Isaac Newton suggested that between any bodies in nature there are forces of mutual attraction. These forces are called gravity forces or forces of gravity. The force of irrepressible gravity manifests itself in space, the solar system and on Earth.

Law of gravity

Newton generalized the laws of motion of celestial bodies and found out that the force \ (F \) is equal to:

\[ F = G \dfrac(m_1 m_2)(R^2) \]

where \(m_1 \) and \(m_2 \) are the masses of interacting bodies, \(R \) is the distance between them, \(G \) is the proportionality coefficient, which is called gravitational constant. The numerical value of the gravitational constant was experimentally determined by Cavendish, measuring the force of interaction between lead balls.

The physical meaning of the gravitational constant follows from the law of universal gravitation. If a \(m_1 = m_2 = 1 \text(kg) \), \(R = 1 \text(m) \) , then \(G = F \) , i.e. the gravitational constant is equal to the force with which two bodies of 1 kg are attracted at a distance of 1 m.

Numerical value:

\(G = 6.67 \cdot() 10^(-11) N \cdot() m^2/ kg^2 \) .

The forces of universal gravitation act between any bodies in nature, but they become tangible at large masses (or if at least the mass of one of the bodies is large). The law of universal gravitation is fulfilled only for material points and balls (in this case, the distance between the centers of the balls is taken as the distance).

Gravity

A special type of universal gravitational force is the force of attraction of bodies to the Earth (or to another planet). This force is called gravity. Under the action of this force, all bodies acquire free fall acceleration.

According to Newton's second law \(g = F_T /m \) , therefore \(F_T = mg \) .

If M is the mass of the Earth, R is its radius, m is the mass of the given body, then the force of gravity is equal to

\(F = G \dfrac(M)(R^2)m = mg \) .

The force of gravity is always directed towards the center of the Earth. Depending on the height \ (h \) above the Earth's surface and the geographical latitude of the position of the body, the free fall acceleration acquires different values. On the surface of the Earth and in middle latitudes, the free fall acceleration is 9.831 m/s 2 .

Body weight

In technology and everyday life, the concept of body weight is widely used.

Body weight denoted by \(P \) . The unit of weight is newton (N). Since the weight is equal to the force with which the body acts on the support, then, in accordance with Newton's third law, the weight of the body is equal in magnitude to the reaction force of the support. Therefore, in order to find the weight of the body, it is necessary to determine what the reaction force of the support is equal to.

It is assumed that the body is motionless relative to the support or suspension.

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

The state of a body in which its weight is zero is called weightlessness. The state of weightlessness is observed in an airplane or spacecraft when moving with the acceleration of free fall, regardless of the direction and value of the speed of their movement. Outside the earth's atmosphere, when the jet engines are turned off, only the force of universal gravitation acts on the spacecraft. Under the action of this force, the spaceship and all the bodies in it move with the same acceleration, so the state of weightlessness is observed in the ship.

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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 speeds and weak gravitational interaction, it is described by Newton's theory of gravitation, in the general case it is 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 appeared such inexplicable guesses 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 the 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 the "unsolvable" mysteries of 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, A life- living matter. He explained what kind of matter can be considered alive, and what physical meaning natural process called a 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 of? 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 about 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 United States, which he then considered a completely normal country, wrote, translated into English 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." It came out as a comedy because, in order to ensure the best performance of 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? A 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 real nature of gravity for the first time in modern history was 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 begins to interact with each other, falling into changed external conditions in certain curvature 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 types of primary 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 is very different from the fictitious law of "mutual attraction", which supposedly exists 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 never 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, internal combustion engines or jet engines have been used almost everywhere, although they are very far from perfect both in terms of the 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 about 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 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 demonstrate very real examples of 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 ...

Newton's classical theory of gravitation (Newton's law of universal gravitation)- a law describing gravitational interaction within the framework of classical mechanics. This law was discovered by Newton around 1666. He says that strength F (\displaystyle F) gravitational attraction between two material points of mass m 1 (\displaystyle m_(1)) and m 2 (\displaystyle m_(2)) separated by distance r (\displaystyle r), is proportional to both masses and inversely proportional to the square of the distance between them - that is:

F = G ⋅ m 1 ⋅ m 2 r 2 (\displaystyle F=G\cdot (m_(1)\cdot m_(2) \over r^(2)))

Here G (\displaystyle G)- gravitational constant, equal to 6.67408(31) 10 −11 m³/(kg s²) .

Encyclopedic YouTube

1 / 5

✪ Introduction to Newton's Law of Gravity

✪ Law of gravity

✪ physics LAW OF UNIVERSAL GRAVITY Grade 9

✪ About Isaac Newton (A Brief History)

✪ Lesson 60. The law of universal gravitation. Gravitational constant

Subtitles

Now let's learn a little about gravitation, or gravity. As you know, gravity, especially in an elementary or even in a fairly advanced physics course, is such a concept that you can calculate and find out the main parameters that determine it, but in fact, gravity is not entirely understandable. Even if you are familiar with the general theory of relativity - if you are asked what gravity is, you can answer: it is the curvature of space-time and the like. However, it is still difficult to get an intuition as to why two objects, just because they have a so-called mass, are attracted to each other. At least for me it's mystical. Having noted this, we proceed to consider the concept of gravitation. We will do this by studying Newton's law of universal gravitation, which is valid for most situations. This law says: the force of mutual gravitational attraction F between two material points with masses m₁ and m₂ is equal to the product of the gravitational constant G times the mass of the first object m₁ and the second object m₂, divided by the square of the distance d between them. This is a pretty simple formula. Let's try transforming it and see if we can get some familiar results. We use this formula to calculate the free fall acceleration near the Earth's surface. Let's draw the Earth first. Just to understand what we are talking about. This is our Earth. Suppose we need to calculate the gravitational acceleration acting on Sal, that is, on me. Here I am. Let's try to apply this equation to calculate the magnitude of the acceleration of my fall to the center of the Earth, or to the center of mass of the Earth. The value denoted by the capital letter G is the universal gravitational constant. Once again: G is the universal gravitational constant. Although, as far as I know, although I am not an expert in this matter, it seems to me that its value can change, that is, it is not a true constant, and I assume that its value differs with different measurements. But for our needs, as well as in most physics courses, it's a constant, a constant equal to 6.67 * 10^(−11) cubic meters divided by a kilogram per second squared. Yes, its dimension looks strange, but it is enough for you to understand that these are arbitrary units necessary to, as a result of multiplying by the masses of objects and dividing by the square of the distance, get the dimension of force - a newton, or a kilogram per meter divided by a second squared. So don't worry about these units, just know that we will have to work with meters, seconds and kilograms. Substitute this number into the formula for force: 6.67 * 10^(−11). Since we need to know the acceleration acting on Sal, then m₁ is equal to the mass of Sal, that is, me. I don't want to expose in this story how much I weigh, so let's leave this mass as a variable, denoting ms. The second mass in the equation is the mass of the Earth. Let's write out its meaning by looking at Wikipedia. So, the mass of the Earth is 5.97 * 10^24 kilograms. Yes, the Earth is more massive than Sal. By the way, weight and mass are different concepts. So, the force F is equal to the product of the gravitational constant G times the mass ms, then the mass of the Earth, and all this is divided by the square of the distance. You may object: what is the distance between the Earth and what stands on it? After all, if objects are in contact, the distance is zero. It is important to understand here: the distance between two objects in this formula is the distance between their centers of mass. In most cases, a person's center of mass is located about three feet above the surface of the earth, unless the person is too tall. Whatever the case, my center of mass may be three feet above the ground. Where is the Earth's center of mass? Obviously at the center of the earth. What is the Earth's radius? 6371 kilometers, or approximately 6 million meters. Since the height of my center of mass is about one millionth of the distance from the center of mass of the Earth, in this case it can be neglected. Then the distance will be equal to 6 and so on, like all other values, you need to write it in the standard form - 6.371 * 10^6, since 6000 km is 6 million meters, and a million is 10^6. We write, rounding all fractions to the second decimal place, the distance is 6.37 * 10 ^ 6 meters. The formula is the square of the distance, so let's square everything. Let's try to simplify now. First, we multiply the values ​​in the numerator and bring forward the variable ms. Then the force F is equal to the mass of Sal on the entire upper part, we calculate it separately. So 6.67 times 5.97 equals 39.82. 39.82. This is the product of the significant parts, which should now be multiplied by 10 to the desired power. 10^(−11) and 10^24 have the same base, so to multiply them, just add the exponents. Adding 24 and −11, we get 13, as a result we have 10^13. Let's find the denominator. It is equal to 6.37 squared times 10^6 also squared. As you remember, if a number written as a power is raised to another power, then the exponents are multiplied, which means that 10^6 squared is 10 times 6 times 2, or 10^12. Next, we calculate the square of the number 6.37 using a calculator and get ... We square 6.37. And this is 40.58. 40.58. It remains to divide 39.82 by 40.58. Divide 39.82 by 40.58, which equals 0.981. Then we divide 10^13 by 10^12, which is 10^1, or just 10. And 0.981 times 10 is 9.81. After simplification and simple calculations, we found that the gravitational force near the surface of the Earth, acting on Sal, is equal to Sal's mass multiplied by 9.81. What does this give us? Is it possible now to calculate the gravitational acceleration? It is known that the force is equal to the product of mass and acceleration, therefore, the force of gravity is simply equal to the product of Sal's mass and gravitational acceleration, which is usually denoted by a lowercase letter g. So, on the one hand, the force of attraction is equal to the number 9.81 times the mass of Sal. On the other hand, it is equal to Sal's mass per gravitational acceleration. Dividing both parts of the equation by Sal's mass, we get that the coefficient 9.81 is the gravitational acceleration. And if we included in the calculations the full record of units of dimensions, then, having reduced kilograms, we would see that gravitational acceleration is measured in meters divided by a second squared, like any acceleration. You can also notice that the value obtained is very close to the one we used when solving problems about the motion of a thrown body: 9.8 meters per second squared. It's impressive. Let's solve another short gravity problem, because we have a couple of minutes left. Suppose we have another planet called Earth Baby. Let Malyshka's radius rS be half the Earth's radius rE, and her mass mS also equal to half the Earth's mass mE. What will be the force of gravity acting here on any object, and how much is it less than the force of the earth's gravity? Although, let's leave the problem for the next time, then I will solve it. See you. Subtitles by the Amara.org community

Properties of Newtonian gravity

In Newtonian theory, each massive body generates a force field of attraction to this body, which is called the gravitational field. This field is potentially , and the function of the gravitational potential for a material point with mass M (\displaystyle M) is determined by the formula:

φ (r) = − G M r . (\displaystyle \varphi (r)=-G(\frac (M)(r)).)

In general, when the density of matter ρ (\displaystyle \rho ) randomly distributed, satisfies the Poisson equation:

Δ φ = − 4 π G ρ (r) . (\displaystyle \Delta \varphi =-4\pi G\rho (r).)

The solution to this equation is written as:

φ = − G ∫ ρ (r) d V r + C , (\displaystyle \varphi =-G\int (\frac (\rho (r)dV)(r))+C,)

where r (\displaystyle r) - distance between volume element dV (\displaystyle dV) and the point at which the potential is determined φ (\displaystyle \varphi ), C (\displaystyle C) is an arbitrary constant.

The force of attraction acting in a gravitational field on a material point with mass m (\displaystyle m), is related to the potential by the formula:

F (r) = − m ∇ φ (r) . (\displaystyle F(r)=-m\nabla \varphi (r).)

A spherically symmetric body creates the same field outside its boundaries as a material point of the same mass located in the center of the body.

The trajectory of a material point in a gravitational field created by a much larger mass point obeys the laws of Kepler. In particular, planets and comets in the Solar System move in ellipses or hyperbolas. The influence of other planets, which distorts this picture, can be taken into account using the perturbation theory.

Accuracy of Newton's law of universal gravitation

An experimental assessment of the degree of accuracy of Newton's law of gravitation is one of the confirmations of the general theory of relativity. Experiments on measuring the quadrupole interaction of a rotating body and a fixed antenna showed that the increment δ (\displaystyle \delta ) in the expression for the dependence of the Newtonian potential r − (1 + δ) (\displaystyle r^(-(1+\delta))) at distances of several meters is within (2 , 1 ± 6 , 2) ∗ 10 − 3 (\displaystyle (2,1\pm 6,2)*10^(-3)). Other experiments also confirmed the absence of modifications in the law of universal gravitation.

Newton's law of universal gravitation was tested in 2007 at distances less than one centimeter (from 55 microns to 9.53 mm). Taking into account the experimental errors, no deviations from Newton's law were found in the investigated range of distances.

Precise laser ranging observations of the Moon's orbit confirm the law of universal gravitation at a distance from the Earth to the Moon with accuracy 3 ⋅ 10 − 11 (\displaystyle 3\cdot 10^(-11)).

Relationship with the geometry of Euclidean space

Equality fact with very high accuracy 10 − 9 (\displaystyle 10^(-9)) the exponent of the distance in the denominator of the expression for the force of gravity to the number 2 (\displaystyle 2) reflects the Euclidean nature of the three-dimensional physical space of Newtonian mechanics. In three-dimensional Euclidean space, the surface area of ​​a sphere is exactly proportional to the square of its radius.

Historical outline

The very idea of ​​a universal gravitational force was repeatedly expressed even before Newton. Earlier, Epicurus, Gassendi, Kepler, Borelli, Descartes, Roberval, Huygens and others thought about it. Kepler believed that gravity is inversely proportional to the distance to the Sun and extends only in the plane of the ecliptic; Descartes considered it to be the result of vortices in the ether. There were, however, guesses with a correct dependence on distance; Newton, in a letter to Halley, mentions Bulliald, Wren, and Hooke as his predecessors. But before Newton, no one was able to clearly and mathematically conclusively link the law of gravitation (a force inversely proportional to the square of distance) and the laws of planetary motion (Kepler's laws).

• law of gravitation;
• the law of motion (Newton's second law);
• system of methods for mathematical research (mathematical analysis).

Taken together, this triad is sufficient for a complete study of the most complex movements of celestial bodies, thereby creating the foundations of celestial mechanics. Prior to Einstein, no fundamental amendments to this model were needed, although the mathematical apparatus turned out to be necessary to be significantly developed.

Note that Newton's theory of gravity was no longer, strictly speaking, heliocentric. Already in the two-body problem, the planet does not rotate around the Sun, but around a common center of gravity, since not only the Sun attracts the planet, but the planet also attracts the Sun. Finally, it turned out to be necessary to take into account the influence of the planets on each other.

During the 18th century, the law of universal gravitation was the subject of active discussion (opposed by supporters of the school of Descartes) and careful testing. By the end of the century, it became generally recognized that the law of universal gravitation makes it possible to explain and predict the movements of celestial bodies with great accuracy. Henry Cavendish in 1798 carried out a direct verification of the validity of the law of gravity in terrestrial conditions, using extremely sensitive torsion balances. An important step was the introduction by Poisson in 1813 of the concept of the gravitational potential and the Poisson equation for this potential; this model made it possible to investigate the gravitational field with an arbitrary distribution of matter. After that, Newton's law began to be regarded as a fundamental law of nature.

At the same time, Newton's theory contained a number of difficulties. The main one is an inexplicable long-range action: the force of gravity was transmitted incomprehensibly how through a completely empty space, and infinitely quickly. Essentially, the Newtonian model was purely mathematical, without any physical content. In addition, if the Universe, as was then assumed, is Euclidean and infinite, and at the same time the average density of matter in it is nonzero, then a gravitational paradox arises. At the end of the 19th century, another problem was discovered: the discrepancy between the theoretical and observed displacement perihelion Mercury.

Further development

General theory of relativity

For more than two hundred years after Newton, physicists have proposed various ways to improve Newton's theory of gravity. These efforts were crowned with success in 1915, with the creation of Einstein's general theory of relativity, in which all these difficulties were overcome. Newton's theory, in full agreement with the correspondence principle, turned out to be an approximation of a more general theory, applicable under two conditions:

In weak stationary gravitational fields, the equations of motion become Newtonian (gravitational potential). To prove this, we show that the scalar gravitational potential in weak stationary gravitational fields satisfies the Poisson equation

Δ Φ = − 4 π G ρ (\displaystyle \Delta \Phi =-4\pi G\rho ).

It is known (Gravitational potential) that in this case the gravitational potential has the form:

Φ = − 1 2 c 2 (g 44 + 1) (\displaystyle \Phi =-(\frac (1)(2))c^(2)(g_(44)+1)).

Let us find the component of the  energy-momentum tensor from the equations of the gravitational field of the general theory of relativity:

R i k = − ϰ (T i k − 1 2 g i k T) (\displaystyle R_(ik)=-\varkappa (T_(ik)-(\frac (1)(2))g_(ik)T)),

where R i k (\displaystyle R_(ik)) is the curvature tensor. For we can introduce the kinetic energy-momentum tensor ρ u i u k (\displaystyle \rho u_(i)u_(k)). Neglecting quantities of the order u/c (\displaystyle u/c), you can put all the components T i k (\displaystyle T_(ik)), Besides T 44 (\displaystyle T_(44)), equal to zero. Component T 44 (\displaystyle T_(44)) is equal to T 44 = ρ c 2 (\displaystyle T_(44)=\rho c^(2)) and therefore T = g i k T i k = g 44 T 44 = − ρ c 2 (\displaystyle T=g^(ik)T_(ik)=g^(44)T_(44)=-\rho c^(2)). Thus, the equations of the gravitational field take the form R 44 = − 1 2 ϰ ρ c 2 (\displaystyle R_(44)=-(\frac (1)(2))\varkappa \rho c^(2)). Due to the formula

R i k = ∂ Γ i α α ∂ x k − ∂ Γ i k α ∂ x α + Γ i α β Γ k β α − Γ i k α Γ α β β (\displaystyle R_(ik)=(\frac (\partial \ Gamma _(i\alpha )^(\alpha ))(\partial x^(k)))-(\frac (\partial \Gamma _(ik)^(\alpha ))(\partial x^(\alpha )))+\Gamma _(i\alpha )^(\beta )\Gamma _(k\beta )^(\alpha )-\Gamma _(ik)^(\alpha )\Gamma _(\alpha \beta )^(\beta ))

value of the curvature tensor component R44 (\displaystyle R_(44)) can be taken equal R 44 = − ∂ Γ 44 α ∂ x α (\displaystyle R_(44)=-(\frac (\partial \Gamma _(44)^(\alpha ))(\partial x^(\alpha )))) and since Γ 44 α ≈ − 1 2 ∂ g 44 ∂ x α (\displaystyle \Gamma _(44)^(\alpha )\approx -(\frac (1)(2))(\frac (\partial g_(44) )(\partial x^(\alpha )))), R 44 = 1 2 ∑ α ∂ 2 g 44 ∂ x α 2 = 1 2 Δ g 44 = − Δ Φ c 2 (\displaystyle R_(44)=(\frac (1)(2))\sum _(\ alpha )(\frac (\partial ^(2)g_(44))(\partial x_(\alpha )^(2)))=(\frac (1)(2))\Delta g_(44)=- (\frac (\Delta \Phi )(c^(2)))). Thus, we arrive at the Poisson equation:

Δ Φ = 1 2 ϰ c 4 ρ (\displaystyle \Delta \Phi =(\frac (1)(2))\varkappa c^(4)\rho ), where ϰ = − 8 π G c 4 (\displaystyle \varkappa =-(\frac (8\pi G)(c^(4))))

quantum gravity

However, the general theory of relativity is not the final theory of gravitation either, since it does not adequately describe gravitational processes on quantum scales (at distances of the order of the Planck scale, about 1.6⋅10 −35 ). The construction of a consistent quantum theory of gravity is one of the most important unsolved problems of modern physics.

From the point of view of quantum gravity, gravitational interaction is carried out by exchanging virtual gravitons between interacting bodies. According to the uncertainty principle, the energy of a virtual graviton is inversely proportional to the time of its existence from the moment of emission by one body to the moment of absorption by another body. The lifetime is proportional to the distance between the bodies. Thus, at small distances interacting bodies can exchange virtual gravitons with short and long wavelengths, and at large distances only long-wavelength gravitons. From these considerations, one can obtain the law of inverse proportionality of the Newtonian potential from distance. The analogy between Newton's law and Coulomb's law is explained by the fact that the graviton mass, like the mass

I. Newton was able to deduce from Kepler's laws one of the fundamental laws of nature - the law of universal gravitation. 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 about times less than the acceleration reported by the Earth to bodies located near the 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 movement of 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, then 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 the planets in the 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 gravitational force of the sun 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.

This article will focus on the history of the discovery of the law of universal gravitation. Here we will get acquainted with the biographical information from the life of the scientist who discovered this physical dogma, consider its main provisions, the relationship with quantum gravity, the course of development, and much more.

Genius

Sir Isaac Newton is an English scientist. At one time, he devoted much attention and effort to such sciences as physics and mathematics, and also brought a lot of new things to mechanics and astronomy. He is rightfully considered one of the first founders of physics in its classical model. He is the author of the fundamental work "Mathematical Principles of Natural Philosophy", where he presented information about the three laws of mechanics and the law of universal gravitation. Isaac Newton laid the foundations of classical mechanics with these works. He also developed an integral type, the light theory. He also made many contributions to physical optics and developed many other theories in physics and mathematics.

Law

The law of universal gravitation and the history of its discovery go far back in time. Its classical form is a law that describes the interaction of a gravitational type that does not go beyond the framework of mechanics.

Its essence was that the indicator of the force F of the gravitational pull arising between 2 bodies or points of matter m1 and m2, separated from each other by a certain distance r, is proportional to both mass indicators and is inversely proportional to the square of the distance between the bodies:

F = G, where by the symbol G we denote the gravitational constant equal to 6.67408(31).10 -11 m 3 /kgf 2.

Newton's gravity

Before considering the history of the discovery of the law of universal gravitation, let's take a closer look at its general characteristics.

In the theory created by Newton, all bodies with a large mass must generate a special field around them, which attracts other objects to itself. It's called the gravitational field, and it has potential.

A body with spherical symmetry forms a field outside of itself, similar to that created by a material point of the same mass located in the center of the body.

The direction of the trajectory of such a point in the gravitational field, created by a body with a much larger mass, obeys. Objects of the universe, such as, for example, a planet or a comet, also obey it, moving along an ellipse or hyperbola. Accounting for the distortion that other massive bodies create is taken into account using the provisions of the perturbation theory.

Analyzing Accuracy

After Newton discovered the law of universal gravitation, it had to be tested and proved many times over. For this, a number of calculations and observations were made. Having come to agreement with its provisions and proceeding from the accuracy of its indicator, the experimental form of estimation serves as a clear confirmation of GR. Measurement of quadrupole interactions of a body that rotates, but its antennas remain motionless, show us that the process of increasing δ depends on the potential r - (1 + δ) , at a distance of several meters and is in the limit (2.1 ± 6.2) .10 -3 . A number of other practical confirmations allowed this law to be established and take a single form, without any modifications. In 2007, this dogma was rechecked at a distance less than a centimeter (55 microns-9.59 mm). Taking into account the experimental errors, the scientists examined the distance range and found no obvious deviations in this law.

Observation of the Moon's orbit with respect to the Earth also confirmed its validity.

Euclidean space

Newton's classical theory of gravity is related to Euclidean space. The actual equality with a sufficiently high accuracy (10 -9) of the distance measures in the denominator of the equality discussed above shows us the Euclidean basis of the space of Newtonian mechanics, with a three-dimensional physical form. At such a point in matter, the area of ​​a spherical surface is exactly proportional to the square of its radius.

Data from history

Consider a brief summary of the history of the discovery of the law of universal gravitation.

Ideas were put forward by other scientists who lived before Newton. Epicurus, Kepler, Descartes, Roberval, Gassendi, Huygens and others visited reflections on it. Kepler put forward the assumption that the gravitational force is inversely proportional to the distance from the star of the Sun and has distribution only in the ecliptic planes; according to Descartes, it was a consequence of the activity of vortices in the thickness of the ether. There was a series of guesses that contained a reflection of the correct guesses about the dependence on distance.

A letter from Newton to Halley contained information that Hooke, Wren and Buyo Ismael were the predecessors of Sir Isaac himself. However, no one before him managed to clearly, with the help of mathematical methods, connect the law of gravity and planetary motion.

The history of the discovery of the law of universal gravitation is closely connected with the work "Mathematical Principles of Natural Philosophy" (1687). In this work, Newton was able to derive the law in question thanks to Kepler's empirical law, which was already known by that time. He shows us that:

• the form of movement of any visible planet testifies to the presence of a central force;
• the attractive force of the central type forms elliptical or hyperbolic orbits.

About Newton's theory

An examination of the brief history of the discovery of the law of universal gravitation can also point us to a number of differences that set it apart from previous hypotheses. Newton was engaged not only in the publication of the proposed formula of the phenomenon under consideration, but also proposed a model of a mathematical type in a holistic form:

• position on the law of gravity;
• position on the law of motion;
• systematics of methods of mathematical research.

This triad was able to investigate even the most complex movements of celestial objects to a fairly accurate extent, thus creating the basis for celestial mechanics. Up to the beginning of Einstein's activity in this model, the presence of a fundamental set of corrections was not required. Only mathematical apparatus had to be significantly improved.

Object for discussion

The discovered and proved law during the whole of the eighteenth century became a well-known subject of active disputes and scrupulous checks. However, the century ended with a general agreement with his postulates and statements. Using the calculations of the law, it was possible to accurately determine the paths of the movement of bodies in heaven. A direct check was made in 1798. He did this using a torsion-type balance with great sensitivity. In the history of the discovery of the universal law of gravitation, it is necessary to allocate a special place to the interpretations introduced by Poisson. He developed the concept of the potential of gravity and the Poisson equation, with which it was possible to calculate this potential. This type of model made it possible to study the gravitational field in the presence of an arbitrary distribution of matter.

There were many difficulties in Newton's theory. The main one could be considered the inexplicability of long-range action. It was impossible to accurately answer the question of how the forces of attraction are sent through vacuum space at infinite speed.

"Evolution" of the law

Over the next two hundred years, and even more, attempts were made by many physicists to propose various ways to improve Newton's theory. These efforts ended in a triumph in 1915, namely the creation of the General Theory of Relativity, which was created by Einstein. He was able to overcome the whole set of difficulties. In accordance with the correspondence principle, Newton's theory turned out to be an approximation to the beginning of work on a theory in a more general form, which can be applied under certain conditions:

1. The potential of the gravitational nature cannot be too large in the systems under study. The solar system is an example of compliance with all the rules for the movement of celestial bodies. The relativistic phenomenon finds itself in a noticeable manifestation of the shift of the perihelion.
2. The indicator of the speed of movement in this group of systems is insignificant in comparison with the speed of light.

The proof that in a weak stationary field of gravitation GR calculations take the form of Newtonian ones is the presence of a scalar gravitational potential in a stationary field with weakly expressed force characteristics, which is able to satisfy the conditions of the Poisson equation.

Quantum Scale

However, in history, neither the scientific discovery of the law of universal gravitation, nor the General Theory of Relativity could serve as the final gravitational theory, since both do not adequately describe the processes of the gravitational type on the quantum scale. An attempt to create a quantum gravitational theory is one of the most important tasks of modern physics.

From the point of view of quantum gravity, the interaction between objects is created by the interchange of virtual gravitons. In accordance with the uncertainty principle, the energy potential of virtual gravitons is inversely proportional to the time interval in which it existed, from the point of emission by one object to the point in time at which it was absorbed by another point.

In view of this, it turns out that on a small scale of distances, the interaction of bodies entails the exchange of virtual type gravitons. Thanks to these considerations, it is possible to conclude the provision on the law of Newton's potential and its dependence in accordance with the reciprocal of proportionality with respect to distance. The analogy between the laws of Coulomb and Newton is explained by the fact that the weight of gravitons is equal to zero. The weight of photons has the same meaning.

Delusion

In the school curriculum, the answer to a question from history, how Newton discovered the law of universal gravitation, is the story of a falling apple fruit. According to this legend, it fell on the head of a scientist. However, this is a widespread misconception, and in fact, everything was able to do without a similar case of a possible head injury. Newton himself sometimes confirmed this myth, but in reality the law was not a spontaneous discovery and did not come in a burst of momentary insight. As it was written above, it was developed for a long time and was presented for the first time in the works on the "Principles of Mathematics", which appeared on public display in 1687.