The moon does not fly away from the earth because... Mountain sky is for you! What does the moon look like

According to the Law universal gravity Newton, all material objects 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. Well, don't think too much about it. I know how much you don’t like to do this. Next I will explain everything in detail! So, keep in mind that when you jump, the Earth pulls you back, the same happens with the Earth, you also attract it to you. But this is not noticeable, because your mass is negligible compared to the mass of the earth!
Now let's remove everything: air, the Sun, satellites, other systems and objects of the universe. Let's leave only the experimental Moon and Earth!


Do you think that in such an ideal system, the Moon will collide with the Earth?
Well, in principle, this is what should happen, based on the above law, the Earth should attract the Moon to itself, the Moon should attract the Earth to itself, and they will unite into one thing! But this doesn't happen! Something is in the way! Now let's add me to our system! Well, for clarity, let’s put a stone in my hand! (that's how it should be)


Please note that I am already on Earth, I was pulled in and can’t get away from it! And the stone in my hand is still reaching for the Earth, but I don’t let it be attracted... I’m gloating over the Earth.
So, the experiment:
I launch a stone with all my strength along the surface of the Earth!


He flies some distance and would happily fly away to another solar system if the insidious Earth had not begun to attract him. He could not resist this law of universal gravitation. From which Newton also suffered. Surely the apple gave him a pretty good bump! So that...
Now I launch this stone with even greater force... Well, in short, with all the force I launched!


He flew around almost half of the Earth. But still, the Earth turned out to be stronger and still pulled him in!
So what do you think...
I won’t rest on this, now I launched the stone at a speed of almost 8000 m/s.
A stone flies to itself and thinks: “Finally, I’m moving away from this hefty planet... Or not?... AAAAAAAAA She’s attracting me to her again...!”


Before I had time to look back, my stone was flying towards the back of my head... What if I ducked down? ... Obviously, it will fly further on the next orbit!
All that remains is to give the stone a second cosmic power and we’ll see...


...Like a stone will leave orbit and possibly the solar system, if, of course, no one else attracts it!
That's it!
The sun turns out to be here and has nothing to do with it! But the Moon is the same stone, and if you slow it down, it will certainly fall to Earth!

Moon, natural satellite The Earth, in the process of its movement in space, is influenced mainly by two bodies - the Earth and the Sun. At the same time, the sun's gravity is twice as strong as the earth's. Therefore, both bodies (Earth and Moon) revolve around the Sun, being close to each other.

With a twofold predominance of solar gravity over the earth's, the curve of the Moon's motion should be concave in relation to the Sun at all its points. The influence of the nearby Earth, which significantly exceeds the Moon in mass, leads to the fact that the curvature of the lunar heliocentric orbit periodically changes.

The movement of the Earth and the Moon in space and the change in their relative position relative to the Sun are shown in the diagram.

Circulating around the Earth, the Moon moves in orbit at a speed of 1 km/sec, that is, slowly enough not to leave its orbit and “fly” into space, but also fast enough not to fall to the Earth. Directly answering the author of the question, we can say that the Moon will fall to the Earth only if it does not move in orbit, i.e. If external forces(some cosmic hand) stop the Moon in its orbit, it will naturally fall to Earth. However, this will release so much energy that talking about the Moon falling on Earth is like solid no need to.

And also by the movement of the Moon.

For clarity, the model of the Moon’s movement in space is simplified. At the same time, we will not lose mathematical and celestial-mechanical rigor if, taking a simpler option as a basis, we do not forget to take into account the influence of numerous factors disturbing the movement.

Assuming the Earth is motionless, we can imagine the Moon as a satellite of our planet, the movement of which obeys Kepler’s laws and occurs along an elliptical orbit. According to a similar scheme, the average value of the eccentricity of the lunar orbit is e = 0.055. The semimajor axis of this ellipse is equal in magnitude to the average distance, i.e. 384,400 km. At the apogee, at the greatest distance, this distance increases to 405,500 km, and at perigee (at the shortest distance) it is 363,300 km. The plane of the lunar orbit is inclined to the ecliptic plane at a certain angle.

Above is a diagram explaining geometric meaning elements of the Moon's orbit.

The elements of the Moon's orbit describe the average, unperturbed motion of the Moon,

However, the influence of the Sun and planets causes the Moon's orbit to change its position in space. The line of nodes moves in the plane of the ecliptic in the direction opposite to the movement of the Moon in its orbit. Consequently, the longitude value of the ascending node is constantly changing. The line of nodes completes a full rotation in 18.6 years.

Relevance:

On April 12, our country remembers a grandiose event - human flight into space. In class we also discussed the topic of space and drew pictures. And the teacher asked us to prepare interesting reports about space. That’s why I chose this particular topic, because I myself am interested in it. And on the eve of this “Cosmonautics Day” holiday, this is relevant for us, I think it will interest you too.

My guesses:

At home, I took out the encyclopedia “Celestial Bodies” and began to read. Then I asked myself, maybe the Moon will fall on us? I replied that the Moon would probably fall if it approached the Earth. Or maybe something holds it with the Earth, so it doesn’t fall and doesn’t fly away anywhere.

The purpose and objectives of my work:

I decided to study in more detail the literature, how the Moon was formed, how it affects the Earth, what connects it with the Earth, and why the Moon does not fly into space and does not fall on the Earth. And here's what I found out.

Introduction

In astronomy, a satellite is a body that revolves around a large body and is held by the force of its gravity. The Moon is a satellite of the Earth. The Earth is a satellite of the Sun. The Moon is a solid, cold, spherical celestial body that is 4 times smaller than the Earth.

The Moon is the celestial body closest to Earth. If it were possible, a tourist would walk to the moon for 40 years

The Earth-Moon system is unique in the solar system, since no planet has such a large satellite. The Moon is the only satellite of the Earth.

It is visible to the naked eye better than any planet through a telescope. Our satellite hides many mysteries.

The Moon is so far the only cosmic body visited by man. The Moon revolves around the Earth in the same way that the Earth revolves around the Sun (see Fig. 1).

The distance between the centers of the Moon and the Earth is approximately 384,467 km.

What does the Moon look like?

The Moon is not at all like the Earth. There is no air, no water, no life. The concentration of gases near the surface of the Moon is equivalent to a deep vacuum. Due to the lack of atmosphere, its gloomy, dusty expanses heat up to + 120 ° C during the day and freeze at night or just in the shade to - 160 ° C. The sky on the Moon is always black, even during the day. The huge disk of the Earth appears from the Moon to be more than 3.5 times larger than the Moon from the Earth, and hangs almost motionless in the sky (see Fig. 2).

The entire surface of the Moon is pitted with craters called craters. You can see them by looking closely at the Moon on a clear night. Some craters are so large that a huge city could fit inside them. There are two main options for the formation of craters - volcanic and meteorite.

The surface of the Moon can be divided into two types: very old mountainous terrain (lunar continent) and relatively smooth and younger lunar maria.

Lunar maria, which make up approximately 16% of the lunar surface, are huge craters created by collisions with celestial bodies that were later flooded with liquid lava. Lunar seas names were given: Sea of ​​Crises, Sea of ​​Abundance, Sea of ​​Tranquility, Sea of ​​Rains, Sea of ​​Clouds, Sea of ​​Moscow and others.

Compared to the Earth, the Moon is very small. The radius of the Moon is 1738 km, the volume of the Moon is 2% of the volume of the Earth, and the area is approximately 7.5%

How was the Moon formed?

The Moon and the Earth are almost the same age. Here is one version of the formation of the Moon.

1. Soon after the formation of the Earth, a huge celestial body crashed into it.

2. From the impact it shattered into many fragments.

3. Under the influence of gravity (attraction) of the Earth, the fragments began to revolve around it.

4. Over time, the fragments came together and formed the Moon.

Moon phases

The moon changes its appearance every day. At first the crescent is narrow, then the Moon gets fuller and after a few days becomes round. A few more days full moon gradually becomes smaller and smaller and again becomes like a sickle. The crescent moon is often called the month. If the sickle is turned convex to the left, like the letter “C,” then they say that the Moon is “aging.” 14 days and 19 hours after the full moon, the old month will disappear completely. The moon is not visible. This phase of the Moon is called “new moon”. Then gradually the Moon turns from a narrow crescent turned to the right into a full Moon again.

For the moon to “grow” again, the same period of time is required: 14 days and 19 hours. Changing the appearance of the Moon, i.e. The change in lunar phases, from full moon to full moon, occurs every four weeks, more precisely in 29 and a half days. This is a lunar month. It served as the basis for compiling lunar calendar. During a full moon, the Moon faces the Earth with its illuminated side, and during a new moon, with its unlit side. Revolving around the Earth, the moon turns towards it either as a fully illuminated surface, or as a partially illuminated surface, or as a dark surface. That is why the appearance of the Moon continuously changes throughout the month.

Ebbs and flows

The gravitational forces between the Earth and the Moon cause some interesting effects. The most famous of them is sea ​​tides and low tides. The difference between high and low tide levels in open areas of the ocean is small and amounts to 30–40 cm. However, near the coast, due to the run-up of a tidal wave onto a hard bottom, a tidal wave increases in height in the same way as ordinary wind waves of the surf.

Taking into account the direction of rotation of the Moon around the Earth, it is possible to create a picture of a tidal wave following the ocean. The maximum tidal wave amplitude on Earth is observed in the Bay of Fundy in Canada and is 18 meters.

Lunar exploration

The moon has attracted the attention of people since ancient times. The invention of telescopes made it possible to distinguish finer details of the relief (surface shape) of the Moon. One of the first lunar maps was compiled by Giovanni Riccioli in 1651, he also gave names to large dark areas, calling them “seas,” which we still use today. In 1881, Jules Janssen compiled a detailed “Photographic Atlas of the Moon.”

With the beginning space age our knowledge of the Moon has increased significantly. The Moon was first visited by the Soviet spacecraft Luna 2 on September 13, 1959.

For the first time I was able to look at reverse side The Moon in 1959, when the Soviet station Luna 3 flew over it and photographed a part of its surface invisible from Earth.

The American manned mission to the Moon was called Apollo.

The first landing took place on July 20, 1969, and the first person to set foot on the surface of the Moon was the American Neil Armstrong. Six expeditions visited the Moon, but last time this was back in 1972, since expeditions are very expensive. Each time, two people landed on it and spent up to three days on the Moon. New expeditions are currently being prepared.

Why doesn't the Moon fall to Earth?

The moon would instantly fall to the Earth if it were stationary. But the Moon does not stand still, it revolves around the Earth.

When we throw an object, such as a tennis ball, gravity pulls it towards the center of the earth. Even a tennis ball thrown at high speed will still fall to the ground, but the pattern will change if the object is much further away and moving much faster.

My experience:

I asked my dad this question and he explained it to me simple example. We tied an ordinary eraser to a thread. Imagine that you are the Earth and the eraser is the moon, and start spinning it. The eraser on the thread will literally tear out of your hand, but the thread will not let it go. The moon is so far away and moving so fast that it never falls in the same direction. Even if it falls constantly, the moon will never fall to the ground. Instead, it moves around the earth in a constant path.

If we rotate the eraser very hard, the thread will break, and if we rotate it slowly, the eraser will fall.

We conclude: if the moon moved even faster, it would overcome the gravity of the earth and fly into space; if the moon moved slower, gravity would pull it to the earth. This precise balance of gravitational speed creates what we call an orbit, where the smaller celestial body constantly orbits the larger one.

The force that prevents the Moon from “escaping” during rotation is the force of gravity of the Earth. And the force that prevents the Moon from falling to Earth is centrifugal force, which occurs when the Moon rotates around the Earth.

Revolving around the Earth, the Moon moves in orbit at a speed of 1 km/sec, that is, slowly enough not to leave its orbit and “fly” into space, but also fast enough not to fall to the Earth.

By the way...

You will be surprised, but in fact the Moon... is moving away from the Earth at a speed of 3-4 cm per year! The movement of the Moon around the Earth can be imagined as a slowly unwinding spiral. The reason for this trajectory of the Moon is the Sun, which attracts the Moon 2 times stronger than the Earth.

Why then does the Moon not fall on the Sun? But because the Moon, together with the Earth, rotates, in turn, around the Sun, and the attractive effect of the Sun is completely spent on constantly transferring both of these bodies from a straight path to a curved orbit.

– The Moon itself does not glow, it only reflects the light falling on it. sunlight;

– The Moon rotates around its axis in 27 Earth days; during the same time it makes one revolution around the Earth;

– The moon, revolving around the earth, always faces us with one side, its reverse side remains invisible to us;

– The Moon, moving in its orbit, gradually moves away from the Earth by about 4 cm per year.

– The force of gravity on the Moon is 6 times less than on Earth.

Therefore, it is much easier for a rocket to take off from the Moon than from the Earth.

It is possible that soon on long interplanetary voyages spaceships will be sent not from the Earth, but from the Moon.

With the beginning this century China has announced its readiness to explore the Moon, as well as build several inhabited lunar bases there. After this statement, space organizations of leading countries, and in particular the USA (NASA) and ESA (European Space Agency), again launched their space programs.

What will come of this?

We'll see in 2020. It was this year that George Bush planned to land people on the moon. This date is ten years ahead of China, since in their space program it was said that the creation of inhabited lunar bases and the landing of people on them will take place only in 2030.

The Moon is the most studied celestial body, but for humans it still conceals many mysteries: perhaps it is the base extraterrestrial civilizations, perhaps life on Earth would be completely different if there were no Moon, perhaps in the future people will settle on the Moon...

Conclusions:

So, we found out that the Moon is a natural satellite of the Earth, it revolves around our planet and, together with the Earth, moves in orbit around the Sun;

– the question of the origin of the Moon still remains controversial;

– changes in the shape of the Moon are called phases. They exist only for us

One of my assumptions turned out to be correct, the Moon is really held up by something, and this is the Earth’s gravitational force and centrifugal force.

And my other assumption, that the Moon will fall if it approaches the Earth, is not entirely correct. The Moon will fall to the Earth when the Moon stops rotating and is motionless, and then the centrifugal force will not work.

Studying encyclopedias and the Internet, I learned a lot of new and interesting things. I will definitely share these discoveries with my classmates in the world around us lesson.

We managed to solve some of the mysteries of the Moon, but this did not make it any less interesting and attractive!

Used literature:

1. “Space. Supernova Atlas of the Universe”, M., “Eksmo”, 2006.

2. New school encyclopedia“Heavenly Bodies”, M., “Rosmen”, 2005

3. “Pochemuchka” Children's Encyclopedia, M., “Rosmen”, 2005.

4. “What is it? Who is this?” Children's Encyclopedia, M.,”Pedagogy –

Press“1995

5. Internet – reference books, pictures about space.

Completed: 3B grade student

Khaliullin Ildar

Supervisor: Sakaeva G.Ch.

Municipal educational institution secondary school No. 79, Ufa

One ancient Greek, supposedly Plutarch, said: as soon as the Moon slows down, it will immediately fall to the Earth, like a stone released from a sling. This was said back when stars, not meteorites, were falling. Seventeen centuries later, Galileo, armed not only with the art of reasonable generalizations, but also with a telescope, continued: The Moon, they say, does not slow down because it moves by inertia, and obviously nothing prevents this movement. He said how he cut it. Another two hundred years later, Newton added his two cents: they say, dear ones, if the Moon moved only by inertia, it would move in a straight line, having long ago disappeared into the abyss of the Universe; The Earth and the Moon are held next to each other by the force of mutual gravity, forcing the latter to move in a circle. Moreover, he said, gravity, being most likely the root cause of any movement in the Universe, is capable of even accelerating the slightly slower run of the Moon in certain sections of the elliptical (Kepler) orbit... A hundred years later, Cavendish, using lead balls and torsion balances, proved the existence of mutual force gravity. That's it. Therefore, it is inertia and gravity, forcing the Moon to move in a closed orbit, that are the reasons that prevent the Moon from falling to the Earth. In short, if the gravitational mass of the Earth suddenly increases, then the Moon will only move away from it in its higher orbit. But... The satellites of the planets cannot have any closed orbits - circular or elliptical. Now we will look at the joint “fall” of the Earth and the Moon on the Sun and make sure of this. So, the Earth and the Moon have been “falling” together in the gravitational space of the Sun for about 4 billion years. At the same time, the speed of the Earth relative to the Sun is approximately 30 km/s, and the Moon – 31. In 30 days, the Earth travels along its trajectory 77.8 million km (30 x 3600 x 24 x 30), and the Moon – 80.3. 80.3 – 77.8 = 2.5 million km. The radius of the Moon's orbit is approximately 400,000 km. Therefore, the circumference of the Moon’s orbit is 400,000 x 2 x 3.14 = 2.5 million km. Only in our reasoning, 2.5 million km is already the “curvature” of the almost straight trajectory of the Moon. A large-scale display of the trajectories of the Earth and the Moon may also look like this: if there are 1 million km in one cell, then the path traveled by the Earth and the Moon in a month will not fit into the entire spread of a notebook in a cell, while the maximum distance between the Moon’s trajectory and the Earth’s trajectory in the full moon and new moon phases it will be equal to only 2 millimeters. However, you can take a segment of arbitrary length, indicating the path of the Earth, and draw the movement of the Moon over a month. The movement of the Earth and the Moon occurs from right to left, that is, counterclockwise. If we have the Sun somewhere at the bottom of the picture, then on the right side of the picture we will mark the Moon in the full moon phase with a dot. Let the Earth at this time be exactly under this point. In 15 days, the Moon will be in the new moon phase, that is, right in the middle of our segment and just under the Earth in the figure. On the left side of the figure we again denote the positions of the Moon and Earth in the full moon phase with dots. Over the course of a month, the Moon crosses the trajectory of the Earth twice at the so-called nodes. The first node will be approximately 7.5 days from the full moon phase. From the Earth at this time, just half of the lunar disk is visible. This phase is called the first quarter, since by this time the Moon has completed a quarter of its monthly path. The second time the Moon crosses the Earth's trajectory is in the last quarter, that is, approximately 7.5 days from the new moon phase. Did you draw it? Here’s what’s interesting: the Moon at the first quarter node is 400,000 km ahead of the Earth, and at the last quarter node it is already 400,000 km behind it. It turns out that the Moon “along the upper crest of the wave” moves with acceleration, and “along the lower crest” - with deceleration; the path of the Moon from the last quarter node to the first quarter node is 800,000 km longer. Of course, the Moon in its movement along the “upper arc” does not accelerate spontaneously, it is the Earth with its gravitational mass that captures it and, as it were, throws it over itself. It is this property of moving planets - to capture and throw - that is used to accelerate space probes during the so-called gravitational maneuver. If the probe crosses the path of the planet in front of it, then we have a gravitational maneuver with the probe slowing down. It's simple. The full moon phase repeats after 29 days, 12 hours and 44 minutes. This is the synodic period of the Moon's revolution. Theoretically, the Moon should complete its orbital journey in 27 days, 7 hours and 43 minutes. This is the sidereal period of revolution. The “inconsistency” of two days in textbooks is explained by the movement of the Earth and the Moon per month relative to the round Sun. We explained this by the absence of any orbit on the Moon. So, Newton explained the “non-fall” of the Moon on the Earth by its temporary accelerations when moving along an elliptical orbit. We, I think, explained this even more simply. And most importantly - more correctly. Viktor Babintsev

Everything in this world is attracted to everything. And for this you do not need to have any special properties ( electric charge, participate in rotation, have a size no less than some.). It is enough to simply exist, just as a person or the Earth or an atom exists. Gravity or, as physicists often say, gravity is the most universal interaction. And yet: everything is attracted to everything. But how exactly? By what laws? Surprisingly, this law is the same, and moreover, it is the same for all bodies in the Universe - both for stars and for electrons.

1. Kepler's laws

Newton argued that between the Earth and all material bodies there is a force of gravity, which is inversely proportional to the square of the distance.

In the 14th century, the Danish astronomer Tycho Brahe spent almost 20 years observing the movements of the planets and recording their positions, and was able to determine their coordinates at various times with the greatest possible accuracy at that time. His assistant, mathematician and astronomer Johannes Kepler, analyzed the teacher’s notes and formulated three laws of planetary motion:

Kepler's first law

Every planet solar system revolves in an ellipse, at one of the foci of which the Sun is located. The shape of the ellipse, the degree of its similarity to a circle will then be characterized by the ratio: e=c/d, where c is the distance from the center of the ellipse to its focus (half the focal length); a - semi-major axis. The quantity e is called the eccentricity of the ellipse. At c = 0 and e = 0, the ellipse turns into a circle with radius a.

Kepler's Second Law (Law of Areas)

Each planet moves in a plane passing through the center of the Sun, and the area of ​​the orbital sector, described by the radius vector of the planets, changes in proportion to time.

In relation to our Solar system, two concepts are associated with this law: perihelion - the point of the orbit closest to the Sun, and aphelion - the most distant point of the orbit. Then we can say that the planet moves unevenly around the Sun: having linear speed more at perihelion than at aphelion.

Every year at the beginning of January, the Earth moves faster when passing through perihelion; therefore, the apparent movement of the Sun along the ecliptic to the east also occurs faster than the average year. At the beginning of July, the Earth, passing aphelion, moves more slowly, and therefore the movement of the Sun along the ecliptic slows down. The law of areas indicates that the force governing the orbital motion of planets is directed towards the Sun.

Kepler's Third Law (Harmonic Law)

Kepler's third, or harmonic, law relates the average distance of a planet from the Sun (a) to its orbital period (t):

where indices 1 and 2 correspond to any two planets.

Newton took up Kepler's baton. Fortunately, many archives and letters remain from England in the 17th century. Let's follow Newton's reasoning.

It must be said that the orbits of most planets differ little from circular ones. Therefore, we will assume that the planet moves not along an ellipse, but along a circle of radius R - this does not change the essence of the conclusion, but greatly simplifies the mathematics. Then Kepler's third law (it remains in force, because a circle is special case ellipse) can be formulated as follows: the square of the time of one revolution in orbit (T2) is proportional to the cube of the average distance (R3) from the planet to the Sun:

T2=CR3 (experimental fact).

Here C is a certain coefficient (the constant is the same for all planets).

Since the time of one revolution T can be expressed through the average speed of the planet’s orbit v: T=2(R/v), then Kepler’s third law takes the following form:

Or after the reduction 4(2 /v2=CR.

Now let us take into account that, according to Kepler’s second law, the movement of the planet along a circular trajectory occurs uniformly, i.e., with a constant speed. From kinematics we know that the acceleration of a body moving in a circle with constant speed, will be purely centripetal and equal to v2/R. And then the force acting on the planet, according to Newton’s second law, will be equal to

Let's express the ratio v2/R from Kepler's law v2/R=4(2 /CR2 and substitute it into Newton's second law:

F= m v2/R=m4(2/СR2 = k(m/R2), where k=4(2/С is a constant value for all planets.

So, for any planet, the force acting on it is directly proportional to its mass and inversely proportional to the square of its distance from the Sun:

The sun is the source of force acting on the planet, follows from Kepler's first law.

But if the Sun attracts a planet with a force F, then the planet (according to Newton’s third law) must attract the Sun with the same magnitude force F. Moreover, this force, by its nature, is no different from the force from the Sun: it is also gravitational and, as we showed, it should also be proportional to the mass (this time - the Sun) and inversely proportional to the square of the distance: F=k1(M/R2), here the coefficient k1 is different for each planet (perhaps it even depends on its mass!) .

Equating both gravitational forces, we get: km=k1M. This is possible provided that k=(M, and k1=(m, i.e. with F=((mM/R2), where ( is a constant - the same for all planets.

Therefore, the universal gravitational constant (cannot be any - with the units of magnitude we have chosen - only the one that nature chose it. Measurements give an approximate value (= 6.7 x10-11 N. m2 / kg2.

2. The law of universal gravitation

Newton obtained a remarkable law describing the gravitational interaction of any planet with the Sun:

The consequences of this law were all three of Kepler's laws. It was a colossal achievement to find (one!) law governing the motion of all the planets in the solar system. If Newton had limited himself to only this, we would still remember him when studying physics at school and would call him an outstanding scientist.

Newton was a genius: he proposed that the same law governed gravitational interaction of any body, it describes the behavior of the Moon orbiting the Earth and an apple falling to the Earth. It was an amazing thought. After all, the general opinion was - celestial bodies move according to their own (heavenly) laws, and earthly bodies - according to their own, “worldly” rules. Newton assumed the unity of the laws of nature for the entire Universe. In 1685, I. Newton formulated the law of universal gravitation:

Any two bodies (or rather, two material points) are attracted towards each other with a force directly proportional to their masses and inversely proportional to the square of the distance between them.

The law of universal gravitation is one of the best examples showing what a person is capable of.

The gravitational force, unlike friction and elastic forces, is not a contact force. This force requires two bodies to touch each other for them to interact gravitationally. Each of the interacting bodies creates a gravitational field in the entire space around itself - a form of matter through which the bodies gravitationally interact with each other. The field created by some body manifests itself in the fact that it acts on any other body with a force determined by the universal law of gravity.

3. Movement of the Earth and Moon in space.

The Moon, a natural satellite of the Earth, in the process of its movement in space is influenced mainly by two bodies - the Earth and the Sun. Let's calculate the force with which the Sun attracts the Moon, applying the law of universal gravitation, we find that the solar attraction is twice as strong as the earth's.

Why doesn't the Moon fall on the Sun? The fact is that both the Moon and the Earth revolve around a common center of mass. The common center of mass of the Earth and Moon revolves around the Sun. Where is the center of mass of the Earth-Moon system? The distance from the Earth to the Moon is 384,000 km. The ratio of the mass of the Moon to the mass of the Earth is 1:81. The distances from the center of mass to the centers of the Moon and Earth will be inversely proportional to these numbers. Dividing 384,000 km by 81 gives approximately 4,700 km. This means that the center of mass is located at a distance of 4700 km from the center of the Earth.

* What is the radius of the Earth?

* About 6400 km.

* Consequently, the center of mass of the Earth-Moon system lies inside the globe. Therefore, if we do not strive for accuracy, we can talk about the Moon’s revolution around the Earth.

The movements of the Earth and the Moon in space and changes in their relative position in relation to the Sun are shown in the diagram.

With a twofold predominance of solar gravity over the earth's, the curve of the Moon's motion should be concave in relation to the Sun at all its points. The influence of the nearby Earth, which significantly exceeds the Moon in mass, leads to the fact that the curvature of the lunar heliocentric orbit periodically changes.

The Moon revolves around the Earth, held by gravity. With what force does the Earth attract the Moon?

This can be determined by the formula expressing the law of gravity: F=G*(Mm/r2) where G is the gravitational constant, Mm is the masses of the Earth and the Moon, r is the distance between them. Having made calculations, we came to the conclusion that the Earth attracts the Moon with a force of about 2-1020 N.

The entire effect of the force of attraction of the Moon by the Earth is expressed only in keeping the Moon in orbit, in imparting centripetal acceleration to it. Knowing the distance from the Earth to the Moon and the number of revolutions of the Moon around the Earth, Newton determined centripetal acceleration Moon, we got the number we already know: 0.0027 m/s2. The good agreement between the calculated value of the Moon's centripetal acceleration and its actual value confirms the assumption that the force holding the Moon in orbit and gravity are of the same nature. The moon could be held in orbit by a steel cable with a diameter of about 600 km. But, despite such a huge gravitational force, the Moon does not fall to the Earth.

The Moon is removed from the Earth at a distance equal to approximately 60 Earth radii. Therefore, Newton reasoned. The Moon, falling with such acceleration, should approach the Earth by 0.0013 m in the first second. But the Moon, in addition, moves by inertia in the direction of instantaneous speed, i.e. along a straight line tangent at a given point to its orbit around the earth

Moving by inertia, the Moon should move away from the Earth, as calculations show, in one second by 1.3 mm. Of course, such a movement in which in the first second the Moon would move radially towards the center of the Earth, and in the second second – along a tangent, does not actually exist. Both movements are continuously added. As a result, the Moon moves along a curved line, close to a circle.

Revolving around the Earth, the Moon moves in orbit at a speed of 1 km/sec, that is, slowly enough not to leave its orbit and “fly” into space, but also fast enough not to fall to the Earth. We can say that the Moon will fall to the Earth only if it does not move in orbit, that is, if external forces (some kind of cosmic hand) stop the Moon in its orbital movement, then it will naturally fall to the Earth. However, this will release so much energy that it is impossible to talk about the Moon falling onto the Earth as a solid body. From all of the above we can draw a conclusion.

The moon is falling, but it cannot fall. And here's why. The movement of the Moon around the Earth is the result of a compromise between the two “desires” of the Moon: to move by inertia - in a straight line (due to the presence of speed and mass) and to fall “down” to the Earth (also due to the presence of mass). You can say this: universal law Gravity encourages the Moon to fall to the Earth, but Galileo's law of inertia "persuades" it not to pay attention to the Earth at all. The result is something in between - orbital motion: a constant, endless fall.