dependence G (s).

The above calculation scheme is also applicable for the exact calculation of the function ρ (λ). For small s≪r, the dependence of G on s goes over to the quadratic one obtained above.

The distance of the center of mass of the nucleus to the axis of rotation of the planet

where m _c = (4/3) πr ³ Δρ is the excess mass of the nucleus, Δρ is the difference between the densities of the nucleus and the medium, m _e is the mass of the planet,

The centrifugal force C = m _c ω ² s _c acts on the core in the fluid, where ω is the angular velocity of the planet’s daily rotation. From here

The distance s (between the centers of mass of the core and mantle) is determined by the equality of the deflecting and returning forces, C (s) = G (s), or

This equation has two solutions:

Thus, the core of the planet has two equilibrium positions. The first coincides with the central position and is unstable at any angular velocity of rotation of the planet. The second is stable and is removed from the central position by a considerable distance, which increases as the square of the angular velocity.

It follows from the obtained result that all, without exception, rotating masses of cosmic origin, including planets and stars, are asymmetric about the axis of rotation.

In accordance with the found shift s, the distance s _c from the axis of rotation of the planet to the center of mass of the nucleus is

The expressions obtained make it possible to consider as the core any inner shell of the planet covered with a layer of liquid:

1) a solid core under the melt in the cavity of the mantle,

2) the mantle under the fluid in the cavity of the lithosphere,

3) the lithosphere under the ocean with a free surface.

In all three cases, the central position of the inner shell is unstable, which violates the symmetry of the planet.

In the first two cases, the shift of the inner shell is small compared to the thickness of the liquid layer and practically does not affect the shape of the outer shell. Insignificant, in particular, the deformation of the mantle during the shift of the solid core. This condition is the basis of the calculation and ensures the accuracy of the shift found. Both cases include precession of the lithosphere around the mantle. In the third case, the calculation is applicable only qualitatively because of the relatively shallow depth of the ocean.

The manifestations of spontaneous nuclear shift in each of the three cases are briefly described below.

For the inner solid core of known planets, the conditions ϑ _О ≤0.01, β≤0.01 are satisfied, whence with acceptable accuracy

For the Earth, ω = 0.7272 · 10 ^-4 s ^-1 , r = 1.67 · 10 ⁶ m (the inner core with a solid baromagnetic shell), ρ = 12 · 10 ⁶ gm ^-3 , ϑ _O = 3.26 · 10 ^-3

Hence β = 0.788 · 10 ^-3 ,

For Jupiter, the values of ω = 1.7585 · 10 ^-4 s ^-1 , r = 8.57 · 10 ⁶ m, ρ = 4.15 · 10 ⁶ gm ^-3 , ϑ _O = 1.53 · 10 ^-2 give β = 1.441 · 10 ^-2 ,

A stable equilibrium displacement of the nucleus is the radius of the orbit along which the center of mass of the nucleus moves when the planet rotates around its own axis. In the simplest case, the displaced core is stationary relative to the planet. In this case, diametrically opposite points on the surface of the core experience a constant pressure difference, which is maximum in the direction along the radius of the planet. On the side with less pressure, the core melts, and on the opposite side it grows, which leads to a lag in the center of mass of the core from the rotation of the planet. It moves in the inner orbit relative to the planet in the opposite direction.

The inertia of the nucleus contributes to its translational movement, that is, without noticeable (in one revolution in the orbit) rotation around its own axis. During the period of revolution in orbit, the angle of rotation of the core relative to the planet is small (in contrast, for example, from the Moon, which makes a complete revolution around its own axis during the period of revolution around the Earth).

The pressure difference on the surface of a progressively moving nucleus fluctuates around zero with a period equal to the period of relative rotation of the center of mass of the nucleus in its orbit. If the period is small enough (about 1 year in the case of the Earth), the pressure difference does not have time to significantly affect the shape of the core.

Observations begun at the end of the 19th century, it was found that the Earth performs a pulsating precession, mainly (but not always) in the direction of its own rotation. The circular movement of the poles leads to fluctuations in the latitude measured by the stars. In 1891, S. Chandler summarized the data of many observatories and singled out pole fluctuations with a period of 1.2 years (430 days) against the background of seasonal fluctuations with a period of 1 year. With respect to the middle position, the pole describes the unrolling and twisting trajectories from west to east (with rare exceptions) within the radius (0.40) "= 12.3 m with an average radius (0.14)" = 4.3 m.

Chandler pole oscillations occur with beats, decreasing to almost zero every 40 years. This indicates the presence of two sources of oscillations with close frequencies. One of the sources recognized the precession of the axis of rotation of the Earth, predicted by Euler. Taking into account the elastic deformation of the Earth, carried out by Love and Larmor, it was possible to obtain agreement with the observed period of 430 days.

The second source of pole oscillations remained unknown until recently. In accordance with the simulation on the proposed device, the second source of pole oscillations is the precession of the lithosphere around the mantle of the planet, caused by a spontaneous shift of the inner core. This lithosphere precession occurs in the direction opposite to the precession of the rotation axis of the planet, which corresponds to the displacement of the pole from east to west. The observed trajectory of the pole is the result of the addition of two opposite periodic motions with a slight predominance of the precession of the axis of rotation of the Earth.

Up to a ratio of the masses of the core and planet (ϑ≤0.01), the spontaneous shift of the Earth's core does not depend on the size of the planet and the position of two solid shells - the mantle and lithosphere. It is also practically not affected by the speed of the lag of the nucleus from the rotation of the planet. However, the lag of the nucleus is expressed in its movement in a circular orbit inside the planet. Oscillation of the mass of the core sways the hard shells, which are surrounded by a liquid and therefore free in relative motion. A spontaneous core shift is a manifestation of the gravitational equilibrium of the system. Inertial vibrations take the system out of this balance.

The inertia force of the vibrating core is directly perceived by the solid mantle, the outer radius of which is approximately 5970 km. Within this radius, the mass m _{O of the} mantle is 0.9 of the mass of the planet.

The significant superiority of the mantle in mass over the core and lithosphere makes it possible to separately assess the oscillations of the mantle caused by the nucleus and the oscillations of the lithosphere caused by the mantle.

The western drift of the center of mass of the core in orbit with radius s _c = 1.3 km relative to the common center of mass leads to the western drift of the center of mass of the mantle in orbit with radius

According to published data, the difference between the average density ρ _{c of the} solid core and the density ρ of the fluid adjacent to the core, ρ _c -ρ = Δρ, can be taken equal to 1 g cm ^-3 . Earth mass m _e = 5.98 · 10 ²⁷ g, ϑ _О = 3.25 · 10 ^-3 . Substitution of the values found above gives the radius of the orbit of the center of mass of the mantle

In a circular orbit inside the Earth, the mantle moves progressively, due to its significant inertia. In itself, such a movement does not change latitude. The observed change in latitude is associated with an additional phenomenon - the rotation of the lithosphere relative to the mantle. Two factors contribute to this: 1) the fluidity of the asthenosphere separating the lithosphere from the solid mantle, 2) the hard bridge 68 connecting the lithosphere to the lower mantle in the south polar region (rod 5 performs the function of the bridge in the described device).

Moving in a circular orbit, the mantle carries with it the polar region of the lithosphere connected to it. The level of the lithosphere relative to the center of mass of the planet is stabilized by currents in the asthenosphere, which restore gravitational equilibrium. The center of mass of the lithosphere remains almost motionless. The axis of symmetry of the lithosphere passing through it leans toward the axis of rotation of the Earth and describes a conical surface, thus making a precession. Under these conditions, the amplitude of the tangential shift of the lithosphere along the meridian coincides with the radius of the mantle orbit (s _m ) and corresponds to the observed latitude vibrations.

Jumper 68 allows small meridional oscillations of the lithosphere, but prevents the continuous rotation of the lithosphere relative to the mantle along the equator. An element of a planet with jumper functions exists in reality. Recent studies using seismic tomography have found under Antarctica an accumulation of dense material of sunken (with subduction) plates in the form of a cone with a height of more than 1000 km (Fukao Y., Maruyama S., Inoue H., J. Geol.Soc.Japan, 1994, vol. 100, p. 7; Dobretsov N.L., Kirdyashkin A.G., Kirdyashkin A.A. Deep Geodynamics, Novosibirsk 2001, p. 108). The base of the cone adjoins Antarctica over its entire area, and the top enters deep into the lower mantle.

In the “lithosphere – asthenosphere – mantle” system (the second of these cases), the rotation of the planet leads to gravitational equilibrium with a spontaneous shift s _{c of the} mantle. To estimate s _c , the following formulas should be substituted with the values: r = 5970 km, ρ = 3.8 g cm ^-3 , Δρ = 1.7 g cm ^-3 . Moreover, ϑ _O = 0.254, β = 2.49 · 10 ^-3 , s _c = 8.3 km.

As a result of a spontaneous shift of the mantle, its center of mass gradually moves inside the planet in an orbit with a radius s _c = 8.3 km. The lithosphere reacts with a precession, in which the pole describes a circle with the same radius of 8.3 km. This is the reason for the displacement of the middle pole around which the Chandler oscillations occur. A distance of 14.5 m, covered by the middle pole over 112 years (from 1890 to 2002), corresponds to a period of approximately 400 thousand years for the orbital center of mass of the mantle, which is associated with the relatively high viscosity of the asthenosphere.

The spontaneous shift of the mantle makes a significant contribution to the difference between the main equatorial moments of inertia of planet A and B:

where R is the radius of the planet. Under Earth conditions, ΔJ = 0.76 · 10 ³⁵ g m ² .

For satellite gravimetry, this value is at the limit of resolution due to the complexity of calculating the system of many bodies and the influence of the magnetic field of the planet. From the shape of the geopotential, the following values of the main moments of inertia of the Earth were calculated (Zh.S. Erzhanov, A.A. Kalybaev. General theory of Earth rotation, Moscow, 1984, p. 214): A = 8.010015 · 10 ⁴⁰ g m ² , B = 8.010131 · 10 ⁴⁰ g m ² , C = 8.036381 · 10 ⁴⁰ g m ² , BA = 12 · 10 ³⁵ g m ² ≈10 ^-5 A without guaranteed accuracy.

In order of magnitude, the ΔJ value due to the shift of the mantle is close to the measured difference BA and makes up its noticeable part.

The third case relates to the spontaneous shift of the lithosphere and means that the planet cannot be covered by a continuous ocean of equal depth. For the bottom of a spherical shape, the difference in depth should be less than the average depth, which excludes the formation of the island only due to a shift of the lithosphere. However, in combination with the internal activity of the planet, a shift in the lithosphere can lead to the formation of the mainland in only one place in the ocean.

Modern continents are separated from the single supercontinent Gondwana, which 500 million years ago was in the equator zone on one side of the globe and was surrounded by the ocean. To a certain extent, the formation of a supercontinent could be related to the spontaneous shift described above.

The trend towards a change in the average level of the ocean floor along the equator is still visible, however, it is masked by tectonic folds. Against the background of local volcanic activity, the spontaneous shift of the lithosphere retains its influence on the global formation of the bottom.

The stated mechanism of oscillations of the planet’s pole makes it possible to estimate the viscosity of the asthenosphere. At a sufficiently high viscosity, excluding the asthenosphere, the displacement of the mantle s _m would be accompanied by the same displacement of the outer layers - the asthenosphere and lithosphere - relative to the center of mass of the planet with the appearance of a force returning them

where r _m is the radius of the mantle (with the transition layer),

g _i , ρ _i , h _i - respectively, the acceleration of gravity at the layer level, the average density and layer thickness for the asthenosphere (index a) and lithosphere (index l). This force is opposed by the force F _{s of the} resistance of the viscous flow of the asthenosphere.

It is known (Loytsyansky L.G. Mechanics of fluid and gas, Moscow, 1978, p. 423) that a ball moving through the center of a spherical cavity with a viscous fluid experiences resistance

where μ _d is the dynamic viscosity,

ε is the gap between a ball of radius r _m and the cavity wall, ε≪r _m ,

u is the speed of the ball.

In this case, u = Ωs _m ,

where T _ch = 430 days is the period of the pole swing, ε = h _a = 300 km is the thickness of the asthenosphere, h _l = 100 km, r _m = 5970 km, ρ _a = 3.8 g cm ^-3 , ρ _l = 3.4 g cm ^{- 3} , g _a = 10 ^{ms -2} , g _l = 9.8 ms ^-2 . With equal forces, F _g = F _s , the flow in the asthenosphere is able to reduce the displacement of the layers by about half, which corresponds to the viscosity

Under these conditions, the amplitude of the oscillations of the surface of the lithosphere of the order of s _m / 2 = 2 m (observed, for example, from the relative fluctuations of the ocean level) would give an estimate of 4 · 10 ¹⁵ P. for the viscosity of the asthenosphere.

However, according to terrestrial and satellite data on the level of sea tides, the amplitude of their component with a frequency of Ω does not exceed 2 cm (Desai SD, J. of Georhysical Research, 2002, vol. 107 (C11) p. 7.1), i.e. orders of magnitude lower than the indicated value s _m / 2. It follows that the viscosity of the molten part of the asthenosphere is of the order of μ _d ≈10 ... 10 ¹⁴ P, which is significantly lower than the value of 10 ¹⁸ P found from the rise of the earth's surface after the removal of the ice load.

At the same time, the estimated viscosity of the asthenosphere is still high enough for conducting transverse seismic waves. The result obtained here relates to the region of the asthenosphere, central in depth, that is, 100 ... 200 km deeper than the bottom of the lithosphere.

The correspondence of the calculated western component of the pole swings to the observed beats allows us to use the Chandler period to calculate the relative angular velocity Ω of the orbital motion of the center of mass of the nucleus against the rotation of the planet, | Ω | ≪ | ω |.

In this case, the absolute angular velocities of the planet and the center of mass of the nucleus are equal to ω and ω- Ω, respectively. If the center of mass of the nucleus moved with the planet (Ω = 0), then the mantle with a melt in its cavity and the solid core would rotate as a monolithic solid, that is, without an angular lag of the core. It follows that the contribution to the angular drift of the nucleus is made only by the relative displacement of its center of mass, described by the parameters Ω and s.

Under conditions of rotational separation of the flow (at Reynolds numbers Re> 30), the time-average velocity of the angular lag of the solid core from the planet is

Substitution of r = 1.67 · 10 ⁶ m and the found values s = s _c = 1320 m, Ω = 1.691 · 10 ^-7 s ^-1 gives the angular velocity of the western drift of the solid core

Observed angular velocity of the western drift of the geomagnetic field

The coincidence of the calculated and observed drift (with an accuracy of 20%), obtained from the first principles, shows that the solid core is the direct source of the geomagnetic field. In combination with the fact of inversions, this implies that the solid core includes a magnetized shell, which periodically heats up to melting and changes polarity upon repeated solidification.

This shell, called baromagnetic, consists mainly of iron hydride and is heated by the α-decay of thorium dioxide, which is distributed in the form of refractory sand in the melt of the mantle cavity and accumulates near the subunit during deposition.

At the present stage, during seismic sounding, the baromagnetic shell manifests itself as a transition layer F 460 km thick above the iron-nickel subnucleus, whose radius is 1210 km. The thickness of the shell and, correspondingly, layer F is determined by the phase transition occurring in iron hydride at a pressure p≈300 GPa, which is reached at a depth of 4700 km (radius 1670 km from the center of the Earth). A likely cause of the transition is the metallization of absorbed hydrogen, which is reflected in a change in the nature of its bond with iron.

Under a pressure of 300 GPa and higher, the temperature of the magnetic ordering of the shell material (Curie temperature) exceeds the melting temperature. Magnetic ordering is ensured by the existence of a bidipole — a combination of electric and magnetic dipole moments in an atom of a transition metal, in this case iron.

Due to bidi fields, an external electric field is able to magnetize metals that do not have a magnetic order in the initial state, in particular, copper, silver, titanium, platinum. This effect was discovered experimentally at the boundary of metals with an electrolyte solution. The source of the external field was a double electric layer. The conjugate moments of the bidipole are oriented so that the north magnetic pole is positively charged, and the south magnetic pole is negative: | S (-) (+) N〉. In relation to external charges, the bidipole is oriented in the opposite way:

Magnetic ordering is achieved by the interaction of the electrical parts of the bidipole:

Ultrahigh pressure significantly increases the concentration of bidipoles, which enhances their interaction due to rapprochement. Spin-uncompensated filled d-electron bands are formed. Due to the increase in the concentration of valence electrons with pressure, the Fermi level is much higher than the filled zone, which weakens the effect of temperature on the magnetic order.

The absence of internal radial nodes in the 3d-wave function is favorable for the formation of a bidipole. The metals of the 4d- and 5d- groups (for example, rhodium and platinum) are not ferromagnetic due to the presence of nodes, respectively, of one and two. In an electric field, nodes can be excluded, which, in particular, occurs during the adsorption of hydrogen on a metal.

Known electromagnetic phenomena are symmetrical. In contrast to the case of ferroelectromagnets with the initial magnetic order, a constant electric field cannot under normal conditions create a magnetic order from zero, since this would mean the unconditional advantage of one orientation of the magnetic field over the opposite. In a bidipole, an electric field prefers a certain orientation of the magnetic field. In this sense, the bidipole is asymmetric (spatial parity is violated).

The electrical part deserves special attention in a bidipole: the appearance of an electric dipole moment at an atom that is not hydrogen-like. Such a moment is common for a molecule, but not for an atom. The electric dipole-dipole interaction between atoms makes a certain contribution to the binding energy between them and is an additional parameter that determines the state of the system. An interaction of this kind is also possible in the absence of a magnetic moment.

Iron hydride filling the mantle cavity loses its ability to magnetize at pressures below 300 GPa, that is, outside the central region with a radius of 1670 km. Inside this region, the vicinity of the iron-nickel subnucleus is magnetized regardless of the state of aggregation — before and after melting.

In the solid state, the substance of the baromagnetic shell has a single-domain structure, which is energetically favorable for large-sized magnetized masses and ensures stability over time. Under these conditions, the shell serves as a permanent magnet.

During melting, due to the destruction of the long-range structural order, the shell loses its residual induction, but acquires significant magnetic permeability, which is characteristic of a soft magnetic amorphous magnet. Preserving the magnetic order, the molten shell material forms a mesophase, capable of making a phase transition to a nonmagnetic state with a further increase in temperature.

Inside the magnetized sphere, the field is uniform (the lines of force are parallel), and outside the sphere it coincides with the field of a point dipole. In the solid magnetized shell and inside it, the field is uniform when the magnetic permeabilities of both regions are equal, which, with sufficient approximation, is fulfilled under Earth conditions. The unhindered penetration of the field from the solid baromagnetic shell into the subnucleus is essential for the mechanism of geomagnetic inversions, during which the subnuclear performs the function of an accumulator of magnetic energy.

Inversions of the geomagnetic field are due to a change in the state of the solid core (Fig.27-33).

The predominant part of the time (in the intervals between inversions) of the solid core 104 of the Earth contains a solid sub-core 105 and a solid baromagnetic shell 106 surrounded by a melt 107 of the mantle cavity. In this case, the shell material is magnetically solid and has its own magnetization.

The subnucleus is not magnetized. The lines of force 108, 109 of the magnetic field of the shell (Fig.27) pass through the sub core, the melt in the cavity of the mantle, the mantle and the lithosphere. In magnitude and direction of the field on the Earth's surface, a homogeneous baromagnetic shell is equivalent to a central dipole.

The inversion process begins by melting the hard shell with the formation of a molten shell 110, the substance of which becomes magnetically soft (Fig.28). A related change in the magnetic flux excites an electric current in the sub-core and the melt of the mantle cavity, which tends to maintain the original magnetic field.

Over time, the induced field dissipates: in the solid subnuclear due to diffusion

in the melt of the mantle cavity - due to diffusion and convection

- вектор магнитной индукции,Where

- vector of magnetic induction,

- вектор скорости расплава относительно твердого субъядра,

is the melt velocity vector relative to the solid subnucleus,

D = 1 / σμ - magnetic viscosity (diffusion coefficient of the magnetic field),

σ is the electrical conductivity,

μ is the magnetic permeability.

The solid subnucleus and the surrounding melt have different σ and μ. The permeability of the sub core is equal to the magnetic constant μ ₀ = 4π · 10 ^-7 GN m ^-1 molten baromagnetic shell μ> μ ₀ .

There is reason to believe that the metal sub-core has a higher electrical conductivity than hydride melt.

, который обусловлен перемешиванием расплавленной оболочки с ее окрестностью в полости мантии. Благодаря такой конвекции магнитное поле в расплаве оболочки рассеивается значительно быстрее, чем в субъядре. Время сохранения магнитного поля в субъядре приблизительно совпадает с длительностью процесса инверсии, которая, согласно данным палеомагнетизма, имеет порядок 10⁴ лет.Under these conditions, regardless of the exact values of σ and μ, the convective term is decisive

, which is due to mixing of the molten shell with its surroundings in the mantle cavity. Due to this convection, the magnetic field in the melt of the shell dissipates much faster than in the subnucleus. The time of conservation of the magnetic field in the subnucleus approximately coincides with the duration of the inversion process, which, according to paleomagnetism, is of the order of 10 ⁴ years.

The latter makes it possible to evaluate the electrical conductivity of the sub core σ _s . The diffusion scattering time of the field in the region with a characteristic size L _d is τ _d ≈L _d ² / D = L _d ² σ / μ.

At L _d ≈600 km (the outer layer of the subnucleus is half its radius), τ _d ≈10 ⁴ years and μ = μ _0, this implies σ _s = 7 · 10 ⁵ cm m ^-1 . This value is an order of magnitude lower than the electrical conductivity of iron under normal conditions: 1.1 · 10 cm m ^-1

When the initial field of the molten shell is scattered, the lines of force 111, 112 move from it into the interior of the liquid core (Fig. 28). Upon completion of convection, the preserved subnuclear field closes on the molten shell and creates in it, as in a shunt, a field of the opposite direction with field lines 113, 114.

At the boundary with the mantle in the surface layer of the melt there is a flow directed from the poles to the equator. The subnucleus is separated from this border by 2,200 km, and the current does not directly reach the subnucleus. However, it contributes to a relative decrease in temperature throughout the equatorial section of the mantle cavity. For this reason, during cooling of the molten shell, the lowest temperature is reached at its equator.

The equatorial region 115 of the shell hardens first, acquiring a constant magnetization in the direction of the induced magnetization of the molten shunt (Fig. 29). The original subnucleus field is gradually weakening. The solidification front 116, 117 of the shell extends to its polar regions 118, 119.

In the hardened part of the shell, the magnetic field lines 120, 121 maintain the direction defined by the equatorial region (Fig. 30). Complete hardening of the shell is accompanied by the penetration of new lines of force 122, 123 into the subnucleus (Fig. 31).

The inversion process ends with the formation of an average stationary magnetic field of the solid core with the direction of the lines of force 124, 125 opposite to the original one (Fig. 32). The hardened shell has significant coercivity, which ensures long-term conservation of the field of the steady direction.

The culmination phase of the described inversion process is the closure of the lines of force 126 of the magnetic field of subunit 105 to the molten baromagnetic shell 110 (Fig. 33). The hardening of the shell freezes the field induced in it as in a shunt. The field orientation is reproduced at the solidification front due to the knot-free ordering, which maintains the parallelism of the spins of the solidified and liquid phases, which is possible without applying an external field. When the hardened baromagnetic shell is heated, the described cycle repeats and ends with the next reorientation of the Earth’s magnetic dipole.

In accordance with the above, modeling of the lithosphere precession and the western drift of the solid core of the planet contributes to solving the problems of gravity in a liquid medium and the origin of the Earth's magnetic field.

During the simulation, a rotational separation of the flow was discovered - a phenomenon important for hydrodynamics. He caused the movement of the core 127, freely weighed in a rotating spherical vessel 128 with a liquid 129 (Fig.34, 35). The vessel serves as a mantle.

The mechanism of rotational separation of the flow consists in the fact that when the fixed center of mass of the nucleus is displaced from the axis of rotation of the vessel, a reverse flow region 130 forms at the surface of the nucleus, the size of which increases with displacement s. The reverse flow slows down the rotation of the core. Using electrodes that are sensitive to the speed of the flow, two vortices 131 and 132 are detected, carried by the flow 133 around the nucleus with a period that is exactly equal to the period of rotation of the vessel. Vortices are attached to certain places of the vessel 134 and follow them for an unlimited time, despite the absence of noticeable deviations of the vessel shape from the symmetry of the body of revolution. After a break in the rotation, the places of localization of the vortices in the vessel are reproduced. The vortex 131, rotating in the direction of rotation of the vessel, is two times larger along the equator than the vortex 132, rotating in the opposite direction.

In a cylindrical vessel — unlike a spherical vessel — there is no synchronization of vortices with the rotation of the vessel.

Claims (14)

1. Device for modeling the precession of the lithosphere around the mantle of the planet, characterized in that it contains a spherical shell, the geometric center of which is fixed in space and which can be rotated relative to this center, a hole is made in the shell through which a vertical rod passing, carrying a ball located inside the shell, the hole of the shell and the cross section of the rod are elongated, the end of the rod protruding from the shell is equipped with a rotation limiter and is inserted into the vertical channel on eriferii wheel which is mounted on a base rotatably around a vertical axis passing through the geometric center of the shell, the wheel connected to the motor. 2. The device according to claim 1, characterized in that the shell is filled with liquid. 3. The device according to claim 1, characterized in that the wheel is located under the shell. 4. The device according to claim 1, characterized in that the wheel is located above the shell. 5. The device according to claim 1, characterized in that the shell is mounted on three rollers with horizontally oriented cylindrical spikes. 6. The device according to claim 5, characterized in that the spikes of the rollers are located in the grooves of the holders mounted on the upper side of the round platform. 7. The device according to claim 6, characterized in that the lower side of the platform has an annular groove and rests on balls located in the annular groove of the base. 8. The device according to claim 1, characterized in that the hole for the rod is made in a rubber sleeve built into the wall of the shell. 9. The device according to claim 8, characterized in that the rubber sleeve is fastened around the perimeter with an elastic cap stretched over the annular protrusion of the rod. 10. The device according to claim 1, characterized in that the rotation limiter is made in the form of a connecting rod, one end of which is fastened to the rod, and the other end has a groove, which includes a fixed cylindrical pin. 11. The device according to claim 3, characterized in that the wheel has a shaft on which a ball bearing and a pulley are mounted, connected by a belt rod to the engine pulley. 12. The device according to claim 1, characterized in that the shell has a neck with a stopper. 13. The device according to claim 1, characterized in that the shell is made detachable from two hemispheres. 14. The device according to claim 1, characterized in that the shell is made of a transparent material.

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