In nature, there are various forces that characterize the interaction of bodies. Consider the forces that are encountered in mechanics.

Gravitational forces. Probably the very first force, the existence of which a person realized, was the force of gravity acting on bodies from the side of the Earth.

And it took many centuries for people to understand that the force of gravity acts between any bodies. And it took many centuries for people to understand that the force of gravity acts between any bodies. The first to understand this fact was the English physicist Newton. Analyzing the laws governing the motion of the planets (Kepler's laws), he came to the conclusion that the observed laws of motion of the planets can be fulfilled only if an attraction force acts between them, which is directly proportional to their masses and inversely proportional to the square of the distance between them.

Newton formulated the law of gravitation. Any two bodies are attracted to each other. The force of attraction between point bodies is directed along a straight line connecting them, is directly proportional to the masses of both and is inversely proportional to the square of the distance between them:

In this case, point bodies are understood as bodies whose dimensions are many times smaller than the distance between them.

The forces of gravity are called gravitational forces. The proportionality coefficient G is called the gravitational constant. Its value was determined experimentally: G = 6.7 10¯¹¹ N m² / kg².

Gravity acting near the surface of the Earth, is directed to its center and is calculated by the formula:

where g is the acceleration free fall(g = 9.8 m / s²).

The role of the force of gravity in living nature is very significant, since the size, shape and proportions of living beings largely depend on its magnitude.

Body weight. Consider what happens when a certain weight is placed on a horizontal plane (support). At the first moment after the load is lowered, it begins to move downward under the influence of gravity (Fig. 8).

The plane bends and an upward elastic force (reaction of the support) arises. After the force of elasticity (Fу) balances the force of gravity, the lowering of the body and the deflection of the support will stop.

The deflection of the support arose under the action of the body, therefore, from the side of the body, a certain force (P) acts on the support, which is called the weight of the body (Fig. 8, b). According to Newton's third law, the weight of a body is equal in magnitude to the reaction force of the support and is directed in the opposite direction.

Р = - Fу = Ftyazh.

Body weight called the force P with which the body acts on a horizontal support fixed relative to it.

Since the force of gravity (weight) is applied to the support, it deforms and, due to its elasticity, opposes the force of gravity. The forces developed in this case from the side of the support are called the reaction forces of the support, and the very phenomenon of the development of reaction is called the reaction of the support. According to Newton's third law, the reaction force of the support is equal in magnitude to the gravity of the body and is opposite to it in direction.

If a person on a support moves with the acceleration of the links of his body directed away from the support, then the reaction force of the support increases by the value ma, where m is the person's mass, and are the accelerations with which the links of his body move. These dynamic effects can be recorded using strain gauge devices (dynamogram).

Weight should not be confused with body mass. The mass of a body characterizes its inert properties and does not depend on either the force of gravity or the acceleration with which it moves.

The weight of a body characterizes the force with which it acts on the support and depends both on the force of gravity and on the acceleration of movement.

For example, on the Moon, the body weight is about 6 times less than the body weight on Earth, while the mass in both cases is the same and is determined by the amount of matter in the body.

In everyday life, technology, sports, weight is often indicated not in newtons (N), but in kilograms of force (kgf). The transition from one unit to another is carried out according to the formula: 1 kgf = 9.8 N.

When the support and the body are motionless, then the mass of the body is equal to the gravity of this body. When the support and the body move with some acceleration, then, depending on its direction, the body can experience either weightlessness or overload. When the acceleration coincides in direction and is equal to the acceleration of gravity, the body weight will be zero, so a state of weightlessness occurs (ISS, high-speed elevator when going down). When the acceleration of the support movement is opposite to the acceleration of free fall, the person experiences an overload (start from the surface of the Earth of a manned spaceship, High-speed elevator going up).

Not only the most mysterious of forces of nature but also the most powerful.

Man on the path of progress

Historically, it turned out that human as it moves forward along paths of progress seized more and more powerful forces of nature. He started when he had nothing but a stick in his fist and his own physical strength. But he was wise, and he attracted the physical strength of animals to his service, making them domestic. The horse accelerated his run, the camel made passable the desert, the elephant made the swampy jungle. But the physical strength of even the most powerful animals is immeasurably small in front of the forces of nature. The first man subdued the element of fire, but only in its most weakened versions. At first - for many centuries - he used only wood as a fuel - a very low-energy-consuming type of fuel. A little later this source of energy he learned to use the energy of the wind, a man raised the white wing of a sail into the air - and a light ship flew like a bird over the waves. Sailboat on the waves. He exposed the blades of a windmill to the gusts of wind - and the heavy stones of the millstones were turning, the pestles of the grinders clattered. But it is clear to everyone that the energy of air jets is far from being concentrated. In addition, both the sail and the windmill were afraid of the blows of the wind: the storm tore sails and sank ships, the storm broke its wings and overturned the mills. Later still, man began to conquer the flowing water. The wheel is not only the most primitive of devices capable of converting the energy of water into rotary motion, but also the least powerful in comparison with various. Man walked all the way forward along the ladder of progress and needed more and more energy. He began to use new types of fuel - already switching to combustion coal raised the energy consumption of a kilogram of fuel from 2500 kcal to 7000 kcal - almost three times. Then came the time for oil and gas. The energy content of each kilogram of fossil fuels has again increased by one and a half to two times. Steam engines were replaced by steam turbines; the mill wheels were replaced by hydraulic turbines. Then the man stretched out his hand to the fissile uranium atom. However, the first use of a new type of energy had tragic consequences - the nuclear flame of Hiroshima in 1945 incinerated 70 thousand human hearts in a matter of minutes. In 1954, the world's first Soviet nuclear power plant went into operation, transforming the power of uranium into a radiant power of electric current. And it should be noted that a kilogram of uranium contains two million times more energy than a kilogram of the best oil. It was a fundamentally new fire that could be called physical, for it was physicists who studied the processes leading to the birth of such fabulous amounts of energy. Uranium is not the only nuclear fuel. A more powerful type of fuel is already being used - isotopes of hydrogen. Unfortunately, man has not yet been able to subdue the hydrogen-helium nuclear flame. He knows how to light his all-burning fire for a moment, igniting the reaction in the hydrogen bomb with the flash of a uranium explosion. But closer and closer, scientists see the hydrogen reactor, which will give birth electricity as a result of the fusion of nuclei of hydrogen isotopes into helium nuclei. Again, the amount of energy that a person can take from each kilogram of fuel will increase almost tenfold. But will this step be the last in the coming history of the power of mankind over the forces of nature? No! Ahead - mastery gravitational view energy. It is even more calculatedly packed by nature than even the energy of hydrogen-helium fusion. Today it is the most concentrated form of energy that a person can even guess about. Nothing further can be seen there, beyond the cutting edge of science. And although we can confidently say that power plants will work for humans, converting gravitational energy into electric current (or maybe into a stream of gas escaping from the nozzle of a jet engine, or into the planned transformation of the ubiquitous silicon and oxygen atoms into atoms of super rare metals), we cannot yet say anything about the details of such a power plant ( rocket engine, physical reactor).

The force of gravity at the origins of the birth of galaxies

The force of gravity is at the origin of the birth of Galaxies from prestellar matter, as Academician V.A.Ambartsumyan is convinced of. It also extinguishes the stars that have burnt out their time and have spent the stellar fuel released by them at birth. Many physicists explain the existence of quasars by the interference of universal gravitation, (in more detail:) Look around: everything on Earth is largely controlled by this force. It is it that determines the layered structure of our planet - the alternation of the lithosphere, hydrosphere and atmosphere. It is she who keeps a thick layer of air gases, at the bottom of which and thanks to which we all exist. If it were not for gravity, the Earth would immediately fall from its orbit around the Sun, and the Earth's sphere itself would fall apart, torn apart by centrifugal forces. It is difficult to find anything that would not be more or less dependent on the force of gravity. Of course, the ancient philosophers, very observant people, could not help but notice that a stone thrown upwards always comes back. Plato in the 4th century BC explained this by the fact that all substances in the Universe tend to where most of similar substances are concentrated: a thrown stone falls to the ground or goes to the bottom, spilled water seeps into the nearest pond or into a river making its way to the sea , the smoke of the fire rushes to its kindred clouds. A student of Plato, Aristotle, clarified that all bodies have special properties of heaviness and lightness. Heavy bodies - stones, metals - rush to the center of the Universe, light bodies - fire, smoke, vapors - to the periphery. This hypothesis, which explains some of the phenomena associated with the force of gravity, existed for more than 2 thousand years.

Scientists on the force of gravity

Probably the first to raise the question of the force of gravity really scientific, was the genius of the Renaissance - Leonardo da Vinci. Leonardo proclaimed that gravitation is inherent not only to the Earth, that there are many centers of gravity. And he also expressed the idea that the force of gravity depends on the distance to the center of gravity. The works of Copernicus, Galileo, Kepler, Robert Hooke brought closer and closer to the idea of ​​the law of universal gravitation, but in its final formulation this law is forever associated with the name of Isaac Newton.

Isaac Newton on the force of gravity

born on January 4, 1643. Graduated from the University of Cambridge, became a bachelor, then - a master of science.
Isaac Newton. Everything further is endless wealth scientific works... But his main work is "Mathematical Principles of Natural Philosophy", published in 1687 and usually called simply "Principles". It is in them that the great is formulated. Probably everyone remembers him from high school.

All bodies are attracted to each other with a force directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them ...

Some of the provisions of this formulation could be anticipated by Newton's predecessors, but no one has yet fully learned it. It took Newton's genius to collect these fragments into a single whole in order to extend the gravity of the Earth to the Moon, and the Sun to the entire planetary system. From the law of universal gravitation, Newton deduced all the laws of motion of the Planets, previously discovered by Kepler. They turned out to be just its consequences. Moreover, Newton showed that not only Kepler's laws, but also deviations from these laws (in the world of three or more bodies) are a consequence of universal gravitation ... This was a great triumph of science. It seemed that the main force of nature, which moves the worlds, the force that is subject to air molecules, apples, and the Sun, was finally discovered and mathematically described. Gigantic, immeasurably huge was the step taken by Newton. The first popularizer of the works of the genius scientist, the French writer François Marie Arouet, world famous under the pseudonym Voltaire, said that Newton suddenly guessed the existence of the law named after him when he looked at a falling apple. Newton himself never mentioned this apple. And it is hardly worth losing time today to refute this beautiful legend. And, apparently, Newton came to comprehend the great power of nature by logical reasoning. Probably, it was precisely this that entered the corresponding chapter of the "Elements".

The force of gravity affects the flight of the nucleus

Suppose that for a very high mountain so high that its summit is already out of the atmosphere, we set up a gigantic artillery piece. Its trunk was placed strictly parallel to the surface. the globe and fired. Having described the arc, the core falls to earth... We increase the charge, improve the quality of the powder, in one way or another we force the core to move at a higher speed after the next shot. The arc described by the nucleus becomes flatter. The core falls much further from the foot of our mountain. We also increase the charge and shoot. The core flies along such a gentle trajectory that it descends parallel to the surface of the globe. The core can no longer fall to the Earth: with the same speed with which it descends, the Earth escapes from under it. And, having described the ring around our planet, the core returns to the point of departure. The weapon can be removed in the meantime. After all, the flight of the nucleus around the globe will take over an hour. And then the core will swiftly sweep over the top of the mountain and set off on a new circumnavigation of the Earth. Fall, if, as we agreed, the core does not experience any air resistance, it will never be able to. The core speed for this should be close to 8 km / sec. And if you increase the speed of the nucleus even more? It will first fly in an arc that is flatter than the curvature. the earth's surface, and will begin to move away from the Earth. At the same time, its speed will decrease under the influence of the Earth's gravity. And finally, having turned, it will begin, as it were, to fall back to the Earth, but it will fly past it and close not a circle, but an ellipse. The core will move around the Earth in exactly the same way as the Earth moves around the Sun, namely along an ellipse, in one of the focuses of which will be the center of our planet. If you increase the initial velocity of the core even more, the ellipse will be more elongated. You can stretch this ellipse so that the core will fly to the lunar orbit or even much further. But as long as starting speed this core will not exceed 11.2 km / sec, it will remain a satellite of the Earth. The nucleus, which received a speed of more than 11.2 km / s when fired, will forever fly off the Earth along a parabolic trajectory. If an ellipse is a closed curve, then a parabola is a curve that has two branches going to infinity. Moving along the ellipse, no matter how elongated it may be, we will inevitably return to the starting point systematically. Moving along a parabola, we will never return to the starting point. But, having left the Earth at this speed, the core will not yet be able to fly away to infinity. The powerful gravity of the Sun will bend the trajectory of its flight, close around itself like the trajectory of a planet. The nucleus will become the sister of the Earth, an independent tiny planet in our family of planets. In order to direct the core out of the planetary system, to overcome the solar attraction, it is necessary to inform it of a speed of more than 16.7 km / s, and direct it so that the speed of the Earth's own motion is applied to this speed. A speed of about 8 km / s (this speed depends on the height of the mountain from which our gun shoots) is called circular speed, speeds from 8 to 11.2 km / s - elliptical, from 11.2 to 16.7 km / s - parabolic , and above this number - by liberating speeds. It should be added here that the given values ​​of these velocities are valid only for the Earth. If we lived on Mars, the circular speed would be much more easily achievable for us - it there is only about 3.6 km / s, and the parabolic speed is only slightly higher than 5 km / s. But sending a nucleus on a space flight from Jupiter would be much more difficult than from Earth: the circular speed on this planet is 42.2 km / sec, and the parabolic speed is even 61.8 km / sec! It would be most difficult for the inhabitants of the Sun to leave their world (if, of course, such could exist). The circular speed of this giant should be 437.6, and the breakaway speed - 618.8 km / s! So Newton's late XVII centuries, a hundred years before the first flight of the Montgolfier brothers 'hot air balloon, two hundred years before the first flights of the Wright brothers' airplane, and almost a quarter of a millennium before the first liquid-propellant rockets took off, showed the way to the sky for satellites and spacecraft.

The force of gravity is inherent in every sphere

By using the law of gravitation unknown planets were discovered, cosmogonic hypotheses of the origin of the solar system were created. The main force of nature, which is subject to stars, planets, apples in the garden, and gas molecules in the atmosphere, has been discovered and described mathematically. But we do not know the mechanism of universal gravitation. Newtonian gravitation does not explain, but clearly presents state of the art the movement of the planets. We do not know what, what causes the interaction of all the bodies of the Universe. And it cannot be said that Newton was not interested in this reason. Over the years, he pondered over its possible mechanism. Incidentally, this is indeed an extremely mysterious force. A force that manifests itself through hundreds of millions of kilometers of space, devoid, at first glance, of any material formations with the help of which the transmission of interaction could be explained.

Newton's hypotheses

AND Newton resorted to hypothesis about the existence of a certain ether that supposedly fills the entire Universe. In 1675, he explained the attraction to the Earth by the fact that the ether filling the entire Universe rushes in continuous streams to the center of the Earth, capturing all objects in this movement and creating the force of gravity. The same stream of ether rushes to the Sun and, dragging planets and comets along with it, provides their elliptical trajectories ... This was not a very convincing, although absolutely mathematically logical hypothesis. But now, in 1679, Newton created a new hypothesis to explain the mechanism of gravitation. This time he endows the ether with the property of having a different concentration near the planets and far from them. The farther from the center of the planet, the supposedly denser the ether. And he has the ability to squeeze out all material bodies from their denser layers into less dense ones. And all bodies are squeezed out to the surface of the Earth. In 1706, Newton sharply denies the very existence of the ether. In 1717 he again returned to the squeezing ether hypothesis. Newton's brilliant brain struggled to solve the great mystery and did not find it. This explains such a sharp throwing from side to side. Newton liked to say:

I do not build hypotheses.

And although, as we could only be convinced, this is not entirely true, we can definitely state something else: Newton was able to clearly distinguish between indisputable things from shaky and controversial hypotheses. And in the "Elements" there is a formula of the great law, but there are no attempts to explain its mechanism. The great physicist bequeathed this riddle to the man of the future. He died in 1727. It has not been solved even today. The discussion about the physical essence of Newton's law took two centuries. And maybe this discussion would not have touched the very essence of the law, if he answered exactly all the questions asked to him. But the fact of the matter is that over time it turned out that this law is not universal. That there are cases when he cannot explain this or that phenomenon. Here are some examples.

The force of gravity in the calculations of Seeeliger

The first is the Seeeliger paradox. Considering the Universe to be infinite and uniformly filled with matter, Seeliger tried to calculate, according to Newton's law, the force of universal gravitation created by the entire infinitely large mass of the infinite Universe at some point. It was not an easy task from the point of view of pure mathematics. Having overcome all the difficulties of the most complex transformations, Seeeliger found that the sought-for force of universal gravitation is proportional to the radius of the Universe. And since this radius is equal to infinity, then the gravitational force must be infinitely large. However, in practice we do not observe this. This means that the law of universal gravitation is not applicable to the entire Universe. However, other explanations of the paradox are also possible. For example, we can assume that matter does not uniformly fill the entire Universe, but its density gradually decreases and, finally, somewhere very far away there is no matter at all. But to present such a picture means to admit the possibility of the existence of space without matter, which is generally absurd. We can assume that the force of universal gravitation is weakening faster than the square of the distance grows. But this casts doubt on the amazing harmony of Newton's law. No, and this explanation did not satisfy the scientists. The paradox remained a paradox.

Observing the movement of Mercury

Another fact, the action of the force of universal gravitation, which cannot be explained by Newton's law, brought observing the movement of Mercury- closest to the planet. Accurate calculations according to Newton's law showed that perehelium - the point of the ellipse closest to the Sun, along which Mercury moves - should shift by 531 arc seconds in 100 years. And astronomers have found that this displacement is 573 arc seconds. This excess - 42 arc seconds - could not be explained by scientists either, using only formulas arising from Newton's law. Explained the Seeeliger paradox, the displacement of the superhelium of Mercury, and many other paradoxical phenomena and unexplained facts Albert Einstein, one of the greatest, if not the most great physicist of all times and peoples. Among the annoying little things was the question of etheric wind.

The experiments of Albert Michelson

It seemed that this question did not directly concern the problem of gravitation. He related to optics, to light. More precisely, to determine its speed. For the first time the speed of light was determined by a Danish astronomer Olaf Roemer observing the eclipse of Jupiter's moons. This happened back in 1675. American physicist Albert Michelson v late XVIII century spent a series of determinations of the speed of light in terrestrial conditions, using devices designed by him. In 1927, he gave the value of 299796 + 4 km / s for the speed of light - this was an excellent accuracy for those times. But the crux of the matter is different. In 1880, he decided to investigate the etheric wind. He wanted to finally establish the existence of that very ether, by the presence of which they tried to explain both the transmission of gravitational interaction and the transmission of light waves. Michelson was probably the most remarkable experimenter of his time. He had excellent equipment. And he was almost sure of success.

The essence of experience

An experience was conceived like this. The earth moves in its orbit at a speed of about 30 km / s... Moves through the ether. This means that the speed of light from a source in front of the receiver relative to the motion of the Earth should be greater than from a source on the other side. In the first case, the speed of the ether wind must be added to the speed of light; in the second case, the speed of light must decrease by this value.
The movement of the Earth in its orbit around the Sun. Of course, the speed of the Earth's orbit around the Sun is only one ten-thousandth the speed of light. It is very difficult to find such a small term, but it is not in vain that Michelson was called the king of accuracy. He used a clever method to capture the "subtle" difference in the speed of light beams. He split the beam into two equal streams and directed them in mutually perpendicular directions: along the meridian and along the parallel. Reflected from the mirrors, the rays returned. If the parallel beam had been influenced by the etheric wind, when it was added to the meridional beam, interference fringes would have appeared, the waves of the two beams would have been phase shifted. However, it was difficult for Michelson to measure the paths of both rays with such great accuracy that they were exactly the same. So he built the apparatus so that there were no fringes, and then turned it 90 degrees. The meridional ray became latitudinal and vice versa. If there is ethereal wind, black and light stripes should appear under the eyepiece! But they weren't. Perhaps, when turning the apparatus, the scientist moved it. He set it up at noon and secured it. After all, besides that, it still rotates around the axis. And therefore, at different times of the day, the latitudinal ray occupies a different position relative to the oncoming etheric wind. Now, when the device is strictly motionless, one can be convinced of the accuracy of the experiment. There were no interference fringes again. The experiment was carried out many times, and Michelson, and with him all the physicists of that time, were amazed. The ethereal wind was not found! Light moved in all directions at the same speed! Nobody was able to explain this. Michelson repeated the experiment again and again, improved the equipment and, finally, achieved an almost incredible measurement accuracy, an order of magnitude greater than was necessary for the success of the experiment. Again, nothing!

The experiments of Albert Einstein

The next big step in knowledge of the force of gravity did Albert Einstein... Albert Einstein was once asked:

- How did you come to your special theory of relativity? Under what circumstances did a brilliant guess dawned on you? The scientist replied: - It always seemed to me that this is the case.

Maybe he didn't want to be frank, maybe he wanted to get rid of the annoying interlocutor. But it is difficult to imagine that Einstein's idea of ​​the connections between time, space and speed was innate. No, of course, at first a guess flashed, bright as lightning. Then her development began. No, there are no contradictions with known phenomena. And then those five pages appeared saturated with formulas, which were published in a physics journal. Pages opened new era in physics. Imagine a starship flying through space. We warn you right away: the starship is very peculiar, one that you have not read about in science fiction stories. Its length is 300 thousand kilometers, and its speed is, say, 240 thousand km / sec. And this spaceship flies past one of the intermediate platforms in space, without stopping at it. Full speed. One of its passengers is standing on the deck of the starship with a clock. And you and I, the reader, are standing on a platform - its length must correspond to the size of the starship, that is, 300 thousand kilometers, because otherwise it will not be able to stick to it. And we also have a watch in our hands. We notice that the moment the starship's nose came up to the rear edge of our platform, a lantern flashed on it, illuminating the space around it. A second later, the beam of light reached the front edge of our platform. We do not doubt this, because we know the speed of light, and we managed to accurately detect the corresponding moment by the clock. And on a spaceship ... But the spaceship flew towards the beam of light. And we definitely saw that the light illuminated its stern at the moment when it was somewhere near the middle of the platform. We definitely saw that the beam of light did not cover 300 thousand kilometers from the bow to the stern of the ship. But passengers on the deck of the starship are sure of something else. They are sure that their beam covered the entire distance from bow to stern of 300 thousand kilometers. After all, he spent a whole second on it. They, too, spotted it absolutely accurately on their watch. And how could it be otherwise: after all, the speed of light does not depend on the speed of movement of the source ... How so? We see one thing from a stationary platform, and another on the deck of a starship? What's the matter?

Einstein's theory of relativity

It should be noted right away: Einstein's theory of relativity at first glance, it absolutely contradicts our established concept of the structure of the world. We can say that it also contradicts common sense, as we are used to presenting it. This has happened more than once in the history of science. But the discovery of the sphericity of the Earth was contrary to common sense. How can this live on opposite side people and not fall into the abyss? For us, the sphericity of the Earth is an undoubted fact, and from the point of view common sense any other assumption is senseless and wild. But look away from your time, imagine the first appearance of this idea, and it becomes clear how difficult it would be to accept it. Well, was it easier to admit that the Earth is not stationary, but flies along its trajectory tens of times faster than a cannonball? These were all crashes of common sense. Therefore, modern physicists never refer to it. Now let's get back to the special theory of relativity. The world recognized her for the first time in 1905 from an article signed by few people famous name - Albert Einstein. And he was at that time only 26 years old. Einstein made a very simple and logical assumption out of this paradox: from the point of view of an observer on the platform, less time passed in a moving carriage than your wristwatch measured. In the car, the passage of time has slowed down compared to time on a stationary platform. Quite surprising things logically flowed from this assumption. It turned out that a person traveling to work in a tram, compared to a pedestrian going the same way, not only saves time at the expense of speed, but it also goes slower for him. However, do not try to preserve eternal youth in this way: even if you become a tram driver and spend a third of your life in a tram, in 30 years you will earn hardly more than a millionth of a second. For the gain in time to become noticeable, it is necessary to move at a speed close to the speed of light. It turns out that an increase in the speed of bodies is reflected in their mass. The closer the speed of a body is to the speed of light, the greater its mass. When the speed of a body is equal to the speed of light, its mass is equal to infinity, that is, it is greater than the mass of the Earth, the Sun, the Galaxy, our entire Universe ... This is how much mass can be concentrated in a simple cobblestone, accelerating it to the speed of light! This also imposes a limitation that does not allow any material body to develop a speed equal to the speed of light. After all, as the mass grows, it becomes more and more difficult to disperse it. And an infinite mass cannot be moved by any force. However, nature has made a very important exception to this law for a whole class of particles. For example, for photons. They can move at the speed of light. More precisely, they cannot move at any other speed. It is unthinkable to imagine a stationary photon. When stationary, it has no mass. Neutrinos also do not have rest mass, and they are also condemned to eternal unrestrained flight through space with the maximum possible speed in our Universe, not overtaking light and not lagging behind it. Isn't it true that each of the consequences of the special theory of relativity that we have listed is surprising, paradoxical! And each, of course, contradicts "common sense"! But here's what's interesting: not in its concrete form, but as a broad philosophical position, all these amazing consequences were predicted by the founders of dialectical materialism. What do these consequences say? On the connections that interconnect energy and mass, mass and speed, speed and time, speed and length of a moving object. .. Einstein's discovery of interdependence, like cement (in more detail:), connecting together reinforcement, or foundation stones, united things and phenomena that seemed independent of each other and created the basis on which for the first time in the history of science it was possible to build a slender building ... This building is a representation of how our universe works. But first, at least a few words about the general theory of relativity, also created by Albert Einstein. Albert Einstein. This name - the general theory of relativity - does not quite correspond to the content of the theory, which will be discussed. It establishes the interdependence between space and matter. Apparently, it would be more correct to call her space-time theory, or theory of gravity... But this name has so grown together with Einstein's theory that it seems indecent for many scientists to even raise the question of replacing it now. General relativity established the interdependence between matter and time, and the space that contains it. It turned out that space and time are not only impossible to imagine existing separately from matter, but their properties also depend on the matter filling them. Einstein published general relativity in 1916 and has been working on it since 1907. It is not realistic to try to lay it out in several pages without using mathematical formulas.

Starting point of reasoning

Therefore, we can only indicate starting point of reasoning and provide some important conclusions. At the beginning space travel an unexpected catastrophe destroyed the library, film fund and other repositories of the mind, memory of people flying through space. And the nature of the native planet is forgotten in the turn of the century. Even the law of universal gravitation has been forgotten, for the rocket flies in intergalactic space, where it is almost not felt. However, the ship's engines work great, the energy supply in the batteries is practically unlimited. Most of the time, the ship moves by inertia, and its inhabitants are accustomed to weightlessness. But sometimes they turn on the engines and slow down or speed up the movement of the ship. When jet nozzles blaze into the void with a colorless flame and the ship moves at an accelerated rate, the inhabitants feel that their bodies are becoming heavy, they are forced to walk around the ship, and not fly along the corridors. And now the flight is close to completion. The ship flies up to one of the stars and lays down in the orbits of the most suitable planet. The starships go outside, walking on the ground covered with fresh greenery, constantly experiencing the same sensation of heaviness, familiar from the time when the ship was moving at an accelerated pace. But the planet moves evenly. It cannot fly towards them with a constant acceleration of 9.8 m / sec2! And they have the first assumption that the gravitational field (the force of attraction) and the acceleration give the same effect, and perhaps have a common nature. None of our contemporaries, earthlings, was in such a long flight, but many felt the phenomenon of "weight" and "relief" of their bodies. Already an ordinary elevator, when it moves at an accelerated rate, creates this feeling. When descending, you feel a sudden loss of weight, while climbing, on the contrary, the floor presses on your legs with more than usual force. But one feeling doesn't prove anything. After all, sensations try to convince us that the Sun moves in the sky around the motionless Earth, that all stars and planets are at the same distance from us, on the firmament, etc. Scientists have subjected sensations experimental verification... Even Newton pondered over the strange identity of the two phenomena. He tried to give them numerical characteristics. Having measured the gravitational and, he made sure that their values ​​are always strictly equal to each other. From whatever materials he made the pendulums of the pilot plant: from silver, lead, glass, salt, wood, water, gold, sand, wheat. The result was the same. Equivalence principle, which we are talking about, lies at the basis of the general theory of relativity, although the modern interpretation of the theory does not need this principle already. Omitting the mathematical conclusions following from this principle, let us go directly to some consequences of the general theory of relativity. The presence of large masses of matter strongly affects the surrounding space. It leads to such changes in it, which can be defined as the inhomogeneity of space. These inhomogeneities direct the movement of any masses that are near the attracting body. This analogy is usually used. Imagine a canvas stretched taut on a frame parallel to the ground. Place a heavy weight on it. This will be our great attractive mass. It will, of course, bend the canvas and end up in some depression. Now roll the ball on this canvas so that part of its path lies next to the attracting mass. There are three options depending on how the ball will be launched.

1. The ball will fly far enough from the depression created by the deflection of the canvas and will not change its movement.
2. The ball will touch the recess, and the lines of its movement will bend towards the attracting mass.
3. The ball will fall into this hole, will not be able to get out of it and will make one or two revolutions around the gravitating mass.

Isn't it true that the third option very nicely simulates the capture by a star or planet of a foreign body inadvertently flying into their field of attraction? And the second case is the bending of the trajectory of a body flying at a speed greater than the possible capture speed! The first case is analogous to flying out of the practical reach of the gravitational field. Yes, it is practical, because theoretically the gravitational field is unlimited. Of course, this is a very distant analogy, primarily because no one can really imagine the deflection of our three-dimensional space. In what physical meaning this deflection, or curvature, as they often say, no one knows. From the general theory of relativity it follows that any material body can move in a gravitational field only along curved lines. Only in private special cases the curve turns into a straight line. The ray of light also obeys this rule. After all, it consists of photons that have a certain mass in flight. And the gravitational field acts on it, as well as on a molecule, asteroid or planet. Another important conclusion is that the gravitational field also changes the course of time. Near a large attracting mass, in a strong gravitational field created by it, the course of time should be slower than far from it. You see, and the general theory of relativity is fraught with paradoxical conclusions, capable of overturning our ideas of "common sense" again and again!

Gravitational collapse

Let's talk about an amazing cosmic phenomenon - gravitational collapse (catastrophic compression). This phenomenon occurs in gigantic accumulations of matter, where the forces of gravity reach such enormous magnitudes that no other forces existing in nature can resist them. Remember Newton's famous formula: the gravitational forces are the greater, the less square distance between gravitating bodies. Thus, the denser the material formation becomes, the smaller its size, the more rapidly the forces of gravity increase, the more inevitable is their destructive embrace. There is a clever trick with the help of which nature fights against the seemingly limitless contraction of matter. To do this, it stops the very course of time in the sphere of action of supergiant gravitational forces, and the chained masses of matter seem to be turned off from our Universe, freeze in a strange lethargic dream. The first of these "black holes" in space has probably already been discovered. According to the assumption of Soviet scientists O. Kh. Guseinov and A. Sh. Novruzova, it is the Gemini delta - a double star with one invisible component. The visible component has a mass of 1.8 solar, and its invisible "partner" should be, according to calculations, four times more massive than the visible one. But there are no traces of it: it is impossible to see the most amazing creation of nature, a "black hole". The Soviet scientist Professor KP Stanyukovich, as they say, "at the tip of the pen," by purely theoretical constructions, showed that the particles of "frozen matter" can be very diverse in size.

• Its gigantic formations are possible, similar to quasars, continuously emitting the same amount of energy as all 100 billion stars of our Galaxy emit.
• Much more modest clumps are possible, equal to only a few solar masses. Both those and other objects can arise themselves from ordinary, not "sleeping" matter.
• And formations of a completely different class are possible, commensurate in mass with elementary particles.

For them to arise, it is necessary to first subject the constituent matter to gigantic pressure and drive it into the Schwarzschild sphere - a sphere where time for an external observer stops completely. And if after that the pressure is even removed, the particles for which time has stopped will remain to exist independently of our Universe.

Plankeons

The author of the hypothesis named such particles in honor of the famous German physicist Max Planck - plankeons. Plankeons are a very special class of particles. They have, according to K.P.Stanyukovich, an extremely interesting property: they carry matter in themselves unchanged, such as it was millions and billions of years ago. Looking inside the plankeon, we could see matter as it was at the time of the birth of our universe. According to theoretical calculations, there are about 10 80 plankeons in the universe, approximately one plankeon in a cube of space with a side of 10 centimeters. By the way, simultaneously with Stanyukovich and (independently of him, the hypothesis of the plankeons was put forward by academician M.A.Markov. Only Markov gave them a different name - maximons. particles never form fragments, but other elementary particles... This is truly amazing: in the ordinary world, breaking a vase, we never get whole cups or even rosettes. But suppose that in the depths of each elementary particle a plankeon is hidden, one or several, and sometimes many plankeons. At the moment of collision of particles, the tightly tied "bag" of the Plankeon opens slightly, some particles will "fall" into it, and instead those that we consider to have arisen during the collision "pop out". At the same time, the Plankeon, as a prudent accountant, will provide all the "conservation laws" adopted in the world of elementary particles. Well, what does the mechanism of universal gravitation have to do with it? "Responsible" for gravitation, according to the hypothesis of KP Stanyukovich, are tiny particles, the so-called gravitons, continuously emitted by elementary particles. Gravitons are as much smaller than the latter, as a speck of dust dancing in a sunbeam is smaller than the globe. The emission of gravitons obeys a number of laws. In particular, they are easier to fly into that area of ​​space. Which contains fewer gravitons. This means that if there are two celestial bodies in space, both will radiate gravitons mainly "outward", in directions opposite to each other. Thus, an impulse is created that makes the bodies come closer, to be attracted to each other. Leaving their elementary particles, gravitons carry away part of their mass. Small as they are, the loss in mass cannot but be noticeable over time. But this time is unimaginably huge. It will take about 100 billion years for all matter in the Universe to turn into a gravitational field.
Gravitational field. But is that all? According to KP Stanyukovich, about 95 percent of the mass of matter is hidden in plankeons of various sizes, is in a state of lethargic sleep, but over time the plankeons open up, and the amount of "normal" matter increases.

The law of universal gravitation was discovered by Newton in 1687 when studying the motion of the moon's satellite around the Earth. The English physicist has clearly formulated the postulate that characterizes the forces of attraction. In addition, analyzing Kepler's laws, Newton calculated that the forces of gravity must exist not only on our planet, but also in space.

History of the issue

The law of universal gravitation was not born spontaneously. Since ancient times, people have studied the sky, mainly for compiling agricultural calendars, calculating important dates, religious holidays. Observations indicated that in the center of the "world" there is a Luminary (the Sun), around which celestial bodies revolve in orbits. Subsequently, the dogmas of the church did not allow to think so, and people lost the knowledge accumulated over thousands of years.

In the 16th century, before the invention of telescopes, a galaxy of astronomers appeared who looked at the firmament in a scientific way, discarding the prohibitions of the church. T. Brahe, observing space for many years, systematized the movements of the planets with particular care. These high-precision data helped I. Kepler subsequently to discover his three laws.

By the time of the discovery (1667) by Isaac Newton of the law of gravitation in astronomy, the heliocentric system of the world of N. Copernicus was finally established. According to her, each of the planets of the system revolves around the Luminary in orbits, which, with an approximation sufficient for many calculations, can be considered circular. At the beginning of the 17th century. I. Kepler, analyzing the work of T. Brahe, established the kinematic laws that characterize the motion of the planets. The discovery became the foundation for elucidating the dynamics of the motion of the planets, that is, the forces that determine exactly this type of their motion.

Description of interaction

Unlike short-period weak and strong interactions, gravity and electromagnetic fields have long-range properties: their influence manifests itself at giant distances. Mechanical phenomena in the macrocosm are influenced by 2 forces: electromagnetic and gravitational. The impact of planets on satellites, the flight of a thrown or launched object, the floating of a body in a liquid - gravitational forces act in each of these phenomena. These objects are attracted by the planet, gravitate towards it, hence the name "law of universal gravitation".

It has been proved that the force of mutual attraction unconditionally acts between physical bodies. Such phenomena as the fall of objects on the Earth, the rotation of the Moon, planets around the Sun, occurring under the action of the forces of universal attraction, are called gravitational.

The law of universal gravitation: formula

Universal gravitation is formulated as follows: any two material objects are attracted to each other with a certain force. The magnitude of this force is directly proportional to the product of the masses of these objects and inversely proportional to the square of the distance between them:

In the formula, m1 and m2 are the masses of the studied material objects; r is the distance determined between the centers of mass of the calculated objects; G is a constant gravitational value expressing the force with which the mutual attraction of two objects weighing 1 kg each, located at a distance of 1 m, is carried out.

What determines the force of attraction

The law of gravitation works differently, depending on the region. Since the force of gravity depends on the latitude values ​​at a certain location, similarly the acceleration of gravity has different meanings in different places. The force of gravity and, accordingly, the acceleration of gravity have the maximum value at the poles of the Earth - the force of gravity at these points is equal to the force of gravity. The minimum values ​​will be at the equator.

The globe is slightly flattened, its polar radius is less than the equatorial one by about 21.5 km. However, this dependence is less significant in comparison with the daily rotation of the Earth. Calculations show that due to the flattening of the Earth at the equator, the acceleration due to gravity is slightly less than its value at the pole by 0.18%, and after daily rotation - by 0.34%.

However, in the same place on the Earth, the angle between the direction vectors is small, so the discrepancy between the force of gravity and the force of gravity is insignificant, and it can be neglected in the calculations. That is, we can assume that the moduli of these forces are the same - the acceleration of gravity near the Earth's surface is the same everywhere and is equal to approximately 9.8 m / s².

Output

Isaac Newton was a scientist who made a scientific revolution, completely rebuilt the principles of dynamics and, on their basis, created scientific picture the world. His discovery influenced the development of science, the creation of material and spiritual culture. The fate of Newton fell to the task of revising the results of the idea of ​​the world. In the XVII century. Scientists have completed the grandiose work of building the foundation new science- physics.

Why does a stone released from the hands fall to the Earth? Because he is attracted by the Earth, each of you will say. Indeed, the stone falls to the Earth with the acceleration of gravity. Consequently, a force directed to the Earth acts on the stone from the side of the Earth. According to Newton's third law, a stone acts on the Earth with the same modulus of force directed to the stone. In other words, the forces of mutual attraction act between the Earth and the stone.

Newton was the first who first guessed, and then strictly proved that the reason causing the fall of the stone to the Earth, the movement of the Moon around the Earth and the planets around the Sun, is the same. This is the force of gravity acting between any bodies in the universe. Here is the course of his reasoning, given in Newton's main work "Mathematical Principles of Natural Philosophy":

“A stone thrown horizontally will deviate from the rectilinear path under the influence of gravity and, having described a curved trajectory, will finally fall to the Earth. If you throw it with a higher speed, then it will fall further ”(Fig. 1).

Continuing this reasoning, Newton comes to the conclusion that if it were not for the air resistance, then the trajectory of a stone thrown from a high mountain at a certain speed could become such that it would never reach the Earth's surface at all, but moved around it “like how the planets describe their orbits in the heavenly space ”.

Now we have become so familiar with the movement of satellites around the Earth that there is no need to explain Newton's thought in more detail.

So, according to Newton, the motion of the Moon around the Earth or planets around the Sun is also a free fall, but only a fall that lasts without stopping for billions of years. The reason for this "fall" (whether it is really about the fall of an ordinary stone to the Earth or about the movement of planets in their orbits) is the force of gravity. What does this force depend on?

The dependence of the force of gravity on the mass of bodies

Galileo proved that during free fall, the Earth imparts the same acceleration to all bodies in a given place, regardless of their mass. But acceleration according to Newton's second law is inversely proportional to the mass \. How can one explain that the acceleration imparted to a body by the Earth's gravity force is the same for all bodies? This is possible only if the force of attraction to the Earth is directly proportional to the mass of the body. In this case, an increase in mass m, for example, twice will lead to an increase in the modulus of force F is also doubled, and the acceleration, which is \ (a = \ frac (F) (m) \), will remain unchanged. Generalizing this conclusion for the forces of gravity between any bodies, we conclude that the force of universal gravitation is directly proportional to the mass of the body on which this force acts.

But at least two bodies are involved in mutual attraction. Each of them, according to Newton's third law, is acted upon by gravitational forces of the same modulus. Therefore, each of these forces must be proportional to both the mass of one body and the mass of another body. Therefore, the force of universal gravity between two bodies is directly proportional to the product of their masses:

\ (F \ sim m_1 \ cdot m_2 \)

Dependence of the force of gravity on the distance between bodies

It is well known from experience that the acceleration of gravity is 9.8 m / s 2 and it is the same for bodies falling from heights of 1, 10 and 100 m, that is, it does not depend on the distance between the body and the Earth. This seems to mean that the force does not depend on distance either. But Newton believed that the distance should be measured not from the surface, but from the center of the Earth. But the radius of the Earth is 6400 km. It is clear that several tens, hundreds, or even thousands of meters above the Earth's surface cannot appreciably change the value of the acceleration due to gravity.

To find out how the distance between bodies affects the strength of their mutual attraction, it would be necessary to find out what is the acceleration of bodies remote from the Earth at sufficiently large distances. However, it is difficult to observe and study the free fall of a body from a height of thousands of kilometers above the Earth. But nature itself came to the rescue here and made it possible to determine the acceleration of a body moving in a circle around the Earth and therefore having a centripetal acceleration, caused, of course, by the same force of attraction to the Earth. Such a body is the natural satellite of the Earth - the Moon. If the force of attraction between the Earth and the Moon did not depend on the distance between them, then the centripetal acceleration of the Moon would be the same as the acceleration of a body freely falling near the Earth's surface. In reality, the centripetal acceleration of the Moon is 0.0027 m / s 2.

Let's prove it... The rotation of the Moon around the Earth occurs under the action of the force of gravity between them. Approximately, the Moon's orbit can be considered a circle. Consequently, the Earth imparts centripetal acceleration to the Moon. It is calculated by the formula \ (a = \ frac (4 \ pi ^ 2 \ cdot R) (T ^ 2) \), where R- the radius of the lunar orbit, equal to approximately 60 radii of the Earth, T≈ 27 days 7 hours 43 minutes ≈ 2.4 ∙ 10 6 s - the period of the Moon's revolution around the Earth. Considering that the radius of the Earth R s ≈ 6.4 ∙ 10 6 m, we obtain that the centripetal acceleration of the Moon is equal to:

\ (a = \ frac (4 \ pi ^ 2 \ cdot 60 \ cdot 6.4 \ cdot 10 ^ 6) ((2.4 \ cdot 10 ^ 6) ^ 2) \ approx 0.0027 \) m / s 2.

The found acceleration value is less than the gravitational acceleration of bodies near the Earth's surface (9.8 m / s 2) by approximately 3600 = 60 2 times.

Thus, an increase in the distance between the body and the Earth 60 times led to a decrease in the acceleration imparted to earthly gravity, and, consequently, the very force of attraction by 60 2 times.

An important conclusion follows from this: the acceleration, which imparts the force of attraction to the bodies to the Earth, decreases in inverse proportion to the square of the distance to the center of the Earth

\ (F \ sim \ frac (1) (R ^ 2) \).

The law of universal gravitation

In 1667 Newton finally formulated the law of universal gravitation:

\ (F = G \ cdot \ frac (m_1 \ cdot m_2) (R ^ 2). \ Quad (1) \)

The force of mutual attraction of two bodies is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them.

Aspect ratio G called gravitational constant.

The law of universal gravitation is valid only for such bodies, the dimensions of which are negligible in comparison with the distance between them. In other words, it is only fair for material points ... In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 2). These kinds of forces are called central.

To find the gravitational force acting on a given body from the side of another, in the case when the size of the bodies cannot be neglected, proceed as follows. Both bodies are mentally divided into such small elements that each of them can be considered pointlike. Adding the forces of gravity acting on each element of a given body from all the elements of another body, we obtain a force acting on this element (Fig. 3). Having performed such an operation for each element of a given body and adding up the forces obtained, they find the total gravitational force acting on this body. This task is difficult.

There is, however, one practically important case when formula (1) is applicable to extended bodies. It can be proved that spherical bodies, the density of which depends only on the distances to their centers, at distances between them larger than the sum of their radii, are attracted with forces, the moduli of which are determined by formula (1). In this case R Is the distance between the centers of the balls.

And finally, since the dimensions of the bodies falling to the Earth are much smaller than the dimensions of the Earth, then these bodies can be considered as point bodies. Then under R in formula (1) one should understand the distance from a given body to the center of the Earth.

The forces of mutual attraction act between all bodies, depending on the bodies themselves (their masses) and on the distance between them.

The physical meaning of the gravitational constant

From formula (1) we find

\ (G = F \ cdot \ frac (R ^ 2) (m_1 \ cdot m_2) \).

Hence it follows that if the distance between the bodies is numerically equal to one ( R= 1 m) and the masses of interacting bodies are also equal to unity ( m 1 = m 2 = 1 kg), then the gravitational constant is numerically equal to the modulus of force F... Thus ( physical meaning ),

the gravitational constant is numerically equal to the modulus of the gravitational force acting on a body with a mass of 1 kg from another body of the same mass with a distance between the bodies equal to 1 m.

In SI, the gravitational constant is expressed in

.

The Cavendish Experience

The value of the gravitational constant G can only be found empirically. To do this, you need to measure the modulus of the gravitational force F acting on a body with a mass m 1 from the side of the body weight m 2 at a known distance R between bodies.

The first measurements of the gravitational constant were carried out in the middle of the 18th century. Estimate, however very roughly, the value G at that time succeeded as a result of considering the attraction of the pendulum to the mountain, the mass of which was determined by geological methods.

Accurate measurements of the gravitational constant were first carried out in 1798 by the English physicist G. Cavendish using a device called a torsion balance. The torsion balance is shown schematically in Figure 4.

Cavendish secured two small lead balls (5 cm in diameter and m 1 = 775 g each) at opposite ends of a 2-meter rod. The rod was suspended from a thin wire. For this wire, the elastic forces arising in it when twisted at various angles were preliminarily determined. Two large lead balls (20 cm in diameter and m 2 = 49.5 kg) could be brought close to small balls. The forces of attraction from the side of the large balls made the small balls move towards them, while the stretched wire twisted slightly. The degree of twisting was a measure of the force acting between the balls. The twist angle of the wire (or the rotation of the rod with small balls) turned out to be so small that it had to be measured with an optical tube. The result obtained by Cavendish is only 1% different from the value of the gravitational constant accepted today:

G ≈ 6.67 ∙ 10 -11 (N ∙ m 2) / kg 2

Thus, the forces of attraction of two bodies with a mass of 1 kg each, located at a distance of 1 m from each other, in terms of modules are only 6.67 ∙ 10 -11 N. This is a very small force. Only in the case when bodies of huge mass interact (or at least the mass of one of the bodies is large), the force of gravity becomes large. For example, the Earth attracts the moon with a force F≈ 2 ∙ 10 20 N.

Gravitational forces are the "weakest" of all the forces of nature. This is due to the fact that the gravitational constant is small. But with large masses cosmic bodies, the forces of universal gravitation become very large. These forces keep all the planets near the Sun.

The meaning of the law of universal gravitation

The law of universal gravitation is the basis of celestial mechanics - the science of planetary motion. With the help of this law, the positions of celestial bodies on the firmament for many decades ahead are determined with great accuracy and their trajectories are calculated. The law of universal gravitation is also used in calculating the motion of artificial earth satellites and interplanetary automatic vehicles.

Disturbances in the motion of the planets... The planets do not move strictly according to Kepler's laws. Kepler's laws would be exactly observed for the motion of a given planet only if this planet alone revolved around the Sun. But in Solar system there are many planets, all of them are attracted by both the Sun and each other. Therefore, there are disturbances in the motion of the planets. In the solar system, perturbations are small, because the attraction of a planet by the sun is much stronger than the attraction of other planets. When calculating the apparent position of the planets, perturbations have to be taken into account. When launching artificial celestial bodies and calculating their trajectories, they use the approximate theory of motion of celestial bodies - the theory of perturbations.

Discovery of Neptune... One of striking examples the triumph of the law of all-peaceful gravitation is the discovery of the planet Neptune. In 1781, the English astronomer William Herschel discovered the planet Uranus. Its orbit was calculated and a table of the positions of this planet was compiled for many years to come. However, a check of this table, carried out in 1840, showed that its data differ from reality.

Scientists have suggested that the deviation in the motion of Uranus is caused by the attraction of an unknown planet, located even further from the Sun than Uranus. Knowing the deviations from the calculated trajectory (perturbations of the motion of Uranus), the Englishman Adame and the Frenchman Leverrier, using the law of universal gravitation, calculated the position of this planet in the sky. Adame had finished his calculations earlier, but the observers to whom he communicated his results were in no hurry to check. Meanwhile, Leverrier, having completed the calculations, showed the German astronomer Halle the place where to look unknown planet... On the very first evening, September 28, 1846, Halle, directing the telescope to the indicated place, discovered new planet... She was named Neptune.

In the same way, on March 14, 1930, the planet Pluto was discovered. Both discoveries are said to have been made "at the tip of the pen."

Using the law of universal gravitation, you can calculate the mass of the planets and their satellites; explain phenomena such as the ebb and flow of water in the oceans, and more.

The forces of gravity are the most universal of all forces of nature. They act between any bodies that have mass, and all bodies have mass. There are no barriers for the forces of gravity. They work through any body.

Literature

1. Kikoin I.K., Kikoin A.K. Physics: Textbook. for 9 cl. wednesday shk. - M .: Education, 1992 .-- 191 p.
2. Physics: Mechanics. 10th grade: Textbook. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakisheva. - M .: Bustard, 2002 .-- 496 p.

There is a force of mutual attraction between any bodies in nature, called by the force of gravity(or the forces of gravity). was discovered by Isaac Newton in 1682. When he was 23 years old, he suggested that the forces holding the Moon in its orbit are of the same nature as the forces that make an apple fall to Earth.

Gravity (mg) is directed vertically strictly to the center of the earth; depending on the distance to the surface of the earth, the acceleration of gravity is different. Near the surface of the Earth in middle latitudes, its value is about 9.8 m / s 2. as you move away from the surface of the Earth g decreases.

Body weight (weight strength) – is the force with which the body acts onhorizontal support or stretching the suspension. In this case, it is assumed that the body motionless relative to the support or suspension. Let the body lie on a horizontal table motionless relative to the Earth. Denoted by a letter R.

Body weight and gravity are different in nature: body weight is a manifestation of the action of intermolecular forces, and gravity is of a gravitational nature.

If acceleration a = 0 , then the weight is equal to the force with which the body is attracted to the Earth, namely. [P] = H.

If the condition is different, then the weight changes:

• if acceleration a not equal 0 then weight P = mg - ma (down) or P = mg + ma (up);
• if the body falls freely or moves with the acceleration of gravity, i.e. a =g(Fig. 2), then the body weight is 0 (P = 0 ). The state of the body in which its weight is zero is called weightlessness.

V weightlessness there are also astronauts. V weightlessness for a moment, you are when you jump up while playing basketball or dancing.

Home experiment: A plastic bottle with a hole at the bottom is filled with water. We release it from the hands from a certain height. As long as the bottle falls, no water flows out of the hole.

The weight of the body moving with acceleration (in the elevator) The body in the elevator is experiencing overload