Universal gravitation definition, formula. Gravitational constant.

What is universal gravitation?

All bodies are attracted to each other. These forces are called the forces of universal gravitation.

Another name for the forces of universal gravitation is gravitational forces.

An example of the manifestation of the forces of universal gravitation is the force of gravity.

A body falls to the ground under the influence of gravity. The earth and this body are attracted to each other.

Universal gravitation definition

Universal gravitation definition:

Two bodies are attracted to each other with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

Gravity Formula

Universal gravitation formula:

F = γ(m 1 m 2)/r 2

where
m 1 is the mass of the first body;
m 2 is the mass of the second body;
r is the distance between the bodies.

Gravitational constant

The coefficient of proportionality γ is called the gravitational constant.

The gravitational constant in SI is:

γ \u003d 6.7 * 10 -11 N * m 2 / kg 2

Important. The above formula for the law of universal gravitation is valid only when the distance between the bodies is much greater than the size of the bodies themselves. In other cases, the formula of the law of universal gravitation cannot be applied.

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 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." 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… Actual picture tidal phenomena differs so much from the theoretical - both qualitatively and quantitatively - that on the basis of such a theory to predict tides 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 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 merging 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 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 efficient use these discoveries, and not to sucked from the finger.

antigravity

As an example of today's scientific profanity we can briefly analyze the "scientists" explanation of the fact that "rays of light are bent near large masses", and therefore we can see that it is closed to 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 chance. 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 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 ...

The phenomenon of universal gravitation

The phenomenon of universal gravitation lies in the fact that between all bodies in the universe there are forces of attraction.

Newton came to the conclusion about the existence of universal gravitational pitchforks (they are also called gravitational pitchforks) as a result of studying the motion of the Moon around the Earth and planets around the Sun. These astronomical observations were made by the Danish astronomer Tycho Brahe. Tycho Brahe measured the position of all the known planets at that time and wrote down their coordinates, but Tycho Brahe failed to finally deduce, create the law of planetary motion relative to the Sun. This was done by his student Johannes Kepler. Johannes Kepler used not only the measurements of Tycho Brahe, but also by that time already sufficiently substantiated, used everywhere and everywhere, the heliocentric system of the world of Copernicus. The system in which it is believed that the Sun is at the center of our system and the planets revolve around it.

Figure 1. Heliocentric system of the world (Copernicus system)

First of all, Newton suggested that all bodies have the property of attraction, i.e. those bodies that have masses are attracted to each other. This phenomenon became known as universal gravitation. And bodies that attract others to each other create force. This force, with which bodies are attracted, began to be called gravitational (from the word gravitas - "gravity").

Law of gravity

Newton managed to obtain a formula for calculating the interaction force of bodies with masses. This formula is called law of gravity. It was discovered in $1667$. I. Newton substantiated his discovery on astronomical observations

The very "law of universal gravitation" sounds like this: two bodies are attracted to each other with a force that is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them.

Let's look at the quantities that are included in this law. So, the law of universal gravitation itself looks like this:

There is one more value here - $G$, gravitational constant. Its physical meaning lies in the fact that it shows the force with which two bodies with a mass of $1$ kg, each $1$ kg, located at a distance of $1$ m interact. This value is very small, it is only $10^ in order of magnitude. (-11).$

$G=6.67\cdot 10^(-11) \frac(H\cdot m^2)(kg^2)$

Its value tells about the ratio in which they are located, with what force the bodies that are nearby interact, and even if they are close enough (for example, two standing people), they will absolutely not feel this interaction, since the order of force is $10^( -11)$ will not give a significant sensation. Action gravitational force begins to affect only when the mass of bodies is large.

Limits of applicability of the law of universal gravitation

In the form in which we use the law of universal gravitation, it is not always true, but only in some cases:

• if the dimensions of the bodies are negligible compared to the distance between them;

Figure 2.

• if both bodies are homogeneous and have a spherical shape - in this case, even if the distances between the bodies are still not so great, the law of universal gravitation is applicable if the bodies have a spherical shape and then the distances are defined as the distances between the centers of the bodies under consideration;

Figure 3

• if one of the interacting bodies is a ball, the dimensions of which are much larger than the dimensions of the second body (of any shape) located on the surface of this ball or near it, this is the case of the movement of satellites in their orbits around the Earth.

Figure 4

Example 1

An artificial satellite moves in a circular orbit around the Earth at a speed of $1$ km/s at an altitude of 350,000 km. We need to determine the mass of the Earth.

Given: $v=1$ km/s, $R=350000$ km.

Find: $M_(3) $-?

Since the satellite is moving around the Earth, it has a centripetal acceleration equal to:

$F=G\frac(mM_(3) )(R^(2) ) =ma$. (2)

Taking into account (1) from (2), we write the expression for finding the mass of the Earth:

$M_(3) =\frac(v^(2) R)(G) =5.24\cdot 10^(24) $kg

Answer: $M_(3) =5.24\cdot 10^(24) $ kg.

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 power 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 ( Short story)

✪ 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 to transform it and see if we can get some results that are familiar to us. 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 weight 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 quantities, you need to write it in standard form - 6.371 * 10^6 because 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, it was found that the gravitational force near the surface of the Earth, acting on Sal, is equal to the mass of Sal, 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 an abandoned 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 precision 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 late XIX 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)). So the equations 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

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 holds 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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