The law of universal gravitation is expressed by the formula. Gravity is not the “Law of Universal Gravity” at all. Gravity and elementary particles

Isaac Newton suggested that between any bodies in nature there are forces of mutual attraction. These forces are called gravity forces or forces of gravity. The force of unrelenting gravity manifests itself in space, solar system and on Earth.

Law of gravity

Newton generalized the laws of motion of celestial bodies and found out that the force \ (F \) is equal to:

\[ F = G \dfrac(m_1 m_2)(R^2) \]

where \(m_1 \) and \(m_2 \) are the masses of interacting bodies, \(R \) is the distance between them, \(G \) is the proportionality coefficient, which is called gravitational constant. The numerical value of the gravitational constant was experimentally determined by Cavendish, measuring the force of interaction between lead balls.

The physical meaning of the gravitational constant follows from the law of universal gravitation. If a \(m_1 = m_2 = 1 \text(kg) \), \(R = 1 \text(m) \) , then \(G = F \) , i.e. the gravitational constant is equal to the force with which two bodies of 1 kg are attracted at a distance of 1 m.

Numerical value:

\(G = 6.67 \cdot() 10^(-11) N \cdot() m^2/ kg^2 \) .

The forces of universal gravitation act between any bodies in nature, but they become tangible at large masses (or if at least the mass of one of the bodies is large). The law of universal gravitation is fulfilled only for material points and balls (in this case, the distance between the centers of the balls is taken as the distance).

Gravity

A special type of universal gravitational force is the force of attraction of bodies to the Earth (or to another planet). This force is called gravity. Under the action of this force, all bodies acquire free fall acceleration.

According to Newton's second law \(g = F_T /m \) , therefore \(F_T = mg \) .

If M is the mass of the Earth, R is its radius, m is the mass of the given body, then the force of gravity is equal to

\(F = G \dfrac(M)(R^2)m = mg \) .

The force of gravity is always directed towards the center of the Earth. Depending on the height \ (h \) above the Earth's surface and the geographical latitude of the position of the body, the free fall acceleration acquires different values. On the surface of the Earth and in middle latitudes, the free fall acceleration is 9.831 m/s 2 .

Body weight

In technology and everyday life, the concept of body weight is widely used.

Body weight denoted by \(P \) . The unit of weight is newton (N). Since the weight is equal to the force with which the body acts on the support, then, in accordance with Newton's third law, the weight of the body is equal in magnitude to the reaction force of the support. Therefore, in order to find the weight of the body, it is necessary to determine what the reaction force of the support is equal to.

It is assumed that the body is motionless relative to the support or suspension.

Body weight and gravity differ in nature: body weight is a manifestation of the action of intermolecular forces, and gravity has a gravitational nature.

The state of a body in which its weight is zero is called weightlessness. The state of weightlessness is observed in an airplane or spacecraft when moving with the acceleration of free fall, regardless of the direction and value of the speed of their movement. Outside the earth's atmosphere, when the jet engines are turned off, only the force of universal gravitation acts on the spacecraft. Under the action of this force, the spaceship and all the bodies in it move with the same acceleration, so the state of weightlessness is observed in the ship.

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« Physics - Grade 10 "

Why does the moon move around the earth?
What happens if the moon stops?
Why do the planets revolve around the sun?

In Chapter 1, it was discussed in detail that the globe imparts the same acceleration to all bodies near the surface of the Earth - the acceleration of free fall. But if the globe imparts acceleration to the body, then, according to Newton's second law, it acts on the body with some force. The force with which the earth acts on the body is called gravity. First, let's find this force, and then consider the force of universal gravitation.

Modulo acceleration is determined from Newton's second law:

AT general case it depends on the force acting on the body and its mass. Since the acceleration of free fall does not depend on the mass, it is clear that the force of gravity must be proportional to the mass:

The physical quantity is the free fall acceleration, it is constant for all bodies.

Based on the formula F = mg, you can specify a simple and practically convenient method for measuring the masses of bodies by comparing the mass of a given body with the standard unit of mass. The ratio of the masses of two bodies is equal to the ratio of the forces of gravity acting on the bodies:

This means that the masses of bodies are the same if the forces of gravity acting on them are the same.

This is the basis for the determination of masses by weighing on a spring or balance scale. By ensuring that the force of pressure of the body on the scales, equal to the force of gravity applied to the body, is balanced by the force of pressure of the weights on the other scales, equal to the force of gravity applied to the weights, we thereby determine the mass of the body.

The force of gravity acting on a given body near the Earth can be considered constant only at a certain latitude near the Earth's surface. If the body is lifted or moved to a place with a different latitude, then the acceleration of free fall, and hence the force of gravity, will change.


The force of gravity.

Newton was the first to rigorously prove that the reason that causes the fall of a stone to the Earth, the movement of the Moon around the Earth and the planets around the Sun, is the same. it gravitational force acting between any bodies of the Universe.

Newton came to the conclusion that if it were not for air resistance, then the trajectory of a stone thrown from high mountain(Fig. 3.1) at a certain speed, it could become such that it would never reach the surface of the Earth at all, but would move around it like the planets describe their orbits in the sky.

Newton found this reason and was able to accurately express it in the form of one formula - the law of universal gravitation.

Since the force of universal gravitation imparts the same acceleration to all bodies, regardless of their mass, it must be proportional to the mass of the body on which it acts:

“Gravity exists for all bodies in general and is proportional to the mass of each of them ... all planets gravitate towards each other ...” I. Newton

But since, for example, the Earth acts on the Moon with a force proportional to the mass of the Moon, then the Moon, according to Newton's third law, must act on the Earth with the same force. Moreover, this force must be proportional to the mass of the Earth. If the gravitational force is truly universal, then from the side of a given body any other body must be acted upon by a force proportional to the mass of this other body. Consequently, the force of universal gravitation must be proportional to the product of the masses of the interacting bodies. From this follows the formulation of the law of universal gravitation.

Law of gravity:

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:

The proportionality factor G is called gravitational constant.

The gravitational constant is numerically equal to the force of attraction between two material points with a mass of 1 kg each, if the distance between them is 1 m. After all, with masses m 1 \u003d m 2 \u003d 1 kg and a distance r \u003d 1 m, we get G \u003d F (numerically).

It must be kept in mind that the law of universal gravitation (3.4) as a universal law is valid for material points. In this case, the forces of gravitational interaction are directed along the line connecting these points (Fig. 3.2, a).

It can be shown that homogeneous bodies having the shape of a ball (even if they cannot be considered material points, Fig. 3.2, b) also interact with the force defined by formula (3.4). In this case, r is the distance between the centers of the balls. The forces of mutual attraction lie on a straight line passing through the centers of the balls. Such forces are called central. The bodies whose fall to the Earth we usually consider are much smaller than the Earth's radius (R ≈ 6400 km).

Such bodies, regardless of their shape, can be considered as material points and the force of their attraction to the Earth can be determined using the law (3.4), bearing in mind that r is the distance from the given body to the center of the Earth.

A stone thrown to the Earth 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 with more speed, it will fall further.” I. Newton

Definition of the gravitational constant.


Now let's find out how you can find the gravitational constant. First of all, note that G has a specific name. This is due to the fact that the units (and, accordingly, the names) of all quantities included in the law of universal gravitation have already been established earlier. The law of gravitation gives a new connection between known quantities with certain names of units. That is why the coefficient turns out to be a named value. Using the formula of the law of universal gravitation, it is easy to find the name of the unit of gravitational constant in SI: N m 2 / kg 2 \u003d m 3 / (kg s 2).

To quantify G, it is necessary to independently determine all the quantities included in the law of universal gravitation: both masses, force and distance between bodies.

The difficulty lies in the fact that the gravitational forces between bodies of small masses are extremely small. It is for this reason that we do not notice the attraction of our body to surrounding objects and the mutual attraction of objects to each other, although gravitational forces are the most universal of all forces in nature. Two people weighing 60 kg at a distance of 1 m from each other are attracted with a force of only about 10 -9 N. Therefore, to measure the gravitational constant, rather subtle experiments are needed.

The gravitational constant was first measured by the English physicist G. Cavendish in 1798 using a device called a torsion balance. The scheme of the torsion balance is shown in Figure 3.3. A light rocker with two identical weights at the ends is suspended on a thin elastic thread. Two heavy balls are motionlessly fixed nearby. Gravitational forces act between weights and motionless balls. Under the influence of these forces, the rocker turns and twists the thread until the resulting elastic force becomes equal to the gravitational force. The angle of twist can be used to determine the force of attraction. To do this, you only need to know the elastic properties of the thread. The masses of bodies are known, and the distance between the centers of interacting bodies can be directly measured.

From these experiments, the following value for the gravitational constant was obtained:

G \u003d 6.67 10 -11 N m 2 / kg 2.

Only in the case when bodies of enormous masses interact (or at least the mass of one of the bodies is very large), the gravitational force reaches of great importance. For example, the Earth and the Moon are attracted to each other with a force F ≈ 2 10 20 N.


Dependence of free fall acceleration of bodies on geographic latitude.


One of the reasons for the increase in the acceleration of free fall when moving the point where the body is located from the equator to the poles is that the globe is somewhat flattened at the poles and the distance from the center of the Earth to its surface at the poles is less than at the equator. Another reason is the rotation of the Earth.


Equality of inertial and gravitational masses.


The most striking property of gravitational forces is that they impart the same acceleration to all bodies, regardless of their masses. What would you say about a football player whose kick would equally accelerate an ordinary leather ball and a two-pound weight? Everyone will say that it is impossible. But the Earth is just such an “extraordinary football player”, with the only difference that its effect on bodies does not have the character of a short-term impact, but continues continuously for billions of years.

In Newton's theory, mass is the source of the gravitational field. We are in the Earth's gravitational field. At the same time, we are also sources of the gravitational field, but due to the fact that our mass is significantly less than the mass of the Earth, our field is much weaker and the surrounding objects do not react to it.

The unusual property of gravitational forces, as we have already said, is explained by the fact that these forces are proportional to the masses of both interacting bodies. The mass of the body, which is included in Newton's second law, determines the inertial properties of the body, i.e., its ability to acquire a certain acceleration under the action of a given force. it inertial mass m and.

It would seem, what relation can it have to the ability of bodies to attract each other? The mass that determines the ability of bodies to attract each other is the gravitational mass m r .

It does not follow at all from Newtonian mechanics that the inertial and gravitational masses are the same, i.e. that

m and = m r . (3.5)

Equality (3.5) is a direct consequence of experience. It means that one can simply speak of the mass of a body as a quantitative measure of both its inertial and gravitational properties.

The law of universal gravitation was discovered in the 17th century and gave a tremendous development to the physics of that time. So who discovered this law, and why is it so important to science?

Definition of the law of universal gravitation

The Danish astronomer Tycho Brahe, who has been observing the motion of the planets for many years, has accumulated a huge amount of interesting data, but has not been able to process them. But this was done by his student Johannes Kepler. Using the idea of ​​Copernicus about the heliocentric system and the results of Tycho Brahe's observations, Kepler established the laws of planetary motion around the Sun. However, he could not explain the dynamics of this movement, that is, why the planets move according to such laws.

And then the time came for Isaac Newton, who had already discovered the three basic laws of dynamics. Newton suggested that a number of phenomena that seem to have nothing in common with each other are caused by one cause - the forces of gravity. After numerous calculations, the scientist came to the conclusion that all bodies in nature 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.

Rice. 1. Portrait of Newton.

Here's how Newton came to this conclusion. It follows from Newton's second law (dynamics) that the acceleration that a body receives under the action of a force is inversely proportional to the mass of the body: $a =( F \over m)$, but the free fall acceleration is $g = 9.8 (m \over s ^2)$ does not depend on the mass of the body. And this seems possible only if the force with which the Earth attracts the body changes in proportion to the mass of the body.

According to Newton's third law, the forces with which bodies interact are equal in absolute value. If the force acting on one body is proportional to the mass of this body, then the force equal to it acting on the second body is obviously proportional to the mass of the second body.

But the forces acting on both bodies are equal, therefore they are proportional to the mass of both the first and second bodies.

Isaac Newton discovered this law at the age of 23, but did not publish it for nine years, since the then available incorrect data on the distance between the Earth and the Moon did not confirm his idea. Only in 1667, after clarifying this distance, was the law of universal gravitation finally published.

Here is the formulation and definition of the law of universal gravitation: all bodies are attracted to each other with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between them. This force is called the force of gravity.

Rice. 2. The formula of the law of universal gravitation.

The gravitational force is very small and becomes noticeable only when at least one of the interacting bodies has a large mass (planet, star).

Rice. 3. Planets of the solar system.

Another essential sign of mass follows from this law: mass reflects the property of a body to be attracted to other bodies and determines the strength of this attraction.

Application of the law of universal gravitation

Like any other laws, the law of universal gravitation has certain limits of applicability. It is valid for:

  • material points;
  • spherical bodies;
  • a ball of large radius interacting with bodies whose dimensions are much smaller than the dimensions of the ball.

The law is not applicable, for example, to the interaction of an infinite rod and a ball. In this case, the force of gravity is only inversely proportional to the distance, not the square of the distance. And, say, the force of attraction between a body and an infinite plane does not depend on the distance at all.

What have we learned?

In the 9th grade, the topic of universal gravitation is very important. This article briefly talks about the discovery and application of this law, as well as the scientists who have contributed to the development of this law.

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We all walk on the Earth because it attracts us. If the Earth did not attract all the bodies on its surface, then we, having repelled from it, would fly away into space. But this does not happen, and everyone knows about the existence of terrestrial gravity.

Are we pulling the earth? Luna attracts!

Do we pull the earth towards us? Ridiculous question, right? But let's see. Do you know what the tides are in the seas and oceans? Every day, the water leaves the coast, wanders around for several hours, and then, as if nothing had happened, returns back.

So the water at this time is not unknown where, but approximately in the middle of the ocean. There is formed something like a mountain of water. Incredible, right? Water, which tends to spread, does not just flow itself, but also forms mountains. And in these mountains a huge mass of water is concentrated.

Just consider the total volume of water that moves away from the coast during low tides, and you will understand that we are talking about gigantic quantities. But if this happens, there must be some reason. And there is a reason. The reason lies in the fact that the moon attracts this water.

As it revolves around the Earth, the Moon passes over the oceans and pulls the ocean waters towards it. The moon revolves around the earth because it is attracted by the earth. But, it turns out that she herself at the same time attracts the Earth to herself. The earth, however, is too big for her, but her influence is sufficient to move water in the oceans.

Force and law of universal gravitation: concept and formula

And now let's go further and think: if two huge bodies, being nearby, both attract each other, is it not logical to assume that smaller bodies will also attract each other? Is it just that they are much smaller and their attractive force will be small?

It turns out that this assumption is absolutely correct. Absolutely between all bodies in the Universe there are forces of attraction or, in other words, forces of universal gravitation.

Isaac Newton was the first to discover and formulate such a phenomenon in the form of a law. The law of universal gravitation says: all bodies are attracted to each other, while the force of their attraction is directly proportional to the mass of each of the bodies and inversely proportional to the square of the distance between them:

F = G * (m_1 * m_2) / r^2 ,

where F is the value of the attraction force vector between the bodies, m_1 and m_2 are the masses of these bodies, r is the distance between the bodies, G is the gravitational constant.

The gravitational constant is numerically equal to the force that exists between bodies of mass 1 kg, located at a distance of 1 meter. This value is found experimentally: G=6.67*〖10〗^(-11) N* m^2⁄〖kg〗^2 .

Returning to our original question, "Are we pulling on the Earth?", we can confidently answer "yes." According to Newton's third law, we attract the Earth with exactly the same force as the Earth pulls us. This force can be calculated from the law of universal gravitation.

And according to Newton's second law, the impact of bodies on each other by any force is expressed in the form of the acceleration they impart to each other. But the acceleration imparted depends on the mass of the body.

The mass of the Earth is great, and it gives us the acceleration of free fall. And our mass is negligible compared to the Earth, and therefore the acceleration that we give to the Earth is practically zero. That is why we are attracted to the Earth and walk on it, and not vice versa.

Newton's law of gravity

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

Gravitational interaction in accordance with N. h. t. plays the main role in the motion of stellar systems such as binary and multiple stars, inside star clusters and galaxies. However, gravitational fields inside star clusters and galaxies are of a very complex nature and have not yet been studied enough, as a result of which movements inside them are studied by methods different from those of celestial mechanics (see Stellar astronomy). The gravitational interaction also plays essential role in all cosmic processes involving accumulations of large masses of matter. N. h. t. is the basis for studying the motion of artificial celestial bodies, in particular artificial satellites Earth and moon, space probes. On N. h. t. relies on Gravimetry. 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 negligibly small compared to the intramolecular and intranuclear forces.

Newton left open the question of the nature of gravity. The assumption of the instantaneous propagation of gravity in space (i.e., the assumption that with a change in the positions of bodies the force of gravity 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 represents 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. Short story 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:

    - (universal gravitation law), see Art. (see GRAVITY). Physical Encyclopedic Dictionary. Moscow: 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 gravity... Big Encyclopedic Dictionary

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

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

    The same as the law of universal gravitation. * * * NEWTON'S LAW OF GRAVATION 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 gravity 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

    THE LAW OF UNIVERSAL 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 gravity force module, m1 and m2, the masses of interacting bodies, R ... ... Great 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 factor G gravitational … Concepts of modern natural science. Glossary of basic terms

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