Gravity: formula, definition. referat

Absolutely all bodies in the Universe are affected by a magical force that somehow attracts them to the Earth (more precisely, to its core). There is nowhere to escape, nowhere to hide from the all-encompassing magical gravity: the planets of our solar system are attracted not only to the huge Sun, but also to each other, all objects, molecules and the smallest atoms are also mutually attracted. known even to small children, having devoted his life to studying this phenomenon, he established one of the greatest laws - the law of universal gravitation.

What is gravity?

The definition and formula have long been known to many. Recall that the force of gravity is a certain quantity, one of the natural manifestations of universal gravitation, namely: the force with which any body is invariably attracted to the Earth.

The force of gravity is denoted by the Latin letter F heavy.

Gravity: formula

How to calculate directed to a certain body? What other quantities do you need to know in order to do this? The formula for calculating gravity is quite simple, it is studied in the 7th grade of a comprehensive school, at the beginning of a physics course. In order not only to learn it, but also to understand it, one should proceed from the fact that the force of gravity, invariably acting on a body, is directly proportional to its quantitative value (mass).

The unit of gravity is named after the great scientist Newton.

It is always directed strictly down to the center of the earth's core, due to its influence all bodies fall down with uniform acceleration. We observe the phenomena of gravity in everyday life everywhere and constantly:

• objects, accidentally or specially released from the hands, necessarily fall down to the Earth (or to any surface preventing free fall);
• a satellite launched into space does not fly away from our planet for an indefinite distance perpendicularly upwards, but remains in orbit;
• all rivers flow from mountains and cannot be reversed;
• it happens that a person falls and is injured;
• the smallest dust particles sit on all surfaces;
• air is concentrated at the surface of the earth;
• hard to carry bags;
• rain falls from clouds and clouds, snow falls, hail.

Along with the concept of "gravity", the term "body weight" is used. If the body is placed on a flat horizontal surface, then its weight and gravity are numerically equal, so these two concepts are often replaced, which is not at all correct.

Acceleration of gravity

The concept of "acceleration of free fall" (in other words, is associated with the term "gravity." The formula shows: in order to calculate the force of gravity, you need to multiply the mass by g (acceleration of St. p.).

"g" = 9.8 N/kg, this is a constant value. However, more accurate measurements show that due to the rotation of the Earth, the value of the acceleration of St. p. is not the same and depends on latitude: at the North Pole it is = 9.832 N / kg, and at the sultry equator = 9.78 N / kg. It turns out that in different places on the planet, different gravity forces are directed to bodies with the same mass (the formula mg still remains unchanged). For practical calculations, it was decided to allow for minor errors in this value and use the average value of 9.8 N/kg.

The proportionality of such a quantity as gravity (the formula proves this) allows you to measure the weight of an object with a dynamometer (similar to ordinary household business). Please note that the instrument only displays force, as the local "g" value must be known to determine the exact body weight.

Does gravity act at any (both close and far) distance from the earth's center? Newton hypothesized that it acts on the body even at a considerable distance from the Earth, but its value decreases inversely with the square of the distance from the object to the Earth's core.

Gravity in the solar system

Is there a Definition and formula regarding other planets retain their relevance. With only one difference in the meaning of "g":

• on the Moon = 1.62 N/kg (six times less than on Earth);
• on Neptune = 13.5 N/kg (almost one and a half times higher than on Earth);
• on Mars = 3.73 N/kg (more than two and a half times less than on our planet);
• on Saturn = 10.44 N/kg;
• on Mercury = 3.7 N/kg;
• on Venus = 8.8 N/kg;
• on Uranus = 9.8 N/kg (practically the same as ours);
• on Jupiter = 24 N/kg (almost two and a half times higher).

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

Man on the way to progress

Historically, it has been Human as you move forward along paths of progress mastered the ever 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 brought the physical strength of animals to his service, making them domestic. The horse accelerated his run, the camel made the desert passable, the elephant the marshy jungle. But the physical forces of even the strongest animals are immeasurably small compared to the forces of nature.

The first person subjugated the element of fire, but only in its most weakened versions. Initially - for many centuries - he used only wood as a fuel - a very low-energy type of fuel. Somewhat later, he learned to use wind energy from this source of energy, a man lifted the white wing of the sail into the air - and a light ship flew over the waves like a bird.

Sailboat on the waves

He exposed the blades of the windmill to the gusts of wind - and the heavy stones of the millstones spun, the pestles of the groats rattled. 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 wind blows: the storm tore the sails and sank the ships, the storm broke the wings and overturned the mills.

Even later, 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 rotational motion, but also the least powerful in comparison with various ones.

Man was moving forward on the ladder of progress and needed more and more energy.
He began to use new types of fuel - already the transition to burning coal increased the energy intensity of a kilogram of fuel from 2500 kcal to 7000 kcal - almost three times. Then came the time for oil and gas. Again, the energy content of each kilogram of fossil fuel has increased by one and a half to two times.

Steam engines were replaced by steam turbines; mill wheels were replaced by hydraulic turbines. Then the man extended 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 within minutes.

In 1954, the world's first Soviet nuclear power plant went into operation, turning the power of uranium into the 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, which could be called physical, because 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 - hydrogen isotopes.

Unfortunately, man has not yet been able to subdue the hydrogen-helium nuclear flame. He knows how to momentarily ignite his all-burning fire, setting fire to the reaction in a hydrogen bomb with a flash of a uranium explosion. But closer and closer, scientists see a hydrogen reactor, which will generate an electric current 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 human power over the forces of nature?

Not! Ahead - the mastery of the gravitational form of energy. It is even more prudently packaged 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 is yet visible there, beyond the cutting edge of science. And although we can confidently say that power plants will work for a person, processing gravitational energy into electric current (or maybe into a jet of gas flying out of a jet engine nozzle, or into the planned transformation of the ubiquitous atoms of silicon and oxygen into atoms of ultra-rare metals), we cannot yet say anything about the details of such a power plant (rocket engine, physical reactor).

The force of universal gravitation at the origins of the birth of galaxies

The force of universal gravitation is at the origins of the birth of galaxies from prestellar matter, as academician V.A. Ambartsumyan is convinced. It also extinguishes the stars that have burnt out their time, having spent the stellar fuel allotted to them at birth.

Yes, look around: everything on Earth is largely controlled by this force.

It is she who 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 there were no gravity, the Earth would immediately break out of its orbit around the Sun, and the globe itself would fall apart, torn apart by centrifugal forces. It is difficult to find anything that would not be, to one degree or another, dependent on the force of universal gravitation.

Of course, the ancient philosophers, very observant people, could not fail to notice that a stone thrown upwards always comes back. Plato in the 4th century BC explained this by the fact that all the substances of the Universe tend to where most of the 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 that makes its way to the sea , the smoke of a 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 - fire, smoke, vapors - to the periphery. This hypothesis, which explains some of the phenomena associated with the force of universal gravitation, has existed for more than 2 thousand years.

Scientists about the force of gravity

Probably the first to raise the question of force of gravity really scientific, was the genius of the Renaissance - Leonardo da Vinci. Leonardo proclaimed that gravitation is characteristic not only of the Earth, that there are many centers of gravity. And he also suggested 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 January 4, 1643. He graduated from the University of Cambridge, became a bachelor, then - a master of science.

Isaac Newton

Everything that follows is an endless wealth of scientific works. But his main work is the "Mathematical Principles of Natural Philosophy", published in 1687 and usually called simply "Beginnings". 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 that is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them ...

Some provisions of this formulation could be anticipated by Newton's predecessors, but it has not yet been given to anyone in its entirety. Newton's genius was needed to assemble these fragments into a single whole in order to spread the attraction of the Earth to the Moon, and the Sun - to the entire planetary system.

From the law of universal gravitation, Newton derived all the laws of motion of the planets, discovered before by Kepler. They were simply 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 the result of universal gravitation ... This was a great triumph of science.

It seemed that the main force of nature, which moves the worlds, was finally discovered and mathematically described, the force to which air molecules, apples, and the Sun are subject. Giant, immeasurably huge was the step taken by Newton.

The first popularizer of the work of a brilliant scientist, the French writer Francois Marie Arouet, world-famous under the pseudonym Voltaire, said that Newton suddenly guessed the existence of a law named after him when he looked at a falling apple.

Newton himself never mentioned this apple. And it is hardly worth wasting time today on the refutation of this beautiful legend. And, apparently, Newton came to comprehend the great power of nature by logical reasoning. It is likely that it was included in the corresponding chapter of the "Beginnings".

The force of gravity affects the flight of the nucleus

Let us suppose that on a very high mountain, so high that its top is already out of the atmosphere, we have set up a gigantic artillery piece. Its barrel was placed strictly parallel to the surface of the globe and fired. Describing the arc the core falls to the ground.

We increase the charge, improve the quality of gunpowder, in one way or another we make the core move at a higher speed after the next shot. The arc described by the core becomes flatter. The core falls much farther from the foot of our mountain.

We also increase the charge and shoot. The nucleus 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 falls, the Earth escapes from under it. And, having described the ring around our planet, the core returns to the point of departure.

The gun can be removed in the meantime. After all, the flight of the nucleus around the globe will take more than an hour. And then the core will swiftly sweep over the top of the mountain and go to a new circle around 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 flight of the core? It will first fly in an arc, more gentle than the curvature of the earth's surface, and begin to move away from the Earth. At the same time, its speed under the influence of the Earth's gravity will decrease.

And, finally, turning around, it will begin, as it were, to fall back to the Earth, but it will fly past it and will no longer complete 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 the center of our planet will be located.

If we further increase the initial velocity of the nucleus, the ellipse will turn out to be more stretched. It is possible to stretch this ellipse in such a way that the nucleus will reach the lunar orbit or even much further. But until the initial velocity of this nucleus exceeds 11.2 km/s, it will remain a satellite of the Earth.

The nucleus, which received a speed of over 11.2 km / s when fired, will forever fly away from 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 an ellipse, no matter how elongated it may be, we will inevitably systematically return to the starting point. Moving along a parabola, we will never return to the starting point.

But, having left the Earth with this speed, the nucleus will not yet be able to fly to infinity. The powerful gravitation of the Sun will bend the trajectory of its flight, close around itself like the trajectory of a planet. The core will become Earth's sister, a tiny planet in our own family of planets.

In order to direct the nucleus outside the planetary system, to overcome the solar attraction, it is necessary to tell it a speed of more than 16.7 km / s, and direct it so that the speed of the Earth's own motion is added 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 are elliptical, from 11.2 to 16.7 km / s are parabolic , and above this number - liberating speeds.

Here it should be added that the given values ​​of these velocities are valid only for the Earth. If we lived on Mars, the circular speed would be much easier for us to achieve - it is only about 3.6 km / s there, and the parabolic speed is only slightly more than 5 km / s.

On the other hand, it would be much more difficult to send the nucleus on a space flight from Jupiter than from Earth: the circular speed on this planet is 42.2 km / s, and the parabolic speed is even 61.8 km / s!

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 separation speed - 618.8 km / s!

So Newton at the end of the 17th century, a hundred years before the first flight of the Montgolfier brothers' balloon filled with warm air, two hundred years before the first flights of the Wright brothers' airplane, and almost a quarter of a millennium before the takeoff of the first liquid rockets, pointed the way to the sky for satellites and spaceships.

The force of gravity is inherent in every sphere

Via law of gravity unknown planets were discovered, cosmogonic hypotheses of the origin of the solar system were created. The main force of nature, which controls the stars, planets, apples in the garden, and gas molecules in the atmosphere, has been discovered and mathematically described.

But we do not know the mechanism of universal gravitation. Newtonian gravitation does not explain, but visually represents the current state of planetary motion.

We do not know what causes the interaction of all bodies of the Universe. And it cannot be said that Newton was not interested in this reason. For many years he pondered over its possible mechanism.

By the way, this is indeed an extremely mysterious power. A force that manifests itself through hundreds of millions of kilometers of space, devoid of any material formations at first glance, with the help of which one could explain the transfer of interaction.

Newton's hypotheses

And Newton resorted to hypothesis about the existence of a certain ether that allegedly fills the entire Universe. In 1675, he explained the attraction to the Earth by the fact that the ether filling the entire Universe rushes to the center of the Earth in continuous streams, capturing all objects in this movement and creating a gravitational force. The same flow of ether rushes to the Sun and, dragging the planets, comets, ensures their elliptical trajectories...

It was not a very convincing, although absolutely mathematically logical hypothesis. But now, in 1679, Newton created a new hypothesis explaining the mechanism of gravity. 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 it has the property of squeezing all material bodies out of 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 returns again to the hypothesis of the squeezing out ether.

The ingenious brain of Newton fought over the solution of the great mystery and did not find it. This explains such sharp throwing from side to side. Newton used to say:

I don't make hypotheses.

And although, as we have only been able to verify, this is not entirely true, we can definitely state something else: Newton was able to clearly distinguish between indisputable things from unsteady and controversial hypotheses. And in the Elements there is a formula of the great law, but there is no attempt 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 perhaps this discussion would not concern the very essence of the law, if he answered exactly all the questions put 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. Let's give examples.

The force of gravity in Seeliger's calculations

The first of these is Seeliger's paradox. Considering the Universe to be infinite and uniformly filled with matter, Seeliger tried to calculate, according to Newton's law, the universal gravitational force created by the entire infinitely large mass of the infinite Universe at some of its points.

It was not an easy task from the point of view of pure mathematics. Having overcome all the difficulties of the most complex transformations, Seeliger found that the desired 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, we do not see this in practice. This means that the law of universal gravitation does not apply to the entire universe.

However, other explanations for the paradox are also possible. For example, we can assume that matter does not evenly fill the entire Universe, but its density gradually decreases and, finally, somewhere very far away there is no matter at all. But to imagine 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 gravity weakens faster than the square of the distance increases. But this casts doubt on the surprising harmony of Newton's law. No, and this explanation did not satisfy scientists. The paradox remained a paradox.

Observations of the movement of Mercury

Another fact, the action of the force of universal gravitation, not explained by Newton's law, brought observation of the motion of Mercury- closest to the planet. Precise calculations according to Newton's law showed that perehelion - the point of the ellipse along which Mercury moves closest to the Sun - should move by 531 arc seconds in 100 years.

And astronomers have found that this shift is equal to 573 arc seconds. This excess - 42 arc seconds - also could not be explained by scientists, using only formulas arising from Newton's law.

He explained both Seeliger's paradox, and the displacement of Mercury's perhelion, and many other paradoxical phenomena and inexplicable facts Albert Einstein, one of the greatest, if not the greatest physicist of all time. Among the annoying little things was the question of ethereal wind.

Experiments by Albert Michelson

It seemed that this question did not directly concern the problem of gravitation. He related to optics, to light. More precisely, to the definition of its speed.

The Danish astronomer was the first to determine the speed of light. Olaf Remer watching the eclipse of Jupiter's moons. This happened as early as 1675.

American physicist Albert Michelson at the end of the 18th century, he conducted a series of determinations of the speed of light under terrestrial conditions, using the apparatus he had designed.

In 1927, he gave the speed of light as 299796 + 4 km/s, which was an excellent accuracy for those times. But the essence of the matter is different. In 1880 he decided to investigate the ethereal 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.

Essence of experience

Experience was conceived like this. The earth moves in its orbit at a speed of about 30 km/sec.. Moves through the air. This means that the speed of light from a source that is ahead of the receiver relative to the motion of the Earth must be greater than from a source that is on the other side. In the first case, the speed of the ethereal wind must be added to the speed of light; in the second case, the speed of light must decrease by this value.

Of course, the speed of the Earth in its orbit around the Sun is only one ten thousandth of the speed of light. Finding such a small term is very difficult, but Michelson was called the king of precision for a reason. He used an ingenious way to catch the "elusive" difference in the speeds of the rays of light.

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 beam going along the parallel experienced the influence of the ethereal wind, when it was added to the meridional beam, interference fringes should have arisen, the waves of the two beams would have been shifted in phase.

However, it was difficult for Michelson to measure the paths of both rays with such great accuracy so that they were exactly the same. Therefore, he built the apparatus so that there were no interference fringes, and then turned it 90 degrees.

The meridional beam became latitudinal and vice versa. If there is an ethereal wind, black and light stripes should appear under the eyepiece! But they weren't. Perhaps, when turning the device, the scientist moved it.

He set it up at noon and fixed it. After all, besides the fact that, it also rotates around an axis. And therefore, at different times of the day, the latitudinal beam occupies a different position relative to the oncoming ethereal wind. Now, when the apparatus 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 detected! The light traveled in all directions at the same speed!

Nobody has been 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. And again nothing!

Experiments by Albert Einstein

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

How did you arrive at your special theory of relativity? Under what circumstances did you come up with a brilliant idea? The scientist replied: “It always seemed to me that this is the case.

Maybe he did not 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 there was a hunch, bright as lightning. Then the development began. No, there are no contradictions with known phenomena. And then those five pages full of formulas appeared, which were published in a physical journal. Pages that opened a new era in physics.

Imagine a spaceship flying through space. We’ll warn you right away: the starship is very peculiar, the kind you haven’t read about in science fiction stories. Its length is 300 thousand kilometers, and its speed is, well, let's say, 240 thousand km / s. And this spaceship flies past one of the intermediate platforms in space, without stopping at it. At full speed.

One of the passengers is standing on the deck of the starship with a watch. And you and I, reader, are standing on a platform - its length must correspond to the size of a starship, that is, 300 thousand kilometers, otherwise it will not be able to stick to it. And we also have a watch in our hands.

We notice that at the moment when the bow of the starship caught up with the rear edge of our platform, a lantern flashed on it, illuminating the space surrounding it. A second later, a beam of light reached the front edge of our platform. We do not doubt this, because we know the speed of light, and we have managed to pinpoint exactly the corresponding moment on the clock. And on a starship...

But the starship also flew towards the beam of light. And we quite 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 the 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, absolutely accurately recorded it on their watches. And how could it be otherwise: after all, the speed of light does not depend on the speed of the source ...

How so? We see one thing from a fixed platform, and another to them on the deck of a starship? What's the matter?

Einstein's theory of relativity

It should be noted immediately: Einstein's theory of relativity at first glance, it absolutely contradicts our established idea 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 many times in the history of science.

But the discovery of the sphericity of the Earth was contrary to common sense. How can people live on the opposite side and not fall into the abyss?

For us, the sphericity of the Earth is an undoubted fact, and from the point of view of common sense, any other assumption is meaningless and wild. But step back from your time, imagine the first appearance of this idea, and you will understand how difficult it would be to accept it.

Well, was it easier to admit that the Earth is not motionless, but flies along its trajectory dozens of times faster than a cannonball?

All these were wrecks of common sense. Therefore, modern physicists never refer to it.

Now back to the special theory of relativity. The world recognized her for the first time in 1905 from an article signed by a little-known name - Albert Einstein. And he was only 26 at the time.

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 has passed in a moving car than your wristwatch measured. In the car, the passage of time slowed down compared to the time on the stationary platform.

Quite amazing things logically followed from this assumption. It turned out that a person traveling to work in a tram, in comparison with a pedestrian going the same way, not only saves time due to speed, but it also goes more slowly for him.

However, do not try to preserve eternal youth in this way: even if you become a carriage driver and spend a third of your life in a tram, in 30 years you will gain hardly more than a millionth of a second. In order 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 the increase in the speed of bodies is reflected in their mass. The closer the speed of a body to the speed of light, the greater its mass. At the speed of a body 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 speed
Sveta!

This 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 motionless photon.

When stationary, it has no mass. Also, neutrinos do not have a rest mass, and they are also condemned to an eternal unrestrained flight through space at the maximum possible speed in our Universe, without overtaking light and keeping up with it.

Isn't it true that each of the consequences of the special theory of relativity listed by us is surprising, paradoxical! And each, of course, is contrary to "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 implications say? About 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 (more:), connecting together reinforcement, or foundation stones, connected together things and phenomena that had previously seemed independent of each other and created the foundation on which for the first time in the history of science it was possible to build a harmonious 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 interdependence between space and matter. Apparently it would be more correct to call it space-time theory, or theory of gravity.

But this name has grown so closely with Einstein's theory that even raising the question of replacing it now seems indecent to many scientists.

The general theory of relativity established the interdependence between matter and the time and space that contain it. It turned out that space and time not only cannot be imagined as existing separately from matter, but their properties also depend on the matter that fills them.

Starting point of discussion

Therefore, one can only specify starting point of discussion and draw some important conclusions.

At the beginning of the space journey, an unexpected catastrophe destroyed the library, the film fund and other repositories of the mind, the memory of people flying through space. And the nature of the native planet is forgotten in the change of centuries. Even the law of universal gravitation is forgotten, because the rocket flies in intergalactic space, where it is almost not felt.

However, the ship's engines work superbly, the energy supply in the batteries is practically unlimited. Most of the time, the ship moves by inertia, and its inhabitants are used 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 become weighty, 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 falls into the orbits of the most suitable planet. The starships go out, walking on fresh green ground, constantly experiencing the same feeling 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/s2! And they have the first assumption that the gravitational field (gravitational force) and acceleration give the same effect, and perhaps have a common nature.

None of our earthling contemporaries was on such a long flight, but many people felt the phenomenon of “weighting” and “lightening” their bodies. Already an ordinary elevator, when it moves at an accelerated pace, creates this sensation. When descending, you feel a sudden loss of weight; when ascending, on the contrary, the floor presses on your legs with more force than usual.

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 the stars and planets are at the same distance from us, in the firmament, etc.

Scientists subjected sensations to experimental verification. Even Newton thought about the strange identity of the two phenomena. He tried to give them numerical characteristics. Having measured the gravitational and , he was convinced 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.

Principle of equivalence, which we are talking about, is the basis of the general theory of relativity, although the modern interpretation of the theory no longer needs this principle. Omitting the mathematical deductions that follow from this principle, let us proceed directly to some consequences of the general theory of relativity.

The presence of large masses of matter greatly affects the surrounding space. It leads to such changes in it, which can be defined as inhomogeneities of space. These inhomogeneities direct the movement of any masses that are close to the attracting body.

Usually resort to such an analogy. Imagine a canvas stretched tightly on a frame parallel to the earth's surface. Put a heavy weight on it. This will be our big attracting mass. She, of course, will bend the canvas and end up in some recess. Now roll the ball over this canvas in such a way that part of its path lies next to the attracting mass. Depending on how the ball will be launched, three options are possible.

1. The ball will fly far enough from the recess 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 beautifully models the capture by a star or planet of an extraneous body carelessly flown 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 similar to flying outside 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. What is the physical meaning of this deflection, or curvature, as they often say, no one knows.

It follows from the general theory of relativity that any material body can move in a gravitational field only along curved lines. Only in particular, special cases does the curve turn 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 has its effect on it, as well as on a molecule, an asteroid or a 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 passage of time should be slower than away from it.

You see, and the general theory of relativity is fraught with paradoxical conclusions that can overturn our ideas of "common sense" again and again!

Gravitational collapse

Let's talk about an amazing phenomenon of a cosmic nature - about gravitational collapse (catastrophic compression). This phenomenon occurs in gigantic accumulations of matter, where gravitational forces reach such enormous magnitudes that no other forces existing in nature can resist them.

Remember Newton's famous formula: the greater the force of gravity, the smaller the square of the distance between gravitating bodies. Thus, the denser the material formation becomes, the smaller its size, the more rapidly the gravitational forces increase, the more inevitable is their destructive embrace.

There is a cunning technique by which nature struggles with the seemingly limitless compression of matter. To do this, it stops the very course of time in the sphere of action of supergiant gravitational forces, and the shackled masses of matter are, as it were, switched off from our Universe, frozen in a strange lethargic dream.

The first of these "black holes" of the cosmos has probably already been discovered. According to the assumption of Soviet scientists O. Kh. Huseynov 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, the "black hole".

The Soviet scientist Professor K.P. Stanyukovich, as they say, “on the tip of a pen”, showed through purely theoretical constructions that particles of “frozen matter” can be very diverse in size.

• Its gigantic formations are possible, similar to quasars, continuously radiating as much energy as all 100 billion stars of our Galaxy radiate.
• 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.

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

plankeons

Plankeons are a very special class of particles. They possess, according to K.P. Stanyukovich, an extremely interesting property: they carry matter in themselves in an unchanged form, 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 1080 plankeons in the Universe, approximately one plankeon in a cube of space with a side of 10 centimeters. By the way, at the same time as Stanyukovich and (regardless of him, the hypothesis of plankeons was put forward by Academician M.A. Markov. Only Markov gave them a different name - maximons.

Special properties of plankeons can also be used to explain sometimes paradoxical transformations of elementary particles. It is known that when two particles collide, fragments never form, but other elementary particles arise. This is truly amazing: in the ordinary world, breaking a vase, we will never get whole cups or even rosettes. But suppose that in the depths of each elementary particle there is a plankeon, 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 of "jump out" those that we consider to have arisen during the collision. At the same time, the plankeon, as a diligent accountant, will ensure 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 K. P. 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 radiation of gravitons obeys a number of regularities. In particular, they are easier to fly into that region of space. Which contains fewer gravitons. This means that if there are two celestial bodies in space, both will radiate gravitons predominantly “outwards”, in directions opposite to each other. This creates an impulse that causes the bodies to approach each other, to attract each other.

Gravitational force is the force with which objects of a certain mass are attracted to each other, located at a certain distance from each other.

The English scientist Isaac Newton in 1867 discovered the law of universal gravitation. This is one of the fundamental laws of mechanics. The essence of this law is as follows:any two material particles are attracted to each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

The force of attraction is the first force that a person felt. This is the force with which the Earth acts on all bodies located on its surface. And any person feels this force as his own weight.

Law of gravity

There is a legend that Newton discovered the law of universal gravitation quite by accident, walking in the evening in the garden of his parents. Creative people are constantly in search, and scientific discoveries are not instantaneous insight, but the fruit of long-term mental work. Sitting under an apple tree, Newton was thinking about another idea, and suddenly an apple fell on his head. It was clear to Newton that the apple fell as a result of the Earth's gravity. “But why doesn’t the moon fall to the Earth? he thought. “It means that some other force is acting on it, keeping it in orbit.” This is how the famous law of gravity.

Scientists who had previously studied the rotation of celestial bodies believed that celestial bodies obey some completely different laws. That is, it was assumed that there are completely different laws of attraction on the surface of the Earth and in space.

Newton combined these supposed kinds of gravity. Analyzing Kepler's laws describing the motion of the planets, he came to the conclusion that the force of attraction arises between any bodies. That is, both the apple that fell in the garden and the planets in space are affected by forces that obey the same law - the law of universal gravitation.

Newton found that Kepler's laws only work if there is an attractive force between the planets. And this force is directly proportional to the masses of the planets and inversely proportional to the square of the distance between them.

The force of attraction is calculated by the formula F=G m 1 m 2 / r 2

m 1 is the mass of the first body;

m2is the mass of the second body;

r is the distance between the bodies;

G is the coefficient of proportionality, which is called gravitational constant or gravitational constant.

Its value was determined experimentally. G\u003d 6.67 10 -11 Nm 2 / kg 2

If two material points with a mass equal to a unit of mass are at a distance equal to a unit of distance, then they are attracted with a force equal to G.

The forces of attraction are the gravitational forces. They are also called gravity. They are subject to the law of universal gravitation and appear everywhere, since all bodies have mass.

Gravity

The gravitational force near the surface of the Earth is the force with which all bodies are attracted to the Earth. They call her gravity. It is considered constant if the distance of the body from the Earth's surface is small compared to the radius of the Earth.

Since gravity, which is the gravitational force, depends on the mass and radius of the planet, it will be different on different planets. Since the radius of the Moon is less than the radius of the Earth, then the force of attraction on the Moon is less than on the Earth by 6 times. And on Jupiter, on the contrary, gravity is 2.4 times greater than gravity on Earth. But body weight remains constant, no matter where it is measured.

Many people confuse the meaning of weight and gravity, believing that gravity is always equal to weight. But it's not.

The force with which the body presses on the support or stretches the suspension, this is the weight. If the support or suspension is removed, the body will begin to fall with the acceleration of free fall under the action of gravity. The force of gravity is proportional to the mass of the body. It is calculated according to the formulaF= m g , where m- body mass, g- acceleration of gravity.

Body weight can change, and sometimes disappear altogether. Imagine that we are in an elevator on the top floor. The elevator is worth it. At this moment, our weight P and the force of gravity F, with which the Earth pulls us, are equal. But as soon as the elevator began to move down with acceleration a , weight and gravity are no longer equal. According to Newton's second lawmg+ P = ma . P \u003d m g -ma.

It can be seen from the formula that our weight decreased as we moved down.

At the moment when the elevator picked up speed and began to move without acceleration, our weight is again equal to gravity. And when the elevator began to slow down its movement, acceleration a became negative and the weight increased. There is an overload.

And if the body moves down with the acceleration of free fall, then the weight will completely become equal to zero.

At a=g R=mg-ma= mg - mg=0

This is a state of weightlessness.

So, without exception, all material bodies in the Universe obey the law of universal gravitation. And the planets around the Sun, and all the bodies that are near the surface of the Earth.

Many rightly call the 16th-17th centuries one of the most glorious periods in history. It was at this time that the foundations were largely laid, without which the further development of this science would be simply unthinkable. Copernicus, Galileo, Kepler have done a great job to declare physics as a science that can answer almost any question. Standing apart in a whole series of discoveries is the law of universal gravitation, the final formulation of which belongs to the outstanding English scientist Isaac Newton.

The main significance of the works of this scientist was not in his discovery of the force of universal gravitation - both Galileo and Kepler spoke about the presence of this quantity even before Newton, but in the fact that he was the first to prove that the same forces act both on Earth and in outer space. same forces of interaction between bodies.

Newton in practice confirmed and theoretically substantiated the fact that absolutely all bodies in the Universe, including those located on the Earth, interact with each other. This interaction is called gravitational, while the process of universal gravitation itself is called gravity.
This interaction occurs between bodies because there is a special type of matter, unlike others, which in science is called the gravitational field. This field exists and acts around absolutely any object, while there is no protection from it, since it has an unparalleled ability to penetrate any materials.

The force of universal gravitation, the definition and formulation of which he gave, is directly dependent on the product of the masses of interacting bodies, and inversely on the square of the distance between these objects. According to Newton, irrefutably confirmed by practical research, the force of universal gravitation is found by the following formula:

In it, of particular importance belongs to the gravitational constant G, which is approximately equal to 6.67 * 10-11 (N * m2) / kg2.

The gravitational force with which bodies are attracted to the Earth is a special case of Newton's law and is called gravity. In this case, the gravitational constant and the mass of the Earth itself can be neglected, so the formula for finding the force of gravity will look like this:

Here g is nothing more than an acceleration whose numerical value is approximately equal to 9.8 m/s2.

Newton's law explains not only the processes occurring directly on the Earth, it gives an answer to many questions related to the structure of the entire solar system. In particular, the force of universal gravitation between has a decisive influence on the motion of the planets in their orbits. The theoretical description of this motion was given by Kepler, but its justification became possible only after Newton formulated his famous law.

Newton himself connected the phenomena of terrestrial and extraterrestrial gravity using a simple example: when fired from it, it does not fly straight, but along an arcuate trajectory. At the same time, with an increase in the charge of gunpowder and the mass of the nucleus, the latter will fly farther and farther. Finally, if we assume that it is possible to obtain so much gunpowder and construct such a cannon that the cannonball will fly around the globe, then, having made this movement, it will not stop, but will continue its circular (ellipsoidal) movement, turning into an artificial one. As a result, the force of the universal gravity is the same in nature both on Earth and in outer space.

DEFINITION

The law of universal gravitation was discovered by I. Newton:

Two bodies are attracted to each other with , which is directly proportional to their product and inversely proportional to the square of the distance between them:

Description of the law of gravity

The coefficient is the gravitational constant. In the SI system, the gravitational constant has the value:

This constant, as can be seen, is very small, so the gravitational forces between bodies with small masses are also small and practically not felt. However, the motion of cosmic bodies is completely determined by gravity. The presence of universal gravitation or, in other words, gravitational interaction explains what the Earth and planets “hold” on, and why they move around the Sun along certain trajectories, and do not fly away from it. The law of universal gravitation allows us to determine many characteristics of celestial bodies - the masses of planets, stars, galaxies and even black holes. This law allows us to calculate the orbits of the planets with great accuracy and create a mathematical model of the Universe.

With the help of the law of universal gravitation, it is also possible to calculate cosmic velocities. For example, the minimum speed at which a body moving horizontally above the Earth's surface will not fall on it, but will move in a circular orbit is 7.9 km / s (the first space velocity). In order to leave the Earth, i.e. to overcome its gravitational attraction, the body must have a speed of 11.2 km / s, (the second cosmic velocity).

Gravity is one of the most amazing natural phenomena. In the absence of gravitational forces, the existence of the Universe would be impossible, the Universe could not even arise. Gravity is responsible for many processes in the Universe - its birth, the existence of order instead of chaos. The nature of gravity is still not fully understood. To date, no one has been able to develop a worthy mechanism and model of gravitational interaction.

Gravity

A special case of the manifestation of gravitational forces is gravity.

Gravity is always directed vertically downward (towards the center of the Earth).

If the force of gravity acts on the body, then the body performs. The type of movement depends on the direction and module of the initial speed.

We deal with the force of gravity every day. , after a while it is on the ground. The book, released from the hands, falls down. Having jumped, a person does not fly away into outer space, but falls down to the ground.

Considering the free fall of a body near the Earth's surface as a result of the gravitational interaction of this body with the Earth, we can write:

whence the free fall acceleration:

The free fall acceleration does not depend on the mass of the body, but depends on the height of the body above the Earth. The globe is slightly flattened at the poles, so bodies near the poles are slightly closer to the center of the earth. In this regard, the acceleration of free fall depends on the latitude of the area: at the pole it is slightly greater than at the equator and other latitudes (at the equator m / s, at the North Pole equator m / s.

The same formula allows you to find the free fall acceleration on the surface of any planet with mass and radius .

Examples of problem solving

EXAMPLE 1 (the problem of "weighing" the Earth)

Exercise	The radius of the Earth is km, the acceleration of free fall on the surface of the planet is m/s. Using these data, estimate the approximate mass of the Earth.
Decision	Acceleration of free fall at the surface of the Earth: whence the mass of the Earth: In the C system, the radius of the Earth m. Substituting the numerical values ​​of physical quantities into the formula, we estimate the mass of the Earth:
Answer	Mass of the Earth kg.

EXAMPLE 2

Exercise

An Earth satellite moves in a circular orbit at an altitude of 1000 km from the Earth's surface. How fast is the satellite moving? How long does it take for a satellite to make one complete revolution around the earth?

Decision

According to , the force acting on the satellite from the Earth is equal to the product of the mass of the satellite and the acceleration with which it moves: From the side of the earth, the force of gravitational attraction acts on the satellite, which, according to the law of universal gravitation, is equal to: where and are the masses of the satellite and the Earth, respectively. Since the satellite is at a certain height above the surface of the Earth, the distance from it to the center of the Earth: where is the radius of the earth.