Gravity, also known as attraction or gravitation, is a universal property of matter that all objects and bodies in the Universe possess. The essence of gravity is that all material bodies attract to themselves all other bodies that are around.
Gravity
If gravity is a general concept and quality that all objects in the Universe possess, then the earth's attraction is a special case of this all-encompassing phenomenon. The earth attracts to itself all the material objects that are on it. Thanks to this, people and animals can safely move around the earth, rivers, seas and oceans can remain within their shores, and air can not fly through the vast expanses of the Cosmos, but form the atmosphere of our planet.
A fair question arises: if all objects have gravity, why does the Earth attract people and animals to itself, and not vice versa? Firstly, we also attract the Earth to ourselves, it's just that compared to its force of attraction, our gravity is negligible. Secondly, the force of gravity is directly proportional to the mass of the body: the smaller the mass of the body, the lower its gravitational forces.
The second indicator on which the force of attraction depends is the distance between objects: the greater the distance, the less the effect of gravity. Including due to this, the planets move in their orbits, and do not fall on each other.
It is noteworthy that the Earth, the Moon, the Sun and other planets owe their spherical shape precisely to the force of gravity. It acts in the direction of the center, pulling towards it the substance that makes up the "body" of the planet.
Earth's gravitational field
The gravitational field of the Earth is a force energy field that is formed around our planet due to the action of two forces:
- gravity;
- centrifugal force, which owes its appearance to the rotation of the Earth around its axis (daily rotation).
Since both gravity and centrifugal force act constantly, the gravitational field is also a constant phenomenon.
The gravitational forces of the Sun, the Moon and some other celestial bodies, as well as the atmospheric masses of the Earth, have an insignificant effect on the field.
Law of gravity and Sir Isaac Newton
The English physicist, Sir Isaac Newton, according to a well-known legend, once walking in the garden during the day, saw the moon in the sky. At the same time, an apple fell from the branch. Newton was then studying the law of motion and knew that an apple falls under the influence of a gravitational field, and the Moon revolves in an orbit around the Earth.
And then the thought came to the mind of a brilliant scientist, illuminated by insight, that perhaps the apple falls to the earth, obeying the same force due to which the Moon is in its orbit, and does not rush randomly throughout the galaxy. This is how the law of universal gravitation, also known as Newton's Third Law, was discovered.
In the language of mathematical formulas, this law looks like this:
F=GMm/D2 ,
where F- force of mutual gravitation between two bodies;
M- mass of the first body;
m- mass of the second body;
D2- distance between two bodies;
G- gravitational constant, equal to 6.67x10 -11.
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 \u003d 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 smallness of the size of any body compared to the size of the Earth), which is considered as a ball of radius R o =6.371030 . 10 6 m. Substituting the values of M o and R o in the last formula, we obtain for the module of the vector g g value "9.81m / s 2. This quantity is called free fall acceleration. Since the Earth is not a perfect 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 the latitude (it varies from 9.780 to 9.832 m/s 2). However, in a given place on the Earth, the acceleration of free fall is the same for all bodies(Galileo's law).
A body with mass m, located on the surface of the Earth, is affected by a force P= m g, which is called gravity. If a body of mass m is 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 -strengthJ, With which the body, due to gravity towards the Earth, acts on a support (or suspension) that keeps the body from free fall. The weight of the body is manifested only when, in addition to the force of gravity, on the bodyP (she tells the body acceleration g), another force is acting (which tells the body acceleration a) : J= m g- m a= m( g-a). Obviously, when acceleration g and a equal in absolute value and directed in opposite directions, then the weight of the body is zero(state of weightlessness). This situation arises, in particular, on space satellites of the Earth.
4.4 Space speeds
First cosmic speed v1 they call such a minimum speed that must be reported to the body so that it can move around the Earth in a circular orbit (turn into an artificial satellite of the Earth). A satellite moving in a circular orbit of radius r is affected by the Earth's gravitational force, giving 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 Earth's radius), we have v 1 = 7.9 km/s.
second cosmic speed v2 called the smallest speed that must be reported to the body so that it can overcome the gravity of the Earth and become a satellite of the Sun. To overcome the earth's 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, whence we have v 2 = 11.2 km/s.
third cosmic speed v 3 call the speed that must be reported to the body and the Earth so that it leaves the solar system(v 3 = 16.7 km/s).
4.5 Non-inertial frames of reference. Forces of inertia.
Newton's laws are valid only in inertial frames of reference. Frames of reference 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, due to the influence of bodies on each other, to 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 frame of reference: the product of the body's mass and acceleration in the considered frame of reference is equal to the sum of all forces acting on this body (including the forces of inertia). Forces of inertia F at the same time, they must be such that, together with the forces F they told the body to accelerate a`, what it has in non-inertial frames of reference, i.e. m a`=F+F in and because F= m a(here a-acceleration of the body in the inertial reference frame), then m a`= m a+F in.
The forces of inertia are due to the accelerated motion of the reference frame relative to the measured frame, and therefore, in the general case, the following cases of manifestation of these forces should be taken into account:
1. Forces of inertia during accelerated translational motion of the frame of reference F n =m a o, here a about- acceleration of the translational motion of the reference system.
2. Forces of inertia acting on a body at rest in a rotating frame of reference F q \u003d -m w 2 R, here w=const - angular velocity of the system in the form of a rotating disk of radius R.
3. Forces of inertia acting on a body moving in a rotating frame of reference F k = 2m[ v`w] where is the power F k (Coriolis force) is perpendicular to the velocity vectors of the body v` and angular velocity of rotation w reference systems in accordance with the rule of the right screw.
In accordance with this, we obtain the basic law of dynamics for non-inertial frames of reference
m a`=F+F n+ F c + F to.
It is significant that inertia forces are caused not by the interaction of bodies, but by the accelerated motion of the frame of reference. Therefore these forces do not obey Newton's third law , since if an inertia force acts on a body, then there is no opposing force applied to this body. The two basic provisions of mechanics, according to which acceleration is always caused by force, and force is always due to the interaction between bodies, are not simultaneously fulfilled in systems moving with acceleration. In this way, inertial forces are not Newtonian forces .
For any body located in a non-inertial frame of reference, the forces of inertia are external and, therefore, there are no closed systems here - this means that in non-inertial frames of reference the laws of conservation of momentum, energy and angular momentum are not fulfilled.
The analogy between the forces of gravity and the forces of inertia underlies the principle of equivalence of gravitational forces and inertial forces (Einstein's equivalence principle): all physical phenomena in the 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.
The study of the Earth's gravitational field is not only scientific, but also of great practical importance for many branches of the national economy of Russia. Being an independent scientific direction, gravimetry is also an integral part of other complex Earth sciences, such as Earth physics, geology, geodesy and astronautics, oceanography and navigation, seismology and forecasting.
All initial concepts of gravimetry are based on the principles of classical Newtonian mechanics. Under the action of gravity, everyone experiences acceleration g. Usually, they are dealing not with gravity, but with its acceleration, numerically equal to the field strength at a given point. Changes in gravity depend on the distribution of masses in the Earth. Under the influence of this force, the modern form (figure) of the Earth was created and its differentiation into geospheres of different composition and density continues. This phenomenon is used in gravimetry to study the geology. Changes in the force of gravity associated with the inhomogeneities of the earth's crust, which do not have an obvious, visible pattern and cause the deviation of the values of the force of gravity from the normal, are called gravity anomalies. These anomalies are not great. Their values fluctuate within several 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. However, it is these changes that are of interest for studying the earth's crust and for searching.
Gravitational anomalies are caused both by masses protruding to the surface (mountains) and by the difference in mass densities inside the Earth. The influence of external visible masses is calculated by excluding corrections for from the obtained anomalies. Changes in densities can occur both by raising and lowering layers, and by changing densities within the layers themselves. Therefore, gravity anomalies reflect both the structural forms and the petrographic composition of the rocks of various layers of the earth's crust. Differentiation of densities in the cortex proceeds both vertically and horizontally. The 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 crustal boundary and reaches 3.0–3.3 g/cm 3 in upper mantle.
The interpretation of gravity anomalies in geology acquires a particularly important role. Directly or indirectly, gravity is involved in all. Finally, 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. This makes it possible to use gravity data to solve geological problems that are very diverse in scale and depth. Gravimetric survey is widely used in prospecting and exploration of ore deposits and oil and gas bearing structures.
The role and importance of gravity data in the study of deep seismic data has especially increased in recent years, when not only the Kola, but also other deep and superdeep wells, including foreign ones (Oberpfalz v, Gravberg v, etc.) did not confirm the results of geological interpretation of deep seismic data, underlying the design of these wells.
For the geological interpretation of gravity anomalies of geomorphologically sharply different regions, the choice of the most justified reduction of the force of gravity acquires a special role, since, for example, in mountainous regions, the Fay and Bouguer anomalies differ sharply not only in intensity, but even in sign. For continental territories, the most recognized is the Bouguer reduction with an intermediate layer density of 2.67 g / cm 3 and adjusted for the influence of the surface topography within a radius of 200 km
The elevations of the earth's surface, as well as the depths of the bottom of the seas and oceans, are measured from the surface of the quasi-geoid (sea level). Therefore, to fully take into account the gravitational influence of the Earth's shape, it is necessary to introduce two corrections: the Bruns correction for deviations of the Earth's figure from a normal Earth ellipsoid or spheroid of rotation, as well as topographic and hydrotopographic corrections for deviations of the solid earth's surface from sea level.
Gravity anomalies are widely used in solving various geological problems. Ideas about the deep geological nature of gravity anomalies so large and heterogeneous across the territory of Russia will largely change depending on what theoretical concepts of the formation and tectonic evolution of the Earth were taken as their basis. A clear connection between gravity anomalies in the Bouguer and hydrotopographic reductions with the daytime relief and with the depths of the sea, when intense minima correspond to mountain structures, and gravity maxima correspond to seas, has long been noted by researchers and has been widely used to study isostasy, the correlation of gravity anomalies with deep seismic sounding data and using it to calculate the "thickness" of the earth's crust in seismically unexplored areas. The Bouguer and hydrotopographic reductions make it possible to remove the influence of the known density inhomogeneities of the Earth and thereby highlight the deeper components of the field. The observed correlation with the daytime relief of gravity anomalies emphasizes that it is isostasy as a physical phenomenon that is the reason that not only the relief, but also all density inhomogeneities of the Earth are mutually balanced in the form of zones of relatively high and low density, often repeatedly alternating with depth and mutually compensating each other. Modern data on the rheological properties of the Earth with its litho- and asthenosphere, which are sharply different in their elasticity and, accordingly, mobility, as well as the tectonic stratification of the earth's crust, with the possible presence of multi-tiered convection of the deep matter of the Earth, testify to the geologically instantaneous relaxation of loads . Therefore, in the Earth, both now and in the past, all anomalous masses of any size and depth of occurrence were and continue to be isostatically compensated, regardless of where they are and in whatever form they appear. And if earlier the amplitudes and signs of gravitational anomalies were tried to be explained only by changes in the total thickness of the earth's crust and for this purpose the coefficients of its correlation with the daytime relief or with gravitational anomalies were calculated, then the subsequent increasingly detailed seismic study of the earth's crust and upper mantle, the use of seismic tomography methods showed that lateral seismic and, consequently, density inhomogeneities are characteristic of all levels of differentiation of the deep masses of the Earth, i.e. not only the earth's crust, but also the upper and lower mantle, and even the core of the Earth.
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 mantle proper levels of lateral density inhomogeneities of the earth. The anomalous gravitational field reflects the total effect of gravitating masses located at different depths and the 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 the rocks of the crystalline basement lie at great depths. The gravitational effect of sedimentary rocks in areas with a shallow basement is much more difficult to observe, since it is obscured by the influences of the 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 minima of the force of gravity. In the anomalous gravitational field, the boundaries of individual blocks are clearly defined by zones of large gradients and stripe maxima of gravity. Within platforms and folded areas, smaller structures, swells, and foredeeps are distinguished.
The most global gravity anomalies characterizing the inhomogeneities of the mantle proper (asthenospheric) level are so great that only their marginal parts enter the territory of Russia under consideration, being traced far beyond its borders, where their intensity increases significantly. The unified zone of the Mediterranean gravity maximum coincides with the basin and is bounded from the north by a small Alpine gravity minimum, and in the east by a single very intense and huge Asian gravity minimum corresponding in general to the Asian megabloat of the Earth, covering the mountain structures of Central and High Asia from to and, respectively, from the Tien Shan to the northeastern system of internal depressions (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, Transbaikalia, Verkhoyansk-Chukotka region), and its branch covers almost the entire area of the Siberian Precambrian platform, which was activated in recent times, in general, slightly elevated (up to 500–1000 m) Siberian Plateau.
Find a logical explanation and different signs of these anomalies, given that the zone melting, as it rises to the surface of the asthenolite, leaves behind at each level melted rocks, relatively denser than the strata containing them laterally. Therefore, in the gravitational field, the entire sum of such remelted rocks creates a single total maximum of gravity, and even the presence of molten “layers” (velocity and density inversion zones) in it will not change its general characteristics, as is observed in the marginal parts of the Arctic Ocean falling within the map. - Atlantic and Pacific global gravity maxima.
The anomalous masses that create the Central Asian global minimum are likely to be at even greater depths, as a result of which the formed zone of the melt led to an increase in the volume of only deep masses and, accordingly, to the formation of a single giant Asian megabulge of the Earth on the surface, and the presence of a molten lens at depth, apparently, it caused basaltoid magmatism, small in volume and scattered throughout this territory, Mesozoic explosion pipes in , extinct Quaternary volcanoes in the Altai-Sayan region, and finally, more intense basaltoid magmatism of the Baikal-Patom highlands, which goes far beyond the Baikal rift itself.
The great depth of the global maxima and minima of gravity, falling within the territory of Russia, is also confirmed by the interpretation of the geoid heights.
Gravitational interaction is one of the four fundamental interactions in our world. Within classical mechanics, the gravitational interaction is described by law of gravity 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 - i.e.
.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, the 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 is also encountered in the study of radiation (see, for example, Light Pressure), and which 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 the area of the entire sphere.
The simplest task 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 problem becomes much more complicated. So, 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, the instability of solutions with respect to the initial conditions sets in rather quickly. When applied to the solar system, this instability makes it impossible to predict the motion of the planets on scales exceeding a hundred million years.
In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly greater than the mass of other bodies (examples: the solar system and the dynamics of Saturn's rings). In this case, in the first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around a massive body. Interactions between them can be taken into account in the framework of perturbation theory, and averaged over time. In this case, non-trivial phenomena may arise, such as resonances, attractors, randomness, etc. A good example of such phenomena is the non-trivial structure of Saturn's rings.
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 Newtonian;
- potential delay associated with the finite propagation velocity of gravitational perturbations; the appearance of gravitational waves;
- non-linear effects: gravitational waves tend to interact with each other, so the principle of superposition of waves in strong fields is no longer valid;
- change in 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: the energy loss in the binary system with the PSR B1913+16 pulsar - the Hulse-Taylor pulsar - is in good agreement with the 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 greatly complicates its detection. Gravity power l-poly source is proportional (v / c) 2l + 2 , if the multipole is of electric type, and (v / c) 2l + 4 - if the multipole is magnetic type , where v is the characteristic velocity of sources in the radiating system, and c is the 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 is the tensor of the quadrupole moment of the mass distribution of the radiating system. Constant 
(1/W) makes it possible to estimate the order of magnitude of the radiation power.
Since 1969 (Weber's experiments (English)) and up 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 are very weak under terrestrial conditions and therefore their detection and experimental verification are therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.
Among them, in particular, one can name the drag of inertial reference frames (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's Gravity Probe B conducted an experiment of unprecedented accuracy to measure these effects near the Earth, but the 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 built. However, at low energies, in the spirit of quantum field theory, the gravitational interaction can be represented as an exchange of gravitons - gauge bosons with spin 2.
Standard Theories of Gravity
Due to the fact that the 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 overwhelming majority of cases one can confine oneself to the classical description of the gravitational interaction.
There is a modern canonical classical theory of gravity - the general theory of relativity, and many hypotheses that refine it and theories of varying degrees of development that compete with each other (see the article Alternative theories of gravity). All of these theories give very similar predictions within the approximation in which experimental tests are currently being carried out. The following are some of the major, 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 the flat Minkowski space, in which the laws of conservation of energy-momentum and angular momentum are unambiguously fulfilled. Then the motion of bodies in the Minkowski space is equivalent to the motion of these bodies in the effective Riemannian space.
- In tensor equations, to determine the metric, one should take into account the mass of the graviton, and also use the gauge conditions associated with the metric of the Minkowski space. This does not allow destroying the gravitational field even locally by choosing some suitable frame of reference.
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, immobile and Euclidean.
On the other hand, there are no less convincing arguments of RTG opponents, which boil down to the following points:
A similar thing happens in RTG, where the second tensor equation is introduced to take into account the connection between the non-Euclidean space and the 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.
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 due to 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 the masses of the earth. The gravitational field of the Earth is characterized by gravity, gravity potential and its various derivatives. The potential has the dimension of m 2 .s -2 , for the unit of measurement of the first derivatives of the potential (including the force of gravity) in gravimetry, a milligal (mGal) equal to 10 -5 m.s -2 is taken, 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 ; average gravity on Earth 979.8 Gal; decrease in the average gravity from the pole to the 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 lunisolar variations in gravity is 0.4 mGal; the possible value of the secular change in gravity<0,01 мГал/год.
The part of the potential of gravity, due only to the attraction of the Earth, is called the geopotential. To solve many global problems (studying the shape of the Earth, calculating satellite trajectories, etc.), the geopotential is represented as an expansion in terms of spherical functions. The second derivatives of the gravity potential are measured by gravitational gradiometers and variometers. There are several expansions of the geopotential, differing in the initial observational data and expansions.
Usually the gravitational field of the Earth is represented as consisting of 2 parts: normal and anomalous. The main - normal part of the field corresponds to the schematized model of the Earth in the form of an ellipsoid of revolution (normal Earth). It is consistent with the real Earth (centers of mass, mass values, angular velocities and axes of daily rotation coincide). The surface of a normal Earth is considered level, i.e. the potential of gravity at all its points has the same value (see geoid); gravity is directed to it along the normal and varies according to a simple law. In gravimetry, the international formula for normal gravity is widely used:
g (p) \u003d 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 (p) \u003d 978030 (1 + 0.005302 sin 2 p - 0.000007 sin 2 2p), mGal.
From the right sides of both formulas, 14 mGal is subtracted to take into account the error in absolute gravity, which was established as a result of repeated measurements of absolute gravity in different places. 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 an anomaly of gravity (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. Since the positions of the Moon and the Sun relative to the Earth change, there is a periodic variation of the Earth's gravitational field. This causes tidal deformations of the Earth, incl. sea tides. There are also non-tidal changes in the Earth's gravitational field in 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 the angular velocity and instantaneous axis of the Earth's daily rotation. Many values of non-tidal changes in the Earth's gravitational field are not observed and are estimated only theoretically.
Based on the gravitational field of the Earth, a geoid is determined that characterizes the gravimetric figure of the Earth, relative to which the heights of the physical surface of the Earth are set. The gravitational field of the Earth, together with other geophysical data, is used to study the model of the radial distribution of the Earth's density. Based on it, conclusions are drawn about the hydrostatic equilibrium state of the Earth and about the associated stresses in it.
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