The forces of gravitational interaction between two homogeneous balls of mass. Gravitational interactions

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 mass, density and other characteristics physical body the gravitational field of some physical bodies is different from others. Larger physical bodies have stronger and more extensive gravitational field and are capable of attracting other, smaller physical bodies. The meaning of their strength mutual attraction to each other is determined by law universal gravity I. Newton - gravity. This applies to any physical body in the Universe.

So what is it physical meaning 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 gravitational interactions between planets and stars in the Universe, already having an idea of gravitational interaction particles, let's 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 V general view consists in the constant desire of the rarefied etheric 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, physical entity 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 density earth's crust or robes. Therefore, the indicators of the Earth’s gravitational force also do not depend on density 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 (acceleration free fall) 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 more dense 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/sec 2, which less than value this indicator at the Earth's poles, which reaches 9.81 m/sec 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 the classical sphere, the most distant points 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, consequently, its gravitational field is more powerful, which leads to more high rates on the acceleration of free fall.

This happens because the rarefied region of a more massive physical body initially captures the rarefied etheric 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 the scale of the Earth, would have long ago 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, pundits, as often happens, introduced a certain constant value into the formula, which, without solving the problem, made it possible to add physical process or natural phenomenon some 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. 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.

History refers to the English physicist Henry Cavendish, who in 1798 put unique experiment using torsion balances. But it should be noted that G. Cavendish performed his experiment only with the aim of determining medium density He never spoke or wrote about the Earth and 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 modern scientific world were forced under the guise of a transition to a single metric system measures to take different gravitational constants for different space systems. So, when calculating the orbits of, for example, satellites relative to the Earth, the geocentric gravitational constant is used equal to GE = 3.98603x10 14 m 3 sec -2 multiplied by the mass of the Earth, and to calculate the orbits celestial bodies relative to the Sun, another gravitational constant is used - heliocentric, equal to GSs = 1.32718x10 20 m 3 sec -2 multiplied by the mass of the Sun. It turns out interesting, the law is one and universal, but constant odds- different! How can such a respected “permanent” be so surprisingly non-permanent?!!

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 point is that everything that exists on planet Earth came from it, belongs to it and will enter 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, on Earth there is a single gravitational field, which conscientiously stands guard over all available earth 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 others 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 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 even if it is transported to 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 in 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 integral part a 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 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 on overcoming the gravitational force of the Earth. Moreover, we seem to be violating usual course 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 on 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 long time, moving further and further from the Earth, and finally take it beyond 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 on the surface of the Earth a meteorite will fall, then his gravitational field will be “absorbed” by the gravitational field of the Earth, and he himself, having lost his 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 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 more more ether is concentrated in the physical body in the form of a set of fundamental ethereal particles - ethereal vortex clots, from which energy fractions, photons, neutrinos, antineutrinos, positrons, electrons, protons, neutrons, atoms, molecules and other physical bodies are respectively composed. 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 significantly bigger 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.

At the same time, than closer to the body are close to each other, the more pronounced and intense this attraction is. Therefore, when, for example, bodies fall to the ground, constant acceleration 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 more stronger desire physical body to balance its rarefied etheric environment, thereby more powerful force 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 the rocket spends huge amount energy to overcome the gravitational force 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 is more than high values near 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 argue 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 and so on. 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.

1. Introduction

All weighty bodies mutually experience gravity; this force determines the movement of planets around the sun and satellites around the planets. The theory of gravity - a theory created by Newton, stood at the cradle modern science. Another theory of gravity, developed by Einstein, is the greatest achievement of theoretical physics of the 20th century. Over the centuries of human development, people have observed the phenomenon of mutual attraction of bodies and measured its magnitude; they tried to put this phenomenon at their service, to surpass its influence, and finally, already at the very lately calculate it with extreme accuracy during the first steps deep into the Universe.

The immense complexity of the bodies around us is due primarily to such a multi-stage structure, the final elements of which - elementary particles - have relatively little a large number types of interaction. But these types of interactions differ sharply in their strength. The particles that form atomic nuclei are bound together by the most powerful forces known to us; In order to separate these particles from each other, it is necessary to expend a colossal amount of energy. The electrons in an atom are bound to the nucleus by electromagnetic forces; it is enough to give them a very modest energy (usually enough energy chemical reaction) as electrons are already separated from the nucleus. If we talk about elementary particles and atoms, then for them the weakest interaction is gravitational interaction.

When compared with the interaction of elementary particles, gravitational forces are so weak that it is difficult to imagine. Nevertheless, they and only they completely regulate the movement of celestial bodies. This happens because gravity combines two features, due to which its effect intensifies when we move to large bodies. Unlike atomic interaction, the forces of gravitational attraction are noticeable even at great distances from the bodies that create them. In addition, gravitational forces are always attractive forces, that is, bodies are always attracted to each other.

The development of the theory of gravity occurred at the very beginning of the development of modern science using the example of the interaction of celestial bodies. The task was made easier by the fact that celestial bodies move in the vacuum of world space without the side influence of other forces. Brilliant astronomers - Galileo and Kepler - with their works prepared the ground for further discoveries in this area. In the future the great Newton managed to come up with a complete theory and give it a mathematical form.

2. Newton and his predecessors

Among all the forces that exist in nature, the force of gravity is distinguished primarily by the fact that it manifests itself everywhere. All bodies have mass, which is defined as the ratio of the force applied to the body to the acceleration that the body acquires under the influence of this force. The force of attraction acting between any two bodies depends on the masses of both bodies; it is proportional to the product of the masses of the bodies under consideration. In addition, the force of gravity is characterized by the fact that it obeys the law of inverse proportionality to the square of the distance. Other forces may depend on distance quite differently; Many such forces are known.

One aspect of universal gravity—the surprising dual role played by mass—served as the cornerstone for the construction of the general theory of relativity. According to Newton's second law, mass is a characteristic of any body, which shows how the body will behave when a force is applied to it, regardless of whether it is gravity or some other force. Since all bodies, according to Newton, accelerate (change their speed) in response to an external force, the mass of a body determines what acceleration the body experiences when a given force is applied to it. If the same force is applied to a bicycle and a car, each will reach a certain speed at a different time.

But in relation to gravity, mass also plays another role, completely different from the one it played as the ratio of force to acceleration: mass is the source of mutual attraction of bodies; If we take two bodies and look at the force with which they act on a third body located at the same distance, first from one and then from the other body, we will find that the ratio of these forces is equal to the ratio of the first two masses. In fact, it turns out that this force is proportional to the mass of the source. Similarly, according to Newton's third law, the forces of attraction experienced by two different bodies and under the influence of the same source of attraction (at the same distance from it), are proportional to the ratio of the masses of these bodies. In engineering and everyday life, the force with which a body is attracted to the ground is referred to as the weight of the body.

So, mass enters into the connection that exists between force and acceleration; on the other hand, mass determines the magnitude of the force of attraction. This dual role of mass leads to the fact that the acceleration of different bodies in the same gravitational field turns out to be the same. Indeed, let us take two different bodies with masses m and M, respectively. Let them both fall freely to Earth. The ratio of the forces of attraction experienced by these bodies is equal to the ratio of the masses of these bodies m/M. However, the acceleration acquired by them turns out to be the same. Thus, the acceleration acquired by bodies in a gravitational field turns out to be the same for all bodies in the same gravitational field and does not depend at all on the specific properties of the falling bodies. This acceleration depends only on the masses of the bodies creating the gravitational field and on the location of these bodies in space. The dual role of mass and the resulting equality of acceleration of all bodies in the same gravitational field is known as the principle of equivalence. This name has historical origin, emphasizing the fact that the effects of gravity and inertia are to a certain extent equivalent.

On the Earth's surface, the acceleration due to gravity is, roughly speaking, 10 m/sec2. The speed of a freely falling body, if you do not take into account air resistance during the fall, increases by 10 m/sec. Every second. For example, if a body begins to freely fall from rest, then by the end of the third second its speed will be 30 m/sec. Typically, the acceleration due to gravity is denoted by the letter g. Due to the fact that the shape of the Earth does not strictly coincide with a sphere, the value of g on Earth is not the same everywhere; it is greater at the poles than at the equator, and less on the tops of large mountains than in the valleys. If the value of g is determined with sufficient accuracy, then it is affected even geological structure. This explains the fact that geological methods for searching for oil and other minerals also include an accurate determination of the value of g.

What's in this place all bodies experience the same acceleration - a characteristic feature of gravity; No other forces possess such properties. And although Newton had no choice but to describe this fact, he understood the universality and unity of the acceleration of gravity. The German physicist and theorist Albert Einstein (1870 - 1955) had the honor of discovering the principle on the basis of which this property of gravity, the principle of equivalence, could be explained. Einstein also belongs to the foundations of the modern understanding of the nature of space and time.

3. Special theory of relativity

Since the time of Newton, it was believed that all reference systems are a set of rigid rods or some other objects that make it possible to establish the position of bodies in space. Of course, in each reference system such bodies were chosen differently. At the same time, it was assumed that all observers had the same time. This assumption seemed intuitively so obvious that it was not specifically stated. In everyday practice on Earth, this assumption is confirmed by all our experience.

But Einstein was able to show that comparisons of clock readings, if we take them into account relative motion, does not require special attention only in the case when the relative speeds of the clocks are significantly less than the speed of light in a vacuum. So, the first result of Einstein's analysis was the establishment of the relativity of simultaneity: two events occurring at a sufficient distance from each other can appear simultaneous for one observer, but for an observer moving relative to him, occurring at different times. Therefore, the assumption of a universal time cannot be justified: it is impossible to specify a specific procedure that allows any observer to establish such a universal time, regardless of the movement in which he participates. The reference system must also contain a clock, moving with the observer and synchronized with the observer's clock.

The next step taken by Einstein was to establish new relationships between the results of measurements of distance and time in two different inertial systems ah countdown. The special theory of relativity, instead of “absolute lengths” and “absolute time”, brought to light a different “absolute value”, which is usually called the invariant space-time interval. For two given events occurring at some distance from each other, the spatial distance between them is not an absolute (i.e., independent of the reference system) value, even in the Newtonian scheme, if there is a certain time interval between the occurrence of these events. Indeed, if two events do not occur simultaneously, an observer moving with a certain frame of reference in one direction and finding himself at the point where the first event occurred can, during the period of time separating these two events, end up at the place where the second event occurs; for this observer both events will occur in the same place in space, although for an observer moving in opposite direction, they may seem to occur at a considerable distance from each other.

4. Relativity and gravity

The deeper they go scientific research into the final constituent substances and the smaller the number of particles and forces acting between them remains, the more insistent the demands for a comprehensive understanding of the action and structure of each component of matter become. It is for this reason that when Einstein and other physicists became convinced that the special theory of relativity had replaced Newtonian physics, they began again fundamental properties particles and force fields. Most important object, requiring revision was gravity.

But why shouldn't the discrepancy between the relativity of time and Newton's law of gravitation be resolved as simply as in electrodynamics? It would be necessary to introduce the concept of a gravitational field, which would propagate in approximately the same way as electric and magnetic field, and which would turn out to be a mediator in the gravitational interaction of bodies, in accordance with the concepts of the theory of relativity. This gravitational interaction would be reduced to Newton's law of gravitation, when the relative speeds of the bodies in question would be small compared to the speed of light. Einstein tried to build a relativistic theory of gravity on this basis, but one circumstance did not allow him to carry out this intention: no one knew anything about the propagation of gravitational interaction with high speed, there was only some information regarding the effects associated with high speeds of movement of the sources of the gravitational field - the masses.

The effect of high speeds on masses is different from the effect of high speeds on charges. If the electric charge of a body remains the same for all observers, the mass of the bodies depends on their speed relative to the observer. The higher the speed, the greater the observed mass. For a given body, the smallest mass will be determined by the observer relative to whom the body is at rest. This mass value is called the rest mass of the body. For all other observers, the mass will be greater than the rest mass by an amount equal to the kinetic energy of the body divided by c. The value of the mass would become infinite in the frame of reference in which the speed of the body would become equal speed Sveta. One can speak only conditionally about such a reference system. Since the magnitude of the gravitational source depends so significantly on the frame of reference in which its value is determined, the field generated by the mass must be more complex than the electromagnetic field. Einstein therefore concluded that the gravitational field appears to be a so-called tensor field, described by a larger number of components than the electromagnetic field.

As a further starting principle, Einstein postulated that the laws of the gravitational field should be derived from a mathematical procedure similar to the procedure leading to the laws of electromagnetic theory; the laws of the gravitational field obtained in this way must obviously be similar in form to the laws of electromagnetism. But even taking all these considerations into account, Einstein found that he could construct several different theories that satisfied all the requirements equally. A different point of view was needed to unambiguously arrive at the relativistic theory of gravity. Einstein found one new point view of the principle of equivalence, according to which the acceleration acquired by a body in the field of gravitational forces does not depend on the characteristics of this body.

5. Relativity of free fall

IN special theory relativity, as in Newtonian physics, postulates the existence of inertial reference systems, i.e. systems relative to which bodies move without acceleration when they are not acted upon external forces. The experimental discovery of such a system depends on whether we can place test bodies in conditions where no external forces act on them, and there must be experimental confirmation of the absence of such forces. But if the presence, for example, of an electric (or any other force) field can be detected by the difference in the effect that these fields have on various test particles, then all test particles placed in the same gravitational field acquire the same acceleration.

However, even in the presence of a gravitational field, there is a certain class of reference systems that can be identified by purely local experiments. Since all gravitational accelerations at a given point ( small area) all bodies are identical both in magnitude and direction, they will all be equal to zero in relation to the reference frame, which is accelerated along with other physical objects that are under the influence only of gravity. Such a frame of reference is called a freely falling frame of reference. Such a system cannot be extended indefinitely to all space and all moments of time. It can be uniquely determined only in the vicinity of a world point, in a limited region of space and for a limited period of time. In this sense, freely falling reference frames can be called local reference frames. In relation to freely falling reference frames, material bodies that are not acted upon by any forces other than gravitational forces do not experience acceleration.

Freely falling reference frames in the absence of gravitational fields are identical to inertial reference frames; in this case they are indefinitely extendable. But such unlimited distribution of systems becomes impossible when gravitational fields appear. The fact that freely falling systems generally exist, even if only as local frames of reference, is a direct consequence of the principle of equivalence, to which all gravitational effects are subject. But the same principle is responsible for the fact that it is impossible to construct inertial frames of reference in the presence of gravitational fields by any local procedures.

Einstein considered the equivalence principle to be the most fundamental property of gravity. He realized that the idea of ​​infinitely extendable inertial frames of reference should be abandoned in favor of local freely falling frames of reference; and only by doing so can the principle of equivalence be accepted as a fundamental part of the foundation of physics. This approach has enabled physicists to look deeper into the nature of gravity. The presence of gravitational fields turns out to be equivalent to the impossibility of propagation in space and time of a local freely falling reference frame; Thus, when studying gravitational fields, attention should be focused not so much on the local field magnitude as on the inhomogeneity of gravitational fields. The value of this approach, which ultimately denies the universality of the existence of inertial reference frames, is that it makes clear that there is no reason to accept without reflection the possibility of constructing inertial reference frames, despite the fact that such frames have been used for several centuries.

6. Gravity in time and space

In Newton's theory of gravity, the gravitational acceleration caused by a given large mass is proportional to that mass and inversely proportional to the square of the distance from that mass. The same law can be formulated a little differently, but at the same time we will be able to reach the relativistic law of gravity. This different formulation is based on the idea of ​​the gravitational field as something that is imprinted in the vicinity of a large gravitating mass. The field can be completely described by specifying at each point in space a vector whose magnitude and direction correspond to that gravitational acceleration. Which is acquired by any test body placed at this point. It is possible to describe the gravitational field graphically by drawing curves in it, the tangent to which at each point in space coincides with the direction of the local gravitational field (acceleration); these curves are drawn with density ( certain number curves per unit area cross section, rice. 2) , equal to the value local field. If one large mass is considered, such curves - they are called lines of force - turn out to be straight lines; these straight lines point directly to the body creating the gravitational field.

Back proportional dependence from the square of the distance is expressed graphically as follows: all lines of force begin at infinity and end at large masses. If the density of field lines is equal to the magnitude of the acceleration, the number of lines passing through spherical surface, the center of which is located on a large mass, is exactly equal to the density of field lines multiplied by the area of ​​a spherical surface of radius r; The area of ​​a spherical surface is proportional to the square of its radius. IN general case Newton's law of inverse dependence on the square of the distance can be given in a form that is equally suitable for the source of gravity in the form of one large mass and for random distribution masses: all lines of force of the gravitational field begin at infinity and end at the masses themselves. The total number of lines of force terminating in some region containing masses is proportional to the total mass contained in this region. In addition, the gravitational field is a conservative field: lines of force cannot take the form of closed curves, and moving a test body along a closed curve cannot lead to either gain or loss of energy.

In the relativistic theory of gravity, the role of sources is assigned to combinations of mass and momentum (momentum acts as a link between the state of the same object in different four-dimensional or Lorentzian reference systems). The inhomogeneities of the relativistic gravitational field are described by the curvature tensor. A tensor is a mathematical object obtained by generalizing the idea of ​​vectors. In a manifold described by coordinates, tensors can be associated with components that completely define the tensor. The relativistic theory connects the curvature tensor with the tensor that describes the behavior of gravitational sources. These tensors are proportional to each other. The proportionality coefficient is determined from the requirement: the law of gravitation in tensor form must be reduced to the Newtonian law of gravitation for weak gravitational fields and at low velocities of bodies; this coefficient of proportionality, up to world constants, is equal to Newton's constant of gravity. With this step, Einstein completed the construction of the theory of gravity, otherwise called the general theory of relativity.

7. Conclusion

The general theory of relativity made it possible to take a slightly different look at issues related to gravitational interactions. It included all Newtonian mechanics only as special case at low speeds of bodies. This opened up a very wide area for exploring the Universe, where gravitational forces play a decisive role.

LITERATURE:

P. BERGMAN “THE MYSTERY OF GRAVITY” LOGUNOV “RELATIVISTIC THEORY OF GRAVITY”

VLADIMIROV “SPACE, TIME, GRAVITY”

GRAVITATIONAL INTERACTION of elementary particles, the weakest of all known fundamental interactions, characterized by the participation of a gravitational field (gravitational field). By modern ideas, any interaction of particles is carried out through the exchange between them of virtual (or real) particles - carriers of interaction. In electromagnetic, weak and strong interactions carriers are photons, intermediate vector bosons and gluons, respectively. For gravitational interaction, the question of carriers is not simple, and the theory of gravitational interaction itself takes special place in the physical picture of the world.

According to Newton's law of universal gravitation, the force of interaction between two point masses (whose sizes are small compared to the distance r between them)

F g =Gm 1 m 2 /r 2 , (1)

where m 2 is the mass of particles, G = 6.67·10 -11 m 3 /kg?s 2 is the gravitational constant. The force of gravitational interaction between two protons is 10 36 times less Coulomb force electrostatic interaction between them. This ratio does not change when taking into account relativistic effects up to distances equal to the Compton wavelength of the proton. The quantity √Gm can be called “gravitational charge”. With this definition of “charge”, formula (1) coincides with Coulomb’s law for the interaction of electric charges. The gravitational charge is proportional to the mass of the body, therefore, according to Newton’s second law (F = ma), the acceleration a caused by force (1) does not depend on the mass of the accelerated body. This fact, verified with great accuracy, is called the equivalence principle. In the relativistic theory of gravitational interaction, due to the relationship between mass and energy (E = mс 2), the gravitational charge is proportional to the energy, that is, the total mass m, and not the rest mass, as in formula (1). This determines the universality of gravitational interaction. There is no type of matter that has zero gravitational charge. It is this property of gravitational interaction that distinguishes it from other fundamental interactions of elementary particles. In addition, at high particle energies, gravitational interaction can no longer be considered weak. At energy >10 18 GeV, the gravitational charge of the particle √GE/c 2 becomes equal to its electric charge e, and at very high energies gravitational interaction may become the main one.

The most important property of the gravitational field is that it determines the geometry of space-time in which matter moves. The geometry of the world cannot be specified initially and changes with the movement of matter creating a gravitational field (see Gravity). A. Einstein made the following conclusion from the property of the universality of gravitational interaction and built a relativistic theory of gravity - general theory relativity (GTR). Experiments confirm the validity of general relativity in the case of weak gravitational fields (when the gravitational potential is absolute value much less with 2). For strong fields, general relativity has not yet been tested, so other theories of gravitational interaction are also possible.

General relativity arose as a generalization of the special theory of relativity. Other theories of gravity arise as a reflection of the successes of particle physics - theoretical and experimental. For example, the Einstein-Cartan-Troutman theory of gravity (the so-called gravity with torsion, Einstein, A. Cartan, A. Trautman, 1922-72) expands the equivalence principle in the sense that the gravitational field in it interacts not only with energy (the energy tensor -momentum) of particles, but also with their spin.

In the so-called f-g theory of gravity by K. J. Isham, A. Salam and J. Strazdi (1973), the existence of two gravitational fields is assumed: the carriers of one of them are massless particles with spin 2 (ordinary, “weak” gravity of general relativity), this field interacts with leptons; the other field is carried by massive particles (f-mesons) with spin 2 (“strong” gravity) and interacts with hadrons.

The Brans-Dicke-Jordan scalar-tensor theory of gravity (K. Brans, R. Dicke, P. Jordan, 1959-61) was a development of P. Dirac's idea about the change in fundamental physical constants and interaction constants over time.

A.D. Sakharov put forward (1967) the idea of ​​gravity as an induced interaction, by analogy with the van der Waals forces, which have electromagnetic nature. In this theory, gravitational interaction is not a fundamental interaction, but the result of quantum fluctuations of all other fields. Success quantum theory fields (QFT) made it possible to calculate the induced gravitational constant G, which in this case is expressed through the parameters of these quantum fields.

Theory of gravity - classical theory, the quantum theory of gravity has not yet been created. The need for quantization is caused by the fact that elementary particles are objects quantum nature, and therefore the connection of classical interaction and quantized sources of this interaction seems inconsistent.

The creation of a quantum theory of gravity faces big challenges math difficulties, arising due to the nonlinearity of the zero equations. There are several methods for quantizing such complex mathematical objects; these methods are being developed and improved (see Quantum theory of gravity). As in quantum electrodynamics(QED), divergences appear during calculations, however, unlike QED, the quantum theory of gravity turns out to be non-renormalizable. There is an analogy here with the theory weak interaction, which also, taken separately, without connection with other interactions, is non-renormalizable. But the unification of weak and electromagnetic interactions (based on the idea of ​​so-called spontaneous symmetry breaking) made it possible to construct a unified renormalizable theory of electroweak interaction. In this regard high hopes are assigned to supergravity - a theory that combines all interactions based on supersymmetry and in which, in addition to gravitons (massless particles with spin 2, bosons), there are other carriers of gravitational interaction - fermions, called gravitinos.

Interest in creating a quantum theory of gravity is not purely academic. The connection of gravitational interaction with all types of matter and with space-time diversity will inevitably lead in the future quantum theory to the quantization of space-time and to a change in our views not only on space and time at ultra-short distances and time intervals, but also on the concept of “particle”, on the measurement procedure in the microcosm, as well as on changes in the structure modern theory elementary particles.

Some outlines of these changes are already visible. This is, first of all, the problem of divergences in QFT. The divergence, for example, of the self-energy of an electrically charged particle appears already in classical electrodynamics. The total mass M of a classical charged thin sphere having a charge e and size r 0 is equal to

M = M 0 + e 2 /2r 0 s 2, (2)

where M 0 is the seed mass. As r 0 → 0, the mass M becomes infinite. This divergence is not eliminated in quantum theory either; it only becomes weaker - logarithmic. If we take into account gravitational interaction and the fact that it depends on total weight M, the divergence of self-energy disappears already in the classical theory.

The issue of divergences can be approached from a different angle. Interaction in QFT is the exchange of virtual particles of arbitrarily high energies. Therefore, when integrating over these energies, divergent expressions are obtained. In general relativity, particles cannot be pointlike. Their minimum size is determined by the gravitational radius r g . How more mass(energy), the larger the gravitational radius:

If a body of mass M is compressed to sizes smaller than rg, then it turns into black hole size r g . In quantum theory there is also a limit to the localization of a particle - its Compton wavelength l С = ћ/М с, which, obviously, cannot be less gravitational radius. Therefore, there is hope that in a theory that takes into account gravitational interaction, intermediate states with arbitrarily high energies will not arise and, therefore, the divergences will disappear. Maximum weight(energy) of particles corresponds to the equality l C = r g, and is equal to МР | =√ћc/G ≈ 10 -5 g. This value is called the Planck mass, and it corresponds to the Planck length l Р| = √ћG/c 3 ≈ 10 -33 cm.

M.A. Markov suggested (1965) that elementary particles of mass M P| and that these particles have the maximum possible mass for an elementary particle. He called these particles maximons. Markov called charged maximons with mass M = e/√G ≈ 10 -6 g friedmons. Freedmons and maximons have a number of unusual properties. Thus, the geometry inside these particles can differ significantly from the geometry outside, and one can imagine such friedmons and maximons, inside of which there are entire universes. It is quite possible that quantum formations similar to maximons and friedmons determined early stages evolution of the Universe and set the initial vacuum of a single interaction, which, during the expansion of the Universe, was divided, for example, through the mechanism of spontaneous symmetry breaking, into four interactions, currently known. The direction of development of elementary particle physics does not exclude, but rather assumes such a possibility.

Not only quantum gravity can have a significant impact on the theory of other interactions, and undoubtedly the opposite effect. Studies of QFT in curved space-time, studies of the evaporation of black holes and the birth of particles in cosmology show that QFT leads to a modification of Einstein's equations. In modern unified theories of interaction of elementary particles, the vacuum energy density can be non-zero and, therefore, have its own gravitational field. The dominance of this energy density leads to an acceleration of expansion modern universe. Finally, in models of multidimensional gravity, processes of non-gravitational interactions occur on a 4-dimensional brane (subspace) in multidimensional space-time. At energies that bring the particle to the brane boundary, a violation of Lorentz invariance can be observed, and the gravitational interaction ceases to be weak.

All this indicates that the creation of a quantum theory of gravitational interaction is impossible without taking into account other fundamental interactions and, conversely, the theory of other interactions will not be complete and free from internal contradictions without taking into account gravitational interaction. It may be possible to achieve such a unification of gravitational interaction with other interactions within the framework of the intensively developing string theory. The study of such unification is facilitated by the methods of cosmomicrophysics, which studies fundamental relationship micro and macro world in combination of its physical, cosmological and astrophysical manifestations.

Lit.: Markov M. A. On the nature of matter. M., 1976; Mizner Ch., Thorne K., Wheeler J. Gravitation. M., 1977. T. 1-3; A. Einstein and the theory of gravity. M., 1979; Grib A. A., Mamaev S. G., Mostepanenko V. M. Quantum effects in intense external fields. M., 1980; Rubakov V. A. Large and endless additional dimensions// Advances in physical sciences. 2001. T. 171. Issue. 9; Landau L. D., Lifshits E. M. Field theory. 8th ed. M., 2003; Khlopov M. Yu. Fundamentals of cosmomicrophysics. M., 2004.

V. A. Berezin, M. Yu. Khlopov.

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 the general principles of classical physics.

1. What is known about gravitational forces

1.1. It is known that the force arising between bodies in gravitational interaction is 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):

Where G" 6.6720H 10 -11 LF m 2H kg -2 - gravitational constant, m, M- masses of interacting bodies and r - shortest distance between the centers of mass of interacting bodies. Assuming that the body has mass M at a 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 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 speed of the body 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 their interaction: with “contact” interaction of bodies, mechanical forces arise, and with 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. We will not consider the rotation of a body around its own axis passing through its center of mass for now. From the general principles of mechanics it is known that force arises when the instantaneous momentum of a body changes. Let us proceed in a similar way as when 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).

Taking into account possible changes in the radial vector, in accordance with equation (7), formula (6) takes the form:

Rice. 1. Relative position of the 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.

Strength F A occurs during rectilinear accelerated motion of a body or during gravitational static interaction of a body with another body. Strength 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. Strength 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. Strength F ω2 is always directed radially. Given equality ¶ r 1 /¶ t=ω· r 1^ , and the direction of the resulting vector in the vector product, we obtain that when each point of the body rotates with angular velocity ω a force acts on her F ω2 = m·ω 2 · r , which coincides with the centrifugal force in formula (3).

Strength F ω3 is the inertial force 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 of gravitational force of inertia of rotational motion

(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:

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:

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 its 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:

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 point of the body that does not coincide with the center of symmetry (center of mass), the vector identity is satisfied:

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 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