The force of gravitational interaction between the two. Strong gravitational fields

21.1. Law universal gravity Newton
Gravitational interactions are inherent in all material bodies (Fig. 111).

Rice. 111
The law describing these forces, discovered by I. Newton and published in 1687, was called the law of universal gravitation: two material points are attracted with forces proportional to the product of the masses of these points, inversely proportional to the square of the distance between the points and directed along the straight line connecting these points:

Since strength is vector quantity, then the formula that determines the force of attraction should be given a vector form.
To do this, we introduce the vector r 12, connecting the points 1 And 2 (Fig. 112).

rice. 112
Then the force of attraction acting on the second body can be written in the form

In formulas (1), (2), the proportionality coefficient b is called the gravitational constant. The value of this quantity cannot be found from others physical laws and determined experimentally. Numerical value gravitational constant depends on the choice of system of units, so in SI it is equal to:

The gravitational constant was first experimentally measured by the English physicist Henry Cavendish. In 1798, he constructed a torsion balance and used it to measure the force of attraction between two spheres, confirming the law of universal gravitation; determined the gravitational constant, mass and average density Earth.
The question of the nature of gravitational interaction is extremely complex. I. Newton himself gave a laconic answer to this question: “I do not invent hypotheses,” thereby refusing to even discuss this topic. It is enough that the law of universal gravitation high degree accurately quantitatively describes gravitational interaction. Tremendous successes Newtonian mechanics for almost two centuries predetermined a similar approach to all physical science, not only mechanics: it is enough to discover, find the laws that correctly describe physical phenomena, and learn to apply them to quantitative description these phenomena.
Thus, in the study of gravity, it was believed that in an incomprehensible way one body can influence another, and this influence is transmitted instantly, that is, a change in the position of one of the bodies instantly changes the forces acting on other bodies, regardless of the distance at which these bodies are located . This general approach to character physical interactions called the theory of long-range action. A similar view of the interactions of bodies was extended to electrical and magnetic phenomena, the study of which was actively carried out during the 18th – 19th centuries. Only in the 30s years XIX century English physicist M. Faraday for electromagnetic interactions the main provisions were formulated alternative theory short-range interaction: to transmit interaction, a “mediator” is required, a certain medium that transmits these interactions; the interactions themselves cannot be transmitted instantly, it requires certain time in order for a change in the position of one of the bodies to be “felt” by other interacting bodies. At the beginning of the 20th century German physicist A. Einstein built a new theory of gravity - the general theory of relativity. Within the framework of this theory, gravitational interactions are explained in the following way: each body with mass changes the properties of the space-time around itself (creates a gravitational field), while other bodies move in this changed space-time (in the gravitational field), which leads to the appearance of observable forces, acceleration, etc. From this point From a perspective, the expression “is in a gravitational field” is equivalent to the expression “gravitational forces act.”
We will turn to these questions later when studying the electromagnetic field.
The most striking thing about the phenomenon of gravity is that gravitational forces are proportional to the masses of bodies. Indeed, earlier we talked about mass as a measure of the inertia of a body. It turned out that mass also determines a fundamentally different property of material bodies - it is a measure of the ability to participate in gravitational interactions. Therefore, we can talk about two masses - inertial and gravitational. The law of universal gravitation states that these masses are proportional to each other. This statement has long been confirmed known fact: All bodies fall to the ground with the same acceleration. Experimented with high accuracy the proportionality of gravitational and inertial masses was confirmed in the works of the Hungarian physicist Lorand Eotvos. Subsequently, the proportionality of inertial and gravitational masses formed the basis new theory gravity − general theory relativity of A. Einstein.
In conclusion, we note that the law of universal gravitation can be used as the basis for determining the unit of mass (of course, gravitational). For example: two point bodies of a unit gravitational mass, located at a distance of one meter, are attracted with a force of one N.

Assignment for independent work : determine the masses of two point bodies located at a distance 1.0 m from each other and interacting with force 1.0 N.

For gravitational forces, the principle of superposition is valid: the force acting on a point body from several other bodies is equal to the sum of the forces acting from each body. This statement is also a generalization of experimental data and a fundamental property of gravitational interactions.
Let's look at the principle of superposition from a mathematical point of view: according to the law of universal gravitation, the force of gravitational interaction is proportional to the mass of these bodies. If the dependence on masses were nonlinear, then the principle of superposition would not apply. Indeed, let a body of mass m o interacts with two point bodies with masses m 1 And m 2. Let's mentally place the bodies m 1 And m 2 to one point (then they can be considered as one body). In this case, the force acting on the body m o, is equal to:

presented as the sum of forces acting on the part of two bodies − m 1 And m 2.
In the case of a nonlinear relationship between force and mass, the superposition principle would not be valid.
The law of universal gravitation for point bodies and the principle of superposition make it possible, in principle, to calculate the forces of interaction between bodies of finite sizes (Fig. 113).

rice. 113
To do this, it is necessary to mentally divide each of the bodies into small sections, each of which can be considered as a material point. Then calculate the double sum of the interaction forces between all pairs of points. IN general case calculating such a sum is a complex mathematical problem.
We emphasize that the force of interaction between bodies of finite sizes is calculated only by the method of breaking up bodies and subsequent summation. It is erroneous to say that the force of interaction between bodies can be calculated as the force of interaction, equal to strength interactions of point bodies located at centers of mass. To substantiate this statement, consider a simple example.
Let one of the interacting bodies be considered a material point of mass m o, and the second body can be represented as two material points equal masses m, located at a fixed distance a from each other (Fig. 114).

rice. 114
All material points are located on the same straight line, the distance from the first body to the center of the second is denoted by r. The force of attraction acting on a body m o, is equal to:

If we connect the material points that make up the second body into one mass 2m, located in the center of the body, then the interaction force will be equal to:

which is different from expression (3). Only when r >> a expression (3) goes into formula (2). Note that in this case the second body should be considered as a material point.

Sokol-Kutylovsky O.L.

About the forces of gravitational interaction

If you ask any student or professor of the physics or mechanics-mathematics departments of any university about the forces of gravitational interaction, seemingly the most studied of all known force interactions, then all they can do is write formulas for the Newtonian force and for the centrifugal force, which They will remember the incomprehensible Coriolis force and the existence of some mysterious gyroscopic forces. And all this despite the fact that all gravitational forces can be obtained from general principles classical physics.

1. What is known about gravitational forces

1.1. It is known that the force arising between bodies in gravitational interaction, directly proportional to the mass of these bodies and inversely proportional to the square of the distance between them (the law of universal gravitation or Newton’s law):

(1)

Where G" 6.6720H 10 -11 LF m 2H kg -2 - gravitational constant, m, M- masses of interacting bodies and r- the shortest distance between the centers of mass of interacting bodies. Assuming that the body has mass M on distance r creates a gravitational acceleration field directed towards its center of mass,

force (1) acting on a body of mass m, are also presented in the form:

where w is the angular velocity of rotation of the body around an axis not passing through the center of mass of the body, v – speed of rectilinear motion of the body and r – radial vector connecting the axis of rotation with the particle or with the center of mass of the rotating body. The first term corresponds to the gravitational force (1), the second term in formula (3) is called the Coriolis force, and the third term is called the centrifugal force. The Coriolis force and centrifugal force are considered fictitious, depending on the reference system, which is absolutely inconsistent with experience and elementary common sense. How can a force be considered fictitious if it can perform real job? Obviously, these are not fictitious physical strength, and the currently available knowledge and ideas about these forces.

Origin numerical coefficient“2” in the Coriolis force is doubtful, since this coefficient was obtained for the case when the instantaneous speed of points of the body in a rotating reference frame coincides with the speed of a moving body or is directed against it, that is, with the radial direction of the Coriolis force. The second case, when the body speed is orthogonal instantaneous speed points of the rotating reference system, not considered. According to the method outlined in, the magnitude of the Coriolis force in the second case turns out to be equal to zero, while for given angular and linear speeds it should be the same.

1.3. Angular velocity is an axial vector, that is, it is characterized by a certain value and is directed along a single selected axis. Direction sign angular velocity determined by the right screw rule. The angular velocity of rotation is defined as the change in the angle of rotation per unit time, ω( t)=¶ φ/¶ t. In this definition φ( t) – periodic function time with a period of 2π radians. At the same time, the angular velocity is inverse function time. This follows, in particular, from its dimension. For these reasons, the derivative of angular velocity with respect to time: ¶ ω /¶ t=-ω 2 . The time derivative of the angular velocity corresponds to the axial vector angular acceleration. According to the conventional definition given in the physical encyclopedic dictionary, the axial vector of angular acceleration is directed along the axis of rotation, in the same direction as the angular velocity if the rotation is accelerated, and against the angular velocity if the rotation is slow.

2. Gravitational forces acting on the center of mass of the body

Gravitational and mechanical forces differ from each other in the nature of the interaction: during the “contact” interaction of bodies, mechanical forces arise, and during the remote gravitational interaction of bodies, gravitational forces arise.

2.1. Let us determine all gravitational forces acting on the center of mass of a material body. Rotating the body around own axis, passing through its center of mass, we will not consider for now. From the general principles of mechanics it is known that force arises when the instantaneous momentum of a body changes. Let's do it In a similar way as in determining the forces associated with rectilinear movement body, and when determining the forces associated with its rotation relative to the external axis:

or in expanded form:

Where r =r·[ cos(ω t)· x + sin(ω t)· y ], x And y – unit vectors in the direction of the corresponding coordinate axes, r– radial vector module r , r 1 =r /r– unit vector in the direction of the radial vector r , t– time, and the coordinate axis z coincides with the axis of rotation. Magnitude of the unit vector derivative r 1 by time, ¶ r 1 /¶ t=ω· r 1^ , where r 1^ – unit vector lying in the plane of rotation and orthogonal to the radial vector r (Fig. 1).

Pay attention to possible changes radial vector, in accordance with equation (7), formula (6) takes the form:

(8)

Rice. 1. Mutual arrangement radial vector r , angular velocity ω and instantaneous speed v m body mass m, in the coordinate system ( x, y, z) with the axis of rotation directed along the axis z. Unit vector r 1 =r /r is orthogonal unit vector r 1^ .

2.2. All forces included in equation (8) are equal and add up according to the rule of vector addition. The sum of forces (8) can be represented as four terms:

F G= F a+F ω1 + F ω2 + F ω3.

Force F A occurs when straight accelerated movement body or during gravitational static interaction of a body with another body. Force F ω1 corresponds to the Coriolis force for the case when material body moves in a rotating system in the radial direction (along the radius of rotation). This force is directed towards or against the instantaneous speed of the body. Force F ω2 is the force acting on any point of the rotating body. It is called centrifugal force, but the same force is called the Coriolis force if a body in a rotating system moves in the direction of instantaneous speed without changing the radius of rotation. Force F ω2 is always directed radially. Given equality ¶ r 1 /¶ t=ω· r 1^, and the direction of the resulting vector in vector product, we find that when each point of the body rotates with angular velocity ω there is a force acting on her F ω2 = m·ω 2 · r , which coincides with the centrifugal force in formula (3).

Force F ω3 is the force of inertia rotational movement. The inertial force of rotational motion arises when the angular velocity of the rotating system and the bodies associated with it changes and is directed along the vector of the instantaneous velocity of the body at dw/dt<0 и против вектора мгновенной скорости тела при dw/dt>0. It occurs only during transient processes, and with uniform rotation of the body this force is absent. Direction gravitational force rotational inertia

(9)

shown in Fig. 2. Here r – radial vector connecting the axis of rotation with the center of mass of the rotating body along the shortest path, ω – axial vector of angular velocity.

Rice. 2. The direction of the gravitational force of inertia of rotational motion, F ω3, when moving a body from point 1 to point 2 at dw / dt<0; r – radial vector , connecting the axis of rotation to the center of mass of a moving body; F T – the force of attraction or the tension force of the rope. Centrifugal force is not shown.

Vector sum of forces F ω1 and F ω2 creates a resultant force (Coriolis force F K) when a body moves in an arbitrary direction in a rotating system:

3. Gravitational and mechanical forces arising when turning the axis of rotation of a body

To determine all gravitational forces acting not only on the center of mass, but also on any other point of a material body, including those arising when the axis of rotation of this body rotates around another axis, it is necessary to return to formula (5).

The general formula for all gravitational and mechanical forces obtained earlier remains in force, but until now all the forces obtained were considered to be applied to the center of mass of the body. The influence of the rotation of the own axis of rotation on individual points of the body that do not coincide with the center of mass was not taken into account. However, formula (5), previously obtained from the general principles of mechanics, contains all the forces acting on any point of a rotating body, including the forces arising during the spatial rotation of the body’s own axis of rotation. Therefore, from formula (5) it is possible to derive in explicit form an equation for the force acting on an arbitrary point of a rotating material body when its own axis of rotation is rotated through a certain angle in space. To do this, we present equation (5) in the following form:

(12)

where S rґ w Ѕ – vector module rґ w , A ( rґ w ) 1 – unit vector directed along the vector rґ w . As has been shown, the time derivative of the vector rґ w when the value of this vector changes, it gives gravitational and mechanical rotational forces, from which centrifugal force, Coriolis force and rotational inertia force are obtained:

where the fifth term is the force, or more precisely, it is the set of forces that arise during the spatial rotation of the axis of rotation of a body at all points of this body, and the force that arises at each point depends on the location of this point. In short notation, the total sum of all gravitational forces can be conveniently represented as:

(15)

Where F a – Newton force with gravitational acceleration vector a , Fw 1 – Fw 3 – forces of rotational motion with gravitational vector of angular velocity w and e Fw W i – a set of forces that arise when turning the axis of rotation of a body in all n points into which the body is evenly divided.

Let us present the fifth term in expanded form. By definition, the radial vector r is orthogonal to the angular velocity vector w, therefore the magnitude of the vector rґ w is equal to the product of the moduli of its constituent vectors:

Time derivative of the unit vector ( rґ w ) 1 when changing it in direction by an angle j gives another unit vector, r 1, located parallel to the plane of rotation S ( x, z) and orthogonal to the vector rґ w (Fig. 3). Moreover, as a factor, it has a coefficient numerically equal to the time derivative of the angle of rotation, W =¶ j /¶ t:

(16)

Since when the axis of rotation is rotated, the movement of the points of a material body is three-dimensional, and the rotation of the axis occurs in a certain plane S ( x, z), then the module of the unit vector relative to the plane of rotation is not constant, and during rotation it varies from zero to one. Therefore, when differentiating such a unit vector, its magnitude relative to the plane in which the rotation of this unit vector occurs must be taken into account. The length of the unit vector ( rґ w ) 1 relative to the plane of rotation S ( x, z) is the projection of this unit vector onto the rotation plane. Derivative of the unit vector ( rґ w ) 1 in the plane of rotation S ( x, z) can be represented as follows:

(17)

where a is the angle between the vector rґ w and rotation plane S ( x, z).

The force acting on any point of a rotating body when turning its axis of rotation is applied not to the center of mass of this body, but directly to each given point. Therefore, the body must be divided into many points, and it is assumed that each such point has a mass m i. Under the mass of a given point of the body, m i, means mass concentrated in a small volume relative to the entire body V i So:

With uniform body density r, the mass is , and the point of application of the force is the center of mass of the given volume V i occupied by a part of a material body with mass m i. The force acting on i-that point of the rotating body when turning its axis of rotation, takes on the following form:

(18)

Where m i– mass of a given point of the body, r i is the shortest distance from a given point (at which the force is determined) to the axis of rotation of the body, w is the angular velocity of rotation of the body, W is the module of the angular velocity of rotation of the axis of rotation, a is the angle between the vector rґ w and rotation plane S ( x, z), and r 1 is a unit vector directed parallel to the plane of rotation and orthogonal to the instantaneous velocity vector rґ w .

Rice. 3. Direction of force Fw W , which occurs when the axis of rotation of the body rotates in the plane S (x, z) with angular speed of rotation W. At the point A with a radius vector emanating from the point With rotation axis, force Fw W =0; at the point b with a radius vector emanating from the center of the body, force Fw W has a maximum value.

The sum of all forces (18) acting on everything n points into which the body is evenly divided,

(19)

creates a moment of forces that rotate the body in the Y plane ( y, z), orthogonal to the rotation plane S ( x, z) (Fig. 4).

From experiments with rotating bodies the very presence of forces (19) is known, but they have not been clearly defined. In particular, in gyroscope theory, the forces acting on the bearing supports of the gyroscope are called “gyroscopic” forces, but the origin of these physical forces is not disclosed. In a gyroscope, when its axis of rotation is rotated, force (18) acts on each point of the body, obtained here from the general principles of classical physics and expressed quantitatively in the form of a specific equation.

From the property of symmetry it follows that each point of the body corresponds to another point, located symmetrically relative to the axis of rotation, in which a force of the same magnitude, but having the opposite direction, acts (18). The combined action of such symmetrical pairs of forces when rotating the axis of a rotating body creates a moment of force that rotates this body in the third plane Y ( y, z), which is orthogonal to the rotation plane S ( x, z) and planes L (x, y), in which the rotation of points of the body occurs:

(20)

Rice. 4. The emergence of a moment of force under the action of pairs of forces at points of the body located symmetrically relative to the center of mass. 1 and 2 – two symmetrical points of a body rotating with angular velocity w, in which, when the axis of rotation of the body rotates with angular velocity W, forces of equal magnitude arise Fw W 1 and Fw W 2, respectively.

In this case, for unit vectors of angular velocities characterizing their direction, at any of the points of the body that do not coincide with the center of symmetry (center of mass), the vector identity is satisfied:

(21)

where Q 1 is the unit axial vector of the angular velocity arising at the moment of action of force (18), w 1 is the unit axial vector of the angular velocity of rotation of the body and W 1 is the unit axial vector of the angular velocity of the rotation axis (Fig. 2). Since the axis of rotation, coinciding with the vector of angular velocity of rotation W, is always orthogonal to the axis of rotation, coinciding with the vector of angular velocity of rotation of the body, w, then the angular velocity vector Q is always orthogonal to the vectors w and W:.

By rotating the coordinate system in space, the problem of finding force (18) can always be reduced to a case similar to that considered in Fig. 3. Only the direction of the axial vector of the angular velocity w and the direction of the axial vector of the speed of rotation of the rotation axis, W, can change, and, as a consequence of their change, can change to the opposite direction of the force Fw W .

The relationship between the absolute values of angular velocities during free rotation of a body along three mutually orthogonal axes can be found by applying the law of conservation of energy of rotational motion. In the simplest case, for a homogeneous body of mass m in the shape of a ball with a radius r we have:

where we get:

4. The total sum of primary gravitational and mechanical forces acting on the body

4.1. Taking into account the forces (19) arising when the rotation axis of a body rotates, the complete equation for the sum of all gravitational forces acting on any point of a material body participating in rectilinear and rotational motion, including spatial rotation of its own rotation axis, has the following form :

(22)

Where a – vector of rectilinear acceleration of a body with mass m, r – radial vector connecting the axis of rotation of the body with the point of application of the force, r– radial vector module r ,r 1 – unit vector coinciding in direction with the radius vector r , w – angular velocity of rotation of the body, S rґ w Ѕ – magnitude of the instantaneous velocity vector rґ w , (rґ w ) 1 – unit vector coinciding in direction with the vector rґ w , r 1^ – unit vector located in the plane of rotation and orthogonal to the vector r 1, W – module of the angular velocity of rotation of the rotation axis, r 1 – unit vector directed parallel to the plane of rotation and orthogonal to the instantaneous velocity vector rґ w , a – angle between vector rґ w and the plane of rotation, m i- weight i-that point of the body concentrated in a small volume of the body V i, the center of which is the point of application of the force, and n– the number of points into which the body is divided. In formula (22) for the second, third and fourth forces the sign can be taken positive, since these forces in the general formula are under the absolute value sign. The signs of the forces are determined taking into account the direction of each specific force. Using the forces included in formula (22), it is possible to describe the mechanical motion of any point of a material body as it moves along an arbitrary trajectory, including the spatial rotation of its axis of rotation.

4.2. So, in gravitational interaction there are only five different physical forces acting on the center of mass and on each of the points of a material body during the translational and rotational motion of this body, and only one of these forces (Newton’s force) can act on a stationary body from the side of another body . Knowledge of all the forces of gravitational interaction makes it possible to understand the reason for the stability of dynamic mechanical systems (for example, planetary), and taking into account electromagnetic forces, to explain the stability of the atom.

Literature:

1. Landau L. D., Akhiezer A. I., Lifshits E. M. Course in general physics. Mechanics and molecular physics. M.: Nauka, 1969.

2. Savelyev I.V. General physics course. T.1. Mechanics. Molecular physics. 3rd ed., rev. M.: Nauka, 1987.

3. Sokol-Kutylovsky O.L. Gravitational and electromagnetic forces. Ekaterinburg, 2005

Sokol-Kutylovsky O.L., On the forces of gravitational interaction // “Academy of Trinitarianism”, M., El No. 77-6567, pub. 13569, 07.18.2006

Introduction

1. A short excursion into the development of the theory of gravity

2. On the nature of gravitational forces

3. Features of gravitational interaction

Conclusion

Bibliography

Application

Introduction

One of the axioms of modern science says: any material objects in the Universe are interconnected by the forces of universal gravity. Thanks to these forces, celestial bodies - planets, stars, galaxies and the Metagalaxy as a whole - are formed and exist. The shape and structure of these bodies and material systems, as well as relative motion and interaction, are determined by the dynamic balance between the forces of their gravity and the forces of inertia of the masses.

Throughout his life, a person feels the gravity of his body and the objects that he has to lift. However, a century and a half earlier before Newton and Hooke, the famous Polish scientist Nicolaus Copernicus wrote about gravity: “Gravity is nothing more than a natural desire that the father of the Universe endowed all particles with, namely to unite into one common whole, forming spherical bodies.” . Other scientists expressed similar thoughts. The formulas for the law of gravity discovered by Newton and Hooke made it possible to calculate the orbits of the planets with great accuracy and create the first mathematical model of the Universe. The question of whether the world around us exists on its own or is it a product of the activity of the mind (belonging to some higher being or to each specific individual) is the essence of the main question of philosophy, classically formulated in the form of a dilemma about the primacy of matter or consciousness. The natural objects around us have an internal structure, i.e. in turn, they themselves consist of other objects (an apple consists of cells of plant tissue, which is composed of molecules, which are combinations of atoms, etc.). In this case, levels of organization of matter of varying complexity naturally arise: cosmic, planetary, geological, biological, chemical, physical.

Does the distribution of all matter in the Universe affect the course of physical processes? Is there any connection between gravitational interaction and the uncertainty principle? Of course, in modern physics there are other questions that have not yet been answered.

Gravity there is interaction through the exchange of impulses between material systems moving in different directions.

Features of gravitational interaction can be understood by studying the dynamics of the most convenient gravitating system - planet Earth, based on the unity of laws operating in any area of physical reality. But it is necessary to study the dynamics of the Earth as a bipolar active (living) system, and not a monolithic, albeit layered-symmetrical, abstract mathematical model. This polarity of gravitational forces is due to the following factors.

1. The universality of gravitational forces in nature. In physical reality there are no other interactions except gravitational ones.

2. Back in 1936–1937, the possibility of such a density distribution was obtained by Bullen, but was regarded as unacceptable.

3. An unambiguous discrepancy between the predicted maximum pressures in the center of the Earth and the existing minimum of gravity - the only reason (according to classical physics) for the occurrence of high pressures.

4. Indicators of decompression of the internal shells can be the excess of the real equatorial swelling of the planet (70 m) and the discrepancy between the normal gravity gradients, correlated with the difference between the equatorial and polar radii.

5. To date, transverse seismic waves passing through the inner core have not been recorded.

6. The assessments of the physical state of the core matter, quite well known to geophysicists, based on calculations of the moment of inertia of the hollow and solid models of the planet, and its comparison with data from the analysis of the dynamics of the Earth-Moon system, were carried out incorrectly.

It is well known that the bulk of the solar system (about 99.8%) lies in its only star – the Sun. The total mass of the planets is only 0.13% of the total. The remaining bodies of the system (comets, planetary satellites, asteroids and meteorite matter) account for only 0.0003% of the mass. From the above figures it follows that Kepler’s laws for the motion of planets in our system should be fulfilled very well. The very attractive theory of the joint origin of the sun and planets from a single gas cloud, compressed under the influence of gravitational forces, turns out to be in contradiction with the observed uneven distribution of rotational moment (momentum ) between a star and planets. Models of the origin of planets as a result of the gravitational capture by the Sun of bodies arriving from deep space, effects caused by supernova explosions are discussed. In most “scenarios” for the development of the solar system, the existence of the asteroid belt is, one way or another, associated with its close proximity to the most massive planet in the system.
1. A short excursion into the development of the theory of gravity Initially, it was believed that the Earth was motionless, and the movement of celestial bodies seemed very complex. Galileo was one of the first to suggest that our planet is no exception and also moves around the Sun. This concept was met with quite hostility. Tycho Brahe decided not to take part in the discussions, but to take direct measurements of the coordinates of bodies on the celestial sphere. Later, Tycho's data came to Kepler, who found a simple explanation for the observed complex trajectories, formulating three laws of motion of the planets (and the Earth) around the Sun: 1. The planets move in elliptical orbits, with the Sun at one of the focuses.2. The speed of the planet's movement changes in such a way that the areas swept by its radius vector in equal periods of time turn out to be equal.3. The orbital periods of the planets of one solar system and the semi-major axes of their orbits are related by the relation: The complex motion of the planets on the “celestial sphere” observed from the Earth, according to Kepler, arose as a result of the addition of these planets in elliptical orbits with the movement of the observer, making orbital motion around the sun together with the Earth and daily rotation around the axis of the planet. Direct evidence of the daily rotation of the Earth was an experiment carried out by Foucault, in which the plane of oscillation of a pendulum was rotated relative to the surface of the rotating Earth. Kepler's laws perfectly described the observed movement of the planets, but did not reveal the reasons leading to such movement (for example, completely it could be assumed that the reason for the movement of bodies in Keplerian orbits was the will of some being or the desire of the celestial bodies themselves for harmony). Newton's theory of gravity indicated the reason that determined the movement of cosmic bodies according to Kepler's laws, correctly predicted and explained the features of their movement in more complex cases, and made it possible to describe in the same terms many phenomena of cosmic and terrestrial scales (the movement of stars in a galactic cluster and the fall of an apple to the surface of the Earth) Newton found the correct expression for the gravitational force arising from the interaction of two point bodies (bodies whose dimensions are small compared to the distance between them), which, together with the second law in the case if the mass of the planet is much less than the mass of the star, led to the differential equation, admitting an analytical solution. Without involving any additional physical ideas, it can be shown using purely mathematical methods that under appropriate initial conditions (a sufficiently small initial distance to the star and the speed of the planet), the cosmic body will rotate in a closed, stable elliptical orbit in full accordance with Kepler’s laws (in particular Kepler's second law is a direct consequence of the law of conservation of angular momentum, which is true during gravitational interactions, since the moment of force relative to a massive center is always zero). At a sufficiently high initial speed (its value depends on the mass of the star and the initial position), the cosmic body moves along a hyperbolic trajectory, ultimately moving away from the star to an infinitely large distance. An important property of the law of gravity is the preservation of its mathematical form in the case of gravitational interaction of non-point bodies in the case of a spherically symmetric distribution of their masses over the volume. In this case, the distance between the centers of these bodies plays a role. 2. On the nature of gravitational forces The law of universal gravitation formulated by Newton belongs to the fundamental laws of classical natural science. The methodological weakness of Newton's concept was his refusal to discuss the mechanisms leading to the emergence of gravitational forces (“I do not invent hypotheses”). After Newton, attempts were made repeatedly to create a theory of gravity. The vast majority of approaches are associated with the so-called hydrodynamic models of gravity, trying to explain the emergence of gravitational forces by the mechanical interactions of massive bodies with an intermediate substance, which is assigned one name or another: “ether”, “flow of gravitons”, “ vacuum" etc. The attraction between bodies arises as a result of the rarefaction of the Medium, which occurs either when it is absorbed by massive bodies, or when they screen its flows. All these theories have a common significant drawback: correctly predicting the dependence of force on distance, they inevitably lead to another unobservable effect: braking of bodies moving relative to the introduced substance. A significantly new step in the development of the concept of gravitational interaction was made by A. Einstein, who created the general theory of relativity .

Newton: “Gravity towards the Sun is composed of gravitation towards its individual particles and, with distance from the Sun, decreases exactly in proportion to the squares of the distances even to the orbit of Saturn, which follows from the rest of the aphelions of the planets and even to the extreme aphelions of comets, if only these aphelions are at rest.” . This feature of gravitational interaction, applied to the conditions inside the body, leads to a decreasing dependence of the gravitational force with decreasing distance from the center of the body.

Gravity (universal gravitation, gravitation)(from Latin gravitas - “gravity”) - a long-range fundamental interaction in nature, to which all material bodies are subject. According to modern data, it is a universal interaction in the sense that, unlike any other forces, it imparts the same acceleration to all bodies without exception, regardless of their mass. Mainly gravity plays a decisive role on a cosmic scale. Term gravity also used as the name of the branch of physics that studies gravitational interaction. The most successful modern physical theory in classical physics that describes gravity is the general theory of relativity; the quantum theory of gravitational interaction has not yet been constructed.

Gravitational interaction

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.

Theories of gravity

Newton's classical theory of gravity	General theory of relativity	Quantum gravity	Alternative
	Mathematical formulation of general relativity Gravity with massive graviton Geometrodynamics (English)		Semiclassical gravity Bimetric theories Scalar-tensor-vector gravity Whitehead's theory of gravity Modified Newtonian dynamics Compound gravity

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.
Ivanenko D. D., Sardanashvili G. A. Gravity, 3rd ed. M.: URSS, 2008. - 200 p.

Links

The law of universal gravitation or “Why doesn’t the Moon fall to Earth?” - Just about difficult things

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It is believed that any physical body in the Universe has its own gravitational field. This gravitational field is formed as a set of gravitational fields of all particles, atoms and molecules that make up this physical body. Depending on the mass, density and other characteristics of the physical body, the gravitational field of some physical bodies is different from others. Large physical bodies have a stronger and more extensive gravitational field and are able to attract other, smaller physical bodies. The value of the force of their mutual attraction to each other is determined by I. Newton’s law of universal gravitation - gravity. This applies to any physical body in the Universe.

So what is the physical meaning of gravity of physical bodies? What did the great genius I. Newton not have time to tell us?

Let's try to clarify this issue. In his theory, I. Newton did not consider particles, but, first of all, planets and stars. We, before moving on to considering the gravitational interactions between planets and stars in the Universe, already having an idea of the gravitational interaction of particles, will try to understand the gravitational interaction between physical bodies on Earth and understand what the general physical meaning of gravity is.

Assumption

I believe that physical meaning of gravity in general terms, it consists in the constant desire of the rarefied ethereal region of the physical body to move into an equilibrium state with the surrounding etheric environment, reducing its tense state, due to the attraction of other rarefied ethereal regions of other physical bodies into the region of its etheric rarefaction.

If we consider the gravitational interaction of our planet and any other physical body raised above the earth or coming to us from space, then we can state that any other physical body always falls on the surface of the Earth. Usually, in this case, we say that the Earth, thanks to gravity, attracts physical bodies to itself. However, no one has yet been able to understand and explain the mechanism of this attraction.

At the same time, the physical essence of this mysterious phenomenon is explained by the fact that the rarefied ethereal medium near the surface of the earth it is more rarefied than at a distance from it. In other words, the gravitational field and force of attraction of the Earth at its surface is more powerful than at a distance from the planet. Note that we are talking only about the ethereal environment, and not about the Earth’s atmosphere, in which there are atoms, molecules and the smallest particles of various chemical substances. It is the filling of the ethereal environment with these chemical substances that gives the rarefied ethereal environment in the Earth’s atmosphere additional density.

The ethereal medium itself constitutes not only the atmosphere of the Earth. It completely unhindered permeates the entire body of the planet. All the particles that make up everything that is on the Earth and what it consists of, including its atmosphere, crust, mantle and core, rotate in an ethereal vortex that has not stopped for many billions of years. At the same time, the rotation of the planet, as well as the rotation of all planets and stars in the Universe, is ensured by the influence of their ethereal vortices. The Earth's ethereal environment rotates in harmony with it and its atmosphere.

The rarefaction of the ethereal medium depends only on the distance to the center of the Earth and does not depend on the density of the earth's crust or mantle. Therefore, the indicators of the Earth’s gravitational force also depend not on the density of rocks, water or air, but only on the distance from the center of the planet we measure this force.

It is quite simple to prove this using data on the gravitational acceleration of physical bodies (gravitational acceleration) at various distances from the surface of the planet. For example, on the surface of the earth it will be equal to 9.806 m/sec 2, at an altitude of 5 km - 9.791 m/sec 2, at an altitude of 10 km - 9.775 m/sec 2, 100 km - 9.505 m/sec 2, 1000 km - 7.36 m/sec 2,

10,000 km - 1.5 m/s 2 , and at an altitude of 400,000 km - 0.002 m/s 2 .

These data indicate that with increasing distance from the center of the Earth, the density of the ethereal medium also increases, which leads to a decrease in the acceleration of gravity and the force of gravity of the Earth.

Closer to the center of the planet, the rarefaction of the ethereal environment increases. An increase in the rarefaction of the ethereal environment predetermines an increase in gravitational acceleration, and, consequently, the weight of the body. This confirms our understanding of the physical essence of gravity as such.

When any other physical body falls into the gravitational field of a planet, it finds itself in a position where the ethereal environment above the falling body is always denser than the ethereal environment below this body. Then, a denser ethereal environment will influence the body, moving it from a denser environment to a less dense one. The body seems to constantly lose support underneath itself and “falls” in space towards the ground.

It is known that the value of the acceleration of a free fall body at the equator is 9.75 m/s 2 , which is less than the value of this indicator at the Earth’s poles, which reaches 9.81 m/s 2 . Scientists explain this difference by the daily rotation of the Earth around its axis, the deviation of the Earth's shape from spherical and the heterogeneous distribution of the density of earth rocks. In fact, only the specific shape of the planet can be taken into account. Everything else, if it has an influence on the value of the acceleration of gravity at the equator and at the poles, is very, very insignificant.

However, our views on gravity and the reasons for its manifestation will be well confirmed if we imagine a classical sphere, the most distant points of which from the center of the Earth will be located at the equator. In this case, at the poles from the surface of this classical speculative sphere to the surface of the Earth, a distance of 21.3 km is formed. This is easily explained by the somewhat flattened shape of the planet. Therefore, the distance from the surface of the earth at the pole to the center of the Earth is less than the same distance at the equator. But then, in accordance with our views, the ethereal environment at the poles of the planet is more rarefied and, therefore, its gravitational field is more powerful, which leads to higher rates of acceleration of free fall.

This happens because the rarefied region of a more massive physical body initially captures the rarefied ethereal region of another physical body, and then brings the physical body itself, which has a smaller mass or a smaller amount of dense ether, closer to itself.

Due to the fact that it is impossible to relieve the tension of the ethereal environment by attracting new physical bodies into the gravitational field of a massive physical body, since in this case its mass will only increase, and, consequently, the gravitational field will only expand, this desire will last continuously, ensuring gravitational constancy of physical bodies. Therefore, a physical body, attracting other physical bodies to itself, will only increase its mass, and, consequently, its gravitational field.

In the etheric space of the Universe, this process will occur until the gravitational forces of one planet or star are balanced with the gravitational forces of other planets and stars, as well as with the core of its galaxy and the core of the Universe. In this case, all planets or stars will be in a tense but equilibrium state in relation to each other.

The gravitational forces between physical bodies begin to manifest themselves from the moment the gravitational fields of these bodies come into contact. Based on this, we can believe that gravity actually has long-range. At the same time, gravitational interaction begins to manifest itself almost instantly and, of course, without any participation of any gravitons or other unknown particles.

From all this it follows that It is not physical bodies that interact, but their gravitational fields interact, which, when deformed, attract physical bodies to each other. Excuse me, but this contradicts the provisions of the laws of the respected I. Newton, which postulate the force of attraction masses physical bodies and who have conscientiously served and are serving humanity for more than one century!

I wouldn't dramatize the situation so much. Our statements do not reject the laws of the highly respected scientist. They only reveal their physical essence, leaving the question of the manifestation of these laws absolutely untouched.

And this is exactly so. But according to I. Newton’s law, any physical body has its own gravitational field and interacts with other physical bodies in accordance with their masses and the distances between their centers. At the same time, I. Newton, first of all, had in mind the interaction of planets and stars. His scientific followers mechanically transferred the features of the interaction of planets and stars to the interaction of any physical bodies, based on the universality of the law of universal gravitation.

At the same time, they did not ignore the fact that on our planet, the Earth regularly attracts any physical bodies, but the physical bodies themselves do not really strive for each other. Except, of course, for magnets. Apparently, in order not to violate the scientific idyll and not to question the law of universal gravitation, scientists postulated that the masses of the physical bodies surrounding us on our planet on a universal scale are extremely small and therefore the force of gravity when they approach each other is very, very weak.

However, we can try to bring conscientiously polished physical bodies of any substance very close to each other, practically eliminating the presence of distance between them. It would seem that, in accordance with the law, the forces of gravity should break out and surprise us with their undivided presence and daring power. But this doesn't happen. The forces of gravity modestly and without much enthusiasm quietly observe our efforts from the most distant corner of each interacting physical body. What's the matter? How to get out of this sticky situation. After all, there is a law? Eat. Does it work? Valid. So everything is fine?!

No, it's not normal. If we adhere to this statement, then many objects located next to each other would “stick together” in an instant, filling our lives with such problems that humanity, without resisting for long, would have long ago ceased its nightmarish existence.

One can object and refer to the fact that these physical bodies are very small. That's why they don't attract. But this is not very convincing. Why? Because the huge Tibetan mountain range, even on an Earth scale, would have long since gathered on its harsh peaks all the planes flying past and would not have allowed tireless travelers and climbers, due to the powerful manifestation of their gravitational forces, to lift even the lightest equipment. And it is unlikely that anyone would suspect the harsh Tibet of insufficient size, density or mass.

What to do? Quite dubious coefficients again came to the aid of adherents of omnipotent formulas in the form of the “gravitational constant” - the not entirely convincing lady “G”, equal to approximately 6.67x10 -11 kg -1 m 3 sec -2. The presence of this constant in I. Newton's formula immediately turned the value of any force into practically nothing. Why this particular number? Simply because humanity simply cannot provide comparable indicators of the mass of any physical body on our planet. Therefore, judging by the value of this constant, the force of attraction of any physical bodies on Earth will be extremely small. And this will perfectly explain the lack of visible interaction of physical bodies on Earth.

Why 10 -11 kg -1? Yes, because the mass of the Earth, which certainly attracts all physical bodies without exception (it is not possible to hide this) is approximately 6x10 24 kg. Therefore, only for her 10 -11 kg -1 is easily overcome. Here is an original solution to the problem.(((

Unable to explain the essence of the problem, scientists, as often happens, introduced a certain constant value into the formula, which, without solving the problem, made it possible to give a physical process or natural phenomenon a certain pseudo-scientific clarity.

By the way, I. Newton seemed to have nothing to do with this. In his works when developing the law of universal gravitation, he never mentioned any gravitational constant. His contemporaries did not mention it either. The gravitational constant was first introduced into the law of universal gravitation only at the beginning of the 19th century by the French physicist, mathematician and mechanic S.D. Poisson. However, history has not recorded a single scientist who would take responsibility for both the method of its calculation and its generally accepted values.

The story refers to the English physicist Henry Cavendish, who in 1798 performed a unique experiment using a torsion balance. But it should be noted that G. Cavendish carried out his experiment only with the aim of determining the average density of the Earth and he never spoke or wrote about any gravitational constant. Moreover, I did not calculate any of its numerical values.

The numerical indicator of the gravitational constant was allegedly calculated much later on the basis of G. Cavendish’s calculations of the average density of the Earth, but who and when calculated it remained a mystery, as did what all this was needed for.

And, apparently, in order to completely confuse humanity and somehow get out of the forest of contradictions and inconsistencies, in the modern scientific world they were forced, under the guise of a transition to a unified metric system of measures, to accept different gravitational constants for different cosmic systems. So, when calculating the orbits of, for example, satellites relative to the Earth, a geocentric gravitational constant equal to GE = 3.98603x10 14 m 3 sec -2 multiplied by the mass of the Earth is used, and to calculate the orbits of celestial bodies relative to the Sun, another gravitational constant is used - heliocentric, equal to GSs = 1.32718x10 20 m 3 sec -2 times the mass of the Sun. It turns out interesting, the law is one and universal, but the constant coefficients are different! How can such a respected “constant” be so surprisingly non-constant?!!

So what should we do? Is the situation hopeless and therefore we must accept it? No. You just need to go back to the basics and define the concepts. The fact is that everything that exists on planet Earth came from it, belongs to it and will enter into it. Everything - mountains, seas and oceans, trees, houses, factories, cars, and you and me - all this was mined, nurtured, nurtured and nurtured on the Earth and created from the Earth. All these are just different virtual reality e variable combinations of a huge number of atoms and molecules that belong only to our planet.

The earth was created from particles and atoms and is a completely independent and almost completely closed system. During its formation, each particle and each atom, creating a single gravitational field of the planet, essentially “transferred” all their gravitational powers to it.

Therefore, there is a single gravitational field on Earth, which conscientiously stands guard over all available earthly resources, without releasing from the planet what was once brought to this planet. Therefore, all objects and everything that is on Earth are not independent gravitational substances and cannot decide whether or not to use their gravitational capabilities when communicating with other physical bodies. Therefore, physical bodies on Earth fall only down onto its surface, and not up, left or right, joining other massive bodies. Therefore, no physical body on Earth, from the point of view of gravity, can be called independent.

What about rockets? Can they be called independent physical bodies? While they are here on Earth, no, it’s impossible. But if they overcome the gravity of the Earth and go beyond the gravitational field of the planet, then yes, it is possible. Only in this case will they be able to become independent physical bodies in relation to the Earth, taking with them their individual part of the gravitational field. The Earth will decrease in size and mass by the size and mass of the rocket. Its gravitational field will also decrease proportionally. The gravitational relationship between the rocket and the Earth will, of course, be interrupted.

And what about the various meteorites that often visit our Earth? Are they independent physical bodies or not? As long as they are outside the gravitational field of the Earth, they are independent. But when they enter the gravitational field of the planet, they, having a less rarefied ethereal environment of their own, will interact with the more rarefied ethereal environment of the Earth.

However, the interaction of the gravitational fields of the Earth and the meteorite differs from the interaction of the gravitational fields of ethereal vortex clots that are almost equal in size to each other. This is due to the huge difference in the sizes of the gravitational fields of the Earth and the meteorite. The gravitational field of a meteorite, when interacting with the gravitational field of the Earth, is practically not deformed, but, remaining part of the meteorite, is absorbed by the gravitational field of the Earth.

The gravitational field of the meteorite seems to fall into the gravitational field of the Earth, since as it approaches the surface of the Earth, its rarefied ethereal environment becomes more and more rarefied. And the closer to the Earth, the more rarefied its rarefied environment becomes and the faster the meteorite moves towards the planet. The Earth seeks to replace its rarefied environment with an unexpected alien from outer space, creating the effect of a meteorite being attracted to its surface.

Having reached the surface of the Earth, the meteorite does not lose its gravitational field, and if it is transported into outer space, it will leave the Earth with its gravitational field. But on Earth he loses his independence of the physical body. Now it belongs to the Earth, its gravitational field is added to the gravitational field of the Earth, and the mass of the Earth increases by the mass of the meteorite.

Therefore, we are forced to state that, being on the planets, all physical bodies from a gravitational point of view cannot be independent physical bodies. Their gravitational capabilities are within the gravitational capabilities of the planets, which are the main generators of gravitational interaction.

Therefore, the law of universal gravitation is absolutely fair to the entire universal system and does not require any additional constants, even gravitational ones.

Assumption

Thus, gravitational field of a physical body- this is an unevenly tense rarefied etheric region, which is part of the physical body and arose as a result of the concentration of the rotating etheric medium in the physical body itself.

The gravitational field of any physical body, in order to achieve equilibrium with the surrounding elastic ethereal environment, tends to increase its density, attracting rarefied ethereal regions of other physical bodies. The interaction of the gravitational fields of physical bodies with each other creates the effect of attraction of physical bodies. This effect is the action of gravitational forces or gravitational interaction of independent physical bodies.

The rarefied ethereal space always strives to restore the initial homogeneous state of the ethereal environment due to the addition of the ethereal environment of other physical bodies. When a physical body or any other physical body appears in the etheric gravitational field, also possessing its own etheric gravitational field, but with less mass, the first physical body tends to “absorb” it and hold it with a force depending on the masses of these bodies and the distance between them .

Consequently, in the etheric gravitational field, when two or more physical bodies appear in it, a the process of their gravitational interactions, which directs them towards each other. Gravitational forces act only to bring some physical bodies or bodies closer to other bodies.

Once again I have to admit that all this is possible only under ideal conditions, when physical bodies are not influenced by the gravitational forces of the planet. On Earth, the gravitational fields of all physical bodies are only an integral part of the single gravitational field of the planet and cannot manifest themselves in relation to each other.

Therefore, on the planet, physical bodies do not have their own individual gravitational field and have gravitational interaction only with the Earth.

Raising the physical body to any height, we do some work and expend a certain amount of energy. Some believe that by lifting the body, we transfer to it energy equivalent to the energy expended in lifting it to a certain height. By falling, the physical body releases this energy.

But that's not true.

We do not transfer energy to it, but spend our energy to overcome the gravitational force of the Earth. Moreover, we seem to disrupt the usual course of events on Earth, changing the location of the physical body relative to the planet. The Earth rightly reacts to this disgrace that is inconsistent with it and strives to return any object to its surface, immediately turning on its gravitational forces.

The gravitational force acts on a raised body in the same way as when this body is on the Earth, but with increasing distance from the Earth’s surface its magnitude will be less than the initial gravitational force. True, it will not be so easy to notice it due to the insignificance of changes in the parameters of this force. If we raise this body to a height of 450 kilometers above the Earth, then the force of gravity will decrease significantly and the body will be in a state of weightlessness.

Here we meet gravity, i.e. With influence gravitational ethereal environment our planet onto the physical body. The raised body is in the gravitational etheric field of the planet, the vector of which is directed towards the center of the Earth. The closer the physical body is to the Earth, the effect gravitational interaction stronger. The farther, the less. Therefore, at long distances, gravitational interaction will also manifest itself, but not so clearly.

But, falling to the Earth, the physical body interacts with it in the same way as two bodies interact in space. The gravitational forces of the Earth act on the body, move it in space, returning it to the mortal earth.

What will happen if we influence the body for a long time, moving it further and further from the Earth, and finally take it outside the solar system? Does this mean that the gravitational interaction between them will disappear? If this is so, is there a possibility that the Earth will lose some of its gravitational capabilities?

Yes, that's exactly how it will happen. Part of the Earth's gravitational capabilities will leave it along with the physical body. The Earth will become smaller by the amount of the mass of this body. And if the mass of the Earth becomes smaller, then it is quite obvious that its gravitational power will proportionally change to a lesser extent, and its gravitational interaction with this physical body will disappear.

But if a meteorite falls on the surface of the Earth, its gravitational field will be “absorbed” by the gravitational field of the Earth, and it itself, having lost its independence, will become part of the Earth, proportionally increasing its gravitational capabilities.

Therefore, larger physical bodies, including planets and stars, have stronger gravity and attract smaller ones, absorbing them. By attracting smaller physical bodies to themselves, they increase their mass and, accordingly, increase their gravitational field. Gravitational interaction will arise between the bodies.

So, around any physical body on our planet there is its own gravitational field, but only conditionally. This gravitational field enters the single gravitational field of the Earth and rotates with it. This is due to the fact that any physical body, including all physical bodies created on Earth or flown from outer space, is already or is becoming belonging to our planet. Any physical body on Earth originated from it and into it and will return. Their gravitational field is part of the single gravitational field of the Earth, which rotates around the planet. Therefore, objects fall to the Earth rather than attaching to each other. They fall down rather than moving parallel to the ground. In addition, the gravitational capabilities of the Earth are incomparably more powerful than the gravitational capabilities of any physical body on the planet, no matter what its size, volume or density. Therefore, any physical body is attracted to the Earth, and not to Everest.

All physical bodies have a gravitational field, but it can only be considered in conjunction with the general gravitational field of the Earth. It is possible to separate it from the Earth’s gravitational field only at a distance beyond the boundaries of the planet’s gravitational field. At this distance, the gravitational field of a physical body, for example, a rocket, will be completely independent and will rotate around the physical body, no matter what its size.

It should be noted that the speed of rotation of the ethereal medium near the surface of a physical body is equal to the speed of rotation of the physical body itself. In relation to the physical body, the environment is motionless. Near a physical body, the force of gravity is much higher than at a distance from it. Let us recall our experience with a rubber circle (Fig. 2). As you move away from the physical body, both the rotation speed of the etheric medium and gravity decrease.

At the same time, we understand that the concentration of ether under the influence of etheric vortices and gravitational forces leads to the emergence of a rarefied etheric region around the physical body. This rarefied ethereal region is larger, the greater the amount of ether concentrated in the physical body in the form of a collection of fundamental ethereal particles - ethereal vortex clots, which respectively consist of energy fractions, photons, neutrinos, antineutrinos, positrons, electrons, protons, neutrons, atoms, molecules and other physical bodies. The rarefied ethereal region, for example, of the planet Earth is much larger in volume than the rarefied region of the Moon, since the Earth is much larger than the Moon. And each rarefied area corresponds to the amount of ether concentrated in the physical body.

The rarefied regions of the ethereal medium are extremely vast. They determine the dimensions gravitational fields physical bodies, i.e. those areas in which gravitational forces act. The actions of these forces begin from the outer boundaries of the rarefied region of the physical body. Since the boundaries of the rarefied region are located quite far from the center of the physical body, these forces can be characterized as long-range forces or long-range interaction.

When the rarefied regions of two or more physical bodies come into contact, each of them, in accordance with the law of balance of opposites, strives to balance its etheric rarefied environment, which leads to attraction and bringing together of the bodies.

Thus, it is not the masses of physical bodies that attract, but the gravitational fields of these physical bodies interact with each other, moving physical bodies towards each other.

Moreover, the closer the bodies are to each other, the more pronounced and intense this attraction is. Therefore, when, for example, bodies fall to the ground, there is a constant acceleration of this fall. This acceleration is called the acceleration of gravity and is approximately 9.806 m/s 2 .

The essence of this acceleration is that the closer the rarefied medium is to the body, the less dense it is and, therefore, the stronger the desire of the physical body to balance its rarefied ethereal environment, the more powerful the force of gravitational interaction. We already talked about this earlier. As one approaches the boundary of a rarefied medium with elastic ethereal space, this tension decreases and, finally, at the boundary it begins to fully correspond to the density of ethereal space. In this case, the gravitational interaction of the physical body completely loses its strength, and the gravitational field of this physical body disappears.

This explains the fact that from the beginning of its launch, a rocket spends a huge amount of energy to overcome the force of gravity of the Earth, but as it flies and moves away from the planet, it enters orbit and practically does not waste its energy.

Here it is necessary to understand that the density of the Earth’s atmosphere and the density of its gravitational field are different concepts. The density of the Earth's atmosphere has higher values at its surface than at altitude. For example, on the surface of the earth the density of the atmosphere is approximately 1.225 kg/m3, at an altitude of 2 kilometers - 1.007 kg/m3, and at an altitude of 3 km - 0.909 kg/m3 i.e. As altitude increases, the density of the atmosphere decreases.

But we assert that the gravitational field of any physical body is more rarefied precisely at its surface, and this rarefaction decreases with increasing distance from the physical body. Contradiction? Not at all. This is confirmation of our reasoning! The fact is that the rarefied ethereal gravitational field will strive to draw into its space everything that is possible to reduce its tension. Therefore, the Earth's gravitational field is filled with molecules of nitrogen, oxygen, hydrogen, etc. In addition, near the surface of the earth in the atmosphere there are not only gas molecules, but also particles of dust, water, ice crystals, sea salt, etc. The higher you are from the Earth’s surface, the less rarefied the gravitational field is, the fewer molecules and particles it can hold in the Earth’s atmosphere, and, accordingly, the lower the density of the planet’s atmosphere. Everything matches. Everything is correct.

To prove this statement, we cite the thoughts of Aristotle and the experiments of G. Galileo and I. Newton. The great Aristotle argued that heavier bodies fall to the ground faster than light bodies and gave the example of a stone and a bird's feather falling from the same height. Unlike Aristotle, G. Galileo suggested that the reason for the difference in the speed of falling objects was air resistance. Allegedly, he simultaneously dropped a rifle bullet and an artillery core from the Leaning Tower of Pisa, which also reached the ground almost simultaneously, despite the significant difference in weight.

To confirm the conclusions of G. Galileo, I. Newton pumped air out of a long glass tube and at the same time threw a bird feather and a gold coin on top. Both the feather and the coin fell to the bottom of the tube almost simultaneously. Subsequently, it was experimentally established that both in air and in vacuum there was an acceleration of the free fall of bodies to the ground.

However, scientists, having recorded the presence of acceleration of free fall of bodies to the ground, limited themselves to only deriving known mathematical dependencies that make it possible to quite accurately measure the magnitude of this acceleration. But the physical essence of this acceleration remained undisclosed.

I believe that the physical essence of this phenomenon lies in the presence of a rarefied ethereal environment around the Earth. The closer the body falling on it is from the surface of the Earth, the more rarefied the etheric environment of the planet is and the faster the body falls on its surface. This can be taken as a clear confirmation of our reasoning about the nature of gravitational fields and the mechanism of their interactions in the Universe.

Of course, our statement about the interaction of the gravitational fields of physical bodies, and not about the mutual influence of their masses, contradicts the views of the highly respected I. Newton and the modern scientific community. However, paying tribute to the great genius, we clearly recognize the fact that the formula he derived is quite indicative and quite rightly allows us to calculate the force of gravitational interaction between two physical bodies. It should also be recognized that the Newtonian formula describes the consequence of a phenomenon, but does not touch its physical essence at all.

Thus, we have determined that the constant desire of the rarefied etheric region of any physical body to move into an equilibrium state with the surrounding etheric environment, reducing its tense state, due to the attraction of other rarefied etheric regions of other physical bodies into the region of its etheric rarefaction constitute a common the physical meaning of gravity or gravitational interaction.

Any physical body has its own gravitational field, but it is not independent. Being on Earth, this gravitational field is combined into a single gravitational field of the planet. The gravitational field of any physical body can only be considered as part of the gravitational field of the planet.

The force of gravitational interaction between the two. Strong gravitational fields

Gravitational interaction

Strong gravitational fields

Gravitational radiation

Subtle effects of gravity

Quantum theory of gravity

Standard theories of gravity

Sources and notes

Literature

see also

Links

Assumption

Assumption