Man has long known the force that makes all bodies fall to the Earth. But until the 17th century believed that only the earth had special property attract bodies that are close to its surface. In 1667, Newton suggested that, in general, forces of mutual attraction act between all bodies. He called these forces the forces of universal gravitation.

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.

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 managed 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.

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. At first glance, this is a very strange property. Indeed, from the formula expressing Newton's second law,

it follows that the acceleration of the body should be the greater, the smaller its mass. Bodies with a small mass must fall with a greater acceleration than bodies with a large mass. Experience has shown (see § 20) that the accelerations of freely falling bodies do not depend on their masses. The only explanation that can be found for this amazing

fact, lies in the fact that the very force with which the Earth attracts a body is proportional to its mass i.e.

Indeed, in this case, for example, a doubling of the mass will also lead to a doubling of the force, and the acceleration, which is equal to the ratio, will remain unchanged. Newton made this one correct conclusion: the force of universal gravitation is proportional to the mass of the body on which it acts. But bodies attract each other. And according to Newton's third law, the forces acting on both attracting bodies are the same in absolute value. This means that the force of mutual attraction must be proportional to the masses of each of the attracting bodies. Then both bodies will receive accelerations that do not depend on their masses.

If the force is proportional to the masses of each of the interacting bodies, then this means that it is proportional to the product of the masses of both bodies.

What else determines the force of mutual attraction of two bodies? Newton suggested that it should depend on the distance between the bodies. From experience it is well known that near the Earth the acceleration of free fall is equal and it is the same for bodies falling from a height of 1, 10 or 100 m. But from this it is still impossible to conclude that the acceleration does not depend on the distance to the Earth. Newton believed that distances should be measured not from the surface of the Earth, but from its center. But the radius of the Earth is 6400 km. It is clear, therefore, that several tens or hundreds of meters above the Earth's surface cannot noticeably change the acceleration of free fall.

To find out how the distance between bodies affects the force of their mutual attraction, you need to know with what acceleration bodies move at great distances from the surface of the Earth.

It is clear that it is difficult to measure the acceleration of gravity along the vertical of bodies located at a height of several thousand kilometers above the Earth's surface. It is more convenient to measure the centripetal acceleration of a body moving around the Earth in a circle under the influence of the force of attraction to the Earth. Recall that we used the same technique when studying the force of elasticity. We measured the centripetal acceleration of a cylinder moving in a circle under the influence of this force.

In studying the force of universal gravitation, nature itself came to the aid of physicists and made it possible to determine the acceleration of a body moving in a circle around the Earth. Such a body is the natural satellite of the Earth - the Moon. After all, if Newton's assumption is correct, then we must assume that the centripetal acceleration of the Moon as it moves in a circle around the Earth is imparted by the force of its attraction to the Earth. If the gravitational force between the Moon and the Earth did not depend on the distance between them, then the centripetal acceleration of the Moon would be the same as the acceleration

free fall of bodies near the surface of the Earth. In fact, the centripetal acceleration with which the Moon moves in its orbit is, as we already know (see exercise 16, problem 9), . And this is approximately 3600 times less than the acceleration of falling bodies near the Earth. At the same time, it is known that the distance from the center of the Earth to the center of the Moon is 384,000 km. This is 60 times the radius of the Earth, that is, the distance from the center of the Earth to its surface. Thus, an increase in the distance between the attracting bodies by 60 times leads to a decrease in acceleration by 602 times. From this we can conclude that the acceleration imparted to bodies by the force of universal gravitation, and hence this force itself, is inversely proportional to the square of the distance between the interacting bodies.

Newton came to this conclusion.

One can, therefore, write that two bodies are attracted by their masses to each other with a force whose absolute value is expressed by the formula

where is the distance between the bodies, y is the coefficient of proportionality, the same for all bodies in nature. This coefficient is called the universal gravitational constant or the gravitational constant.

The above formula expresses the law of universal gravitation discovered by Newton:

All 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.

Under the influence of the force of universal gravitation, the planets move around the Sun, and artificial satellites around the Earth.

But what should be understood by the distance between interacting bodies? Let's take two bodies of arbitrary shape (Fig. 109). The question immediately arises: what distance should be substituted into the formula for the law of universal gravitation? The distance between

the farthest points of the surface of both bodies, or, conversely, the distance between the nearest points? Or maybe the distance between some other points on the body?

It turns out that formula (1), which expresses the law of universal gravitation, is valid when the distance between the bodies is so large compared to their sizes that the bodies can be considered material points. Material points in calculating the gravitational force between them can be considered the Earth and the Moon, the planets and the Sun.

If the bodies are in the form of balls, then even if their dimensions are comparable to the distance between them, they are attracted to each other as material points located at the centers of the balls (Fig. 110). In this case, this is the distance between the centers of the balls.

Formula (1) can also be used when calculating the force of attraction between a ball of large radius and a body of arbitrary shape small sizes, located close to the surface of the ball (Fig. 111). Then the dimensions of the body can be neglected in comparison with the radius of the ball. This is what we do when we consider attraction. various bodies to the globe.

The force of gravity is another example of a force that depends on the position (coordinates) of the body on which this force acts, relative to the body that acts. After all, the force of gravity depends on the distance between the bodies.

Page 1

The mutual attraction of bodies, as experience shows, is carried out through the space that separates these bodies, even when they are in a vacuum. This is explained by the fact that any body changes the properties of the surrounding space.

The total force of mutual attraction of bodies is the sum of the forces acting from the elements of one body on all the elements of another body.

Gravitational interaction is manifested in the mutual attraction of bodies and is inherent in all bodies, regardless of their structure, chemical composition and other properties. Newton established the law that determines the force of mutual attraction of bodies.

Let us assume that under the influence of mutual attraction the bodies approached a little.

This coefficient is so small that the mutual attraction of bodies located on the earth's surface cannot be noticed even in very subtle experiments, so that, generally speaking, they can be neglected.

With such an approximation, it remains to take into account only the mutual attraction of the bodies of the planetary system. The Earth is attracted by the Sun and other bodies solar system; both the Sun and these other bodies are at distances comparable to each other from the Earth.

Mass is also included in the law that determines the force of mutual attraction of bodies. The mass in the law of universal gravitation serves as a measure of the ability of bodies to create gravitational fields and experience the effects of gravitational fields, therefore it is called gravitational.

The gravitational field is a special kind of matter, through which the mutual attraction of bodies is carried out. Formally, the gravitational field can be defined as the space in which gravitational forces. However, it must be clearly understood that the field is material.

The law of universal gravitation only indicates what the force of mutual attraction of bodies depends on, but does not explain the mechanism for transmitting action at a distance through a vacuum. Newton himself found it meaningless to act at a distance without the help of an intermediary, but he avoided expressing his attitude to the nature of the forces of gravity.

The gravitational field is a special kind of matter, through which the mutual attraction of bodies is carried out.

Such a small value of the gravitational constant explains why we do not observe the mutual attraction of bodies in Everyday life when we are dealing with bodies of small mass. For the same reason, gravitational interaction plays no role in atomic-molecular phenomena. But with increasing mass, the role of gravitational interaction increases.

We considered the gravitational field on the basis of Newton's law of universal gravitation, but this law does not take into account the dependence of the force of mutual attraction of bodies on time.

When studying movement celestial bodies- both natural and artificial - it is necessary first of all to take into account the forces of mutual attraction of bodies in space. Classical celestial mechanics saw its main task in studying the motion of bodies precisely under the influence of their mutual attraction.

The laws of motion of the planets and their satellites, the fall of bodies to the Earth, the motion of artillery shells, the oscillations of pendulums testify to the existence of forces of mutual attraction of bodies to each other. These forces obey the law of universal gravitation (gravity), established by I.

“If we did not observe every minute the fall of bodies, it would be the most amazing phenomenon for us,” wrote the famous French astronomer Arago. Habit makes the attraction of all terrestrial objects by the Earth seem to us a natural and ordinary phenomenon. But when we are told that objects also attract each other, we are not inclined to believe this, because in everyday life we ​​do not notice anything of the kind.

Why, in fact, the law of universal attraction does not manifest itself constantly around us in ordinary situations? Why don't we see that tables, watermelons, people attract each other? Because for small objects, the force of attraction is extremely small. I will bring good example. Two people, separated by two meters from each other, attract each other, but the force of this attraction is negligible: for people of average weight - less than 0.01 milligrams. This means that two people attract each other with the same force with which a weight of 0.00001 grams presses on a scale pan; only extremely sensitive scales scientific laboratories able to detect such an insignificant weight! Such a force, of course, cannot budge us - this is hindered by the friction of our soles on the floor. To move us, for example, on a wooden floor (the friction force of the soles on the floor is 30% of the body weight), we need a force of at least 20 kg. It is ridiculous even to compare this force with an insignificant force of attraction of one hundredth of a milligram. A milligram is a thousandth of a gram; gram - a thousandth of a kilogram; so 0.01 milligrams is half a billionth of the force it takes to move us! Is it surprising that at normal conditions do we not notice even a hint of the mutual attraction of earthly bodies?

It would be another matter if friction did not exist; then nothing would prevent even a weak attraction from causing the bodies to approach each other. But with a force of 0.01 mg, the speed of this rapprochement of people should be completely negligible. It can be calculated that in the absence of friction, two people separated by a distance of 2 m, during the first hour, would move closer to each other by 3 cm; during next hour they would get closer by another 9 cm; during the third hour - by another 15 cm. The movement would have accelerated, but both people would have come close to each other not earlier than after five hours.

Figure 43. The attraction of the Sun bends the path of the Earth E. Due to inertia Earth tends to rush along the tangent line ER.

The attraction of terrestrial bodies can be detected in cases where the force of friction does not serve as an obstacle. A load suspended on a thread is under the influence of the earth's gravity, and therefore the thread has a vertical direction; but if there is some massive body near the load, which attracts the load to itself, then the thread deviates slightly from the vertical position and is directed along the resultant of the earth's attraction and the attraction of another body, relatively very weak. Such a deviation of the plumb near a large mountain was first observed in 1775 by Maskelyne in Scotland; he compared the direction of a plumb line with the direction towards the pole of the starry sky from two sides of the same mountain. Subsequently, more advanced experiments with the attraction of terrestrial bodies using weights of a special device made it possible to accurately measure the force of gravity.

The force of gravity between small masses is negligible. With increasing masses, it increases in proportion to their product. But here many tend to exaggerate this power. One scientist - though not a physicist, but a zoologist - tried to assure me that the mutual attraction often observed between sea vessels is caused by the force of universal gravitation! It is easy to show by calculation that gravity has nothing to do with it: two ships of the line, 25,000 tons each, at a distance of 100 m, attract each other with a force of only 400 g. Of course, such a force is insufficient to impart even an insignificant movement to ships in the water. the true reason We will explain the mysterious attraction of ships in the chapter on the properties of liquids.

Negligible for small masses, the gravitational force becomes very noticeable when we are talking about the colossal masses of celestial bodies. So, even Neptune, a planet very far from us, slowly circling almost at the edge of the solar system, sends us its "hello" by the Earth's attraction with a force of 18 million tons! In spite of huge distance, separating us from the Sun, the Earth is kept in its orbit solely by the force of gravity. If the force of solar attraction for some reason disappeared, the Earth would fly along a line tangent to its orbit, and forever rush off into the bottomless depths of world space.

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 occur when during strong compression With a larger 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 huge forces gravity, but there is no way out. modern science revealed the connection between time and 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 the 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 great power gravity than the moon.

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