How is the force of gravity directed? Gravity: formula, definition. Experiments by Albert Michelson

Absolutely all bodies in the Universe are affected by a magical force that somehow attracts them to the Earth (more precisely, to its core). There is nowhere to escape, nowhere to hide from the all-encompassing magical gravity: the planets of our solar system are attracted not only to the huge Sun, but also to each other, all objects, molecules and the smallest atoms are also mutually attracted. known even to small children, having devoted his life to studying this phenomenon, he established one of the greatest laws - the law of universal gravitation.

What is gravity?

The definition and formula have long been known to many. Recall that gravity is a certain quantity, one of the natural manifestations of universal gravitation, namely: the force with which any body is invariably attracted to the Earth.

The force of gravity is denoted by the Latin letter F heavy.

Gravity: formula

How to calculate directed to a certain body? What other quantities do you need to know in order to do this? The formula for calculating gravity is quite simple, it is studied in the 7th grade secondary school, at the beginning of the physics course. In order not only to learn it, but also to understand it, one should proceed from the fact that the force of gravity, invariably acting on a body, is directly proportional to its quantitative value (mass).

The unit of gravity is named after the great scientist Newton.

It is always directed strictly down to the center of the earth's core, due to its influence all bodies fall down with uniform acceleration. The phenomena of gravity in Everyday life We observe everywhere and constantly:

• objects, accidentally or specially released from the hands, necessarily fall down to the Earth (or to any surface preventing free fall);
• a satellite launched into space does not fly away from our planet for an indefinite distance perpendicularly upwards, but remains in orbit;
• all rivers flow from mountains and cannot be reversed;
• it happens that a person falls and is injured;
• the smallest dust particles sit on all surfaces;
• air is concentrated at the surface of the earth;
• hard to carry bags;
• rain falls from clouds and clouds, snow falls, hail.

Along with the concept of "gravity", the term "body weight" is used. If the body is placed on a flat horizontal surface, then its weight and gravity are numerically equal, so these two concepts are often replaced, which is not at all correct.

Acceleration of gravity

The concept of "acceleration of free fall" (in other words, is associated with the term "gravity." The formula shows: in order to calculate the force of gravity, you need to multiply the mass by g (acceleration of St. p.).

"g" = 9.8 N/kg, this is a constant value. However, more accurate measurements show that due to the rotation of the Earth, the value of the acceleration of St. p. is not the same and depends on latitude: at the North Pole it is = 9.832 N / kg, and at the sultry equator = 9.78 N / kg. It turns out that in different places of the planet a different force of gravity is directed to bodies with equal mass (the formula mg still remains unchanged). For practical calculations, it was decided to allow for minor errors in this value and use the average value of 9.8 N/kg.

The proportionality of such a quantity as gravity (the formula proves this) allows you to measure the weight of an object with a dynamometer (similar to ordinary household business). Please note that the instrument only displays force, as the local "g" value must be known to determine the exact body weight.

Does gravity act at any (both close and far) distance from the earth's center? Newton hypothesized that it acts on the body even at a considerable distance from the Earth, but its value decreases inversely with the square of the distance from the object to the Earth's core.

Gravity in the solar system

Is there a Definition and formula regarding other planets retain their relevance. With only one difference in the meaning of "g":

• on the Moon = 1.62 N/kg (six times less than on Earth);
• on Neptune = 13.5 N/kg (almost one and a half times higher than on Earth);
• on Mars = 3.73 N/kg (more than two and a half times less than on our planet);
• on Saturn = 10.44 N/kg;
• on Mercury = 3.7 N/kg;
• on Venus = 8.8 N/kg;
• on Uranus = 9.8 N/kg (practically the same as ours);
• on Jupiter = 24 N/kg (almost two and a half times higher).

XVI - XVII centuries, many rightly call one of the most glorious periods in it. It was at this time that the foundations were largely laid, without which further development 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 work 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 her special meaning 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 special case Newton's law is called the force of 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 construct 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.

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 thought 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 we are really talking about the fall of an ordinary stone on the Earth or 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

It is well known from experience that the free fall acceleration 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. Thus ( 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 with 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 physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G.Ya. Myakishev. – M.: Bustard, 2002. – 496 p.

The most important phenomenon constantly studied by physicists is motion. Electromagnetic phenomena, laws of mechanics, thermodynamic and quantum processes - all this is a wide range of fragments of the universe studied by physics. And all these processes come down, one way or another, to one thing - to.

In contact with

Everything in the universe moves. Gravity is a familiar phenomenon for all people since childhood, we were born in the gravitational field of our planet, this physical phenomenon is perceived by us at the deepest intuitive level and, it would seem, does not even require study.

But, alas, the question is why and How do all bodies attract each other?, remains to this day not fully disclosed, although it has been studied up and down.

In this article, we will consider what Newton's universal attraction is - the classical theory of gravity. However, before moving on to formulas and examples, let's talk about the essence of the problem of attraction and give it a definition.

Perhaps the study of gravity was the beginning of natural philosophy (the science of understanding the essence of things), perhaps natural philosophy gave rise to the question of the essence of gravity, but, one way or another, the question of gravity of bodies interested in ancient Greece.

Movement was understood as the essence of the sensual characteristics of the body, or rather, the body moved while the observer sees it. If we cannot measure, weigh, feel a phenomenon, does this mean that this phenomenon does not exist? Naturally, it doesn't. And since Aristotle understood this, reflections on the essence of gravity began.

As it turned out today, after many tens of centuries, gravity is the basis not only of the earth's attraction and the attraction of our planet to, but also the basis of the origin of the Universe and almost all existing elementary particles.

Movement task

Let's do a thought experiment. Take a small ball in your left hand. Let's take the same one on the right. Let's release the right ball, and it will start to fall down. The left one remains in the hand, it is still motionless.

Let's mentally stop the passage of time. The falling right ball "hangs" in the air, the left one still remains in the hand. The right ball is endowed with the “energy” of movement, the left one is not. But what is the deep, meaningful difference between them?

Where, in what part of the falling ball is it written that it must move? It has the same mass, the same volume. It has the same atoms, and they are no different from the atoms of a ball at rest. Ball has? Yes, this is the correct answer, but how does the ball know that it has potential energy, where is it recorded in it?

This is the task set by Aristotle, Newton and Albert Einstein. And all three brilliant thinkers partly solved this problem for themselves, but today there are a number of issues that need to be resolved.

Newtonian gravity

In 1666, the greatest English physicist and mechanic I. Newton discovered a law capable of quantitatively calculating the force due to which all matter in the universe tends to each other. This phenomenon is called universal gravitation. When asked: "Formulate the law of universal gravitation", your answer should sound like this:

The force of gravitational interaction, which contributes to the attraction of two bodies, is in direct proportion to the masses of these bodies and inversely proportional to the distance between them.

Important! Newton's law of attraction uses the term "distance". This term should be understood not as the distance between the surfaces of bodies, but as the distance between their centers of gravity. For example, if two balls with radii r1 and r2 lie on top of each other, then the distance between their surfaces is zero, but there is an attractive force. The point is that the distance between their centers r1+r2 is nonzero. On a cosmic scale, this clarification is not important, but for a satellite in orbit, this distance is equal to the height above the surface plus the radius of our planet. The distance between the Earth and the Moon is also measured as the distance between their centers, not their surfaces.

For the law of gravity, the formula is as follows:

,

• F is the force of attraction,
• - masses,
• r - distance,
• G is the gravitational constant, equal to 6.67 10−11 m³ / (kg s²).

What is weight, if we have just considered the force of attraction?

Force is a vector quantity, but in the law of universal gravitation it is traditionally written as a scalar. In a vector picture, the law will look like this:

.

But this does not mean that the force is inversely proportional to the cube of the distance between the centers. The ratio should be understood as a unit vector directed from one center to another:

.

Law of gravitational interaction

Weight and gravity

Having considered the law of gravity, one can understand that there is nothing surprising in the fact that we personally we feel the attraction of the sun is much weaker than the earth's. The massive Sun, although it has a large mass, is very far from us. also far from the Sun, but it is attracted to it, as it has a large mass. How to find the force of attraction of two bodies, namely, how to calculate the gravitational force of the Sun, the Earth and you and me - we will deal with this issue a little later.

As far as we know, the force of gravity is:

where m is our mass, and g is the free fall acceleration of the Earth (9.81 m/s 2).

Important! There are no two, three, ten kinds of forces of attraction. Gravity is the only force that quantifies attraction. Weight (P = mg) and gravitational force are one and the same.

If m is our mass, M is the mass of the globe, R is its radius, then the gravitational force acting on us is:

Thus, since F = mg:

.

The masses m cancel out, leaving the expression for the free fall acceleration:

As you can see, the acceleration of free fall is indeed a constant value, since its formula includes constant values ​​- the radius, the mass of the Earth and the gravitational constant. Substituting the values ​​of these constants, we will make sure that the acceleration of free fall is equal to 9.81 m / s 2.

At different latitudes, the radius of the planet is somewhat different, since the Earth is still not a perfect sphere. Because of this, the acceleration of free fall at different points on the globe is different.

Let's return to the attraction of the Earth and the Sun. Let's try to prove by example that the globe attracts us stronger than the Sun.

For convenience, let's take the mass of a person: m = 100 kg. Then:

• The distance between a person and the globe is equal to the radius of the planet: R = 6.4∙10 6 m.
• The mass of the Earth is: M ≈ 6∙10 24 kg.
• The mass of the Sun is: Mc ≈ 2∙10 30 kg.
• Distance between our planet and the Sun (between the Sun and man): r=15∙10 10 m.

Gravitational attraction between man and the Earth:

This result is fairly obvious from a simpler expression for the weight (P = mg).

The force of gravitational attraction between man and the Sun:

As you can see, our planet attracts us almost 2000 times stronger.

How to find the force of attraction between the Earth and the Sun? In the following way:

Now we see that the Sun pulls on our planet more than a billion billion times stronger than the planet pulls you and me.

first cosmic speed

After Isaac Newton discovered the law of universal gravitation, he became interested in how fast a body should be thrown so that it, having overcome the gravitational field, left the globe forever.

True, he imagined it a little differently, in his understanding it was not a vertically standing rocket directed into the sky, but a body that horizontally makes a jump from the top of a mountain. It was a logical illustration, since at the top of the mountain, the force of gravity is slightly less.

So, at the top of Everest, the acceleration of gravity will not be the usual 9.8 m / s 2, but almost m / s 2. It is for this reason that there is so rarefied, the air particles are no longer as attached to gravity as those that "fell" to the surface.

Let's try to find out what cosmic speed is.

The first cosmic velocity v1 is the velocity at which the body leaves the surface of the Earth (or another planet) and enters a circular orbit.

Let's try to find out the numerical value of this quantity for our planet.

Let's write Newton's second law for a body that revolves around the planet in a circular orbit:

,

where h is the height of the body above the surface, R is the radius of the Earth.

In orbit, the centrifugal acceleration acts on the body, thus:

.

The masses are reduced, we get:

,

This speed is called the first cosmic speed:

As you can see, the space velocity is absolutely independent of the mass of the body. Thus, any object accelerated to a speed of 7.9 km / s will leave our planet and enter its orbit.

first cosmic speed

Second space velocity

However, even having accelerated the body to the first cosmic speed, we will not be able to completely break its gravitational connection with the Earth. For this, the second cosmic velocity is needed. Upon reaching this speed, the body leaves the gravitational field of the planet and all possible closed orbits.

Important! By mistake, it is often believed that in order to get to the Moon, astronauts had to reach the second cosmic velocity, because they first had to "disconnect" from the planet's gravitational field. This is not so: the Earth-Moon pair are in the Earth's gravitational field. Their common center of gravity is inside the globe.

In order to find this speed, we set the problem a little differently. Suppose a body flies from infinity to a planet. Question: what speed will be achieved on the surface upon landing (without taking into account the atmosphere, of course)? It is this speed and it will take the body to leave the planet.

The law of universal gravitation. Physics Grade 9

The law of universal gravitation.

Conclusion

We have learned that although gravity is the main force in the universe, many of the reasons for this phenomenon are still a mystery. We learned what Newton's universal gravitational force is, learned how to calculate it for various bodies, and also studied some useful consequences that follow from such a phenomenon as the universal law of gravity.

Absolutely all material bodies, both located directly on the Earth and existing in the Universe, are constantly attracted to each other. The fact that this interaction is by no means always possible to see or feel, only indicates that this attraction is relatively weak in these specific cases.

The interaction between material bodies, which consists in their constant striving for each other, according to basic physical terms, is called gravitational, while the phenomenon of attraction itself is called gravity.

The phenomenon of gravity is possible because there is a gravitational field around absolutely any material body (including around a person). This field is a special kind of matter, from the action of which nothing can be protected, and with the help of which one body acts on another, causing acceleration towards the center of the source of this field. It served as the basis for the universal gravitation formulated in 1682 by the English naturalist and philosopher I..

The basic concept of this law is the gravitational force, which, as mentioned above, is nothing but the result of the action of a gravitational field on a particular material body. lies in the fact that the force with which the mutual attraction of bodies occurs both on Earth and in outer space directly depends on the product of the mass of these bodies and is inversely related to the distance separating these objects.

Thus, the gravitational force, the definition of which was given by Newton himself, depends only on two main factors - the mass of the interacting bodies and the distance between them.

Confirmation that this phenomenon depends on the mass of matter can be found by studying the interaction of the Earth with the bodies surrounding it. Soon after Newton, another famous scientist, Galileo, convincingly showed that at , our planet gives all bodies exactly the same acceleration. This is possible only if the body to the Earth directly depends on the mass of this body. After all, indeed, in this case, with an increase in mass by several times, the force of acting gravity will increase exactly the same number of times, while the acceleration will remain unchanged.

If we continue this thought and consider the interaction of any two bodies on the surface of the "blue planet", then we can conclude that the same force acts on each of them from our "mother Earth". At the same time, relying on the famous law formulated by the same Newton, we can say with confidence that the magnitude of this force will directly depend on the mass of the body, therefore the gravitational force between these bodies is directly dependent on the product of their masses.

To prove that it depends on the size of the gap between the bodies, Newton had to involve the Moon as an "ally". It has long been established that the acceleration with which bodies fall to the Earth is approximately equal to 9.8 m / s ^ 2, but the Moon in relation to our planet, as a result of a series of experiments, turned out to be only 0.0027 m / s ^ 2.

Thus, the gravitational force is the most important physical quantity that explains many processes occurring both on our planet and in the surrounding outer space.