Gravitational forces. Law of Gravity

The force of universal gravity

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

Why don’t we notice the mutual attraction between the bodies around us? Maybe this is explained by the fact that the attractive forces between them are too small?

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

"HOLES" IN SPACE AND TIME

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

The role of the masses of attracting bodies

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

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

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

But bodies attract each other, and the forces of interaction are always of the same nature. Consequently, the force with which a body attracts the Earth is proportional to the mass of the Earth. According to Newton's third law, these forces are equal in magnitude. This means that if one of them is proportional to the mass of the Earth, then the other force equal to it is also proportional to the mass of the Earth. From this it follows that the force of mutual attraction is proportional to the masses of both interacting bodies. This means that it is proportional to the product of the masses of both bodies.

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

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

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

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

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.

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 Newton’s universal gravity is - classical theory 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 in left hand small ball. 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 thinker We have partially solved this problem for ourselves, 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 a straight line proportional connection with 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. The massive Sun, although it has large mass, however, 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 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? As follows:

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 numerical value 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.

Gravitational forces. The law of universal gravitation. Gravity.

The interaction characteristic of all bodies of the Universe and manifested in their mutual attraction to each other is called gravitational, and the phenomenon of universal gravitation itself gravity .

Gravitational interaction carried out through a special type of matter called gravitational field.

Gravitational forces (forces of gravity) are caused by the mutual attraction of bodies and are directed along the line connecting the interacting points.

Newton received the expression for the force of gravity in 1666 when he was only 24 years old.

Law of Gravity: two bodies are attracted to each other with forces directly proportional to the product of the masses of the bodies and inversely proportional to the square of the distance between them:

The law is valid provided that the sizes of the bodies are negligible compared to the distances between them. Also, the formula can be used to calculate the forces of universal gravity, for spherical bodies, for two bodies, one of which is a ball, the other a material point.

The proportionality coefficient G = 6.68·10 -11 is called gravitational constant.

Physical meaning The gravitational constant is that it is numerically equal to the force with which two bodies weighing 1 kg each, located at a distance of 1 m from each other, are attracted.

Gravity

The force with which the Earth attracts nearby bodies is called gravity , and the Earth’s gravitational field is gravity field .

The force of gravity is directed downward, towards the center of the Earth. In the body it passes through a point called center of gravity. The center of gravity of a homogeneous body having a center of symmetry (a ball, a rectangular or round plate, a cylinder, etc.) is located at this center. Moreover, it may not coincide with any of the points of a given body (for example, near a ring).

In the general case, when you need to find the center of gravity of a body irregular shape, one should proceed from the following pattern: if the body is suspended on a thread attached in series to different points body, then the directions marked by the thread will intersect at one point, which is precisely the center of gravity of this body.

The modulus of gravity is determined using the law of universal gravitation and is determined by the formula:

F t = mg, (2.7)

where g is the acceleration of free fall of the body (g=9.8 m/s 2 ≈10 m/s 2).

Since the direction of acceleration of free fall g coincides with the direction of gravity F t, we can rewrite the last equality in the form

From (2.7) it follows that, that is, the ratio of the force acting on a body of mass m at any point in the field to the mass of the body determines the acceleration of gravity at a given point in the field.

For points located at a height h from the Earth's surface, the acceleration of free fall of a body is equal to:

(2.8)

where RZ is the radius of the Earth; MZ - mass of the Earth; h is the distance from the center of gravity of the body to the surface of the Earth.

From this formula it follows that,

Firstly, the acceleration of free fall does not depend on the mass and size of the body and,

secondly, with increasing height above the Earth, the acceleration of free fall decreases. For example, at an altitude of 297 km it turns out to be not 9.8 m/s 2, but 9 m/s 2.

A decrease in the acceleration of gravity means that the force of gravity also decreases as the height above the Earth increases. The further a body is from the Earth, the weaker it attracts it.

From formula (1.73) it is clear that g depends on the radius of the Earth R z.

But due to the oblateness of the Earth in different places has different meaning: it decreases as you move from the equator to the pole. At the equator, for example, it is equal to 9.780 m/s 2, and at the pole - 9.832 m/s 2. In addition, local g values ​​may differ from their average g av values ​​due to the heterogeneous structure earth's crust and subsoil, mountain ranges and depressions, as well as mineral deposits. The difference between the values ​​of g and g cf is called

In 1667. Newton understood that in order for the Moon to revolve around the Earth, and the Earth and other planets around the Sun, there must be a force to keep them in a circular orbit. He suggested that the force of gravity acting on all bodies on Earth and the force that holds the planets in their circular orbits are one and the same force. This force is called force of universal gravity or gravitational force. This force is an attractive force and acts between all bodies. Newton formulated law of universal gravitation : two material points 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.

The proportionality coefficient G was unknown in Newton's time. It was first measured experimentally by the English scientist Cavendish. This coefficient is called gravitational constant. Her modern meaning equals . The gravitational constant is one of the most fundamental physical constants. The law of universal gravitation can be written in vector form. If the force acting on the second point from the first is equal F 21, and the radius vector of the second point relative to the first is equal to R 21, That:

The presented form of the law of universal gravitation is valid only for the gravitational interaction of material points. It cannot be used for bodies of arbitrary shape and size. Calculating the gravitational force in the general case is a very difficult task. However, there are bodies that are not material points for which the gravitational force can be calculated using the given formula. These are bodies that have spherical symmetry, for example, having the shape of a ball. For such bodies, the above law is valid if by distance R we mean the distance between the centers of the bodies. In particular, the force of gravity acting on all bodies from the Earth can be calculated using this formula, since the Earth has the shape of a ball, and all other bodies can be considered material points compared to the radius of the Earth.

Since gravity is a gravitational force, we can write that the force of gravity acting on a body of mass m is equal to

Where MZ and RZ are the mass and radius of the Earth. On the other hand, the force of gravity is equal to mg, where g is the acceleration of gravity. So the acceleration of free fall is equal to

This is the formula for the acceleration of gravity on the surface of the Earth. If you move away from the surface of the Earth, the distance to the center of the Earth will increase, and the acceleration of gravity will correspondingly decrease. So at a height h above the Earth’s surface, the acceleration of gravity is equal to:

In nature, there are various forces that characterize the interaction of bodies. Let us consider the forces that occur in mechanics.

Gravitational forces. Probably the very first force whose existence man realized was the force of gravity acting on bodies from the Earth.

And it took many centuries for people to understand that the force of gravity acts between any bodies. And it took many centuries for people to understand that the force of gravity acts between any bodies. The English physicist Newton was the first to understand this fact. Analyzing the laws that govern the motion of planets (Kepler's laws), he came to the conclusion that the observed laws of motion of planets can be fulfilled only if there is an attractive force between them, directly proportional to their masses and inversely proportional to the square of the distance between them.

Newton formulated law of universal gravitation. Any two bodies attract each other. The force of attraction between point bodies is directed along the straight line connecting them, is directly proportional to the masses of both and inversely proportional to the square of the distance between them:

In this case, point bodies are understood as bodies whose dimensions are many times smaller than the distance between them.

The forces of universal gravity are called gravitational forces. The proportionality coefficient G is called the gravitational constant. Its value was determined experimentally: G = 6.7 10¯¹¹ N m² / kg².

Gravity acting near the surface of the Earth is directed towards its center and is calculated by the formula:

where g is the acceleration of gravity (g = 9.8 m/s²).

The role of gravity in living nature is very significant, since the size, shape and proportions of living beings largely depend on its magnitude.

Body weight. Let's consider what happens when some load is placed on a horizontal plane (support). At the first moment after the load is lowered, it begins to move downward under the influence of gravity (Fig. 8).

The plane bends and an elastic force (support reaction) directed upward appears. After the elastic force (Fу) balances the force of gravity, the lowering of the body and the deflection of the support will stop.

The deflection of the support arose under the action of the body, therefore, a certain force (P) acts on the support from the side of the body, which is called the weight of the body (Fig. 8, b). According to Newton's third law, the weight of a body is equal in magnitude to the ground reaction force and is directed in the opposite direction.

P = - Fу = Fheavy.

Body weight is called the force P with which a body acts on a horizontal support that is motionless relative to it.

Since the force of gravity (weight) is applied to the support, it is deformed and, due to its elasticity, counteracts the force of gravity. The forces developed in this case from the side of the support are called support reaction forces, and the very phenomenon of the development of counteraction is called the support reaction. According to Newton's third law, the support reaction force is equal in magnitude to the force of gravity of the body and opposite in direction.

If a person on a support moves with the acceleration of the parts of his body directed from the support, then the reaction force of the support increases by the amount ma, where m is the mass of the person, and is the acceleration with which the parts of his body move. These dynamic effects can be recorded using strain gauge devices (dynamograms).

Weight should not be confused with body weight. The mass of a body characterizes its inert properties and does not depend either on the force of gravity or on the acceleration with which it moves.

The weight of a body characterizes the force with which it acts on the support and depends on both the force of gravity and the acceleration of movement.

For example, on the Moon the weight of a body is approximately 6 times less than the weight of a body on Earth. The mass in both cases is the same and is determined by the amount of matter in the body.

In everyday life, technology, and sports, weight is often indicated not in newtons (N), but in kilograms of force (kgf). The transition from one unit to another is carried out according to the formula: 1 kgf = 9.8 N.

When the support and the body are motionless, then the mass of the body is equal to the gravity of this body. When the support and the body move with some acceleration, then, depending on its direction, the body can experience either weightlessness or overload. When the acceleration coincides in direction and is equal to the acceleration of gravity, the weight of the body will be equal to zero, therefore a state of weightlessness arises (ISS, high-speed elevator when lowering down). When the acceleration of the support movement is opposite to the acceleration of free fall, the person experiences an overload (a manned launch from the surface of the Earth spaceship, High-speed elevator going up).