How is the force of universal gravity directed. Gravity: formula, definition. The experiments of 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 run away, nowhere to hide from the all-encompassing magical gravitation: 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 young children, having devoted his life to the study of this phenomenon, he established one of the greatest laws - the law of gravity.

What is gravity?

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

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

Gravity: formula

How to calculate the directional to a specific body? What other values \u200b\u200bdo you need to know for this? The formula for calculating gravity is quite simple, it is studied in the 7th grade of a comprehensive school, at the beginning of a 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, which invariably acts 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 downward, to the center of the earth's core, thanks to its effect, all bodies fall down at uniform acceleration. We observe the phenomena of gravitation in everyday life everywhere and constantly:

• objects, accidentally or deliberately released from the hands, must fall down to the Earth (or on any surface that prevents free fall);
• a satellite launched into space does not fly away from our planet for an indefinite distance perpendicularly upward, but remains in orbit;
• all rivers flow from the mountains and cannot be reversed;
• it happens that a person falls and is injured;
• the smallest dust particles settle on all surfaces;
• air is concentrated near the surface of the earth;
• hard to carry bags;
• rain is falling from clouds and clouds, snow is falling, 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, thus, these two concepts are often substituted, which is not at all correct.

Acceleration of gravity

The concept of "acceleration of gravity" (in other words, it is associated with the term "gravity."

"g" \u003d 9.8 N / kg, this is a constant. However, more accurate measurements show that due to the rotation of the Earth, the value of the acceleration of St. n. is not the same and depends on latitude: at the North Pole it \u003d 9.832 N / kg, and at the sultry equator \u003d 9.78 N / kg. It turns out that in different places of the planet, different gravity is directed at bodies with equal mass (the formula mg still remains unchanged). For practical calculations, it was decided to insignificant errors of this value and to use the average value of 9.8 N / kg.

The proportionality of such a quantity as the force of gravity (the formula proves this) allows you to measure the weight of an object with a dynamometer (similar to an ordinary household bizarre). Note that the meter only displays strength, as the regional "g" value must be known to obtain an accurate body weight.

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

Gravity in the solar system

Is there a definition and a formula for other planets remain relevant. With only one difference in the meaning of "g":

• on the Moon \u003d 1.62 N / kg (six times less than on Earth);
• on Neptune \u003d 13.5 N / kg (almost one and a half times higher than on Earth);
• on Mars \u003d 3.73 N / kg (more than two and a half times less than on our planet);
• on Saturn \u003d 10.44 N / kg;
• on Mercury \u003d 3.7 N / kg;
• on Venus \u003d 8.8 N / kg;
• on Uranus \u003d 9.8 N / kg (almost the same as ours);
• on Jupiter \u003d 24 N / kg (almost two and a half times higher).

The 16th - 17th centuries are rightly called by many as one of the most glorious periods in. It was at this time that the foundations were largely laid, without which the further development of this science would be simply unthinkable. Copernicus, Galileo, Kepler did a great job to declare physics as a science that can provide an answer to almost any question. The law of universal gravitation stands apart in a whole series of discoveries, 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 of the presence of this value even before Newton, but in the fact that he was the first to prove that both on Earth and in outer space the same the 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 Earth, interact with each other. This interaction is called gravitational, while the very process of universal gravitation is gravity.
This interaction occurs between bodies because there is a special, unlike others, type of matter, 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 a unique ability to penetrate any material.

The force of universal gravitation, the definition and formulation of which he gave, is in direct dependence on the product of the masses of interacting bodies, and in inverse dependence on the square of the distance between these objects. According to Newton's opinion, irrefutably confirmed by practical research, the force of gravity is found by the following formula:

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

The force of gravity with which bodies are attracted to the Earth is a special case of Newton's law and 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 9.8 m / s2.

Newton's law explains not only the processes taking place directly on the Earth, it answers many questions related to the structure of the entire solar system. In particular, the force of universal gravity between has a decisive influence on the movement of planets in their orbits. A theoretical description of this motion 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 from, it flies not directly, but along an arcuate trajectory. In this case, with an increase in the charge of the powder and the mass of the nucleus, the latter will fly away further and further. Finally, if we assume that it is possible to get so much gunpowder and design such a cannon so that the nucleus flew 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 world gravitation is the same in nature both on Earth and in outer space.

Why does a stone released from the hands fall to the Earth? Because he is attracted by the Earth, each of you will say. In fact, the stone falls to the Earth with the acceleration of gravity. Therefore, a force directed to the Earth acts on the stone from the side of the Earth. According to Newton's third law, a stone acts on the Earth with the same modulus of force directed to 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 for the fall of a stone on the Earth, the movement of the Moon around the Earth and the planets around the Sun, is the same. This is the force of gravity acting between any bodies in the universe. Here is the course of his reasoning, given in Newton's main work "Mathematical Principles of Natural Philosophy":

“A stone thrown horizontally will deviate from a straight path under the action of gravity and, having described a curved trajectory, will finally fall to the Earth. If you throw it with a higher speed, it will fall further ”(fig. 1).

Continuing this reasoning, Newton comes to the conclusion that if it were not for the air resistance, then the trajectory of a stone thrown from a high mountain with a certain speed could become such that it would never reach the Earth's surface at all, but moved around it “like how the planets describe their orbits in heavenly space ”.

Now we have become so familiar with 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 planets around the Sun is also a free fall, but only a fall that lasts without stopping for billions of years. The reason for this "fall" (whether we are talking really about the fall of an ordinary stone to the Earth or about the movement of planets in their orbits) is the force of gravity. 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 force 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 mass m, for example, twice will lead to an increase in the modulus of force F is also doubled, but the acceleration, which is \\ (a \u003d \\ frac (F) (m) \\), will remain unchanged. Generalizing this conclusion for the forces of gravity between any bodies, we conclude that the force of universal gravity is directly proportional to the mass of the body on which this force acts.

But at least two bodies are involved in mutual attraction. Each of them, according to Newton's third law, is subject to gravitational forces of the same magnitude. Therefore, each of these forces must be proportional to both the mass of one body and the mass of another body. Therefore, the force of universal gravity 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 acceleration of gravity is 9.8 m / s 2 and it is the same for bodies falling from heights 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 the force does not depend on distance either. But Newton believed that the distance 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 appreciably change the value of the acceleration due to gravity.

To find out how the distance between bodies affects the strength 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 having a 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 Earth's surface. In reality, the centripetal acceleration of the Moon is 0.0027 m / s 2.

Let's prove it... The rotation of the Moon around the Earth occurs under the action of the force of gravity between them. Approximately, the Moon's orbit can be considered a circle. Consequently, the Earth imparts centripetal acceleration to the Moon. It is calculated by the formula \\ (a \u003d \\ 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 hours 43 minutes ≈ 2.4 ∙ 10 6 s - the period of the Moon's revolution around the Earth. Considering that the radius of the Earth R s ≈ 6.4 ∙ 10 6 m, we obtain that the centripetal acceleration of the Moon is equal to:

\\ (a \u003d \\ 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 the acceleration is less than the gravitational acceleration of bodies near the Earth's surface (9.8 m / s 2) by approximately 3600 \u003d 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 gravity itself by 60 2 times.

An important conclusion follows from this: the acceleration that gives the bodies the force of gravity 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) \\).

The law of universal gravitation

In 1667, Newton finally formulated the law of universal gravitation:

\\ (F \u003d 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.

Aspect ratio G called gravitational constant.

The law of universal gravitation is valid only for those bodies whose dimensions are negligible in comparison with 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). These kinds of 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 pointlike. Adding the forces of gravity acting on each element of a given body from all the elements of another body, we obtain a force acting on this element (Fig. 3). Having performed such an operation for each element of a given body and adding up the forces obtained, they find the total force of gravity acting on this body. This task is difficult.

However, there is 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 larger than the sum of their radii, are attracted with forces, the moduli of which 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 on the Earth are much smaller than the dimensions of the Earth, then these bodies can be considered as point bodies. Then under R in formula (1), the distance from the given body to the center of the Earth should be understood.

The forces of mutual attraction act between all bodies, 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 \u003d F \\ cdot \\ frac (R ^ 2) (m_1 \\ cdot m_2) \\).

Hence it follows that if the distance between the bodies is numerically equal to one ( R \u003d 1 m) and the masses of the interacting bodies are also equal to unity ( m 1 = m 2 \u003d 1 kg), then the gravitational constant is numerically equal to the modulus of force F... In this way ( physical meaning ),

the gravitational constant is numerically equal to the modulus of the gravitational force acting on a body with a mass of 1 kg from another body of the same mass with a distance between the bodies equal to 1 m.

In SI, the gravitational constant is expressed in

.

The Cavendish Experience

The value of the gravitational constant G can only be found empirically. To do this, you need to measure the modulus of gravity Facting on the body with mass m 1 from the side of the body weight m 2 at a known distance R between bodies.

The first measurements of the gravitational constant were carried out 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 carried out in 1798 by the English physicist G. Cavendish using a device called a torsion balance. The torsion balance is shown schematically in Figure 4.

Cavendish secured two small lead balls (5 cm in diameter and m 1 \u003d 775 g each) at opposite ends of a 2-meter rod. The rod was suspended from a thin wire. For this wire, the elastic forces arising in it when twisted at various angles were preliminarily determined. Two large lead balls (20 cm in diameter and m 2 \u003d 49.5 kg) could be brought close to small balls. The forces of attraction from the side of the large balls made the small balls move towards them, while the stretched wire twisted slightly. The degree of twisting was a measure of the force acting between the balls. The angle of twisting of the wire (or rotation of the rod with small balls) was 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 forces of attraction of two bodies weighing 1 kg each, located at a distance of 1 m from each other, in terms of modules are only 6.67 ∙ 10 -11 N. 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 force of gravity becomes large. For example, the Earth attracts the moon with a 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 universal gravitation

The law of universal gravitation is the basis of celestial mechanics - the science of planetary motion. With the help of this law, the positions of celestial bodies on the firmament for many decades ahead are determined with great accuracy and their trajectories are calculated. The law of universal gravitation is also used in calculating the motion of artificial earth satellites and interplanetary automatic vehicles.

Disturbances in the motion of the planets... The planets do not move strictly according to Kepler's laws. Kepler's laws would be exactly 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, disturbances arise in the motion of the planets. In the solar system, disturbances are small, because the attraction of a planet by the sun is much stronger than the attraction of other planets. When calculating the apparent position of the planets, perturbations have to be taken into account. When launching artificial celestial bodies and calculating their trajectories, an approximate theory of the motion of celestial bodies is used - the theory of perturbations.

Discovery of Neptune... One of the striking 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 motion of Uranus), the Englishman Adam and the Frenchman Leverrier, using the law of universal gravitation, calculated the position of this planet in the sky. Adame had finished his calculations earlier, but the observers to whom he communicated his results were in no hurry to check. Meanwhile, Leverrier, having completed the calculations, showed the German astronomer Halle the place where to look for an unknown planet. On the first evening, September 28, 1846, Halle, aiming the telescope at the indicated place, discovered a new planet. She was named 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 the 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 more.

The forces of gravity 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 for the forces of gravity. They work through any body.

Literature

1. Kikoin I.K., Kikoin A.K. Physics: Textbook. for 9 cl. Wednesday shk. - M .: Education, 1992 .-- 191 p.
2. Physics: Mechanics. 10 cl .: Textbook. for in-depth study of physics / M.M. Balashov, A.I. Gomonova, A.B. Dolitsky and others; Ed. G. Ya. Myakisheva. - M .: Bustard, 2002 .-- 496 p.

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.

In contact with

Everything in the universe is moving. 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 all bodies are attracted to each other, remains to this day not fully disclosed, although it has been studied up and down.

In this article, we will look at what Newton's universal attraction is - the classical theory of gravity. However, before moving on to formulas and examples, let us 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 became interested in ancient Greece.

Movement was understood as the essence of the sensory 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 realized this, thoughts about 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 gravity and the attraction of our planet to, but also the basis of the origin of the Universe and almost all available elementary particles.

Movement task

Let's do a thought experiment. Take a small ball in our left hand. Let's take the same on the right. Let go of the right ball and it will start falling down. The left one remains in the hand, it is still motionless.

Let's stop mentally 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 "energy" of movement, the left one is not. But what is the profound, 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. He has the same atoms, and they are no different from the atoms of the resting ball. Ball possesses? Yes, this is the correct answer, but how does the ball know that it has potential energy, where is it fixed in it?

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

Newton's 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 proportional relationship with 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 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 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 surfaces.

For the law of gravitation, 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 have just considered the force of gravity?

Force is a vector quantity, however 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:

.

The 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 much weaker than the earth... The massive Sun, although it has a large mass, 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 force of attraction of two bodies, namely how to calculate the force of gravity of the Sun, Earth and you and me - we will deal with this issue a little later.

As far as we know, gravity is:

where m is our mass and g is the acceleration of the Earth's gravity (9.81 m / s 2).

Important! There are no two, three, ten types of attraction forces. Gravity is the only force that quantifies attraction. Weight (P \u003d mg) and gravity 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 equal to:

Thus, since F \u003d mg:

.

The masses m contract, and the expression for the acceleration of gravity remains:

As you can see, the acceleration of gravity is really a constant value, since its formula includes constant values \u200b\u200b- the radius, the mass of the Earth and the gravitational constant. Substituting the values \u200b\u200bof these constants, we will make sure that the acceleration due to gravity is 9.81 m / s 2.

At different latitudes, the radius of the planet is slightly different, since the Earth is still not a perfect ball. Because of this, the acceleration of gravity is different at different points of the globe.

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

For convenience, let's take the mass of a person: m \u003d 100 kg. Then:

• The distance between a person and the earth is equal to the radius of the planet: R \u003d 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 \u003d 15 ∙ 10 10 m.

Gravitational attraction between man and the Earth:

This result is fairly obvious from a simpler weight expression (P \u003d 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 gravity between the Earth and the Sun? In the following way:

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

First space speed

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

True, he imagined it somewhat differently, in his understanding there was not a vertically standing rocket aimed at the sky, but a body that horizontally makes a jump from the top of the mountain. This 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 be equal not to 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 so attached to gravity as those that "fell" to the surface.

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

The first cosmic speed 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 Newton's second law for a body that revolves around the planet in a circular orbit:

,

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

In orbit, 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 cosmic speed is absolutely independent of body weight. Thus, any object accelerated to a speed of 7.9 km / s will leave our planet and enter its orbit.

First space speed

Second space speed

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. This is what the second space speed is for. 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 speed, because they had to first "disconnect" from the gravitational field of the planet. This is not so: the pair "Earth - Moon" are in the gravitational field of the Earth. Their common center of gravity is within the globe.

To find this speed, let's set the problem a little differently. Let's say a body flies from infinity to the planet. The question is: what speed will be achieved on the surface upon landing (excluding 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 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 gravitational force is, learned to count it for various bodies, and also studied some useful consequences that follow from such a phenomenon as the universal law of gravitation.

Absolutely all material bodies, both located directly on Earth and existing in the Universe, are constantly attracted to each other. The fact that this interaction can not always be seen or felt, says only that this attraction in these specific cases is relatively weak.

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

The phenomenon of gravity is possible because a gravitational field exists 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 to 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 force of gravity, which, as indicated above, is nothing more than the result of the action of the gravitational field on a particular material body. lies in the fact that the force with which the mutual attraction of bodies 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 force of gravity, the definition of which was given by Newton himself, depends only on two main factors - the mass of 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 around it. Soon after Newton, another famous scientist - Galileo - convincingly showed that when our planet sets all bodies exactly the same acceleration. This is possible only if the body to the Earth directly depends on the mass of this body. Indeed, in this case, with an increase in mass by several times, the force of the acting gravity will increase by exactly the same amount, 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 come to the conclusion that the same force acts on each of them from the side of 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 in direct proportion to the product of their masses.

To prove that 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 9.8 m / s ^ 2, but the Moon in relation to our planet, as a result of a number of experiments, turned out to be only 0.0027 m / s ^ 2.

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