Formula for gravity. The force of universal gravity: characteristics and practical significance

The most important phenomenon constantly studied by physicists is movement. 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.

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Everything in the Universe moves. Gravity is a common 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 far and wide.

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

Perhaps the study of gravity became 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 the gravitation of bodies became interested in ancient Greece.

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

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

Movement task

Let's conduct a thought experiment. Let's take a small ball in our left hand. Let's take the same one on the right. Let's release the right ball and it will begin 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 should 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 what has potential energy, where is it recorded in it?

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

Newton's gravity

In 1666, the greatest English physicist and mechanic I. Newton discovered a law that can quantitatively calculate the force due to which all matter in the Universe tends to each other. This phenomenon is called universal gravity. When you are asked: “Formulate the law of universal gravitation,” your answer should sound like this:

The force of gravitational interaction contributing to the attraction of two bodies is located in direct proportion to the masses of these bodies and in inverse proportion 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 of 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 thing is that the distance between their centers r1+r2 is different from zero. 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 – force of attraction,
– masses,
r – distance,
G – gravitational constant equal to 6.67·10−11 m³/(kg·s²).

What is weight, if we just looked at the force of gravity?

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 relation should be perceived 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 it is not surprising that we personally we feel the Sun's gravity much weaker than the Earth's. Although the massive Sun has a large mass, it is very far from us. is also far from the Sun, but it is attracted to it, since it has a large mass. How to find the gravitational force of two bodies, namely, how to calculate the gravitational force of the Sun, 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 acceleration of free fall of the Earth (9.81 m/s 2).

Important! There are not two, three, ten types of attractive forces. Gravity is the only force that gives a quantitative characteristic of attraction. Weight (P = mg) and gravitational force are the same thing.

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

Thus, since F = mg:

The masses m are reduced, and the expression for the acceleration of free fall remains:

As we can see, the acceleration of gravity is truly a constant value, since its formula includes constant quantities - 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 gravity is equal to 9.81 m/s 2.

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

Let's return to the attraction of the Earth and the Sun. Let's try to prove with an example that the globe attracts you and me more strongly 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 Earth:

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

The force of gravitational attraction between man and the Sun:

As we 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 attracts our planet more than a billion billion times stronger than the planet attracts you and me.

First escape velocity

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

True, he imagined it a little differently, in his understanding it was not a vertically standing rocket aimed at the sky, but a body that horizontally made a jump from the top of a mountain. This was a logical illustration because 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 the air there is so thin, the air particles are no longer as tied to gravity as those that “fell” to the surface.

Let's try to find out what escape velocity is.

The first escape velocity v1 is the speed 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 value for our planet.

Let's write down Newton's second law for a body that rotates around a 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, a body is subject to centrifugal acceleration, thus:

The masses are reduced, we get:

This speed is called the first escape velocity:

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

First escape velocity

Second escape velocity

However, even having accelerated the body to the first escape velocity, we will not be able to completely break its gravitational connection with the Earth. This is why we need a second escape velocity. When this speed is reached the body leaves the planet's gravitational field and all possible closed orbits.

Important! It is often mistakenly believed that in order to get to the Moon, astronauts had to reach the second escape velocity, because they first had to “disconnect” from the gravitational field of the planet. 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, let's pose the problem a little differently. Let's say a body flies from infinity to a planet. Question: what speed will be reached on the surface upon landing (without taking into account the atmosphere, of course)? This is exactly the speed the body will need to leave the planet.

Second escape velocity

Let's write down the law of conservation of energy:

where on the right side of the equality is the work of gravity: A = Fs.

From this we obtain that the second escape velocity is equal to:

Thus, the second escape velocity is times greater than the first:

The law of universal gravitation. Physics 9th grade

Law of Universal Gravitation.

Conclusion

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

The 16th - 17th centuries are rightfully called by many one of the most glorious periods in the world. It was at this time that the foundations were largely laid, without which the further development of this science would have been simply unthinkable. Copernicus, Galileo, Kepler did a great job of establishing 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 this scientist’s work lay 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. the same forces of interaction between bodies.

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

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

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

The force of universal gravity 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 Earth, it answers many questions related to the structure of the entire solar system. In particular, the force of universal gravitation has a decisive influence on the movement of planets in their orbits. A 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 gravity using a simple example: when fired, it does not fly straight, but along an arcuate trajectory. Moreover, with an increase in the charge of gunpowder and the mass of the core, the latter will fly further and further. Finally, if we assume that it is possible to get so much gunpowder and construct such a cannon so that the cannonball flies 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 consequence, the force of the universal gravity is the same in nature both on Earth and in outer space.

In the 7th grade physics course, you studied the phenomenon of universal gravitation. It lies in the fact that there are gravitational forces between all bodies in the Universe.

Newton came to the conclusion about the existence of universal gravitational forces (they are also called gravitational forces) as a result of studying the movement of the Moon around the Earth and the planets around the Sun.

Newton's merit lies not only in his brilliant guess about the mutual attraction of bodies, but also in the fact that he was able to find the law of their interaction, that is, a formula for calculating the gravitational force between two bodies.

The law of universal gravitation says:

any two bodies attract each other with a force directly proportional to the mass of each of them and inversely proportional to the square of the distance between them

where F is the magnitude of the vector of gravitational attraction between bodies of masses m 1 and m 2, g is the distance between the bodies (their centers); G is the coefficient, which is called gravitational constant.

If m 1 = m 2 = 1 kg and g = 1 m, then, as can be seen from the formula, the gravitational constant G is numerically equal to the force F. In other words, the gravitational constant is numerically equal to the force F of attraction of two bodies weighing 1 kg each, located at a distance 1 m apart. Measurements show that

G = 6.67 10 -11 Nm 2 /kg 2.

The formula gives an accurate result when calculating the force of universal gravity in three cases: 1) if the sizes of the bodies are negligible compared to the distance between them (Fig. 32, a); 2) if both bodies are homogeneous and have a spherical shape (Fig. 32, b); 3) if one of the interacting bodies is a ball, the dimensions and mass of which are significantly greater than that of the second body (of any shape) located on the surface of this ball or near it (Fig. 32, c).

Rice. 32. Conditions defining the limits of applicability of the law of universal gravitation

The third of the cases considered is the basis for calculating, using the given formula, the force of attraction to the Earth of any of the bodies located on it. In this case, the radius of the Earth should be taken as the distance between bodies, since the sizes of all bodies located on its surface or near it are negligible compared to the Earth’s radius.

According to Newton's third law, an apple hanging on a branch or falling from it with the acceleration of free fall attracts the Earth to itself with the same magnitude of force with which the Earth attracts it. But the acceleration of the Earth, caused by the force of its attraction to the apple, is close to zero, since the mass of the Earth is incommensurably greater than the mass of the apple.

Questions

What was called universal gravity?
What is another name for the forces of universal gravity?
Who discovered the law of universal gravitation and in what century?
Formulate the law of universal gravitation. Write down a formula expressing this law.
In what cases should the law of universal gravitation be applied to calculate gravitational forces?
Is the Earth attracted to an apple hanging on a branch?

Exercise 15

Give examples of the manifestation of gravity.
The space station flies from the Earth to the Moon. How does the modulus of the vector of its force of attraction to the Earth change in this case; to the moon? Is the station attracted to the Earth and the Moon with equal or different magnitude forces when it is in the middle between them? If the forces are different, which one is greater and by how many times? Justify all answers. (It is known that the mass of the Earth is about 81 times the mass of the Moon.)
It is known that the mass of the Sun is 330,000 times greater than the mass of the Earth. Is it true that the Sun attracts the Earth 330,000 times stronger than the Earth attracts the Sun? Explain your answer.
The ball thrown by the boy moved upward for some time. At the same time, its speed decreased all the time until it became equal to zero. Then the ball began to fall down with increasing speed. Explain: a) whether the force of gravity towards the Earth acted on the ball during its upward movement; down; b) what caused the decrease in the speed of the ball as it moved up; increasing its speed when moving down; c) why, when the ball moved up, its speed decreased, and when it moved down, it increased.
Is a person standing on Earth attracted to the Moon? If so, what is it more attracted to - the Moon or the Earth? Is the Moon attracted to this person? Justify your answers.

Newton's law of gravity

the law of universal gravitation, one of the universal laws of nature; according to N. z. i.e. all material bodies attract each other, and the magnitude of the gravitational force does not depend on the physical and chemical properties of the bodies, on the state of their motion, on the properties of the environment where the bodies are located. On Earth, gravity manifests itself primarily in the existence of gravity, which is the result of the attraction of any material body by the Earth. Associated with this is the term “gravity” (from the Latin gravitas - heaviness), equivalent to the term “gravity”.

Gravitational interaction in accordance with the New Law. m plays a major role in the movement of stellar systems such as double and multiple stars, inside star clusters and galaxies. However, the gravitational fields inside star clusters and galaxies are of a very complex nature and have not yet been sufficiently studied, as a result of which the movements inside them are studied by methods different from the methods of celestial mechanics (see Stellar astronomy). Gravitational interaction also plays a significant role in all cosmic processes in which accumulations of large masses of matter participate. N. z. t. is the basis for studying the movement of artificial celestial bodies, in particular artificial satellites of the Earth and the Moon, and space probes. On N. z. t. relies on Gravimetry. The forces of attraction between ordinary macroscopic material bodies on Earth can be detected and measured, but do not play any noticeable practical role. In the microcosm, the forces of attraction are negligible compared to intramolecular and intranuclear forces.

Newton left open the question of the nature of gravity. The assumption about the instantaneous propagation of gravity in space (i.e., the assumption that with a change in the positions of bodies the gravitational force between them instantly changes), which is closely related to the nature of gravity, was also not explained. The difficulties associated with this were eliminated only in Einstein's theory of gravitation, which represented a new stage in the knowledge of the objective laws of nature.

Lit.: Isaac Newton. 1643-1727. Sat. Art. to the tercentenary of his birth, ed. acad. S. I. Vavilova, M. - L., 1943; Berry A., A Brief History of Astronomy, trans. from English, M. - L., 1946; Subbotin M.F., Introduction to theoretical astronomy, M., 1968.

Yu. A. Ryabov.

Great Soviet Encyclopedia. - M.: Soviet Encyclopedia. 1969-1978 .

See what "Newton's law of gravity" is in other dictionaries:

- (law of universal gravitation), see Art. (see GRAVITY). Physical encyclopedic dictionary. M.: Soviet Encyclopedia. Editor-in-chief A. M. Prokhorov. 1983 ... Physical encyclopedia

NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation... Modern encyclopedia

The same as the law of universal gravitation... Big Encyclopedic Dictionary

Newton's law of gravity- NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation. ... Illustrated Encyclopedic Dictionary

NEWTON'S LAW OF GRAVITY- the same as (see) ...

The same as the law of universal gravitation. * * * NEWTON'S LAW OF GRAVITY NEWTON'S LAW OF GRAVITY, the same as the law of universal gravitation (see UNIVERSAL GRAVITATION LAW) ... encyclopedic Dictionary

Newton's law of gravity- Niutono gravitacijos dėsnis statusas T sritis fizika atitikmenys: engl. Newton's law of gravitation vok. Newtonsches Gravitationsgesetz, n; Newtonsches Massenanziehungsgesetz, n rus. Newton's law of gravity, m; Newton's law of gravity, m pranc.… … Fizikos terminų žodynas

Gravity (universal gravitation, gravitation) (from Latin gravitas “gravity”) is a long-range fundamental interaction in nature to which all material bodies are subject. According to modern data, it is a universal interaction in that... ... Wikipedia

LAW OF GRAVITY- (Newton’s law of gravity) all material bodies attract each other with forces directly proportional to their masses and inversely proportional to the square of the distance between them: where F is the modulus of the gravitational force, m1 and m2, the masses of interacting bodies, R... ... Big Polytechnic Encyclopedia

Law of Gravity- I. Newton’s law of gravitation (1643–1727) in classical mechanics, according to which the force of gravitational attraction of two bodies with masses m1 and m2 is inversely proportional to the square of the distance r between them; proportionality coefficient G gravitational... Concepts of modern natural science. Glossary of basic terms

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

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 that a computer and a mouse attract each other? Or a pencil and pen lying on the table? In this case, we substitute the mass of the pen and the mass of the pencil into the formula, divide by the square of the distance between them, taking into account the gravitational constant, and obtain the force of their mutual attraction. But it will be so small (due to the small masses of the pen and pencil) that we do not feel its presence. It's a different matter when it comes to the Earth and the chair, or the Sun and the Earth. The masses are significant, which means we can already evaluate the effect of the force.

Let's remember the acceleration of free fall. This is the effect of the law of attraction. Under the influence of force, a body changes speed the more slowly, the greater its mass. As a result, all bodies fall to Earth with the same acceleration.

What causes this invisible unique force? Today 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 it, what is gravity? Where is it from? What is it? Surely it cannot be that the planet looks at the Sun, sees how far away it is, and 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 to 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 downward, and it is applied from the center of gravity of the body, it is called the force of gravity.

The main thing to remember

Some methods of geological exploration, tide prediction and, more recently, calculation of the movement of artificial satellites and interplanetary stations. Advance calculation of planetary positions.

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

Such 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 towards them from the side. 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 a device, 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 between charges, and the thought involuntarily arises that there is a deep meaning hidden in this pattern. Until now, no one has been able to imagine 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 the electrical and gravitational forces is striking. Trying to establish the general nature of gravity and electricity, we discover such a superiority of electrical forces over the forces of gravity that it is difficult to believe that both have the same source. How can you say that one is more powerful than the other? After all, everything depends on what the mass is and what the charge is. When discussing how strongly 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 itself offers us (her own numbers and measures, which have nothing to do with our inches, years, with our measures), then we will be able to compare. We take an elementary charged particle, such as an electron. Two elementary particles, two electrons, due to an 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? Gravity is to electrical repulsion as one is to a number with 42 zeros. This causes deepest bewilderment. Where could such a huge number come from?

People look for this huge coefficient in other natural phenomena. They try all sorts of big numbers, and if you need 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 so 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 idea, but as the Universe gradually expands, the gravitational constant 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 gravitational constant 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 states that a distance x cannot be overcome instantly, whereas according to Newton's theory, forces act instantly. Einstein had to change Newton's laws. These changes and clarifications are very small. One of them is this: since light has energy, energy is equivalent to mass, and all masses are attracted, light is also attracted 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 gravitation is just sufficient to explain some of the apparent irregularities in the motion of Mercury.

Physical phenomena in the microworld are subject to different laws than phenomena in the world on a large scale. The question arises: how does gravity manifest itself in the 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.