Changes in the earth's gravitational field. Earth gravity
GRAVITATIONAL FIELD OF THE EARTH (a. gravitational field of the Earth, Earth gravitational field; n. Schwerefeld der Erde; f. champ de gravite de la Terre; i. campo de gravedad de la tierra) - a force field caused by the attraction of masses and centrifugal force , which arises due to the daily rotation of the Earth; also slightly depends on the attraction of the Moon and the Sun and other celestial bodies and earth masses. The Earth's gravitational field is characterized by gravity, gravity potential and its various derivatives. The potential has the dimension m 2 .s -2, the unit of measurement for the first derivatives of the potential (including gravity) in gravimetry is taken to be milligal (mGal), equal to 10 -5 m.s -2, and for the second derivatives - etvos ( E, E), equal to 10 -9 .s -2.
Values of the main characteristics of the Earth's gravitational field: gravity potential at sea level 62636830 m 2 .s -2; the average gravity on Earth is 979.8 Gal; decrease in average gravity from pole to equator 5200 mGal (including due to the daily rotation of the Earth 3400 mGal); maximum gravity anomaly on Earth 660 mGal; normal vertical gravity gradient 0.3086 mGal/m; the maximum deviation of the plumb line on Earth is 120"; the range of periodic lunar-solar variations in gravity is 0.4 mGal; possible value secular change in gravity<0,01 мГал/год.
The part of the gravitational potential due only to the Earth's gravity is called geopotential. To solve many global problems (studying the figure of the Earth, calculating satellite trajectories, etc.), the geopotential is presented in the form of an expansion in spherical functions. The second derivatives of the gravitational potential are measured by gravity gradiometers and variometers. There are several expansions of geopotential, differing in the initial observational data and degrees of expansion.
Usually the Earth's gravitational field is represented as consisting of 2 parts: normal and anomalous. The main - normal part of the field corresponds to a schematized model of the Earth in the form of an ellipsoid of rotation (normal Earth). It is consistent with the real Earth (the centers of mass, mass values, angular velocities and daily rotation axes coincide). The surface of a normal Earth is considered level, i.e. the gravity potential at all its points has the same value (see geoid); the force of gravity is directed normal to it and changes according to a simple law. In gravimetry, the international formula for normal gravity is widely used:
g(p) = 978049(1 + 0.0052884 sin 2 p - 0.0000059 sin 2 2p), mGal.
In other socialist countries, the formula of F.R. Helmert is mainly used:
g(р) = 978030(1 + 0.005302 sin 2 р - 0.000007 sin 2 2р), mGal.
14 mGal is subtracted from the right-hand sides of both formulas to account for the error in absolute gravity, which was established as a result of repeated measurements of absolute gravity at different locations. Other similar formulas have been derived that take into account changes in the normal force of gravity due to the triaxiality of the Earth, the asymmetry of its northern and southern hemispheres, etc. The difference between the measured force of gravity and the normal force is called a gravity anomaly (see geophysical anomaly). The anomalous part of the Earth's gravitational field is smaller in magnitude than the normal part and changes in a complex way. As the positions of the Moon and Sun relative to the Earth change, periodic variations in the Earth's gravitational field occur. This causes tidal deformations of the Earth, incl. sea tides. There are also non-tidal changes in the Earth's gravitational field over time, which arise due to the redistribution of masses in the Earth's interior, tectonic movements, earthquakes, volcanic eruptions, movement of water and atmospheric masses, changes in angular velocity and the instantaneous axis of the Earth's daily rotation. Many magnitudes of non-tidal changes in the Earth's gravitational field are not observed and are estimated only theoretically.
Based on the Earth’s gravitational field, the geoid is determined, which characterizes the gravimetric figure of the Earth, relative to which the heights of the physical surface of the Earth are specified. The Earth's gravitational field, in conjunction with other geophysical data, is used to study the model of the Earth's radial density distribution. Based on it, conclusions are drawn about the hydrostatic equilibrium state of the Earth and the associated stresses in it.
Earth's gravitational field- this is the material environment of interaction of mechanical (physical) masses, determined by the general mechanical state of the Earth’s figure. To understand the physical meaning of the gravitational field, the concept is introduced gravity, as the equivalence of the forces of gravity of the Earth and centrifugal, due to rotation.
The basis of the physical interaction of masses is Newton’s law of universal gravitation:
m 1 And m 2– mechanical masses; r – distance between masses; f – gravitational gradual, equal to 6.67 * 10 -8 cm 3 / g * s 2, in the SI system = 6.67 * 10 -11 m 3 / kg * s 2.
Indicators of gravitational field.
If placed in formula (1) m 1=1 and m 2=M and accept M for the mass of the Earth, then the acceleration of gravity on the Earth's surface will be:
g– a vector quantity, which is the equal action of the forces of attraction (F), centrifugal force (P) and celestial bodies.
In gravimetry, the acceleration due to gravity is abbreviated as " gravity»: g average = 9.81 m/s 2, g pole= 9.83 m/s 2, g equator= 9.78 m/s 2 .
g h atmosphere: g h =g, Where h – height, R– radius of the Earth.
g inside the Earth it changes according to a complex pattern from 9.82 m/s 2 at the surface to 10.68 m/s 2 at the base of the lower mantle at a depth of 2900 km.
g in the core it decreases at a depth of 6000 m to 1.26 m/s2, and in the center of the Earth to 0.
To determine absolute values g use the pendulum method and the method of free fall of bodies. For a pendulum:
T = 2, where T- period of oscillation of the pendulum, h– length of the pendulum.
Gravimetry and gravity surveying primarily use relative measurements of gravitational acceleration. The increments of g are determined in relation to any value. Pendulum instruments and gravimeters are used.
Isostasia.
The heterogeneity of the outer shell of the Earth, due to the presence of land and oceans, is one of its main density features.
Because of this, it would seem that gravitational anomalies on land should be positive and have a higher intensity than in the oceans. However, gravitational measurements on the daytime surface and from satellites do not confirm this. The geoid height map shows that deviations of g from the normal field are not associated with oceans and continents.
From this, theorists conclude that continental regions are isostatically compensated: less dense continents float in a denser subcrustal substrate, like giant icebergs in the polar seas. (!?) That is, the concept of isostasy is that the light crust of the earth is balanced on a heavier mantle, despite the fact that the upper layer of the mantle is rigid and the lower layer is plastic. The rigid layer of the mantle came up with a name lithosphere, and plastic asthenosphere.
However, the upper mantle is not liquid, because Transverse waves pass through it. At the same time, on a time scale ( T) the asthenosphere behaves at small T(hours, days) like an elastic body, and at large T(tens of thousands of years) like a liquid. The viscosity of the asthenosphere substance is estimated at 10 20 Pa*s (pascal second).
Hypotheses of isostasy include: 1) Elastic deformation of the earth's crust, which is shown in the diagram; 2) the block structure of the Earth and involves the immersion of these blocks into the underlying mantle substrate to varying depths.
It should be noted that, following the mathematical language, the conclusion follows: the existence of isostatic equilibrium of the earth’s crust is a sufficient, but by no means necessary condition for the natural connection between g anomalies and crustal thickness; nevertheless, for regional territories this connection exists.
If you perform gravitational measurements across the ocean, then the protrusions of the oceanic crust will be characterized by gravitational minima, and the depressions - by maxima. The introduction of the isostatic Bouguer correction makes the territory (region) isostatically balanced.
It follows from the figure that the intensity of the gravitational field is 2.5-3.0 times greater in those places where the oceanic crust is thinner, i.e. in these areas, the defect in the density of the underlying mantle substrate, in particular the Moch surface layer, is more pronounced. The density of this subcrustal layer = 3.3 g/cm 3, and the basalt layer = 2.9 g/cm 3.
Thus, there is a direct connection between regional gravity anomalies and the thickness of the earth's crust. These studies constitute second level of detail in gravimetry.
Third level of detail is directly related to various corrections during gravimetric surveys for the purpose of studying local geological objects, in particular mineral deposits. Here, all measurements are carried out to the Bouguer reduction (the difference between observations and theoretical fields) and provide corrections for: 1) “free air”, 2) the intermediate layer, 3) relief.
In general and structural geology, the results of gravimetric observations are used to study tectonic zoning of geosynclinal and platform areas.
The structure of the gravitational field is different here.
In geosynclinal areas Negative anomalies are confined to areas of uplifts g, and to the depressions - positive. This pattern is associated with the history of the development of the earth’s crust due to inversions geotectonic conditions (redistribution of zones of uplift and subsidence). In places of uplifts there was previously and has been preserved a bend of the Moho boundary.
Anomalies on platform areas g are associated mainly with the material and petrographic composition of rocks. Minimum values g large zones are formed from “light” rocks “rapakivi granites”.
Variations in gravity.
In the general structure of the Earth's gravitational field, periodic changes in gravity occur; they are caused by the approach of the Moon and the Sun and depend on the internal structure of the Earth.
The most noticeable movement of geosphere particles in the horizontal direction is sea tides.
Under the influence of the gravitational forces to a greater extent of the Moon and to a lesser extent of the Sun, the waters of the World Ocean are driven to points Z And N(high tide), and at this time at points A And IN The water level of the World Ocean is falling (low tide). The spherical layer of the Earth experiences periodic vibrations and, accordingly, acceleration of gravity. During oscillations, this layer takes the shape of an ellipsoid.
Due to the daily rotation of the Earth, tides occur with a period of 24 hours (“solar day”) and 24 hours 50 minutes. (“lunar day”). Therefore, there are two high tides and two low tides.
Under the influence of tidal forces, the surface of the earth's crust continuously pulsates: it rises and falls twice a day.
The study of the tides in the solid body of the Earth allows us to obtain information about its density and internal structure.
The anomalies of the gravitational field are not great. Their values fluctuate within a few units of 10-3 m/s 2, which is 0.05% of the total value of gravity and an order of magnitude less than its normal change. Density differentiation in the crust occurs both vertically and horizontally. Density increases with depth from 1.9–2.3 g/cm 3 on the surface to 2.7–2.8 g/cm 3 at the level of the lower boundary of the crust and reaches 3.0–3.3 g/cm 3 in the area upper mantle. Gravity anomalies, due to their physical nature and the methods used to calculate them, make it possible to simultaneously study any density inhomogeneities of the Earth, no matter where and at what depth they are located.
The role and importance of gravity data in the study of the deep interior of the Earth has especially increased in recent years, when not only the Kola, but also other deep and ultra-deep wells, including foreign ones (Oberpfalz in Germany, Gravberg in Sweden, etc.) did not confirm the results of geological interpretation deep seismic data used as the basis for the design of these wells.
For the geological interpretation of gravity anomalies in geomorphologically distinctly different regions, the choice of the most justified reduction of gravity plays a special role since, for example, in mountainous areas the Fay and Bouguer anomalies differ sharply not only in intensity, but even in sign. Bouguer reduction and hydrotopographic make it possible to remove the influence of known density inhomogeneities of the Earth and thereby highlight the deeper components of the field.
Previously, they tried to explain the amplitudes and signs of gravitational anomalies only by changes in the total thickness of the earth's crust and calculated for this purpose the coefficients of its correlation with the daytime relief or with gravitational anomalies, then subsequent increasingly detailed seismic studies of the earth's crust and upper mantle, the use of seismic tomography methods showed that that lateral seismic, and therefore density, inhomogeneities are characteristic of all levels of differentiation of the Earth's deep masses, i.e., not only the Earth's crust, but also the upper and lower mantle, and even the Earth's core. The field of gravity anomalies changes by a huge amount - over 500 mGal - from –245 to +265 mGal, forming a system of global, regional and more local gravity anomalies of different sizes and intensity, characterizing the crustal, crust-mantle and actual mantle levels of lateral density inhomogeneities of the Earth. The anomalous gravitational field reflects the total effect of gravitating masses located at various depths in the earth's crust and upper mantle. Thus, the structure of sedimentary basins is better manifested in an anomalous gravitational field in the presence of sufficient density differentiation in areas where crystalline basement rocks lie at great depths. The gravitational effect of sedimentary rocks in areas with shallow foundations is much more difficult to observe, since it is obscured by the influence of basement features. Areas with a large thickness of the “granite layer” are distinguished by negative gravity anomalies. Outcrops of granite massifs on the surface are characterized by minimum gravity. In an anomalous gravitational field, zones of large gradients and strip maximums of gravity clearly outline the boundaries of individual blocks. Within the platforms and folded areas, smaller structures, depressions, swells, and marginal troughs are distinguished. The most global gravity anomalies, which characterize the inhomogeneities of the mantle (asthenospheric) level proper, are so large that only their marginal parts extend into the boundaries of the Russian territory under consideration, being traced far beyond its borders, where their intensity increases significantly. A single zone of the Mediterranean maximum of gravity coincides with the Mediterranean Sea basin and is limited in the north by a small Alpine minimum of gravity, and in the east by a single very intense and huge in area Asian minimum of gravity, corresponding in general to the Asian mega-inflation of the Earth, covering mountain structures of the Middle and High Asia from Transbaikalia to the Himalayas and, accordingly, from the Tien Shan to the northeastern system of depressions in inland China (Ordos, Sichuan, etc. ). This global Asian minimum of gravity decreases in intensity and can be traced further to the territory of the North-East of Russia (mountain structures of Altai, Transbaikalia, Verkhoyansk-Chukchi region), and its branch covers almost the entire area of the Siberian Precambrian platform activated in recent times as a whole slightly elevated (up to 500–1000 m) Siberian Plateau. The extreme northern part of the Aegean High partially falls within the territory of Russia, where, after a slight compression, a new maximum begins, obliquely crossing the Russian Platform, the Urals, Western Siberia and leaving in the north into the Arctic Ocean. In the extreme east and northeast, also only partially entering the territory of Russia, there is another one - the Pacific giant gravity maximum, the marginal part of which stretches in the form of an intense linear zone of gravitational gradient from the Shantar Islands to the Bering Strait across the entire margin of the Eurasian continent and the surrounding its seas. There is a logical explanation for the different signs of these anomalies, if we take into account that zone melting, as it rises to the surface of the asthenolite, leaves behind at each level remelted rocks that are relatively denser than the strata containing them laterally. Therefore, in a gravitational field, the entire sum of such melted rocks creates a single total maximum of gravity, and even the presence of molten “layers” (zones of velocity and density inversion) in it will not change its overall characteristics, as is observed in the marginal parts of the Arctic that fall within the map -Atlantic and Pacific global gravity maxima. The anomalous masses creating the Central Asian global minimum are probably located at an even greater depth, as a result of which the resulting melt zone led to an increase in the volume of only the deep masses and, accordingly, to the formation of a single giant Asian mega-bloat of the Earth on the surface, and the presence of a molten lens at depth, apparently caused basaltoid magmatism, small in volume and scattered throughout this territory, Mesozoic explosion pipes in the Tien Shan, extinct Quaternary volcanoes in the Altai-Sayan region, and finally, more intense basaltoid magmatism of the Baikal-Patom Highlands, extending far beyond the boundaries of the Baikal rift itself .
If we are dealing with the gravitational attraction of a body of mass m to the Earth (earth gravity), then on the surface of the Earth g= (GM o /R o 2) r o,where M o is the mass of the Earth (M o = 5.976.10 24 kg), r o - a unit vector directed from the body to the center of the Earth (any body on the surface of the Earth can always be considered as a material point due to the small size of any body compared to the size of the Earth), which is considered in the form of a ball of radius R o = 6.371030. 10 6 m. Substituting the values of M o and R o into the last formula, we obtain for the vector modulus g value g"9.81 m/s 2. This quantity is usually called acceleration of free fall. Since the Earth is not an ideal sphere (at the poles R o =6.356799.10 6 m, at the equator R o =6.378164.10 6 m), the value of g somewhat depends on latitude (it varies from 9.780 to 9.832 m/s 2). However, in a given place on the Earth, the acceleration of gravity is the same for all bodies(Galileo's law).
A body with mass m located on the surface of the Earth is acted upon by a force P= m g, which is called gravity. If a body of mass m is located at a height h above the Earth’s surface, then P = m(GM o /(R o + h) 2, in other words, gravity decreases with distance from the Earth's surface.
The concept is often used - body weight -forceJ, With in which the body, due to its gravity towards the Earth, acts on a support (or suspension) that holds the body from free fall. The weight of the body appears only when the body, in addition to the force of gravity,P (it imparts acceleration to the body g), another force acts (which imparts acceleration to the body A) : J= m g-m a= m( g-a). Obviously, when acceleration g And a equal in magnitude and directed in opposite directions, then the weight of the body is zero(state of weightlessness). This situation arises, in particular, on Earth’s space satellites.
4.4.Space speeds
First cosmic speed v 1 they call the minimum speed that must be imparted to a body so that it can move around the Earth in a circular orbit (turn into an artificial Earth satellite). A satellite moving in a circular orbit of radius r is acted upon by the Earth's gravitational force, imparting to it a normal acceleration v 1 2 /r. According to Newton's second law, GmM/r 2 = mv 1 2 /r and, therefore, if the satellite moves near the Earth's surface (r = R is the radius of the Earth), we have v 1 = 7.9 km/s.
Second escape velocity v 2 they call the minimum speed that must be imparted to a body so that it can overcome the gravity of the Earth and turn into a satellite of the Sun. To overcome gravity, the kinetic energy of the body must be equal to the work done against the forces of gravity: mv 2 2 /2 = (GmM/r 2)dr = GmM/R, from which we have v 2 = = 11.2 km/s.
Third cosmic speed v 3 they call the speed that must be imparted to a body on the Earth in order for it to leave the solar system(v 3 = 16.7 km/s).
4.5. Non-inertial reference systems. Inertia forces.
Newton's laws are satisfied only in inertial frames of reference. Reference frames moving relative to inertial frames with acceleration are callednon-inertial. In non-inertial systems, Newton's laws are not valid. However, the laws of dynamics can also be used for non-inertial systems if, in addition to forces F, caused by the influence of bodies on each other, introduce into consideration inertia forces F in. If we take into account the forces of inertia, then Newton’s second law will be valid for any reference system: the product of the mass of a body and the acceleration in the reference frame under consideration is equal to the sum of all forces acting on a given body (including inertial forces). Inertia forces F in this case must be such that, together with the forces F they imparted acceleration to the body a`, what it has in non-inertial frames of reference, i.e. m a`=F+F in and since F= m a(Here a- acceleration of the body in the inertial frame), then m a`= m a+F in.
Inertial forces are caused by the accelerated movement of the reference system relative to the measured system and therefore, in the general case, the following cases of manifestation of these forces must be taken into account:
1. Inertia forces during accelerated translational motion of the reference system F n =m a o, Here A O- acceleration of translational motion of the reference system.
2. Inertial forces acting on a body at rest in a rotating frame of reference F c = -m w 2 R, here w=const - angular velocity of the system in the form of a rotating disk of radius R.
3. Inertial forces acting on a body moving in a rotating frame of reference F k = 2m[ v`w] where is the strength F k (Coriolis force) is perpendicular to the body velocity vectors v` and angular velocity w reference system in accordance with the right screw rule.
In accordance with this, we obtain the basic law of dynamics for non-inertial reference systems
m a`=F+F n + F ts + F To.
It is essential that inertia forces are caused not by the interaction of bodies, but by the accelerated motion of the reference system. Therefore these forces do not obey Newton's third law , since if a force of inertia acts on any body, then there is no opposing force applied to this body. The two basic principles of mechanics, according to which acceleration is always caused by force, and force is always caused by the interaction between bodies, are not simultaneously satisfied in systems moving with acceleration. Thus, inertial forces are not Newtonian forces .
For any body located in a non-inertial reference frame, the inertial forces are external and, therefore, there are no closed systems here - this means that in non-inertial reference frames the laws of conservation of momentum, energy and angular momentum are not satisfied.
The analogy between gravitational forces and inertial forces underlies the principle of equivalence of gravitational forces and inertial forces (Einstein's equivalence principle): all physical phenomena in a gravitational field occur in exactly the same way as in the corresponding field of inertial forces, if the strengths of both fields at the corresponding points in space coincide. This principle underlies the general theory of relativity.
There is a gravitational field around the Earth due to its mass. This field is called gravitational. The force of attraction is inherent in both small and large bodies. The greater the mass of a body, the more powerful its gravitational field. At the Earth's surface its average value is about 9.8 m/s2. The field strength decreases with height. Theoretically, the Earth's gravitational field extends to infinity. Closer to the surface of the Earth, the force of gravity takes on a slightly different character. Here forces appear that not only attract, but also repel bodies located on the surface of the Earth. The repulsive force is caused by the rotation of the Earth around its axis and is called centrifugal. The resultant of two forces - gravitational and centrifugal - is called gravity. The force of attraction is determined by the mass of bodies. Mass, in fact, is the force with which bodies are attracted towards the center of the Earth. The force of gravity holds bodies and objects on the surface of the Earth, and the gravitational field keeps the Earth's satellite, the Moon, at a distance.
The distribution of gravity on the Earth's surface depends on geographic latitude: it increases with latitude. The decrease in gravity in the direction of the equator is explained by two reasons: an increase in centrifugal force in this direction and an increase in the distance from the center of the planet, as well as the peculiarities of its internal structure. If the Earth were a regular stationary bullet, homogeneous in composition from the surface to the center, then its force of attraction would be the same everywhere and directed towards the center of the planet.
At the poles, where there is practically no centrifugal force and the distance to the center of the Earth is the smallest, the force of attraction is greatest and amounts to 9.83 m/s2. At the equator, the centrifugal force and distance are the greatest, so the force of attraction is the smallest - 9.78 m/s2.
The influence of the gravitational field on the development of the planet and its geographical envelope is enormous. The force of gravity determines the true shape of the earth's surface - the geoid, and leads to the movements of the earth's crust. Under its influence, loose rocks, masses of water, ice, and air move. The Earth's gravitational field is one of the causes of circulation in the lithosphere, atmosphere and hydrosphere.
The gravitational field itself is determined, as already noted, by the mass of the Earth. It is calculated that the total mass of the Earth (F) is 5.976 ten twenty-seven g. It is impossible to measure this mass directly, but it is relatively simple to calculate it using the gravitational attraction formula:
Where k e- gravitational constant equal to 6.67 +10 +8; m 1, m 2- mass of bodies attracted, g d- distance between the centers of bodies, cm.
The volume of a spherical Earth is also easy to roughly calculate, since the radius of the arcs of its circle is known. The volume of our planet found in this way is 1.083 ten two +7 cm 3.
Knowing the mass and volume of the Earth, you can find its average density. It is 5.52 g / cm 3, that is, twice the density of granite."
It has been established that the earth's crust has an average density of 2.7 g/cm3. Thus, for the average density of the Earth to be 5.52 g/cm3, the interior of the Earth must be denser than the exterior. The increase in density with depth can be explained by differences in chemical composition and the enormous force with which the outer parts of the Earth press on the inner ones. The inner core is assumed to have a density of about 13 g/cm3.
Terrestrial magnetism
The Earth is a huge spherical magnet. Although people have known about the presence of magnetism on the planet for a long time, and scientists from various countries around the world are studying its properties, much about the nature of its magnetic field still remains unclear. It is known that among metals only iron and nickel can be permanent magnets. These materials are called ferromagnetic. But ferromagnetic substances cease to be a magnet if they are heated above the Curie point (770 ° C for iron and 358 ° C for nickel). Since the temperature in the interior of the Earth is much higher than these values, the earth's core, consisting mainly of iron and nickel, cannot be ferromagnetic due to the lack of appropriate conditions for this.
Of the many theories that have been put forward to explain the origin of the Earth's magnetic field, the most popular currently is the dynamo theory. According to it, the Earth is an electromagnet rather than a permanent magnet: the electric current, driven by turbulent convection in the liquid core, forms around itself a field of uniform magnetization, or a permanent field. The question remains unclear about the source of energy that causes convection in the earth's core, where there are very few or no radioactive elements. Three options are allowed: 1) at the boundary between the inner and outer cores, gradual crystallization of iron occurs with the release of heat; 2) due to the sinking of iron from the mantle, gravitational energy is released; 3) heat is released during phase changes in substances that occur as a result of the hypothetical expansion of the Earth.
The Earth's magnetic field reaches a height of 80-90 thousand km from its surface. Up to an altitude of 44 thousand km, the magnetic field is constant, its value gradually decreases with distance from the earth's surface. At an altitude of 44 to 90 thousand km, the magnetic field is variable, depending on the sign it captures and holds electrons or protons. The sphere of near-Earth space in which there are charged parts captured by the Earth's magnetic field is called the magnetosphere.
The structure of the Earth's magnetosphere, that is, the surrounding space, the physical properties of which are determined by the Earth's magnetic field and its interaction with the flow of charged particles of the solar wind, seemed quite simple in the past. It was believed that the magnetosphere forms a symmetrical dipole. But even the first direct measurements of magnetic fields, which were made directly in space, did not confirm this hypothesis. It turned out that the Earth’s magnetosphere is extremely asymmetrical: on the side of the Sun, the magnetic field is highly compressed, and on the opposite side, on the contrary, it is very elongated and forms a long, up to 1 million km, magnetospheric tail (Fig. 5). This is a consequence of the solar wind flowing around the magnetosphere. Moreover, here, depending on the pressure of the solar wind, the boundary of the magnetosphere on the side of the Sun - the magnetopause - either approaches the Earth (as the pressure increases), or moves away (as it weakens). The solar wind plasma flows around the Earth's magnetosphere at supersonic speed, resulting in the formation of a shock wave in front of the magnetosphere, which is separated from the magnetopause by a transition region.
Rice. 5.
The geomagnetic field lines move back under the influence of the solar wind, forming a tail, or “plume” of the magnetosphere. It is divided by a magnetically neutral layer into two sectors - northern and southern. Magnetic field lines of sectors associated with the polar regions of the Earth. In the magnetically neutral layer, dense and hot plasma with a temperature of about a million degrees is concentrated, which, with its pressure, prevents the annihilation of field lines of opposite directions in the “trail” sectors.
There are radiation belts inside the magnetosphere. They consist of charged particles, protons and electrons, captured by the Earth's magnetic field from the solar wind. Radiation belts form a layer of the ionosphere in the atmosphere and are considered an area of trapped radiation; they would be magnetic traps for charged particles in space.
The magnetic field is clearly manifested when working with a compass: the magnetic needle at any point on the earth’s surface is set in a certain direction. The angle formed by the magnetic and geographic meridians is called magnetic declination. It is calculated by the north end of the compass needle and can be western or eastern (Fig. 6).
Rice. 6.
Lines connecting points with the same declination are called isogons. The zero isogon is a line that connects the points at which the compass needle points simultaneously to the magnetic and geographic poles. It divides the globe into two parts. Now the line of zero declination passes through the middle parts of North and South America, and in Eurasia it makes a very winding path from Scandinavia through Central Europe to Egypt, then to Somalia and through the Himalayas into the Laptev Sea, from where it turns south again (see Fig. 7 ). In order to characterize the earth's magnetism, the magnetic inclination is also determined, that is, the angle formed by the magnetic needle and the horizontal plane. A freely suspended magnetic needle maintains a horizontal position only on the line of the magnetic equator, which does not coincide with the geographical one. To the north and south of the magnetic equator, the needle tilts towards the earth's surface, and the higher the latitude, the more. Lines connecting points with the same inclination are called isoclines. Since magnetic poles do not coincide with geographic poles, isoclines also do not coincide with parallels.
Rice. 7.
The magnetic poles change their position from year to year. Now the north magnetic pole is located among the islands of Canada and has coordinates of 77 ° N. w. and one hundred and second zap. and the south magnetic pole is located in Antarctica at about 65°S. w. and 139°E. d. It is considered proven that 300 million years ago the magnetic poles were in the modern equatorial region.
The magnetic field at the Earth's surface is also characterized by the magnitude of the voltage of the earth's magnetism. It is determined by the number of oscillations of the magnetic needle per unit of time, or the period of its oscillation, just as the force of gravity is determined by the period of oscillation of a pendulum. The magnetic tension at the poles is greater than at the equator. The places of greatest magnetic field tension are called voltage poles.
As the measurement results show, magnetic anomalies are often observed on the surface of the planet. They manifest themselves in the deviation of the values of the elements of terrestrial magnetism from their average values for a given place. There are regional and local magnetic anomalies. Regional ones cover large areas and are caused by deep processes. An example of a regional anomaly is the East Siberian anomaly, where there is a western declination instead of an eastern one. Local magnetic anomalies are associated with local structural features of the earth's crust (for example, with iron ore deposits), as, for example, in Kursk and Kharkov.
The magnetic field experiences periodic and non-periodic oscillations. The strongest periodic magnetic oscillations are called magnetic storms. They are caused by changes in electrical currents in the atmosphere under the influence of the solar wind.
Magnetism is of great practical importance. Using a magnetic needle, the directions of the sides of the horizon are determined. Magnetometric methods for searching for minerals are based on establishing connections between magnetic elements and geological structures. The study of Earth's paleomagnetism makes it possible to reconstruct the history of the development of the earth's crust. The magnetosphere protects the geographic envelope of the Earth from the direct influence of the solar wind, from the penetration of high-energy electrons and protons into the lower layers of the atmosphere, and therefore changes the influence of space on living nature.
Gravitational interaction is one of the four fundamental interactions in our world. Within the framework of classical mechanics, gravitational interaction is described law of universal gravitation Newton, who states that the force of gravitational attraction between two material points of mass m 1 and m 2 separated by distance R, is proportional to both masses and inversely proportional to the square of the distance - that is
.Here G- gravitational constant, equal to approximately 
m³/(kg s²). The minus sign means that the force acting on the body is always equal in direction to the radius vector directed to the body, that is, gravitational interaction always leads to the attraction of any bodies.
The law of universal gravitation is one of the applications of the inverse square law, which also occurs in the study of radiation (see, for example, Light Pressure), and is a direct consequence of the quadratic increase in the area of the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to area of the entire sphere.
The simplest problem of celestial mechanics is the gravitational interaction of two bodies in empty space. This problem is solved analytically to the end; the result of its solution is often formulated in the form of Kepler's three laws.
As the number of interacting bodies increases, the task becomes dramatically more complicated. Thus, the already famous three-body problem (that is, the motion of three bodies with non-zero masses) cannot be solved analytically in a general form. With a numerical solution, instability of the solutions relative to the initial conditions occurs quite quickly. When applied to the Solar System, this instability makes it impossible to predict the motion of planets on scales larger than a hundred million years.
In some special cases, it is possible to find an approximate solution. The most important case is when the mass of one body is significantly greater than the mass of other bodies (examples: the solar system and the dynamics of the rings of Saturn). In this case, as a first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around the massive body. The interactions between them can be taken into account within the framework of perturbation theory, and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, chaos, etc. A clear example of such phenomena is the non-trivial structure of the rings of Saturn.
Despite attempts to describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.
Strong gravitational fields
In strong gravitational fields, when moving at relativistic speeds, the effects of general relativity begin to appear:
- deviation of the law of gravity from Newton's;
- delay of potentials associated with the finite speed of propagation of gravitational disturbances; the appearance of gravitational waves;
- nonlinearity effects: gravitational waves tend to interact with each other, so the principle of superposition of waves in strong fields no longer holds true;
- changing the geometry of space-time;
- the emergence of black holes;
Gravitational radiation
One of the important predictions of general relativity is gravitational radiation, the presence of which has not yet been confirmed by direct observations. However, there is indirect observational evidence in favor of its existence, namely: energy losses in the binary system with the pulsar PSR B1913+16 - the Hulse-Taylor pulsar - are in good agreement with a model in which this energy is carried away by gravitational radiation.
Gravitational radiation can only be generated by systems with variable quadrupole or higher multipole moments, this fact suggests that the gravitational radiation of most natural sources is directional, which significantly complicates its detection. Gravity power l-field source is proportional (v / c) 2l + 2 , if the multipole is of electric type, and (v / c) 2l + 4 - if the multipole is of magnetic type, where v is the characteristic speed of movement of sources in the radiating system, and c- speed of light. Thus, the dominant moment will be the quadrupole moment of the electric type, and the power of the corresponding radiation is equal to:
Where Q ij- quadrupole moment tensor of the mass distribution of the radiating system. Constant 
(1/W) allows us to estimate the order of magnitude of the radiation power.
From 1969 (Weber's experiments) to the present (February 2007), attempts have been made to directly detect gravitational radiation. In the USA, Europe and Japan, there are currently several operating ground-based detectors (GEO 600), as well as a project for a space gravitational detector of the Republic of Tatarstan.
Subtle effects of gravity
In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which under terrestrial conditions are very weak and their detection and experimental verification are therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.
Among them, in particular, we can name the entrainment of inertial frames of reference (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's unmanned Gravity Probe B conducted an unprecedented precision experiment to measure these effects near Earth, but its full results have not yet been published.
Quantum theory of gravity
Despite more than half a century of attempts, gravity is the only fundamental interaction for which a consistent renormalizable quantum theory has not yet been constructed. However, at low energies, in the spirit of quantum field theory, gravitational interaction can be represented as an exchange of gravitons - gauge bosons with spin 2.
Standard theories of gravity
Due to the fact that quantum effects of gravity are extremely small even under the most extreme experimental and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the vast majority of cases one can limit oneself to the classical description of gravitational interaction.
There is a modern canonical classical theory of gravity - general theory of relativity, and many hypotheses and theories of varying degrees of development that clarify it, competing with each other (see the article Alternative theories of gravity). All of these theories make very similar predictions within the approximation in which experimental tests are currently carried out. The following are several basic, most well-developed or known theories of gravity.
- Gravity is not a geometric field, but a real physical force field described by a tensor.
- Gravitational phenomena should be considered within the framework of flat Minkowski space, in which the laws of conservation of energy-momentum and angular momentum are unambiguously satisfied. Then the motion of bodies in Minkowski space is equivalent to the motion of these bodies in effective Riemannian space.
- In tensor equations to determine the metric, the graviton mass should be taken into account, and gauge conditions associated with the Minkowski space metric should be used. This does not allow the gravitational field to be destroyed even locally by choosing some suitable reference frame.
As in general relativity, in RTG matter refers to all forms of matter (including the electromagnetic field), with the exception of the gravitational field itself. The consequences of the RTG theory are as follows: black holes as physical objects predicted in General Relativity do not exist; The universe is flat, homogeneous, isotropic, stationary and Euclidean.
On the other hand, there are no less convincing arguments by opponents of RTG, which boil down to the following points:
A similar thing occurs in RTG, where the second tensor equation is introduced to take into account the connection between non-Euclidean space and Minkowski space. Due to the presence of a dimensionless fitting parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments.
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Sources and notes
Literature
- Vizgin V. P. Relativistic theory of gravity (origins and formation, 1900-1915). M.: Nauka, 1981. - 352c.
- Vizgin V. P. Unified theories in the 1st third of the twentieth century. M.: Nauka, 1985. - 304c.
