The force of gravity

Newton discovered the laws of motion of bodies. According to these laws, movement with acceleration is possible only under the action of a force. Since falling bodies move with acceleration, they must be subjected to a force directed downward towards the Earth. Is it only the Earth that has the property of attracting bodies that are near its surface to itself? In 1667, Newton suggested that, in general, forces of mutual attraction act between all bodies. He called these forces the forces of universal gravitation.

Why do we not notice the mutual attraction between the bodies around us? Perhaps this is due to the fact that the forces of attraction between them are too small?

Newton was able to show that the force of attraction between bodies depends on the masses of both bodies and, as it turned out, reaches a noticeable value only when the interacting bodies (or at least one of them) have a sufficiently large mass.

"HOLES" IN SPACE AND TIME

Black holes are the product of gigantic gravitational forces. They arise when, in the course of a strong compression of a large mass of matter, its increasing gravitational field becomes so strong that it does not even let out light, nothing can come out of a black hole at all. You can only fall into it under the influence of huge gravitational forces, but there is no way out. Modern science has revealed the connection of time with physical processes, called to "probe" the first links of the chain of time in the past and follow its properties in the distant future.

The role of the masses of attracting bodies

The acceleration of free fall is distinguished by the curious feature that it is the same in a given place for all bodies, for bodies of any mass. How to explain this strange property?

The only explanation that can be found for the fact that acceleration does not depend on the mass of the body is that the force F with which the Earth attracts the body is proportional to its mass m.

Indeed, in this case, an increase in the mass m, for example, by a factor of two will lead to an increase in the modulus of force F also by a factor of two, while the acceleration, which is equal to the ratio F/m, will remain unchanged. Newton made this only correct conclusion: the force of universal gravitation is proportional to the mass of the body on which it acts.

But after all, bodies are attracted mutually, and the forces of interaction are always of the same nature. Consequently, the force with which the body attracts the Earth is proportional to the mass of the Earth. According to Newton's third law, these forces are equal in absolute value. Hence, if one of them is proportional to the mass of the Earth, then the other force equal to it is also proportional to the mass of the Earth. From here it follows that the force of mutual attraction is proportional to the masses of both interacting bodies. And this means that it is proportional to the product of the masses of both bodies.

WHY IS GRAVITY IN SPACE NOT THE SAME AS ON EARTH?

Every object in the universe acts on another object, they attract each other. The force of attraction, or gravity, depends on two factors.

Firstly, it depends on how much substance the object, body, object contains. The greater the mass of the substance of the body, the stronger the gravity. If a body has very little mass, its gravity is small. For example, the mass of the Earth is many times greater than the mass of the Moon, so the earth has a greater gravitational force than the Moon.

Secondly, the force of gravity depends on the distances between the bodies. The closer the bodies are to each other, the greater the force of attraction. The farther they are from each other, the less gravity.

Why does a stone released from the hands fall to the ground? Because it is attracted by the Earth, each of you will say. In fact, the stone falls to the Earth with free fall acceleration. Consequently, a force directed towards the Earth acts on the stone from the side of the Earth. According to Newton's third law, the stone also acts on the Earth with the same modulus of force directed towards the stone. In other words, forces of mutual attraction act between the Earth and the stone.

Newton was the first who first guessed, and then strictly proved, that the reason causing the fall of a stone to the Earth, the movement of the Moon around the Earth and the planets around the Sun, is one and the same. This is the gravitational force acting between any bodies of the Universe. Here is the course of his reasoning given in Newton's main work "The Mathematical Principles of Natural Philosophy":

“A stone thrown horizontally will deviate under the action of gravity from a straight path and, having described a curved trajectory, will finally fall to the Earth. If you throw it at a higher speed, then it will fall further” (Fig. 1).

Continuing these reasoning, Newton comes to the conclusion that if it were not for air resistance, then the trajectory of a stone thrown from a high mountain at a certain speed could become such that it would never reach the Earth’s surface at all, but would move around it “like how the planets describe their orbits in celestial space.

Now we have become so accustomed to the movement of satellites around the Earth that there is no need to explain Newton's idea in more detail.

So, according to Newton, the movement of the Moon around the Earth or the planets around the Sun is also a free fall, but only a fall that lasts without stopping for billions of years. The reason for such a “fall” (whether it is really about the fall of an ordinary stone on the Earth or about the movement of the planets in their orbits) is the force of universal gravitation. What does this force depend on?

The dependence of the force of gravity on the mass of bodies

Galileo proved that during free fall, the Earth imparts the same acceleration to all bodies in a given place, regardless of their mass. But acceleration, according to Newton's second law, is inversely proportional to mass. How can one explain that the acceleration imparted to a body by the Earth's gravity is the same for all bodies? This is possible only if the force of attraction to the Earth is directly proportional to the mass of the body. In this case, an increase in the mass m, for example, by a factor of two will lead to an increase in the modulus of force F is also doubled, and the acceleration, which is equal to \(a = \frac (F)(m)\), will remain unchanged. Generalizing this conclusion for the forces of gravity between any bodies, we conclude that the force of universal gravitation is directly proportional to the mass of the body on which this force acts.

But at least two bodies participate in mutual attraction. Each of them, according to Newton's third law, is subject to the same modulus of gravitational forces. Therefore, each of these forces must be proportional both to the mass of one body and to the mass of the other body. Therefore, the force of universal gravitation between two bodies is directly proportional to the product of their masses:

\(F \sim m_1 \cdot m_2\)

The dependence of the force of gravity on the distance between bodies

From experience it is well known that the acceleration of free fall is 9.8 m / s 2 and it is the same for bodies falling from a height of 1, 10 and 100 m, that is, it does not depend on the distance between the body and the Earth. This seems to mean that force does not depend on distance. But Newton believed that distances should be measured not from the surface, but from the center of the Earth. But the radius of the Earth is 6400 km. It is clear that several tens, hundreds or even thousands of meters above the Earth's surface cannot noticeably change the value of the free fall acceleration.

To find out how the distance between bodies affects the force of their mutual attraction, it would be necessary to find out what is the acceleration of bodies remote from the Earth at sufficiently large distances. However, it is difficult to observe and study the free fall of a body from a height of thousands of kilometers above the Earth. But nature itself came to the rescue here and made it possible to determine the acceleration of a body moving in a circle around the Earth and therefore possessing centripetal acceleration, caused, of course, by the same force of attraction to the Earth. Such a body is the natural satellite of the Earth - the Moon. If the force of attraction between the Earth and the Moon did not depend on the distance between them, then the centripetal acceleration of the Moon would be the same as the acceleration of a body freely falling near the surface of the Earth. In reality, the centripetal acceleration of the Moon is 0.0027 m/s 2 .

Let's prove it. The revolution of the Moon around the Earth occurs under the influence of the gravitational force between them. Approximately, the orbit of the Moon can be considered a circle. Therefore, the Earth imparts centripetal acceleration to the Moon. It is calculated by the formula \(a = \frac (4 \pi^2 \cdot R)(T^2)\), where R- the radius of the lunar orbit, equal to approximately 60 radii of the Earth, T≈ 27 days 7 h 43 min ≈ 2.4∙10 6 s is the period of the Moon's revolution around the Earth. Given that the radius of the earth R h ≈ 6.4∙10 6 m, we get that the centripetal acceleration of the Moon is equal to:

\(a = \frac (4 \pi^2 \cdot 60 \cdot 6.4 \cdot 10^6)((2.4 \cdot 10^6)^2) \approx 0.0027\) m/s 2.

The found value of acceleration is less than the acceleration of free fall of bodies near the surface of the Earth (9.8 m/s 2) by approximately 3600 = 60 2 times.

Thus, an increase in the distance between the body and the Earth by 60 times led to a decrease in the acceleration imparted by the earth's gravity, and, consequently, the force of attraction itself by 60 2 times.

This leads to an important conclusion: the acceleration imparted to bodies by the force of attraction to the earth decreases in inverse proportion to the square of the distance to the center of the earth

\(F \sim \frac (1)(R^2)\).

Law of gravity

In 1667, Newton finally formulated the law of universal gravitation:

\(F = G \cdot \frac (m_1 \cdot m_2)(R^2).\quad (1)\)

The force of mutual attraction of two bodies is directly proportional to the product of the masses of these bodies and inversely proportional to the square of the distance between them.

Proportionality factor G called gravitational constant.

Law of gravity is valid only for bodies whose dimensions are negligibly small compared to the distance between them. In other words, it is only fair for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 2). Such forces are called central.

To find the gravitational force acting on a given body from the side of another, in the case when the size of the bodies cannot be neglected, proceed as follows. Both bodies are mentally divided into such small elements that each of them can be considered a point. Adding up the gravitational forces acting on each element of a given body from all the elements of another body, we obtain the force acting on this element (Fig. 3). Having done such an operation for each element of a given body and adding the resulting forces, they find the total gravitational force acting on this body. This task is difficult.

There is, however, one practically important case when formula (1) is applicable to extended bodies. It can be proved that spherical bodies, the density of which depends only on the distances to their centers, at distances between them that are greater than the sum of their radii, attract with forces whose modules are determined by formula (1). In this case R is the distance between the centers of the balls.

And finally, since the dimensions of the bodies falling to the Earth are much smaller than the dimensions of the Earth, these bodies can be considered as point ones. Then under R in formula (1) one should understand the distance from a given body to the center of the Earth.

Between all bodies there are forces of mutual attraction, depending on the bodies themselves (their masses) and on the distance between them.

The physical meaning of the gravitational constant

From formula (1) we find

\(G = F \cdot \frac (R^2)(m_1 \cdot m_2)\).

It follows that if the distance between the bodies is numerically equal to one ( R= 1 m) and the masses of the interacting bodies are also equal to unity ( m 1 = m 2 = 1 kg), then the gravitational constant is numerically equal to the force modulus F. In this way ( physical meaning ),

the gravitational constant is numerically equal to the modulus of the gravitational force acting on a body of mass 1 kg from another body of the same mass with a distance between bodies equal to 1 m.

In SI, the gravitational constant is expressed as

.

Cavendish experience

The value of the gravitational constant G can only be found empirically. To do this, you need to measure the modulus of the gravitational force F, acting on the body mass m 1 side body weight m 2 at a known distance R between bodies.

The first measurements of the gravitational constant were made in the middle of the 18th century. Estimate, though very roughly, the value G at that time succeeded as a result of considering the attraction of the pendulum to the mountain, the mass of which was determined by geological methods.

Accurate measurements of the gravitational constant were first made in 1798 by the English physicist G. Cavendish using a device called a torsion balance. Schematically, the torsion balance is shown in Figure 4.

Cavendish fixed two small lead balls (5 cm in diameter and weighing m 1 = 775 g each) at opposite ends of a two meter rod. The rod was suspended on a thin wire. For this wire, the elastic forces arising in it when twisting through various angles were preliminarily determined. Two large lead balls (20 cm in diameter and weighing m 2 = 49.5 kg) could be brought close to small balls. Attractive forces from the large balls forced the small balls to move towards them, while the stretched wire twisted a little. The degree of twist was a measure of the force acting between the balls. The twisting angle of the wire (or the rotation of the rod with small balls) turned out to be so small that it had to be measured using an optical tube. The result obtained by Cavendish is only 1% different from the value of the gravitational constant accepted today:

G ≈ 6.67∙10 -11 (N∙m 2) / kg 2

Thus, the attraction forces of two bodies weighing 1 kg each, located at a distance of 1 m from each other, are only 6.67∙10 -11 N in modules. This is a very small force. Only in the case when bodies of enormous mass interact (or at least the mass of one of the bodies is large), the gravitational force becomes large. For example, the Earth pulls the Moon with force F≈ 2∙10 20 N.

Gravitational forces are the "weakest" of all the forces of nature. This is due to the fact that the gravitational constant is small. But with large masses of cosmic bodies, the forces of universal gravitation become very large. These forces keep all the planets near the Sun.

The meaning of the law of gravity

The law of universal gravitation underlies celestial mechanics - the science of planetary motion. With the help of this law, the positions of celestial bodies in the firmament for many decades to come are determined with great accuracy and their trajectories are calculated. The law of universal gravitation is also used in calculations of the motion of artificial earth satellites and interplanetary automatic vehicles.

Disturbances in the motion of the planets. Planets do not move strictly according to Kepler's laws. Kepler's laws would be strictly observed for the motion of a given planet only if this planet alone revolved around the Sun. But there are many planets in the solar system, all of them are attracted by both the Sun and each other. Therefore, there are disturbances in the motion of the planets. In the solar system, perturbations are small, because the attraction of the planet by the Sun is much stronger than the attraction of other planets. When calculating the apparent position of the planets, perturbations must be taken into account. When launching artificial celestial bodies and when calculating their trajectories, they use an approximate theory of the motion of celestial bodies - perturbation theory.

Discovery of Neptune. One of the clearest examples of the triumph of the law of universal gravitation is the discovery of the planet Neptune. In 1781, the English astronomer William Herschel discovered the planet Uranus. Its orbit was calculated and a table of the positions of this planet was compiled for many years to come. However, a check of this table, carried out in 1840, showed that its data differ from reality.

Scientists have suggested that the deviation in the motion of Uranus is caused by the attraction of an unknown planet, located even further from the Sun than Uranus. Knowing the deviations from the calculated trajectory (disturbances in the movement of Uranus), the Englishman Adams and the Frenchman Leverrier, using the law of universal gravitation, calculated the position of this planet in the sky. Adams completed the calculations earlier, but the observers to whom he reported his results were in no hurry to verify. Meanwhile, Leverrier, having completed his calculations, indicated to the German astronomer Halle the place where to look for an unknown planet. On the very first evening, September 28, 1846, Halle, pointing the telescope to the indicated place, discovered a new planet. They named her Neptune.

In the same way, on March 14, 1930, the planet Pluto was discovered. Both discoveries are said to have been made "at the tip of a pen".

Using the law of universal gravitation, you can calculate the mass of the planets and their satellites; explain phenomena such as the ebb and flow of water in the oceans, and much more.

The forces of universal gravitation are the most universal of all the forces of nature. They act between any bodies that have mass, and all bodies have mass. There are no barriers to the forces of gravity. They act through any body.

Literature

1. Kikoin I.K., Kikoin A.K. Physics: Proc. for 9 cells. avg. school - M.: Enlightenment, 1992. - 191 p.
2. Physics: Mechanics. Grade 10: Proc. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakishev. – M.: Bustard, 2002. – 496 p.

As you know, weight is the force with which the body presses on the support due to gravity towards the Earth.

According to the second law of mechanics, the weight of a body is related to the free fall acceleration and to the mass of this body by the ratio

The weight of a body is due to the resultant of all the forces of attraction between each particle of the body and the Earth. Therefore, the weight of any body must be proportional to the mass of this body, as it is in reality. If we neglect the influence of the daily rotation of the Earth, then according to the Newtonian law of gravity, the weight is determined by the formula

where is the gravitational constant, the mass of the Earth, the distance of the body from the center of the Earth. Formula (3) shows that the weight of the body decreases with distance from the earth's surface. Average

the radius of the Earth is therefore, when lifted by weight, it decreases in relation to 0.00032 of its magnitude.

Since the earth's crust is not uniform in density, in areas under which dense rocks lie in the depths of the earth's crust, the force of gravity is somewhat greater than in areas (at the same geographical latitude), the bed of which is less dense rocks. Massifs of mountains cause a deviation of the plumb line towards the mountains.

Comparing equations (2) and (3), we obtain an expression for the acceleration of gravity without taking into account the influence of the Earth's rotation:

Each body lying quietly on the surface of the Earth, participating in the daily rotation of the Earth, obviously has a centripetal acceleration common with the given area, lying in a plane parallel to the equator and directed to the axis of rotation (Fig. 48). The force with which the Earth attracts any body lying quietly on its surface, partly manifests itself statically in the pressure that the body exerts on the support (this component is called “weight”, another geometric component of the force manifests itself dynamically, giving the body a centripetal acceleration, involving it in the daily rotation of the Earth. For the equator, this acceleration is the greatest, for the poles it is equal to zero. Therefore, if any body is moved from the pole to the equator, it will somewhat "lose in weight."

Rice. 48. Due to the rotation of the Earth, the force of attraction to the Earth has static (weight) and dynamic components.

If the Earth were exactly spherical, then the weight loss at the equator would be:

where is the circumferential velocity at the equator. Let mean the number of seconds in a day, then

Hence, given that we find the relative weight loss:

Therefore, if the Earth were exactly spherical in shape, then each kilogram of mass transferred from the Earth's pole to the equator would lose approximately in weight (this could be detected by weighing on a spring balance). The actual weight loss is even greater (about 1000 lbs) because the Earth is somewhat flattened and its poles are closer to the center of the Earth than the equatorial regions.

The centripetal acceleration of the daily rotation lies in a plane parallel to the equator (Fig. 48); it is directed at an angle to the radius drawn from the given locality to the center of the Earth latitude of the locality). We consider the centripetal force as one component of the gravitational force and as another geometric component of the same force. Therefore, the direction of the plumb line for all localities, except for the equator and the poles, does not coincide with the direction of the straight line drawn to the center of the Earth. However, the angle between them is small because the centripetal component of the gravitational force is small compared to the weight. The compression of the Earth due to the diurnal rotation is just such that a plumb line (and not a straight line drawn to the center of the Earth) is everywhere perpendicular to the surface of the Earth. The shape of the Earth is a triaxial ellipsoid.

The most accurate dimensions of the earth's ellipsoid, calculated under the guidance of prof. F. N. Krasovsky, are as follows:

To calculate the acceleration of gravity depending on the geographical latitude of the area and, consequently, to determine the weight of bodies at sea level, the International Geodetic Congress in 1930 adopted the formula

Here are the values ​​of the acceleration of gravity for different latitudes (at sea level):

At latitude 45° ("normal acceleration")

Consider how the force of gravity changes as you go deeper into the Earth. Let the average radius of the terrestrial spheroid. Consider the force of gravity at point K, located at a distance from the center of the Earth.

The attraction at this point is determined by the total action of the outer spherical layer of thickness and the inner sphere of radius. An accurate mathematical calculation shows that the spherical layer has no effect on the material points located inside it, since the attractive forces caused by its individual parts are mutually balanced. Thus, there remains only the action of an inner spheroid of radius and, therefore, a smaller mass than the mass of the globe.

If the globe were uniform in density, then the mass inside the sphere would be determined by the expression

where is the average density of the earth. In this case, the acceleration of gravity, numerically equal to the force acting on a unit mass in the gravitational field, will be equal to

and, therefore, will decrease linearly as it approaches the center of the Earth. The acceleration of gravity has a maximum value on the surface of the Earth.

However, due to the fact that the Earth's core consists of heavy metals (iron, nickel, cobalt) and has an average density greater than that, while the average density of the Earth's crust then near the Earth's surface at first even slightly increases with depth and reaches its maximum value at a depth of about i.e. on the border of the upper layers of the earth's crust and the ore shell of the earth. Further, the force of gravity begins to decrease as it approaches the center of the Earth, but somewhat more slowly than the linear dependence requires.

Of considerable interest is the history of one of the instruments designed to measure the acceleration of gravity. In 1940, at an international conference of gravimetrists, the device of the German engineer Gaalck was considered. In the course of the debate, it turned out that this device is fundamentally no different from the so-called "universal barometer" designed by Lomonosov and described in detail in his work "On the relationship between the amount of matter and weight", published in 1757. Lomonosov's device was arranged as follows (Fig. 49).

This makes it possible to take into account very small changes in the acceleration of free fall.

By what law are you going to hang me?
- And we hang everyone according to one law - the law of universal gravitation.

Law of gravity

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

Mathematically, we can express this great law by the formula

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

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

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

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

Direction of gravity

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

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

The main thing to remember

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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