I. Newton managed to derive from Kepler's laws one of the fundamental laws of nature - the law gravity. Newton knew that for all the planets of the solar system, the acceleration is inversely proportional to the square of the distance from the planet to the Sun and the coefficient of proportionality is the same for all planets.

From this it follows, first of all, that the force of attraction acting from the side of the Sun on a planet must be proportional to the mass of this planet. Indeed, if the acceleration of the planet is given by formula (123.5), then the force causing the acceleration,

where is the mass of the planet. On the other hand, Newton knew the acceleration that the Earth imparts to the Moon; it was determined from observations of the motion of the moon as it revolved around the earth. This acceleration is approximately one times less than the acceleration reported by the Earth to bodies located near earth's surface. The distance from the Earth to the Moon is approximately equal to the Earth's radii. In other words, the Moon is farther from the center of the Earth than the bodies on the surface of the Earth, and its acceleration is several times less.

If we accept that the Moon moves under the influence of the Earth's gravity, then it follows that the force of the Earth's attraction, as well as the force of attraction of the Sun, decreases inversely with the square of the distance from the center of the Earth. Finally, the force of gravity of the Earth is directly proportional to the mass of the attracted body. Newton established this fact in experiments with pendulums. He found that the swing period of a pendulum does not depend on its mass. This means that the Earth imparts the same acceleration to pendulums of different masses, and, consequently, the force of the Earth's attraction is proportional to the mass of the body on which it acts. The same, of course, follows from the same acceleration of free fall for bodies of different masses, but experiments with pendulums make it possible to verify this fact with greater accuracy.

These similar features of the forces of attraction of the Sun and the Earth led Newton to the conclusion that the nature of these forces is the same and that there are universal gravitational forces acting between all bodies and decreasing inversely with the square of the distance between the bodies. In this case, the gravitational force acting on a given body of mass must be proportional to the mass.

Based on these facts and considerations, Newton formulated the law of universal gravitation in this way: any two bodies are attracted to each other with a force that is directed along the line connecting them, is directly proportional to the masses of both bodies and inversely proportional to the square of the distance between them, i.e. force of mutual attraction

where and are the masses of the bodies, is the distance between them, and is the proportionality coefficient, called the gravitational constant (the method of its measurement will be described below). Splicing this formula with formula (123.4), we see that , where is the mass of the Sun. The forces of universal gravitation satisfy Newton's third law. This was confirmed by all astronomical observations of the motion celestial bodies.

In this formulation, the law of universal gravitation is applicable to bodies that can be considered material points, i.e. to bodies, the distance between which is very large compared to their sizes, otherwise it would be necessary to take into account that different points of the bodies are separated from each other by different distances . For homogeneous spherical bodies, the formula is true for any distance between the bodies, if we take the distance between their centers as the quality. In particular, in the case of attraction of the body by the Earth, the distance must be counted from the center of the Earth. This explains the fact that the force of gravity almost does not decrease as the height above the Earth increases (§ 54): since the radius of the Earth is approximately 6400, when the position of the body above the Earth's surface changes within even tens of kilometers, the force of gravity of the Earth remains practically unchanged.

The gravitational constant can be determined by measuring all other quantities included in the law of universal gravitation, for any particular case.

For the first time, it was possible to determine the value of the gravitational constant using torsion balances, the device of which is schematically shown in Fig. 202. A light rocker, at the ends of which two identical balls of mass are fixed, is hung on a long and thin thread. The rocker is equipped with a mirror, which allows you to optically measure small turns of the rocker around the vertical axis. Two balls of much larger mass can be approached from different sides of the balls.

Rice. 202. Diagram of a torsion balance for measuring the gravitational constant

The forces of attraction of small balls to large ones create a couple of forces that rotate the rocker clockwise (when viewed from above). By measuring the angle at which the rocker turns when approaching the balls of balls , and knowing the elastic properties of the thread on which the rocker is suspended, it is possible to determine the moment of a pair of forces with which the masses are attracted to the masses . Since the masses of the balls and and the distance between their centers (at a given position of the rocker arm) are known, the value can be found from formula (124.1). It turned out to be equal

After the value was determined, it turned out to be possible to determine the mass of the Earth from the law of universal gravitation. Indeed, in accordance with this law, a body of mass located at the surface of the Earth is attracted to the Earth with a force

where is the mass of the Earth and is its radius. On the other hand, we know that . Equating these quantities, we find

.

Thus, although the forces of universal gravitation acting between bodies of different masses are equal, a body of small mass receives a significant acceleration, and a body of large mass experiences a small acceleration.

Since the total mass of all planets solar system is slightly more than the mass of the Sun, the acceleration that the Sun experiences as a result of the gravitational forces acting on it from the planets is negligible compared to the accelerations that the Sun's gravitational force imparts to the planets. The gravitational forces acting between the planets are also relatively small. Therefore, when considering the laws of planetary motion (Kepler's laws), we did not take into account the motion of the Sun itself and approximately considered that the trajectories of the planets are elliptical orbits, in one of the focuses of which the Sun is located. However, in precise calculations, one has to take into account those “perturbations” that are introduced into the motion of the Sun itself or any planet by gravitational forces from other planets.

124.1. How much will the force of gravity acting on a rocket projectile decrease when it rises 600 km above the Earth's surface? The radius of the Earth is taken equal to 6400 km.

124.2. The mass of the Moon is 81 times less than the mass of the Earth, and the radius of the Moon is approximately 3.7 times less than the radius of the Earth. Find the weight of a man on the moon if his weight on earth is 600N.

124.3. The mass of the Moon is 81 times less than the mass of the Earth. Find on the line connecting the centers of the Earth and the Moon, a point at which the forces of attraction of the Earth and the Moon are equal to each other, acting on a body placed at this point.

I decided, to the best of my ability and ability, to focus on lighting in more detail. scientific heritage academician Nikolai Viktorovich Levashov, because I see that today his works are not yet in the demand that they should be in a society of truly free and reasonable people. people still do not understand the value and importance of his books and articles, because they don't realize the extent of the deception in which we have been living for the last couple of centuries; do not understand that the information about nature, which we consider familiar and therefore true, is 100% false; and they are deliberately imposed on us in order to hide the truth and prevent us from developing in the right direction ...

Law of gravity

Why do we need to deal with this gravity? Is there anything else we don't know about her? What are you! We already know a lot about gravity! For example, Wikipedia kindly informs us that « gravity (attraction, worldwide, gravity) (from lat. gravitas - "gravity") - a universal fundamental interaction between all material bodies. In the approximation of low velocities and weak gravitational interaction, it is described by Newton's theory of gravitation, in general case described by Einstein's general theory of relativity ... " Those. simply put, this Internet chatterbox says that gravity is the interaction between all material bodies, and even more simply - mutual attraction material bodies to each other.

We owe the appearance of such an opinion to Comrade. Isaac Newton, credited with the discovery in 1687 "Law of gravity", according to which all bodies are allegedly attracted to each other in proportion to their masses and inversely proportional to the square of the distance between them. I am glad that Comrade. Isaac Newton is described in Pedia as a highly educated scientist, unlike Comrade. who is credited with discovering electricity…

It is interesting to look at the dimension of the "Force of Attraction" or "Force of Gravity", which follows from Com. Isaac Newton, having the following form: F=m 1 *m2 /r2

The numerator is the product of the masses of the two bodies. This gives the dimension of "kilograms squared" - kg 2. The denominator is "distance" squared, i.e. square meters - m 2. But strength is not measured in strange kg 2 / m 2, and in no less strange kg * m / s 2! It turns out to be a mismatch. To remove it, the "scientists" came up with a coefficient, the so-called. "gravitational constant" G , equal to approximately 6.67545×10 −11 m³/(kg s²). If we now multiply everything, we get the correct dimension of "Gravity" in kg * m / s 2, and this abracadabra is called in physics "newton", i.e. force in today's physics is measured in "".

Interesting: what physical meaning has a coefficient G , for something reducing the result in 600 billion times? None! "Scientists" called it "proportionality coefficient". And they brought it in for fit dimension and result under the most desired! This is the kind of science we have today ... It should be noted that, in order to confuse scientists and hide contradictions, measurement systems have changed several times in physics - the so-called. "systems of units". Here are the names of some of them, replacing each other, as the need to create the next disguises arose: MTS, MKGSS, SGS, SI ...

It would be interesting to ask Comrade. Isaac: a how did he guess that there is a natural process of attracting bodies to each other? How did he guess that the “Force of Attraction” is proportional precisely to the product of the masses of two bodies, and not to their sum or difference? How did he so successfully comprehend that this Force is inversely proportional precisely to the square of the distance between the bodies, and not to the cube, doubling or fractional power? Where at comrade did such inexplicable guesses appear 350 years ago? After all, he did not conduct any experiments in this area! And, if you believe the traditional version of history, in those days even the rulers were not yet completely even, but here such an inexplicable, simply fantastic insight! Where?

Yes out of nowhere! Tov. Isaac knew nothing of the kind, nor did he investigate anything of the kind, and did not open. Why? Because in reality physical process « attraction tel" to each other does not exist, and, accordingly, there is no Law that would describe this process (this will be convincingly proved below)! In reality, Comrade Newton in our indistinct, just attributed the discovery of the law of "Universal gravitation", simultaneously awarding him the title of "one of the founders of classical physics"; in the same way as Comrade was attributed at one time. bene Franklin, which had 2 classes education. In “Medieval Europe”, this did not happen: there was a lot of tension not only with the sciences, but simply with life ...

But, fortunately for us, at the end of the last century, the Russian scientist Nikolai Levashov wrote several books in which he gave "alphabet and grammar" undistorted knowledge; returned to earthlings the previously destroyed scientific paradigm, with the help of which easily explained almost all "unsolvable" riddles earthly nature; explained the fundamentals of the structure of the Universe; showed under what conditions on all planets on which necessary and sufficient conditions appear, Life- living matter. He explained what kind of matter can be considered alive, and what physical meaning natural process called life". Then he explained when and under what conditions "living matter" acquires Intelligence, i.e. realizes its existence - becomes intelligent. Nikolai Viktorovich Levashov conveyed to people in his books and films very much undistorted knowledge. He also explained what "gravity", where does it come from, how does it work, what is its actual physical meaning. Most of all this is written in books and. And now let's deal with the "Law of Universal Gravitation" ...

The "Law of Gravity" is a hoax!

Why do I so boldly and confidently criticize physics, the "discovery" of Comrade. Isaac Newton and the "great" "Law of Universal Gravitation" itself? Yes, because this “Law” is a fiction! Deception! Fiction! A worldwide scam to lead earthly science to a dead end! The same scam with the same goals as the notorious "Theory of Relativity" comrade. Einstein.

Proof? If you please, here they are: very precise, strict and convincing. They were splendidly described by the author O.Kh. Derevensky in his wonderful article. Due to the fact that the article is quite voluminous, I will give here a very brief version of some of the evidence for the falsity of the "Law of Universal Gravity", and citizens who are interested in the details will read the rest for themselves.

1. In our solar system only the planets and the Moon, the Earth's satellite, have gravity. The satellites of the other planets, and there are more than six dozen of them, do not have gravity! This information is completely open, but not advertised by "scientific" people, because it is inexplicable from the point of view of their "science". Those. b O Most of the objects in our solar system do not have gravity - they do not attract each other! And this completely refutes the "Law of General Gravity".

2. Henry Cavendish Experience by attracting massive blanks to each other is considered irrefutable proof of the presence of attraction between bodies. However, despite its simplicity, this experience is not openly reproduced anywhere. Apparently, because it does not give the effect that some people once announced. Those. today, with the possibility of strict verification, experience does not show any attraction between bodies!

3. Launch of an artificial satellite into orbit around the asteroid. In the middle of February 2000 the Americans drove a space probe NEAR close enough to the asteroid Eros, leveled the speeds and began to wait for the capture of the probe by the gravity of Eros, i.e. when the satellite is gently attracted by the gravity of the asteroid.

But for some reason the first date didn't work out. The second and subsequent attempts to surrender to Eros had exactly the same effect: Eros did not want to attract the American probe NEAR, and without engine work, the probe did not stay near Eros . This space date ended in nothing. Those. no attraction between probe with mass 805 kg and an asteroid weighing over 6 trillion tons could not be found.

Here it is impossible not to note the inexplicable stubbornness of the Americans from NASA, because the Russian scientist Nikolai Levashov, living at that time in the USA, which he then considered a completely normal country, wrote, translated into English language and published in 1994 year of his famous book, in which he explained everything that NASA specialists needed to know in order to make their probe NEAR did not hang out as a useless piece of iron in space, but brought at least some benefit to society. But, apparently, exorbitant self-conceit played a trick on the “scientists” there.

4. Next try repeat the erotic experiment with the asteroid Japanese. They chose an asteroid called Itokawa, and sent on May 9 2003 year to him a probe called ("Falcon"). In September 2005 year, the probe approached the asteroid at a distance of 20 km.

Taking into account the experience of the “stupid Americans”, the smart Japanese equipped their probe with several engines and an autonomous short-range navigation system with laser rangefinders, so that it could approach the asteroid and move around it automatically, without the participation of ground operators. “The first number of this program was a comedy stunt with the landing of a small research robot on the surface of an asteroid. The probe descended to the calculated height and carefully dropped the robot, which was supposed to slowly and smoothly fall to the surface. But... it didn't fall. Slow and smooth he got carried away somewhere far away from the asteroid. There he went missing ... The next number of the program turned out to be, again, a comedy trick with a short landing of the probe on the surface "to take a soil sample." He came out comedy because, to ensure best work laser rangefinders, a reflective marker ball was dropped onto the surface of the asteroid. There were no engines on this ball either, and ... in short, there was no ball in the right place ... So, did the Japanese Sokol land on Itokawa, and what did he do on it if he sat down, science does not know ... "Conclusion: the Japanese miracle of Hayabusa is not was able to discover no attraction between probe ground 510 kg and an asteroid with mass 35 000 tons.

Separately, I would like to note that an exhaustive explanation of the nature of gravity by a Russian scientist Nikolai Levashov gave in his book, which he first published in 2002 year - almost a year and a half before the start of the Japanese "Falcon". And, despite this, the Japanese "scientists" followed exactly in the footsteps of their American colleagues and carefully repeated all their mistakes, including landing. Here is such an interesting continuity of "scientific thinking" ...

5. Where do hot flashes come from? Very interesting phenomenon described in the literature, to put it mildly, is not entirely correct. “... There are textbooks on physics, where it is written what should be - in accordance with the "law of universal gravitation". There are also textbooks oceanography, where it is written what they are, tides, In fact.

If the law of universal gravitation operates here, and ocean water is attracted, including to the Sun and the Moon, then the "physical" and "oceanographic" patterns of the tides must coincide. So do they match or not? It turns out that to say that they do not match is to say nothing. Because the "physical" and "oceanographic" pictures have no relationship at all nothing in common... The actual picture of tidal phenomena is so different from the theoretical one - both qualitatively and quantitatively - that on the basis of such a theory, tides can be predicted impossible. Yes, no one is trying to do it. Not crazy after all. They do this: for each port or other point of interest, the dynamics of the ocean level is modeled by the sum of oscillations with amplitudes and phases that are found purely empirically. And then they extrapolate this sum of fluctuations forward - so you get the pre-calculations. The captains of the ships are happy - well, okay! .. ”This all means that our earthly tides are also do not obey"Law of universal gravitation".

What is gravity really

The true nature of gravity for the first time in recent history clearly described by academician Nikolai Levashov in a fundamental scientific work. In order for the reader to better understand what has been written regarding gravity, I will give a little preliminary explanation.

The space around us is not empty. It is all completely filled with many different matters, which Academician N.V. Levashov named "first matter". Previously, scientists called all this riot of matter "ether" and even received convincing evidence of its existence (the famous experiments of Dayton Miller, described in the article by Nikolai Levashov "Theory of the Universe and Objective Reality"). Modern "scientists" have gone much further and now they "ether" called "dark matter". Enormous progress! Some matters in the "ether" interact with each other to one degree or another, some do not. And some primary matter begin to interact with each other, getting into the changed external conditions in certain curvatures of space (heterogeneities).

Curvature of space appears as a result of various explosions, including "supernova explosions". « When a supernova explodes, fluctuations in the dimensionality of space occur, similar to the waves that appear on the surface of water after a stone is thrown. The masses of matter ejected during the explosion fill these inhomogeneities in the dimensionality of the space around the star. From these masses of matter, planets ( and ) begin to form ... "

Those. planets are not formed from space debris, as modern “scientists” for some reason claim, but are synthesized from the matter of stars and other primary matters that begin to interact with each other in suitable inhomogeneities of space and form the so-called. "hybrid matter". It is from these “hybrid matters” that the planets and everything else in our space are formed. our planet, just like the rest of the planets, is not just a "piece of stone", but a very complex system consisting of several spheres nested one into another (see). The densest sphere is called the "physically dense level" - this is what we see, the so-called. physical world. Second in terms of density, a slightly larger sphere is the so-called. "ethereal material level" of the planet. Third sphere - "astral material level". 4th the sphere is the "first mental level" of the planet. Fifth the sphere is the "second mental level" of the planet. AND sixth the sphere is the "third mental level" of the planet.

Our planet should only be considered as the totality of these six spheres– six material levels of the planet nested one into another. Only in this case it is possible to get a complete picture of the structure and properties of the planet and the processes occurring in nature. The fact that we are not yet able to observe the processes taking place outside the physically dense sphere of our planet does not indicate that “there is nothing there”, but only that at present our sense organs are not adapted by nature for these purposes. And one more thing: our Universe, our planet Earth and everything else in our Universe is formed from seven various kinds primal matter merged into six hybrid materials. And it is neither divine nor unique. This is just a qualitative structure of our Universe, due to the properties of the heterogeneity in which it was formed.

Let's continue: the planets are formed by the merger of the corresponding primary matter in the areas of space inhomogeneities that have properties and qualities suitable for this. But in these, as in all other regions of space, a huge number of primal matter(free forms of matter) of various types, not interacting or very weakly interacting with hybrid matters. Getting into the area of ​​heterogeneity, many of these primary matters are affected by this heterogeneity and rush to its center, in accordance with the gradient (difference) of space. And, if a planet has already formed in the center of this heterogeneity, then the primary matter, moving towards the center of heterogeneity (and the center of the planet), creates directional flow, which creates the so-called. gravitational field. And, accordingly, under gravity you and I need to understand the impact of the directed flow of primary matter on everything that is in its path. That is, to put it simply, gravity is pressure material objects to the surface of the planet by the flow of primary matter.

Is not it, reality very different from the fictional law " mutual attraction”, allegedly existing everywhere for no clear reason. Reality is much more interesting, much more complex and much simpler at the same time. Therefore, the physics of real natural processes is much easier to understand than fictional ones. And the use of real knowledge leads to real discoveries and the effective use of these discoveries, and not to sucked from the finger.

antigravity

As an example of today's scientific profanity one can briefly analyze the "scientists" explanation of the fact that "rays of light are bent near large masses", and therefore we can see what is hidden from us by stars and planets.

Indeed, we can observe objects in the Cosmos that are hidden from us by other objects, but this phenomenon has nothing to do with the masses of objects, because the “universal” phenomenon does not exist, i.e. no stars, no planets NOT attract no rays to themselves and do not bend their trajectory! Why then are they "curved"? There is a very simple and convincing answer to this question: rays are not bent! They just do not spread in a straight line, as we are accustomed to understand, and in accordance with form of space. If we consider a beam passing near a large cosmic body, then we must keep in mind that the beam goes around this body, because it is forced to follow the curvature of space, as if along a road of the corresponding shape. And there is simply no other way for the beam. The beam cannot help but go around this body, because the space in this area has such a curved shape ... Small to what has been said.

Now, returning to antigravity, it becomes clear why Mankind can not manage to catch this nasty "anti-gravity" or achieve at least something of what the clever functionaries of the dream factory show us on TV. We are specifically forced for more than a hundred years, engines have been used almost everywhere internal combustion or jet engines, although they are very far from perfect both in principle of operation, and in design, and in efficiency. We are specifically forced mine using various generators of cyclopean sizes, and then transmit this energy through wires, where b O most of it is scattered in space! We are specifically forced live the life of unreasonable beings, so we have no reason to be surprised that we can’t do anything sensible either in science, or in technology, or in economics, or in medicine, or in organizing a decent life for society.

I will now give you a few examples of the creation and use of antigravity (aka levitation) in our lives. But these ways of achieving anti-gravity are most likely discovered by accident. And in order to consciously create a really useful device that implements antigravity, you need to know the real nature of the phenomenon of gravity, explore it, analyze and understand all its essence! Only then can something sensible, effective and really useful to society be created.

The most common anti-gravity device we have is balloon and many of its variations. If it is filled with warm air or a gas that is lighter than the atmospheric gas mixture, then the ball will tend to fly up, and not fall down. This effect has been known to people for a very long time, but still does not have a complete explanation- one that would no longer give rise to new questions.

A short search on YouTube led to the discovery of a large number of videos that show quite real examples antigravity. I will list some of them here so that you can be sure that antigravity ( levitation) really exists, but ... so far none of the "scientists" has explained it, apparently, pride does not allow ...

Law of gravity

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

Gravitational interaction

Gravitational interaction is one of the four fundamental interactions in our world. Within classical mechanics, the gravitational interaction is described by law of gravity Newton, who states that the force of gravitational attraction between two material points of mass m 1 and m 2 separated by distance R, is proportional to both masses and inversely proportional to the square of the distance - i.e.

.

Here G- gravitational constant, equal to approximately m³/(kg s²). The minus sign means that the force acting on the body is always equal in direction to the radius vector directed to the body, that is, the gravitational interaction always leads to the attraction of any bodies.

The law of universal gravitation is one of the applications of the inverse square law, which is also encountered in the study of radiation (see, for example, Light Pressure), and which is a direct consequence of the quadratic increase in the area of ​​the sphere with increasing radius, which leads to a quadratic decrease in the contribution of any unit area to the area of ​​the entire sphere.

The simplest task of celestial mechanics is the gravitational interaction of two bodies in empty space. This problem is solved analytically to the end; the result of its solution is often formulated in three Kepler's laws.

As the number of interacting bodies increases, the problem becomes much more complicated. So, the already famous three-body problem (that is, the movement three bodies with nonzero masses) cannot be solved analytically in general view. With a numerical solution, the instability of solutions with respect to initial conditions. When applied to the solar system, this instability makes it impossible to predict the motion of the planets on scales exceeding a hundred million years.

In some special cases, it is possible to find an approximate solution. The most important is the case when the mass of one body is significantly greater than the mass of other bodies (examples: the solar system and the dynamics of Saturn's rings). In this case, in the first approximation, we can assume that light bodies do not interact with each other and move along Keplerian trajectories around a massive body. Interactions between them can be taken into account in the framework of perturbation theory, and averaged over time. In this case, non-trivial phenomena can arise, such as resonances, attractors, randomness, etc. illustrative example such phenomena - non-trivial structure of the rings of Saturn.

Despite attempts to describe the behavior of a system of a large number of attracting bodies of approximately the same mass, this cannot be done due to the phenomenon of dynamic chaos.

Strong gravitational fields

In strong gravitational fields, when moving at relativistic speeds, the effects of general relativity begin to appear:

  • deviation of the law of gravity from Newtonian;
  • potential delay associated with the finite propagation velocity of gravitational perturbations; the appearance of gravitational waves;
  • non-linear effects: gravitational waves tend to interact with each other, so the principle of superposition of waves in strong fields is no longer valid;
  • change in the geometry of space-time;
  • the emergence of black holes;

Gravitational radiation

One of the important predictions of general relativity is gravitational radiation, the presence of which has not yet been confirmed by direct observations. However, there is indirect observational evidence in favor of its existence, namely: the energy loss in the binary system with the PSR B1913+16 pulsar - the Hulse-Taylor pulsar - is in good agreement with the model in which this energy is carried away by gravitational radiation.

Only systems with variable quadrupole or higher multipole moments can generate gravitational radiation, this fact suggests that the gravitational radiation of most natural sources directional, which significantly complicates its detection. Gravity power l-poly source is proportional (v / c) 2l + 2 , if the multipole is of electric type, and (v / c) 2l + 4 - if the multipole is magnetic type , where v is the characteristic velocity of sources in the radiating system, and c is the speed of light. Thus, the dominant moment will be the quadrupole moment of the electric type, and the power of the corresponding radiation is equal to:

Where Q ij is the tensor of the quadrupole moment of the mass distribution of the radiating system. Constant (1/W) makes it possible to estimate the order of magnitude of the radiation power.

Since 1969 (Weber's experiments (English)) and up to the present (February 2007), attempts have been made to directly detect gravitational radiation. In the USA, Europe and Japan in currently there are several active ground-based detectors (GEO 600), as well as a project for a space gravitational detector of the Republic of Tatarstan.

Subtle effects of gravity

In addition to the classical effects of gravitational attraction and time dilation, the general theory of relativity predicts the existence of other manifestations of gravity, which are very weak under terrestrial conditions and therefore their detection and experimental verification are therefore very difficult. Until recently, overcoming these difficulties seemed beyond the capabilities of experimenters.

Among them, in particular, one can name the drag of inertial reference frames (or the Lense-Thirring effect) and the gravitomagnetic field. In 2005, NASA's robotic Gravity Probe B conducted an experiment of unprecedented accuracy to measure these effects near the Earth, but the full results have not yet been published.

quantum theory of gravity

Despite more than half a century of attempts, gravity is the only fundamental interaction for which a consistent renormalizable quantum theory has not yet been built. However, at low energies, in the spirit of quantum field theory, the gravitational interaction can be represented as an exchange of gravitons - gauge bosons with spin 2.

Standard Theories of Gravity

Due to the fact that the quantum effects of gravity are extremely small even under the most extreme experimental and observational conditions, there are still no reliable observations of them. Theoretical estimates show that in the overwhelming majority of cases one can confine oneself to the classical description of the gravitational interaction.

There is a modern canonical classical theory of gravity - the general theory of relativity, and many hypotheses that refine it and theories of varying degrees of development that compete with each other (see the article Alternative theories of gravity). All of these theories give very similar predictions within the approximation in which experimental tests are currently being carried out. The following are some of the major, most well developed or known theories of gravity.

  • Gravity is not a geometric field, but a real physical force field described by a tensor.
  • Gravitational phenomena should be considered within the framework of the flat Minkowski space, in which the laws of conservation of energy-momentum and angular momentum are unambiguously fulfilled. Then the motion of bodies in the Minkowski space is equivalent to the motion of these bodies in the effective Riemannian space.
  • In tensor equations, to determine the metric, one should take into account the mass of the graviton, and also use the gauge conditions associated with the metric of the Minkowski space. This does not allow destroying the gravitational field even locally by choosing some suitable frame of reference.

As in general relativity, in RTG, matter refers to all forms of matter (including the electromagnetic field), with the exception of the gravitational field itself. The consequences of the RTG theory are as follows: black holes as physical objects predicted in general relativity do not exist; The universe is flat, homogeneous, isotropic, immobile and Euclidean.

On the other hand, there are no less convincing arguments of RTG opponents, which boil down to the following points:

A similar thing happens in RTG, where the second tensor equation is introduced to take into account the connection between the non-Euclidean space and the Minkowski space. Due to the presence of a dimensionless fitting parameter in the Jordan-Brans-Dicke theory, it becomes possible to choose it so that the results of the theory coincide with the results of gravitational experiments.

Theories of gravity
Newton's classical theory of gravity General theory of relativity quantum gravity Alternative
  • Mathematical formulation of general relativity
  • Gravity with massive graviton
  • Geometrodynamics (English)
  • Semiclassical gravity (English)
  • Bimetric theories
    • Scalar-Tensor-Vector Gravity
    • Whitehead's theory of gravity
  • Modified Newtonian Dynamics
  • Composite gravity

Sources and notes

Literature

  • Vizgin V.P. Relativistic theory of gravity (origins and formation, 1900-1915). M.: Nauka, 1981. - 352c.
  • Vizgin V.P. Unified theories in the 1st third of the twentieth century. M.: Nauka, 1985. - 304c.
  • Ivanenko D. D., Sardanashvili G. A. Gravity, 3rd ed. M.: URSS, 2008. - 200p.

see also

  • gravimeter

Links

  • The law of universal gravitation or "Why does the moon not fall to the Earth?" - Just about the complex
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By what law are you going to hang me?
- And we hang everyone according to one law - the law of universal gravitation.

Law of gravity

The phenomenon of gravity is the law of universal gravitation. Two bodies act on each other with a force that is inversely proportional to the square of the distance between them and directly proportional to the product of their masses.

Mathematically, we can express this great law by the formula


Gravity acts over vast distances in the universe. But Newton argued that all objects are mutually attracted. Is it true that any two objects attract each other? Just imagine, it is known that the Earth attracts you sitting on a chair. But have you ever thought about the fact that a computer and a mouse attract each other? Or a pencil and pen on the table? In this case, we substitute the mass of the pen, the mass of the pencil into the formula, divide by the square of the distance between them, taking into account the gravitational constant, we obtain the force of their mutual attraction. But, it will come out so small (due to the small masses of the pen and pencil) that we do not feel its presence. Another thing is when we are talking about the Earth and the chair, or the Sun and the Earth. The masses are significant, which means that we can already evaluate the effect of force.

Let's think about free fall acceleration. This is the operation of the law of attraction. Under the action of a force, the body changes speed the slower, the greater the mass. As a result, all bodies fall to the Earth with the same acceleration.

What is the cause of this invisible unique power? To date, the existence of a gravitational field is known and proven. You can learn more about the nature of the gravitational field in the additional material on the topic.

Think about what gravity is. Where is it from? What does it represent? After all, it cannot be that the planet looks at the Sun, sees how far it is removed, calculates the inverse square of the distance in accordance with this law?

Direction of gravity

There are two bodies, let's say body A and B. Body A attracts body B. The force with which body A acts begins on body B and is directed towards body A. That is, it "takes" body B and pulls it towards itself. Body B "does" the same thing with body A.



Every body is attracted by the earth. The earth "takes" the body and pulls it towards its center. Therefore, this force will always be directed vertically downwards, and it is applied from the center of gravity of the body, it is called gravity.

The main thing to remember

Some methods of geological exploration, tide prediction and in Lately calculation of the movement of artificial satellites and interplanetary stations. Early calculation of the position of the planets.

Can we set up such an experiment ourselves, and not guess whether planets, objects are attracted?

Such a direct experience made Cavendish (Henry Cavendish (1731-1810) - English physicist and chemist) using the device shown in the figure. The idea was to hang a rod with two balls on a very thin quartz thread and then bring two large lead balls to the side of them. The attraction of the balls will twist the thread slightly - slightly, because the forces of attraction between ordinary objects are very weak. With the help of such an instrument, Cavendish was able to directly measure the force, distance and magnitude of both masses and, thus, determine gravitational constant G.

The unique discovery of the gravitational constant G, which characterizes the gravitational field in space, made it possible to determine the mass of the Earth, the Sun and other celestial bodies. Therefore, Cavendish called his experience "weighing the Earth."

Interestingly, the various laws of physics have some common features. Let's turn to the laws of electricity (Coulomb force). Electric forces are also inversely proportional to the square of the distance, but already between the charges, and the thought involuntarily arises that this pattern hides deep meaning. Until now, no one has been able to represent gravity and electricity as two different manifestations the same entity.

The force here also varies inversely with the square of the distance, but the difference in the magnitude of electric forces and gravitational forces is striking. Trying to install common nature gravity and electricity, we find such a superiority of electric forces over gravitational forces that it is difficult to believe that both have the same source. How can you say that one is stronger than the other? After all, it all depends on what is the mass and what is the charge. Arguing about how strong gravity acts, you have no right to say: "Let's take a mass of such and such a size," because you choose it yourself. But if we take what Nature herself offers us (her own numbers and measures, which have nothing to do with our inches, years, our measures), then we can compare. We will take an elementary charged particle, such as, for example, an electron. Two elementary particles, two electrons, due to the electric charge repel each other with a force inversely proportional to the square of the distance between them, and due to gravity they are attracted to each other again with a force inversely proportional to the square of the distance.

Question: What is the ratio of gravitational force to electrical force? Gravitation is related to electrical repulsion as one is to a number with 42 zeros. This is deeply puzzling. Where could such a huge number come from?

People are looking for this huge factor in other natural phenomena. They go through all sorts of big numbers, and if you want a big number, why not take, say, the ratio of the diameter of the universe to the diameter of a proton - surprisingly, this is also a number with 42 zeros. And they say: maybe this coefficient is equal to the ratio of the diameter of the proton to the diameter of the universe? This is an interesting thought, but as the universe gradually expands, the constant of gravity must also change. Although this hypothesis has not yet been refuted, we do not have any evidence in its favor. On the contrary, some evidence suggests that the constant of gravity did not change in this way. This huge number remains a mystery to this day.

Einstein had to modify the laws of gravity in accordance with the principles of relativity. The first of these principles says that the distance x cannot be overcome instantly, while according to Newton's theory, forces act instantly. Einstein had to change Newton's laws. These changes, refinements are very small. One of them is this: since light has energy, energy is equivalent to mass, and all masses attract, light also attracts and, therefore, passing by the Sun, must be deflected. This is how it actually happens. The force of gravity is also slightly modified in Einstein's theory. But this very slight change in the law of gravity is just enough to explain some of the apparent irregularities in Mercury's motion.

Physical phenomena in the microcosm are subject to other laws than phenomena in the world of large scales. The question arises: how does gravity manifest itself in a world of small scales? The quantum theory of gravity will answer it. But quantum theory there is no gravity yet. People have not yet been very successful in creating a theory of gravity that is fully consistent with quantum mechanical principles and with the uncertainty principle.

You already know that between all bodies there are attractive forces called forces of gravity.

Their action is manifested, for example, in the fact that bodies fall to the Earth, the Moon revolves around the Earth, and the planets revolve around the Sun. If the forces of gravity disappeared, the Earth would fly away from the Sun (Fig. 14.1).

The law of universal gravitation was formulated in the second half of the 17th century by Isaac Newton.
Two material points of mass m 1 and m 2 located at a distance R attract with forces directly proportional to the product of their masses and inversely proportional to the square of the distance between them. The modulus of each force

The coefficient of proportionality G is called gravitational constant. (From the Latin "gravitas" - gravity.) Measurements showed that

G \u003d 6.67 * 10 -11 N * m 2 / kg 2. (2)

The law of universal gravitation reveals another important property of a body's mass: it is a measure not only of the body's inertia, but also of its gravitational properties.

1. What are the attractive forces of two material points with a mass of 1 kg each, located at a distance of 1 m from each other? How many times is this force greater or less than the weight of a mosquito, whose mass is 2.5 mg?

Such a small value of the gravitational constant explains why we do not notice the gravitational attraction between the objects around us.

Gravitational forces noticeably manifest themselves only when at least one of the interacting bodies has a huge mass - for example, it is a star or a planet.

3. How will the force of attraction between two material points change if the distance between them is increased by 3 times?

4. Two material points of mass m each are attracted with force F. With what force are material points of mass 2m and 3m located at the same distance attracted?

2. Movement of planets around the Sun

The distance from the Sun to any planet is many times more sizes Sun and planets. Therefore, when considering the motion of the planets, they can be considered material points. Therefore, the gravitational force of the planet to the Sun

where m is the mass of the planet, M С is the mass of the Sun, R is the distance from the Sun to the planet.

We will assume that the planet moves around the Sun uniformly in a circle. Then the speed of the planet can be found if we take into account that the acceleration of the planet a = v 2 /R is due to the action of the force F of the attraction of the Sun and the fact that, according to Newton's second law, F = ma.

5. Prove that the speed of the planet

the larger the radius of the orbit, the lower the speed of the planet.

6. The radius of Saturn's orbit is about 9 times the radius of the Earth's orbit. Find verbally, what is the approximate speed of Saturn if the Earth moves in its orbit at a speed of 30 km / s?

In a time equal to one revolution period T, the planet, moving at a speed v, covers a path equal to the circumference of a circle of radius R.

7. Prove that the orbital period of the planet

From this formula it follows that the larger the radius of the orbit, the longer period planet rotation.

9. Prove that for all planets of the solar system

Clue. Use formula (5).
From formula (6) it follows that for all the planets of the solar system, the ratio of the cube of the radius of the orbit to the square of the period of revolution is the same. This pattern (it is called Kepler's third law) was discovered by the German scientist Johannes Kepler based on the results of many years of observations by the Danish astronomer Tycho Brahe.

3. Conditions for the applicability of the formula for the law of universal gravitation

Newton proved that the formula

F \u003d G (m 1 m 2 / R 2)

for the force of attraction of two material points, you can also apply:
- for homogeneous balls and spheres (R is the distance between the centers of balls or spheres, Fig. 14.2, a);

- for a homogeneous ball (sphere) and a material point (R is the distance from the center of the ball (sphere) to the material point, Fig. 14.2, b).

4. Gravity and the law of universal gravitation

The second of the above conditions means that by formula (1) one can find the force of attraction of a body of any shape to a homogeneous ball, which is much larger than this body. Therefore, according to formula (1), it is possible to calculate the force of attraction to the Earth of a body located on its surface (Fig. 14.3, a). We get the expression for gravity:

(The earth is not a uniform sphere, but it can be considered spherically symmetrical. This is sufficient for formula (1) to be applicable.)

10. Prove that near the surface of the Earth

Where M Earth is the mass of the Earth, R Earth is its radius.
Clue. Use formula (7) and that F t = mg.

Using formula (1), you can find the acceleration of free fall at a height h above the Earth's surface (Fig. 14.3, b).

11. Prove that

12. What is the free fall acceleration at a height above the Earth's surface equal to its radius?

13. How many times is the acceleration of free fall on the surface of the Moon less than on the surface of the Earth?
Clue. Use formula (8), in which the mass and radius of the Earth are replaced by the mass and radius of the Moon.

14. The radius of a white dwarf star can be equal to the radius of the Earth, and its mass - equal to the mass Sun. What is the weight of a kilogram weight on the surface of such a "dwarf"?

5. First space velocity

Imagine that for a very high mountain they set up a huge cannon and shoot from it in a horizontal direction (Fig. 14.4).

The greater the initial velocity of the projectile, the further it will fall. It won't fall at all if you pick it up initial speed so that it moves around the Earth in a circle. Flying in a circular orbit, the projectile will then become an artificial satellite of the Earth.

Let our projectile-satellite move in a low near-Earth orbit (the so-called orbit, the radius of which can be taken equal to the radius of the Earth R Earth).
When moving uniformly along a circle, the satellite moves with centripetal acceleration a = v2/Rzem, where v is the speed of the satellite. This acceleration is due to the action of gravity. Consequently, the satellite moves with free fall acceleration directed towards the center of the Earth (Fig. 14.4). Therefore a = g.

15. Prove that when moving in low Earth orbit, the speed of the satellite

Clue. Use the formula a \u003d v 2 / r for centripetal acceleration and the fact that when moving along an orbit of radius R Earth, the satellite's acceleration is equal to the acceleration of free fall.

The speed v 1 that must be reported to the body so that it moves under the action of gravity in a circular orbit near the surface of the Earth is called the first cosmic velocity. It is approximately equal to 8 km/s.

16. Express the first cosmic velocity in terms of the gravitational constant, mass and radius of the Earth.

Clue. In the formula obtained from the previous task, replace the mass and radius of the Earth with the mass and radius of the Moon.

In order for a body to forever leave the vicinity of the Earth, it must be informed of a speed equal to approximately 11.2 km / s. It is called the second space velocity.

6. How the gravitational constant was measured

If we assume that the free fall acceleration g near the Earth's surface, the mass and radius of the Earth are known, then the value of the gravitational constant G can be easily determined using formula (7). The problem, however, is that until the end of the 18th century, the mass of the Earth could not be measured.

Therefore, in order to find the value of the gravitational constant G, it was necessary to measure the force of attraction of two bodies of known mass, located at a certain distance from each other. At the end of the 18th century, the English scientist Henry Cavendish was able to put such an experiment.

He hung a light horizontal rod with small metal balls a and b on a thin elastic thread, and measured the attractive forces acting on these balls from large metal balls A and B by the angle of rotation of the thread (Fig. 14.5). The scientist measured the small angles of rotation of the thread by the displacement of the "bunny" from the mirror attached to the thread.

This experiment of Cavendish was figuratively called "weighing the Earth", because this experiment for the first time made it possible to measure the mass of the Earth.

18. Express the mass of the Earth in terms of G, g and R Earth.


Additional questions and tasks

19. Two ships weighing 6000 tons each are attracted with forces of 2 mN. What is the distance between ships?

20. With what force does the Sun attract the Earth?

21. With what force does a person weighing 60 kg attract the Sun?

22. What is the free fall acceleration at a distance from the Earth's surface equal to its diameter?

23. How many times the acceleration of the Moon, due to the attraction of the Earth, is less than the acceleration of free fall on the surface of the Earth?

24. Acceleration of free fall on the surface of Mars is 2.65 times less than the acceleration of free fall on the surface of the Earth. The radius of Mars is approximately 3400 km. How many times the mass of Mars is less than the mass of the Earth?

25. What is the period of revolution of an artificial Earth satellite in low Earth orbit?

26. What is the first space velocity for Mars? The mass of Mars is 6.4 * 10 23 kg, and the radius is 3400 km.