The force of gravity on the moon g. What is gravity? Like stones in a well

As science knows, the moon is natural satellite Earth, a spherical celestial body, cold, but not cooled (it is believed that the Moon was originally cold). The Moon is located at a distance of 384,000 kilometers from the Earth, its radius is 1738 kilometers. There is no water on the Moon, no atmosphere, and any weight there is six times lighter than on Earth.

There is no water on the moon. But its connection with water is the most direct.

Most Earth's surface is covered by seas and oceans. There is a lot of water on our planet. If it were not so, life would hardly have appeared here. All living things need a large amount of fluid. The human body is more than sixty percent water. This is water, which is contained in the composition of every cell of the body, and blood, and other fluids.

The ebb and flow of the terrestrial seas and oceans are connected with the Moon. Moon with huge force attracts the water surface of the part of the Earth over which it is located. Imagine: a huge tidal wave all the time "runs" after the moon along earth's surface when the moon makes a complete revolution around the earth.

This happens for a completely natural reason - according to the law gravity, which operates throughout the universe. Everything celestial bodies, including the Sun, Moon and Earth, have an attractive force - some more, others less, depending on their size. It is thanks to this force that we all stand firmly on the ground: the forces of gravity, the forces of gravity attract us. Due to the force of solar attraction, the Earth revolves around the Sun and does not fly away from it. And the Earth's gravity keeps the Moon in Earth orbit.

The moon is much smaller than the Earth, and therefore it is, of course, not able to attract the Earth to itself. But it can attract terrestrial water masses. And not only them: scientists have found that the Moon deforms even the solid shell of the Earth by gravity, stretching it by about 50 centimeters! The Earth seems to be breathing all the time, inhaling and exhaling with its different parts following the attraction of the Moon moving around it.

But the deformation of the solid surface of the Earth is less noticeable to us than the ebbs and flows. This phenomenon was observed by everyone who was by the sea. Arriving at the beach in the morning, you see that the water has receded, exposing the coastal stones, leaving algae and jellyfish on the wet pebbles. And after a few days it turns out that the strip of the beach, on which you were conveniently located yesterday for relaxation, today disappeared under water.

The strongest tides occur on the new moon. Why? Because in the new moon, both the Sun and the Moon are on the same side of the Earth. Therefore, at the new moon, the moon is not visible in the sky: the sun at this time illuminates it reverse side. At this moment, the attraction of the Sun is added to the attraction of the Moon and both luminaries pull the Earth in one direction. Ground water masses rush in this direction. The tide begins, while the tide is observed on the opposite side of the Earth.

During a full moon, the Sun and Moon are on opposite sides of the Earth; The Earth is between the Sun and the Moon, and both luminaries are on opposite sides of it. Then the water masses partly rush towards the Sun, and partly towards the Moon, tides are observed both there and there, but less than on a new moon.

In other phases of the Moon - when the Moon and the Sun are not on the same side of the Earth, and not on opposite sides, but occupy intermediate positions - the ebbs and flows are almost imperceptible, since the Sun and Moon neutralize each other's attraction and the water shell is distributed evenly over the entire the surface of the earth.

Since there is a lot of water on Earth, the earth's climate depends on the state of water. Oceans and seas are the kitchen where earthly weather is “cooked”. And of course, any change in the state of the seas and oceans immediately affects the state of the weather. Weather changes are directly related to the tides. The behavior of the atmosphere depends on this, the emergence of cyclones and anticyclones in it, and hence the humidity of the air, the direction and speed of the wind, and other factors. And our well-being and many processes in the body depend on the weather: changes in blood pressure, blood flow velocity, activity of various organs - you can’t list everything. Not to mention the mood and state of the nerves, psyche, soul - all this is directly affected by the weather. Sunny, clear weather excites and tones us, quiet, cloudy - soothes, low clouds depress, and a strong wind with dampness and cold can lead to depression.

We depend on the weather, the weather originates in the oceans, and the state of the oceans is related to the moon. It turns out that our state ultimately depends on the moon.

But this is just one example of the not very strong and very indirect influence of the Moon on us - through the ebbs and flows of the seas and oceans. In addition, the Moon affects us in many other ways - absolutely directly and very diversely.

As we already know, the human body is more than sixty percent water. But if the Moon attracts earthly water, then the water that is part of our body is no exception.

At the new moon, at the strongest tides, the water inside the body, together with the water of the seas and oceans, rushes up to the Moon. At this moment, it seems that we have become lighter, that we are not walking, but as if we are flying above the ground, and we even want to jump, our legs themselves come off the ground. At this time, you need to be more careful - not to lose your balance and fulcrum in the physical and mental sense. It is difficult to be active, to go about your usual earthly affairs - after all, the body, as it were, breaks away from the earth, it is pulled upwards.

After the new moon, the attraction of the moon weakens and we quietly descend from heaven to earth. The attraction of the Earth again affects us with the usual force. We again acquire the usual sense of our own weight. You can gradually return to normal activity and daily affairs, it's easier now.

As the lunar crescent grows and approaches the full moon, the Sun and Moon diverge further and further. They begin to attract all terrestrial liquids from different sides. And our body begins to burst, as it were, liquids stretch in different directions, the process of expansion is underway. Imagine: you have just been pulled up, then down, and now suddenly to the sides. This is a serious stress for the body: it just needs to have time to rebuild.

During the full moon, the Sun and the Moon act on us from opposite sides. Therefore, all liquids human body drawn closer to the surface of the body. The body bursts as much as possible from the inside, as if a void is formed inside, but energy splashes out from the outside - it literally whips with a powerful stream.

But now the Moon begins to decrease, and the organism, which was expanding before, passes to contraction. All liquids from the surface rush inward, energy also flows inward. Such a restructuring is stress again. But as the liquids rush inward, a person feels stronger and more active: after all, now the energy is concentrated inside, and he is ready to act, to use this energy to achieve various goals in his life.

After the maximum compression of energy inside the body, new changes occur - the new moon comes again, and the fluids again rush to the head.

As you can see, the body is not frozen in immobility: something in it is constantly changing, transforming, moving from one state to another; moreover, changes occur synchronously with the moon, and hence with the entire universe. If we know and take into account the changes taking place in us, then health, inner harmony, and well-being will come. If we live in unison with the Universe, then the Universe helps us and supports us with all its immense forces.

The waning or waxing Moon is not only the cause of terrestrial tides; the well-being of a person depends on it, which can be taken care of in advance by referring to the lunar calendar.

How exactly to take into account the lunar rhythms will be discussed more than once in this book. In the meantime, we will understand to the end the mechanisms of our relationship with the moon.

All that we have talked about is the physical influence of the moon. But there is another effect - energy.

Let us imagine that we are going on a journey through solar system. What is the force of gravity on other planets? On which ones will we be easier than on Earth, and on which ones it will be harder?

While we have not yet left the Earth, let's do the following experiment: let's mentally descend to one of the earth's poles, and then imagine that we have been transported to the equator. I wonder if our weight has changed?

It is known that the weight of any body is determined by the force of attraction (gravity). It is directly proportional to the mass of the planet and inversely proportional to the square of its radius (we first learned about this from a school physics textbook). Therefore, if our Earth were strictly spherical, then the weight of each object when moving over its surface would remain unchanged.

But the Earth is not a sphere. It is flattened at the poles and elongated along the equator. The equatorial radius of the Earth is 21 km longer than the polar one. It turns out that the force of gravity acts on the equator as if from afar. That is why the weight of the same body in different parts of the Earth is not the same. The heaviest objects should be at the earth's poles and the easiest - at the equator. Here they become 1/190 lighter than their weight at the poles. Of course, this change in weight can only be detected using a spring balance. A slight decrease in the weight of objects at the equator also occurs due to the centrifugal force arising from the rotation of the Earth. Thus, the weight of an adult person arriving from the high polar latitudes to the equator will decrease by a total of approximately 0.5 kg.

Now it is appropriate to ask: how will the weight of a person traveling through the planets of the solar system change?

Our first space station is Mars. How much would a person weigh on Mars? It is not difficult to make such a calculation. To do this, you need to know the mass and radius of Mars.

As is known, the mass of the "red planet" is 9.31 times less than the mass of the Earth, and the radius is 1.88 times smaller than the radius of the globe. Consequently, due to the action of the first factor, the force of gravity on the surface of Mars should be 9.31 times less, and due to the second - 3.53 times greater than ours (1.88 * 1.88 = 3.53 ). Ultimately, it is there a little more than 1/3 of the earth's gravity (3.53: 9.31 = 0.38). In the same way, one can determine the stress of gravity on any celestial body.

Now let's agree that on Earth an astronaut-traveler weighs exactly 70 kg. Then for other planets we get the following weight values ​​(the planets are arranged in order of increasing weight):

Pluto 4.5 Mercury 26.5 Mars 26.5 Saturn 62.7 Uranus 63.4 Venus 63.4 Earth 70.0 Neptune 79.6 Jupiter 161.2
As you can see, the Earth occupies an intermediate position between the giant planets in terms of gravity. On two of them - Saturn and Uranus - the force of gravity is somewhat less than on Earth, and on the other two - Jupiter and Neptune - more. True, for Jupiter and Saturn, the weight is given taking into account the action of centrifugal force (they rotate rapidly). The latter reduces body weight at the equator by a few percent.

It should be noted that for the giant planets, the weight values ​​are given at the level of the upper cloud layer, and not at the level of the solid surface, as for terrestrial planets (Mercury, Venus, Earth, Mars) and Pluto.

On the surface of Venus, a person will be almost 10% lighter than on Earth. On the other hand, on Mercury and Mars, the weight reduction will occur by a factor of 2.6. As for Pluto, a person will be 2.5 times lighter on it than on the Moon, or 15.5 times lighter than on Earth.

But on the Sun, gravity (attraction) is 28 times stronger than on Earth. Human body it would weigh 2 tons there and would be instantly crushed by its own weight. However, before reaching the Sun, everything would turn into hot gas. Another thing is tiny celestial bodies, such as the satellites of Mars and asteroids. On many of them, in terms of ease, you can become like ... a sparrow!

It is quite clear that a person can travel to other planets only in a special sealed spacesuit equipped with life support system devices. The weight of the American astronauts' space suit, in which they went to the surface of the moon, is approximately equal to the weight of an adult. Therefore, the values ​​given by us for the weight of a space traveler on other planets should be at least doubled. Only then will we obtain weight values ​​close to the real ones.

Objects or people, such as the hopping astronaut shown in the figure, weigh less on the Moon than on Earth, due to the weaker gravitational field of the Moon. Gravity is the fundamental gravitational force that propagates through outer space and acts on all physical bodies.

The gravitational attraction between any two bodies, for example, between a planet and a person, can be quantified if the mass of each body and the distance between them are known. Mass, which remains constant, is a quantitative measure of the matter contained in the body. As for weight, it is a measure of the force of gravity acting on a body. The stronger the gravitational field, the greater will be the weight of the body and the higher will be its acceleration; the weaker the gravitational field, the less will be the weight of the body and the less acceleration it will experience. The force characteristics of gravitational fields depend on the size of the bodies they surround, so the weight of any body is not a fixed value.

On the image Moon(left) and Earth(on right):

1. On the Moon, an astronaut's weight is reduced by six times compared to his weight on Earth, since the force of gravity on the Moon is only one-sixth of that of Earth.
2. Upon returning from the moon (fig. on the right), the astronaut shown in the figure below the text weighs six times more on Earth than he weighed on the Moon. Having more mass than the Moon, the Earth develops a higher gravitational attraction force.

Like stones in a well

In the gravitational fields shown schematically in the figure below the text, the Moon (left side of the picture) creates a smaller force of attraction than the more massive Earth (right side of the picture). Overcoming gravity is like climbing out of a well. The greater the force of gravity, the deeper the well and the steeper its walls.

The essence of the mutual gravity of bodies

The Moon and the Earth (respectively, the left and right drawings above the text) attract bodies that are near their surface; bodies in turn also create an attractive force proportional to their mass. The greater distance between the Moon and the person in the left figure and the smaller mass of the Moon contribute to a weaker gravitational connection, while for the couple in the right figure, the greater mass of the Earth provides a stronger attraction.

In this chapter, we will consider how the Moon affects the Earth itself with its gravitational field, i.e. on her body and her movement in orbit. The consequences of this impact for various terrestrial spheres - the lithosphere, hydrosphere, core, atmosphere, magnetosphere, etc., as well as for the biosphere, will be considered in the following chapters.

ATTENTION!
Graphs of the gravitational interaction of the Moon and the Earth, see using the service
MOON FACTOR

Design ratios and constants

To calculate the gravitational influence of the Moon, we use the formula of classical physics that determines the force F of mutual attraction of two bodies with masses M1 and M2, whose centers of mass are at a distance R from each other:

(1) F (n) \u003d (G x M1 x M2) / R 2,

where G = 6.67384 x 10 -11 is the gravitational constant.

This formula gives the value of the attractive force in SI units - newtons (n). For the purposes of our treatise, it will be more convenient and clearer to operate with kilograms of force (kgf), which are obtained by dividing F by a factor of 9.81, i.e.:

(2) F (kgf) = (G x M1 x M2) / (9.81 x R 2)

For further calculations, we need the following constants:

1. the mass of the moon is 7.35 x 10 22 kg;
2. the average distance from the Earth to the Moon is 384,400 km;
3. the average radius of the Earth - 6371 km;
4. the mass of the Sun is 1.99 x 10 30 kg;
5. the average distance from the Earth to the Sun is 149.6 million km;

Lunar attraction on earth

In accordance with formula (2), the force of attraction by the Moon of a body with a mass of 1 kg, located in the center of the Earth, with a distance between the Moon and the Earth equal to its average value, is equal to:

(3) F \u003d (6.67 x 10 -11 x 7.35 x 10 22 x 1) / (9.81 x 384400000 2) \u003d 0.000003382 kgf

those. only 3.382 micrograms. For comparison, we calculate the force of attraction of the same body by the Sun (also for the average distance):

(4) F \u003d (6.67 x 10 -11 x 1.99 x 10 30 x 1) / (9.81 x 149600000000 2) \u003d 0.000604570 kgf,

those. 604.570 micrograms, which is almost 200 (two hundred!) times greater than the gravitational force of the Moon.

In addition, the weight of a body located on the surface of the Earth changes to a much more significant extent due to the deviation of the Earth's shape from the ideal, the uneven topography and density, and the influence of centrifugal forces. So, for example, the weight of a body weighing 1 kg at the poles is more than the weight at the equator by about 5.3 grams, and one third of this difference is due to the oblateness of the Earth from the poles, and two thirds is due to centrifugal force at the equator directed against gravity.

As can be seen, the direct gravitational effect of the Moon on a specific body located on the Earth is literally microscopic and, at the same time, is significantly inferior to the gravitational effect of the Sun and geophysical anomalies.

lunar gravity gradient

Let's turn to Fig.3.1. For the average value of the distance Earth - Moon, the force of attraction by the Moon of a body with a mass of 1 kg, located on the surface of the Earth at the point closest to the Moon, is 3.495 micrograms, which is 0.113 micrograms more than the force of attraction of the same body, but located in the center of the Earth. The force of attraction of a body located on the surface of the Earth by the Sun (also for the average distance) will be 604.622 micrograms, which is more than the force of attraction of the same body, but located in the center of the Earth, by 0.052 micrograms.

Fig.3.1 Lunar and solar gravity

Thus, despite the immeasurably smaller mass of the Moon compared to the Sun, the gradient of its gravitational force in the Earth's orbit is, on average, more than two times greater than the gradient of the Sun's gravitational force.

To illustrate the effect of the gravitational field of the Moon on the body of the Earth, let us turn to Fig. 3.2.

Fig.3.2 Influence of the gravitational field of the Moon on the body of the Earth.

This figure represents a very, very simplified picture of the reaction of the Earth's body to the influence of lunar gravity, but it reliably reflects the essence of the process - a change in the shape of the globe under the influence of the so-called. tidal (or tide-forming) forces directed along the Earth-Moon axis, and the forces of elasticity of the Earth's body that counteract them. Tidal forces arise from the fact that points of the Earth located closer to the Moon are attracted to it more strongly than points located farther from it. In other words, the deformation of the Earth's body is a consequence of the gradient of the Moon's attraction force and the forces of elasticity of the Earth's body that counteract it. As a result of these forces, the size of the Earth increases in the direction of tidal forces and decreases in the transverse direction, as a result of which a wave called a tidal wave forms on the surface. This wave has two maxima located on the Earth-Moon axis and moving along the Earth's surface in the direction opposite to the direction of its rotation. The amplitude of the wave depends on the latitude of the area and the current parameters of the Moon's orbit and can reach several tens of centimeters. It will have a maximum value at the equator when the Moon passes its perigee.

The sun also causes a tidal wave in the body of the Earth, but much smaller due to the smaller gradient of its gravitational force. The joint gravitational effect of the Moon and the Sun on the body of the Earth depends on their relative position. The maximum value of tidal forces and, accordingly, the maximum amplitude of the tidal wave is achieved when all three objects are located on the same axis, i.e. in the state of the so-called. syzygy(alignment), which takes place during a new moon (Moon and Sun in "conjunction") or a full moon (Moon and Sun in "opposition"). The configuration data is illustrated in fig. 3.3 and 3.4.

Fig.3.3 Joint influence of the gravitational fields of the Moon and the Sun on the body of the Earth
in "conjunction" (on the new moon).

Fig.3.4 Joint influence of the gravitational fields of the Moon and the Sun on the body of the Earth
in "opposition" (on the full moon).

As the Moon and Sun deviate from the syzygy line, the tidal forces they cause and, accordingly, the tidal waves begin to acquire an independent character, their sum decreases, and the degree of their opposition to each other increases. The counteraction reaches its maximum when the angle between the directions to the Moon and the Sun from the center of the Earth is 90°, i.e. these bodies are in a “square”, and the Moon, respectively, is in a quarter phase (first or last). In this configuration, the tidal forces of the Moon and the Sun act on the shape of the Earth's body in exactly the opposite way, the corresponding tidal waves on the surface are maximally separated, and their amplitude is minimal, which is illustrated in Fig. 3.5.

Fig.3.5 Joint influence of the gravitational fields of the Moon and the Sun on the body of the Earth in the "square".

The physics of terrestrial tidal processes under the influence of the gravitational fields of the Moon and the Sun is very complex and requires taking into account a large number of parameters. This topic has been developed big number various theories, many experimental studies, written a huge number of articles, monographs and dissertations. Even today in this area there are many "white" spots, conflicting points of view and alternative approaches. For those who want to delve into the problems of terrestrial tides, we can recommend fundamental research P. Melchior "Tides of the Earth" (translated from English, M., "Mir", 1968, 483 pages).

The consequence of the influence of lunar gravity on the Earth are two fundamental phenomena:

1. Lunar tides on the surface of the Earth - periodic changes in the level of the earth's surface, synchronized with the daily rotation of the Earth and the movement of the Moon in orbit.
2. The imposition of a variable component on the earth's orbit, synchronized with the rotation of the Earth-Moon system around a common center of mass.

These phenomena are the main mechanisms of the Moon's influence on the earth's spheres - the lithosphere, hydrosphere, earth's core, atmosphere, magnetosphere, etc. More on this in the next chapter.