Equation of gravity. The history of the discovery of the law of universal gravitation - description, features and interesting facts. Isaac Newton on the force of universal gravitation
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 ways of progress mastered the increasingly powerful forces of nature. He started when he had nothing but a stick clutched in his fist and his own physical strength. But he was wise, and he brought the physical strength of animals into his service, making them domesticated. The horse sped up his run, the camel made the desert passable, the elephant made the swampy jungle. But physical strength even the strongest animals are immeasurably weak before the forces of nature. Man was the first to subjugate the element of fire, but only in its most weakened versions. At first - for many centuries - he used only wood as fuel - a very low-energy type of fuel. Somewhat later, he learned to use this source of energy to use the energy of the wind, the man raised the white wing of the sail into the air - and the light ship flew like a bird across the waves. Sailboat on the waves. He exposed the windmill blades to the gusts of wind - and the heavy stones of the millstones began to spin, and the pestles of the grinders began to rattle. 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 the sails and sank the ships, the storm broke the wings and overturned the mills. Even later, man began to conquer flowing water. The wheel is not only the most primitive of devices capable of converting water energy into rotational movement, but also the least powerful compared to the various ones. Man walked ever forward along the ladder of progress and needed everything large quantities 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 the time came for oil and gas. The energy content of each kilogram of fossil fuel has again increased by one and a half to two times. Steam engines replaced steam turbines; mill wheels were replaced by hydraulic turbines. Next, the man extended his hand to the fissioning uranium atom. However, the first use of a new type of energy had tragic consequences - the nuclear fire of Hiroshima in 1945 incinerated 70 thousand human hearts within a matter of minutes. In 1954, the world's first Soviet nuclear power plant came online, turning the power of uranium into the radiant force 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. This 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 subjugate the hydrogen-helium nuclear flame. He knows how to light his all-burning fire for a moment, igniting the reaction in hydrogen bomb flash of a uranium explosion. But scientists are seeing a hydrogen reactor, which will give birth, closer and closer. electricity as a result of the fusion of hydrogen isotope nuclei 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 mankind’s power over the forces of nature? No! Ahead is mastering the gravitational form of energy. It is even more prudently packaged by nature than even the energy of hydrogen-helium fusion. Today this is the most concentrated form of energy that a person can even imagine. Nothing further is yet visible there, beyond the cutting edge of science. And although we can confidently say that power plants that process gravitational energy into an electric current (or perhaps into a stream of gas escaping from the nozzle of a jet engine, or into the planned transformations 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
Force universal gravity stands at the origins of the birth of Galaxies from prestellar matter, as Academician V.A. Ambartsumyan is convinced of. It extinguishes stars that have burned out their time, having used up the stellar fuel they were given at birth. Many physicists explain the existence of quasars by the intervention of universal gravity (more details:) Look around: here on Earth everything is largely controlled by this force. It is this that determines the layered structure of our planet - the alternation of lithosphere, hydrosphere and atmosphere. It is she who holds 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 out of its orbit around the Sun, and the globe itself would fall apart, torn apart centrifugal forces. It is difficult to find anything that would not be, to one degree or another, dependent on the force of universal gravity. Of course, the ancient philosophers, very observant people, could not help but notice that a stone thrown upward always comes back. Plato in the 4th century BC explained this by saying 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 making its way to the sea , the smoke of the fire rushes towards its kindred clouds. Plato's student, 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 phenomena associated with the force of universal gravity, has existed for more than 2 thousand years.Scientists about the force of universal gravity
Probably the first to raise the question about force of universal gravity truly scientifically, there was a genius of the Renaissance - Leonardo da Vinci. Leonardo proclaimed that gravity is not unique 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 universal gravitation
born January 4, 1643. He graduated from Cambridge University, became a bachelor, then a master of science.
Isaac Newton. Everything further is endless wealth scientific works. But his main work is “ Mathematical principles 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 attract 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 were able to anticipate Newton's predecessors, but no one had ever succeeded in achieving it in its entirety. It took the genius of Newton to assemble 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 planetary motion previously discovered by Kepler. They turned out to be 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 a consequence of universal gravitation... This was a great triumph of science. It seemed that the main force of nature that moves the worlds had finally been discovered and mathematically described, a force that controls air molecules, apples, and the Sun. The step taken by Newton was gigantic, immeasurably huge. The first popularizer of the works of the brilliant scientist, the French writer François Marie Arouet, world-famous under the pseudonym Voltaire, said that Newton suddenly realized the existence of the law named after him when he looked at a falling apple. Newton himself never mentioned this apple. And it’s hardly worth wasting time today to refute this beautiful legend. And, apparently, Newton came to comprehend the great power of nature through logical reasoning. Probably, it was this that was included in the corresponding chapter of “Beginnings”.
The force of universal gravity affects the flight of the nucleus
Let's assume that very high mountain, so high that its top is already out of the atmosphere, we installed a giant artillery piece. Its barrel was positioned strictly parallel to the surface globe and fired. Having described the arc, the core falls to Earth. We increase the charge, improve the quality of the gunpowder, and in one way or another force the cannonball to move at a higher speed after the next shot. The arc described by the core 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 flat trajectory that it descends parallel to the surface of the globe. The core can no longer fall to the Earth: at the same speed with which it decreases, the Earth escapes from under it. And, having described a 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 core around the globe will take over an hour. And then the core will quickly fly over the top of the mountain and set off on a new flight around the Earth. If, as we agreed, the core does not experience any air resistance, it will never be able to fall. For this, the core speed should be close to 8 km/sec. What if we increase the speed of the core's flight? It will first fly in an arc, flatter than the curvature 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, turning around, it will begin to fall back to Earth, but 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, at one of the foci of which the center of our planet will be located. If you further increase the initial speed of the core, the ellipse will become more stretched. It is possible to stretch this ellipse so that the core will reach the lunar orbit or even much further. But until the initial speed of this core exceeds 11.2 km/sec, it will remain a satellite of the Earth. The core, which received a speed of over 11.2 km/sec 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 at this speed, the core will not yet be able to fly to infinity. The powerful gravity of the Sun will bend the trajectory of its flight, closing it around itself like the trajectory of a planet. The core will become the sister of the Earth, an independent tiny planet in our family of planets. In order to direct the core beyond the planetary system, to overcome solar gravity, it is necessary to give it a speed of over 16.7 km/sec, and direct it so that the speed is added to this speed own movement Earth. A speed of about 8 km/sec (this speed depends on the height of the mountain from which our cannon fires) is called circular speed, speeds from 8 to 11.2 km/sec are elliptical, from 11.2 to 16.7 km/sec are parabolic , and above this number - at 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 is only about 3.6 km/sec, and the parabolic speed is only slightly higher than 5 km/sec. But sending the core into space 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/sec! So Newton at the end of the 17th century, a hundred years before the first flight filled with warm air hot air balloon The Montgolfier brothers, 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-propellant rockets, showed the way to the sky for satellites and spacecraft.The force of universal gravity is inherent in every sphere
By using law of universal gravitation unknown planets were discovered, cosmogonic hypotheses of origin were created solar system. The main force of nature, which controls the stars, the 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 gravity does not explain, but clearly represents current state planetary movements. We do not know what causes the interaction of all bodies in the Universe. And it cannot be said that Newton was not interested in this reason. For many years he pondered 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 at first glance of any material formations with the help of which the transfer 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, which fills 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 flow of ether rushes towards the Sun and, carrying planets and comets with it, ensures their elliptical trajectories... This was not a very convincing, although absolutely mathematically logical, hypothesis. But then, in 1679, Newton created a new hypothesis explaining the mechanism of gravity. This time he gives the ether the property of having different concentrations 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 out all material bodies from their denser layers into less dense ones. And all the bodies are squeezed out onto the surface of the Earth. In 1706, Newton sharply denied the very existence of the ether. In 1717, he again returned to the hypothesis of extruding ether. Newton's brilliant brain struggled to solve the great mystery and did not find it. This explains such sharp throwing from side to side. Newton liked to say:I don't make hypotheses.And although, as soon as we were able to verify, this is not entirely true, something else can be stated for sure: Newton knew how to clearly distinguish between indisputable things and unsteady and controversial hypotheses. And in “Principles” there is a formula for 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 to this day. 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 it answered exactly all the questions asked of it. 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 universal gravitation in Seeliger's calculations
The first of them is the Seeliger 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. This was not an easy task from the point of view of pure mathematics. Having overcome all the difficulties of the most complex transformations, Seeliger established 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, in practice we do not observe this. This means that the law of universal gravitation does not apply to the entire Universe. However, other explanations for the paradox are 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 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 universal gravity weakens faster than the square of the distance increases. But this calls into question the amazing 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 observations of the movement of Mercury- closest to the planet. Accurate calculations According to Newton's law, they showed that perhelion - the point of the ellipse along which Mercury moves closest to the Sun - should shift by 531 arcseconds in 100 years. And astronomers have determined that this displacement is equal to 573 arcseconds. This excess - 42 arc seconds - also could not be explained by scientists, using only formulas arising from Newton's law. Explained the Seeliger paradox, the shift of the perihelion of Mercury, 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.Albert Michelson's experiments
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. The speed of light was first determined by a Danish astronomer Olaf Roemer, observing the eclipse of the satellites of Jupiter. This happened back in 1675. American physicist Albert Michelson at the end of the 18th century, he carried out a series of determinations of the speed of light under terrestrial conditions, using the apparatus he designed. In 1927, he gave the speed of light a value of 299796 + 4 km/sec - this was excellent accuracy for those times. But the point is different. In 1880, he decided to explore the ethereal wind. He wanted to finally establish the existence of that very ether, the presence of which they tried to explain the transmission gravitational interaction, and transmission of light waves. Michelson was probably the most remarkable experimentalist of his time. He had excellent equipment. And he was almost sure of success.The essence of experience
Experience was intended this way. The Earth moves in its orbit at a speed of about 30 km/sec. Moves through the ether. This means that the speed of light from a source standing in front of the receiver relative to the movement of the Earth must be greater than from a source standing on the other side. In the first case, the speed of the etheric wind must be added to the speed of light; in the second case, the speed of light must decrease by this amount.
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 detect such a small term, but it is not for nothing that Michelson was called the king of accuracy. He used a clever method to capture the “elusive” difference in the speed of light rays. He split the beam into two equal streams and directed them in mutually perpendicular directions: along the meridian and along the parallel. Having reflected from the mirrors, the rays returned. If a beam traveling along a parallel were influenced by the ethereal wind, when it was added to a meridional beam, interference fringes would appear, and the waves of the two beams would be out of phase. However, it was difficult for Michelson to measure the paths of both rays with such great accuracy so that they were absolutely identical. So he built the apparatus so that there were no interference fringes, and then rotated it 90 degrees. The meridional ray became latitudinal and vice versa. If there is an etheric wind, black and light stripes should appear under the eyepiece! But they were not there. Perhaps, when turning the apparatus, the scientist moved it. He set it up at noon and secured it. After all, in addition to the fact that it also rotates around an axis. And therefore in different time day, the latitude beam occupies a different position relative to the oncoming ethereal 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. No ethereal wind was detected! The light moved in all directions at the same speed! No one has been able to explain this. Michelson repeated the experiment again and again, improved the equipment, and finally achieved almost incredible measurement accuracy, an order of magnitude greater than what was necessary for the success of the experiment. And again nothing! Albert Einstein's experiments
The next big step in knowledge of the force of universal gravity did Albert Einstein. Albert Einstein was once asked:- How did you come to your special theory relativity? Under what circumstances did the brilliant idea strike you? The scientist replied: “I always imagined that this was the case.”Maybe he didn’t want to be frank, maybe he wanted to get rid of his annoying interlocutor. But it is difficult to imagine that the concept of the connections between time, space and speed discovered by Einstein was innate. No, of course, first a guess flashed through, bright as lightning. Then its development began. No, there are no contradictions with known phenomena. And then those five pages, filled with formulas, appeared that were published in a physics journal. Pages that opened a new era in physics. Imagine a starship flying in space. Let us warn you right away: the starship is very unique, the kind you have never read about in science fiction stories. Its length is 300 thousand kilometers, and its speed is, let’s say, 240 thousand km/sec. And this spaceship flies past one of the intermediate platforms in space, without stopping at it. At full speed. One of its 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 the starship, i.e. 300 thousand kilometers, because otherwise it will not be able to land on it. And we also have a watch in our hands. We notice: at that moment, when the nose of the spaceship reached the rear edge of our platform, a lantern flashed on it, illuminating the space surrounding it. A second later, the beam of light reached the front edge of our platform. We have no doubt about this, because we know the speed of light, and we managed to accurately detect the corresponding moment on the clock. And on the spaceship... But the spaceship was also flying 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 travel 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 confident that their beam covered the entire distance from bow to stern of 300 thousand kilometers. After all, he spent a whole second on this. They also absolutely accurately detected this on their watch. And how could it be otherwise: after all, the speed of light does not depend on the speed of the source... How can this be? We see one thing from a stationary platform, and they see something else 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 understanding of the structure of the world. We can say that it also contradicts common sense, as we are accustomed to represent it. This has happened more than once in the history of science. But the discovery of the spherical shape of the Earth also contradicted 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 common sense any other assumption is senseless and wild. But step back from your time, imagine the first appearance of this idea, and it becomes clear how difficult it would be to accept. Well, would it be easier to admit that the Earth is not motionless, but flies along its trajectory tens of times faster than a cannonball? These were all failures of common sense. That's why modern physicists never refer to it. Now let's return to the special theory of relativity. The world first learned about it in 1905 from an article signed by a little-known name - Albert Einstein. And he was only 26 years old at that time. Einstein made a very simple and logical assumption from this paradox: from the point of view of an observer on the platform, less time has passed in a moving carriage than was measured by your wristwatch. In the carriage, the passage of time slowed down compared to time on the stationary platform. Absolutely amazing things logically flowed from this assumption. It turned out that a person going to work on a tram, compared to a pedestrian walking the same way, not only saves time due to speed, but it also goes slower 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 on a tram, in 30 years you will gain hardly more than a millionth of a second. For the gain in time to become noticeable, you need 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, i.e. 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 imposes a limitation that does not allow any material body to develop speed, equal to the speed Sveta. After all, as the mass grows, it becomes more and more difficult to accelerate it. And an infinite mass cannot be moved from its place 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. Neutrinos also do not have a rest mass, and they are also condemned to eternal uncontrolled flight through space at the maximum speed possible in our Universe, without overtaking light or falling behind it. Isn’t it true that each of the consequences of the special theory of relativity that we have listed is surprising and paradoxical! And each, of course, contradicts “common sense”! But here’s what’s interesting: not in their specific form, but as a broad philosophical position, all these amazing consequences were predicted by the founders of dialectical materialism. What do these results indicate? About the connections that interconnect energy and mass, mass and speed, speed and time, the speed and length of a moving object... Einstein's discovery of interdependence, like cement (more details:), connecting together reinforcement, or foundation stones, connected together the seemingly before this, things and phenomena were independent of each other and created the basis on which, for the first time in the history of science, it became possible to build a harmonious building. This building is an idea 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 - general theory of relativity - does not quite correspond to the content of the theory that will be discussed. It establishes the 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 become so intertwined 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 filling them. Einstein published the general theory of relativity in 1916 and had been working on it since 1907. It is not realistic to try to present it in several pages without using mathematical formulas. Starting point for reasoning
Therefore, we can only indicate starting point and provide some important conclusions. At first space travel An unexpected catastrophe destroyed the library, film collection and other repositories of the mind and memory of people flying through space. And nature is forgotten in the change of centuries home planet. 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 great, and 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 the jet nozzles blaze into the void with a colorless flame and the ship moves at an accelerated pace, the inhabitants feel that their bodies are becoming 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 orbit of the most suitable planet. The spaceships go outside, walk on the soil covered with fresh greenery, continuously 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 can’t fly towards them with a constant acceleration of 9.8 m/sec2! 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 were on such a long flight, but many felt the phenomenon of “heaviness” and “lightening” of their body. Even an ordinary elevator, when it moves at an accelerated pace, creates this feeling. When going down, you feel a sudden loss of weight; when going up, on the contrary, the floor presses on your legs with greater force than usual. But one feeling does not prove anything. After all, sensations are trying to convince us that the Sun moves across the sky around the motionless Earth, that all the stars and planets are at the same distance from us, in the firmament, etc. Scientists have subjected sensations to experimental testing. Newton also thought about the strange identity of the two phenomena. He tried to give them numerical characteristics. Having measured gravitational and , he was convinced that their values were always strictly equal to each other. He made the pendulums of the pilot plant from all kinds of materials: 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 no longer needs this principle. Skipping the mathematical conclusions that follow from this principle, let us move 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 that can be defined as heterogeneity of space. These inhomogeneities direct the movement of any masses that find themselves near the attracting body. Usually they resort to this analogy. Imagine a canvas stretched tightly onto a frame parallel to the earth's surface. Place a heavy weight on it. This will be our large attracting mass. It will, of course, bend the canvas and end up in some kind of depression. Now roll the ball along this canvas so that part of its path lies next to the attracting mass. Depending on how the ball is launched, there are three possible options.- The ball will fly far enough from the depression created by the deflection of the canvas and will not change its movement.
- The ball will touch the depression, and the lines of its movement will bend towards the attracting mass.
- 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.
Gravitational collapse
Let's talk about an amazing phenomenon that has a cosmic character - 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 smaller the square of the distance between gravitating bodies, the greater the gravitational force. Thus, the denser a material formation becomes, the smaller its size, the more rapidly the forces of gravity increase, the more inevitable their destructive embrace. There is a cunning technique with which nature fights the seemingly limitless compression of matter. To do this, it stops the very passage of time in the sphere of action of supergiant gravitational forces, and the bound masses of matter seem to be turned off from our Universe, frozen in a strange lethargic sleep. 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 - double star with one invisible component. The visible component has a mass of 1.8 solar, and its invisible “companion” should be four times more massive than the visible one, according to calculations. 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, “at the tip of his pen,” through purely theoretical constructions, showed that particles of “frozen matter” can be very diverse in size.- Its giant formations are possible, similar to quasars, continuously emitting as much energy as all 100 billion stars of our Galaxy emit.
- Much more modest clumps, equal to only a few solar masses, are possible. Both objects can arise themselves from ordinary, non-sleeping matter.
- And formations of a completely different class are possible, comparable in mass to elementary particles.
Plankeons
The author of the hypothesis named such particles in honor of the famous German physicist Max Planck - plankeons. Plankeons are a completely special class of particles. They have, according to K. P. Stanyukovich, an extremely interesting property: they carry matter in an unchanged form, the way it was millions and billions of years ago. Looking inside the plankeon, we would be able to see matter as it was at the moment 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 from him), the hypothesis about plankeons was put forward by Academician M.A. Markov. Only Markov gave them another name - maximons. The special properties of plankeons can also be used to explain the sometimes paradoxical transformations of elementary particles. It is known that in the collision of two particles never form fragments, but others arise elementary particles. 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 hidden 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 in return those that we consider to have arisen during the collision will “pop out”. At the same time, plankeon, like a prudent accountant, will ensure all the “laws of conservation” accepted in the world of elementary particles. Well, what does the mechanism of universal gravitation have to do with it? “Responsible” for gravity, 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 sunbeam, smaller than the globe. The emission of gravitons obeys a number of laws. In particular, they fly more easily into that area of space. Which contains fewer gravitons. This means that if there are two celestial bodies in space, both will emit gravitons predominantly “outward”, in directions opposite to each other. This creates an impulse that causes the bodies to come closer and attract each other. Leaving their elementary particles, gravitons take part of the mass with them. No matter how small they are, the loss of mass cannot but be noticeable over time. But this time is unimaginably huge. It will take about 100 billion years for all the matter in the Universe to turn into a gravitational field.
Gravitational field. But is that all? According to K.P. Stanyukovich, about 95 percent of the mass of matter is hidden in plankeons of various sizes and is in a state of lethargic sleep, but over time the plankeons open up, and the amount of “normal” matter increases. We all walk on the Earth because it attracts us. If the Earth did not attract all the bodies on its surface, then we would push off from it and fly into space. But this does not happen, and everyone knows about the existence of gravity.
Are we attracting the Earth? The Moon attracts!
Do we attract the Earth to ourselves? Funny question, isn't it? But let's figure it out. Do you know what tides are in the seas and oceans? Every day the water leaves the shores, hangs around somewhere unknown for several hours, and then, as if nothing had happened, returns back.
So the water at this time is not somewhere unknown, but approximately in the middle of the ocean. Something like a mountain of water is formed there. Incredible, right? Water, which has the property of spreading, not only flows down, but also forms mountains. And in these mountains a huge mass of water is concentrated.
Just estimate the entire volume of water that moves away from the shores during low tides, and you will understand that we're talking about about gigantic quantities. But if this happens, there must be some reason. And there is a reason. The reason lies in the fact that this water is attracted to the Moon.
As the Moon revolves around the Earth, it passes over the oceans and attracts ocean waters. The moon revolves around the Earth because it is attracted by the Earth. But it turns out that she herself also attracts the Earth to herself. The earth, however, is too big for it, but its influence is sufficient to move water in the oceans.
Force and law of universal gravitation: concept and formula
Now let's go further and think: if two huge bodies, being nearby, both attract each other, isn't it logical to assume that smaller bodies will also attract each other? Are they simply much smaller and their attractive force will be small?
It turns out that this assumption is absolutely correct. Between absolutely all bodies in the Universe there are forces of attraction or, in other words, forces of universal gravity.
Isaac Newton was the first to discover this phenomenon and formulate it in the form of a law. The law of universal gravitation states: all bodies are attracted to each other, and the force of their attraction is directly proportional to the mass of each of the bodies and inversely proportional to the square of the distance between them:
F = G * (m_1 * m_2) / r^2 ,
where F is the magnitude of the vector of attraction between the bodies, m_1 and m_2 are the masses of these bodies, r is the distance between the bodies, G is the gravitational constant.
The gravitational constant is numerically equal to the force that exists between bodies of mass 1 kg located at a distance of 1 meter. This value was found experimentally: G=6.67*〖10〗^(-11) N* m^2⁄〖kg〗^2.
Returning to our original question: “are we attracting the Earth?”, we can confidently answer: “yes.” According to Newton's third law, we attract the Earth with exactly the same force with which the Earth attracts us. This force can be calculated from the law of universal gravitation.
And according to Newton’s second law, the influence of bodies on each other by any force is expressed in the form of the acceleration they impart to each other. But the acceleration imparted depends on the mass of the body.
The mass of the Earth is large, and it gives us the acceleration of gravity. And our mass is negligible compared to the Earth, and therefore the acceleration that we give to the Earth is practically zero. This is why we are attracted to the Earth and walk on it, and not vice versa.
In physics, there are a huge number of laws, terms, definitions and formulas that explain all natural phenomena on earth and in the Universe. One of the main ones is the law of universal gravitation, which was discovered by the great and well-known scientist Isaac Newton. Its definition looks like this: any two bodies in the Universe are mutually attracted to each other with a certain force. The formula for universal gravitation, which calculates this force, will have the form: F = G*(m1*m2 / R*R).
In contact with
History of the discovery of the law
For a very long time people have studied the sky. They wanted to know all its features, everything that reigns in inaccessible space. They made a calendar based on the sky, calculated important dates and dates religious holidays. People believed that the center of the entire Universe was the Sun, around which all celestial objects revolved.
Really stormy scientific interest to space and to astronomy in general appeared in the 16th century. Tycho Brahe, a great astronomer, during his research observed the movements of the planets, recorded and systematized his observations. By the time Isaac Newton discovered the law of universal gravitation, the Copernican system had already been established in the world, according to which everything celestial bodies revolve around a star in certain orbits. The great scientist Kepler, based on Brahe's research, discovered the kinematic laws that characterize the motion of planets.
Based on Kepler's laws, Isaac Newton discovered his and found out, What:
- The movements of the planets indicate the presence of a central force.
- The central force causes the planets to move in their orbits.
Parsing the formula
There are five variables in the Newton's law formula:
How accurate are the calculations?
Since Isaac Newton's law is a mechanics law, calculations do not always reflect as accurately as possible the actual force with which objects interact. Moreover , this formula can only be used in two cases:
- When two bodies between which interaction occurs are homogeneous objects.
- When one of the bodies is material point, and the other is a homogeneous ball.
Gravitational field
According to Newton's third law, we understand that the forces of interaction between two bodies are equal in value, but opposite in direction. The direction of forces occurs strictly along a straight line that connects the centers of mass of two interacting bodies. The interaction of attraction between bodies occurs due to the gravitational field.
Description of interaction and gravity
Gravity has very long-range interaction fields. In other words, its influence extends over very large, cosmic distances. Thanks to gravity, people and all other objects are attracted to the earth, and the earth and all the planets of the solar system are attracted to the Sun. Gravity is the constant influence of bodies on each other; it is a phenomenon that determines the law of universal gravitation. It is very important to understand one thing - the more massive the body, the more gravity it has. The Earth has enormous mass, so we are attracted to it, and the Sun weighs several million times more than the Earth, so our planet is attracted to the star.
Albert Einstein, one of the greatest physicists, argued that gravity between two bodies occurs due to the curvature of space-time. The scientist was sure that space, like fabric, can be pressed through, and the more massive the object, the more strongly it will press through this fabric. Einstein became the author of the theory of relativity, which states that everything in the Universe is relative, even such a quantity as time.
Calculation example
Let's try, using the already known formula of the law of universal gravitation, solve a physics problem:
- The radius of the Earth is approximately 6350 kilometers. Let's take the acceleration of free fall as 10. It is necessary to find the mass of the Earth.
Solution: The acceleration of gravity near the Earth will be equal to G*M / R^2. From this equation we can express the mass of the Earth: M = g*R^2 / G. All that remains is to substitute the values into the formula: M = 10*6350000^2 / 6.7 * 10^-11. In order not to worry about degrees, let’s reduce the equation to the form:
- M = 10* (6.4*10^6)^2 / 6.7 * 10^-11.
After doing the math, we find that the mass of the Earth is approximately 6*10^24 kilograms.
The phenomenon of universal gravity
The phenomenon of universal gravitation is that attractive forces act between all bodies in the Universe.
Newton came to the conclusion about the existence of universal gravity (they are also called gravitational) as a result of studying the movement of the Moon around the Earth and the planets around the Sun. These astronomical observations were made by the Danish astronomer Tycho Brahe. Tycho Brahe measured the position of all the known planets at that time and wrote down their coordinates, but Tycho Brahe failed to finally derive and create the law of planetary motion relative to the Sun. This was done by his student Johannes Kepler. Johannes Kepler used not only the measurements of Tycho Brahe, but also by that time the heliocentric system of the world of Copernicus, which was already quite substantiated and used everywhere. That system in which it is believed that the Sun is at the center of our system and the planets revolve around it.
Figure 1. Heliocentric system of the world (Copernican system)
First of all, Newton assumed that all bodies have the property of attraction, i.e. those bodies that have masses are attracted to each other. This phenomenon came to be called universal gravity. And bodies that attract others to each other create force. This force with which bodies are attracted began to be called gravitational (from the word gravitas - “gravity”).
Law of Gravity
Newton managed to obtain a formula for calculating the force of interaction between bodies with masses. This formula is called law of universal gravitation. It was discovered in $1667$. I. Newton based his discovery on astronomical observations
The “law of universal gravitation” itself sounds like this: two bodies attract 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.
Let's look at the quantities that are included in this law. So, the law of universal gravitation itself looks like this:
There is one more value here - $G$, gravitational constant. Its physical meaning is that it shows the force with which two bodies weighing $1$ kg, each $1$ kg, located at a distance of $1$ m interact. This value is very small, it is only on the order of magnitude $10^ (-11).$
$G=6.67\cdot 10^(-11) \frac(H\cdot m^2)(kg^2)$
This value indicates the relationship in which they are located, with what force the bodies nearby interact, and even if they are located close enough (for example, two standing people), they will not feel this interaction at all, since the order of force is $10^( -11)$ will not give a significant sensation. The effect of gravitational force begins to be felt only when the mass of bodies is large.
Limits of applicability of the law of universal gravitation
In the form in which we use the law of universal gravitation, it is not always valid, but only in some cases:
- if the sizes of the bodies are negligible compared to the distance between them;
Figure 2.
- if both bodies are homogeneous and have spherical shape- in this case, even if the distances between the bodies are not so great, the law of universal gravitation is applicable if the bodies have a spherical shape and then the distances are defined as the distances between the centers of the bodies in question;
Figure 3.
- if one of the interacting bodies is a ball, the dimensions of which are significantly larger than the dimensions of the second body (of any shape) located on the surface of this ball or near it - this is the case of satellites moving in their orbits around the Earth.
Figure 4.
Example 1
Artificial satellite moves in a circular orbit around the Earth at a speed of $1$ km/s at an altitude of 350,000 km. We need to determine the mass of the Earth.
Given: $v=1$ km/s, $R=350000$ km.
Find: $M_(3) $-?
Since the satellite moves around the Earth, it has a centripetal acceleration equal to:
$F=G\frac(mM_(3) )(R^(2) ) =ma$. (2)
Taking into account (1) from (2), we write the expression for finding the mass of the Earth:
$M_(3) =\frac(v^(2) R)(G) =5.24\cdot 10^(24) $kg
Answer: $M_(3) =5.24\cdot 10^(24) $ kg.