Causes of ebb and flow. Natural phenomenon ebb and flow

The Moon moves around the Earth at an average speed of 1.02 km / s in an approximately elliptical orbit in the same direction in which the vast majority of other bodies in the Solar System move, that is, counterclockwise when viewed from the Moon's orbit from the North Pole of the World. The semi-major axis of the Moon's orbit, equal to the average distance between the centers of the Earth and the Moon, is 384,400 km (approximately 60 Earth radii). Due to the ellipticity of the orbit, the distance to the Moon fluctuates between 356,400 and 406,800 km. The period of revolution of the Moon around the Earth, the so-called sidereal month, is subject to small fluctuations from 27.32166 to 29.53 days, but also to a very small secular reduction. The moon shines only with light reflected from the sun, so one half of it, facing the sun, is illuminated, while the other is plunged into darkness. What part of the illuminated half of the moon is visible to us in this moment, depends on the position of the Moon in its orbit around the Earth. As the Moon moves in its orbit, its shape is gradually but continuously changing. The various visible shapes of the moon are called its phases.

Ebb and flow is familiar to every surfer. Twice a day, the level of ocean waters rises and falls, and in some places by a very significant amount. Every day the tide comes 50 minutes later than the previous day.

The Moon is kept in its orbit around the Earth for the reason that between these two celestial bodies there are gravitational forces that attract them to each other. The Earth always tries to pull the Moon towards itself, and the Moon pulls the Earth towards itself. Since the oceans are large masses of fluid and can flow, they are easily deformed by the Moon's gravity, taking the shape of a lemon. The ball of solid rock, which is the Earth, remains in the middle. As a result, on the side of the Earth that faces the Moon, a water bulge appears and another similar bulge appears on the opposite side.

Insofar as solid earth rotates around its axis, tides occur on the ocean shores, this happens twice during every 24 hours and 50 minutes when the ocean shores pass through water mounds. The length of the period is more than 24 hours due to the fact that the Moon itself also moves in its orbit.

Due to the ocean tides, a friction force arises between the surface of the Earth and the waters of the oceans, slowing down the speed of the Earth's rotation around its axis. Our days are gradually getting longer and longer, each century the length of the day increases by about two thousandths of a second. This is evidenced by some types of corals that grow in such a way that each day leaves a clear scar in the body of the coral. The increase varies throughout the year, so that each year has its own stripe, like an annual ring on a tree cut. Studying fossil corals dating back 400 million years, oceanologists discovered that at that time the year consisted of 400 days with a duration of 22 hours. Fossilized remains of even more ancient forms of life indicate that about 2 billion years ago, a day lasted only 10 hours. In the distant future, the length of a day will be equal to our month. The moon will always stand in the same place, since the speed of the Earth's rotation around its axis will exactly coincide with the speed of the Moon's movement in its orbit. Even now, thanks to the tidal forces between the Earth and the Moon, the Moon constantly faces the Earth with the same side, except for small fluctuations. In addition, the speed of the moon in its orbit is constantly increasing. As a result, the Moon is gradually moving away from the Earth at a rate of about 4 cm per year.

The earth casts a long shadow in space, blocking the light of the sun. When the Moon enters the Earth's shadow, a lunar eclipse occurs. If you were on the Moon during a lunar eclipse, you could see the Earth passing in front of the Sun, blocking it. Often, the Moon remains faintly visible, glowing with a dim reddish light. Although it is in shadow, the moon is illuminated by a small amount of red sunlight, which is refracted by the earth's atmosphere in the direction of the moon. A total lunar eclipse can last up to 1 hour 44 minutes. Unlike solar, lunar eclipses can be observed from any place on Earth where the Moon is above the horizon. Although the Moon passes through its entire orbit around the Earth once a month, eclipses cannot occur monthly due to the fact that the plane of the Moon's orbit is tilted relative to the plane of the Earth's orbit around the Sun. At the most, seven eclipses can occur in a year, of which two or three must be lunar. solar eclipses occur only on the new moon, when the moon is exactly between the earth and the sun. Lunar eclipses always occur on a full moon when the Earth is between the Moon and the Sun.

Before scientists saw the moon rocks, they had three theories about the origin of the moon, but there was no way to prove any of them were correct. Some believed that the newly formed Earth rotated so fast that it threw off part of the substance that then became the Moon. Others suggested that the moon came from the depths of space and was captured by the force of the earth's gravity. The third theory was that the Earth and the Moon formed independently, almost simultaneously and at about the same distance from the Sun. Differences in chemical composition The earths and moons indicate that these celestial bodies are unlikely to have ever been one.

Not so long ago, a fourth theory arose, which is now accepted as the most plausible. This is the giant impact hypothesis. The basic idea is that when the planets that we see now were just forming, some celestial body the size of Mars crashed into the young Earth at a glancing angle with great force. In this case, the lighter substances of the outer layers of the Earth would have to break away from it and scatter in space, forming a ring of debris around the Earth, while the core of the Earth, consisting of iron, would have been preserved intact. Eventually, this ring of debris stuck together to form the Moon.

By studying radioactive substances contained in lunar rocks, scientists were able to calculate the age of the moon. Rocks on the moon became solid about 4.4 billion years ago. The moon had apparently formed not long before; its most probable age is about 4.65 billion years. This is consistent with the age of meteorites, as well as with estimates of the age of the Sun.
The most ancient rocks on the Moon are found in mountainous regions. The age of the rocks taken from the seas of solidified lava is much less. When the Moon was very young, its outer layer was liquid due to the very high temperature. As the moon cooled, its outer covering, or crust, formed, parts of which are now found in mountainous regions. For the next half a billion years, the lunar crust was bombarded by asteroids, that is, small planets, and giant rocks that arose during the formation of the solar system. After the strongest blows, huge dents remained on the surface.

Between 4.2 and 3.1 billion years ago, lava flowed out through holes in the crust, flooding the circular basins left on the surface by colossal impacts. Lava, flooding vast flat areas, created lunar seas, which in our time are solidified oceans of rock.

The content of the article

Ebb and flow, periodic fluctuations in the water level (ups and downs) in the water areas on the Earth, which are due to the gravitational attraction of the Moon and the Sun, acting on the rotating Earth. All large water areas, including oceans, seas and lakes, are subject to tides to one degree or another, although they are small on lakes.

Reversible waterfall

(reversing direction) is another phenomenon associated with tides on rivers. Typical example- a waterfall on the St. John River (prov. New Brunswick, Canada). Here, along a narrow gorge, water at high tide penetrates into a basin located above the low water level, but somewhat below the high water level in the same gorge. Thus, a barrier arises, flowing through which water forms a waterfall. At low tide, the flow of water rushes downstream through a narrowed passage and, overcoming an underwater ledge, forms an ordinary waterfall. At high tide, a steep wave that has penetrated the gorge falls like a waterfall into the overlying basin. The reverse current continues until the water levels on both sides of the threshold are equal and the tide begins to ebb. Then the waterfall is restored again, facing downstream. The average water level difference in the gorge is approx. 2.7 m, however, at the highest tides, the height of a direct waterfall can exceed 4.8 m, and a reverse one - 3.7 m.

The greatest amplitudes of the tides.

The world's highest tide is formed by strong currents in Minas Bay in the Bay of Fundy. Tidal fluctuations here are characterized by a normal course with a semidiurnal period. The water level at high tide often rises by more than 12 m in six hours, and then drops by the same amount over the next six hours. When the action of the spring tide, the position of the Moon at perigee, and the maximum declination of the Moon occur in one day, the tide level can reach 15 m. the top of the bay.

wind and weather.

Wind has a significant effect on tidal phenomena. The wind from the sea drives the water towards the shore, the height of the tide rises above normal, and at low tide the water level also exceeds the average. On the contrary, when the wind blows from the land, the water is driven away from the coast, and the sea level drops.

By increasing atmospheric pressure over a vast area of ​​water there is a decrease in the level of water, as the superimposed weight of the atmosphere is added. When atmospheric pressure increases by 25 mm Hg. Art., the water level drops by about 33 cm. A decrease in atmospheric pressure causes a corresponding increase in the water level. Therefore, a sharp drop in atmospheric pressure, combined with hurricane-force winds, can cause a noticeable rise in the water level. Such waves, although they are called tidal waves, are in fact not associated with the influence of tidal forces and do not have the periodicity characteristic of tidal phenomena. The formation of the mentioned waves can be associated either with hurricane force winds or with underwater earthquakes (in the latter case they are called seismic sea ​​waves or tsunami).

The use of tidal energy.

Four methods have been developed to harness the energy of the tides, but the most practical of these is the creation of a system of tidal pools. At the same time, water level fluctuations associated with tidal phenomena are used in the lock system in such a way that the level difference is constantly maintained, which makes it possible to obtain energy. The power of tidal power plants directly depends on the area of ​​the trap pools and the potential level difference. The latter factor, in turn, is a function of the amplitude of the tidal fluctuations. The achievable level difference is by far the most important for power generation, although the cost of facilities depends on the size of the pools. At present, large tidal power plants operate in Russia on the Kola Peninsula and in Primorye, in France in the estuary of the Rance River, in China near Shanghai, and also in other regions of the globe.

The level of the surface of the oceans and seas periodically, approximately twice a day, changes. These fluctuations are called ebbs and flows. At high tide, the ocean level gradually rises and reaches its highest position. At low tide, the level gradually drops to the lowest. At high tide, water flows towards the shores; at low tide, it flows away from the shores.

Ebb and flow are standing tides. They are formed as a result of the influence of such cosmic bodies as the Sun. According to the laws of interaction of cosmic bodies, our planet and the Moon mutually attract each other. The lunar attraction is so strong that the surface of the ocean seems to curve towards it. The moon moves around the Earth, and a tidal wave “runs” across the ocean behind it. A wave will reach the shore - that's the tide. A little time will pass, the water, following the Moon, will move away from the shore - that's the ebb. According to the same universal cosmic laws, ebbs and flows are also formed from the attraction of the Sun. However, the tide-forming force of the Sun, due to its remoteness, is much less than the lunar one, and if there were no Moon, then the tides on Earth would be 2.17 times less. The explanation of tidal forces was first given by Newton.

Tides vary in duration and magnitude. Most often during the day there are two high and two low tides. On the arcs and coasts of Eastern and Central America, there is one high tide and one low tide during the day.

The magnitude of the tides is even more varied than their period. Theoretically, one lunar tide is 0.53 m, solar - 0.24 m. Thus, the largest tide should have a height of 0.77 m. In the open ocean and near the islands, the tide is quite close to theoretical: in the Hawaiian Islands - 1 m , on the island of St. Helena - 1.1 m; on the islands - 1.7 m. On the continents, the tide ranges from 1.5 to 2 m. In the inland seas, the tides are very small: - 13 cm, - 4.8 cm. It is considered tideless, but near Venice, tides are up to 1 m. The largest can be noted the following tides recorded in:

In the Bay of Fundy (), the tide reached a height of 16-17 m. This is the largest tide indicator on the entire globe.

In the north, in the Penzhina Bay, the tide height reached 12-14 m. This is the largest tide off the coast of Russia. However, the above tide figures are the exception rather than the rule. At the vast majority of tide level measurement points, they are small and rarely exceed 2 m.

The significance of the tides is very great for maritime navigation and port facilities. Each tidal wave carries a huge amount of energy.

There is a rise and fall of water. This phenomenon sea ​​tides and ebbs. Already in antiquity, observers noticed that the tide comes some time after the culmination of the Moon at the place of observation. Moreover, the tides are strongest on the days of new and full moons, when the centers of the Moon and the Sun are approximately on the same straight line.

Given this, I. Newton explained the tides by the action of gravity from the Moon and the Sun, namely, that different parts of the Earth are attracted by the Moon in different ways.

The Earth rotates on its axis much faster than the Moon revolves around the Earth. As a result, the tidal hump (the relative position of the Earth and the Moon is shown in Figure 38) moves, a tidal wave runs along the Earth, and tidal currents arise. When approaching the shore, the height of the wave increases as the bottom rises. In the inland seas, the height of the tidal wave is only a few centimeters, while in the open ocean it reaches about one meter. In well-located narrow bays, the height of the tide increases several times more.

The friction of the water against the bottom, as well as the deformation of the solid shell of the Earth, are accompanied by the release of heat, which leads to the dissipation of the energy of the Earth-Moon system. Since the tide hump is due east, the maximum tide occurs after the Moon's culmination, the attraction of the hump causes the Moon to accelerate and the Earth's rotation to slow. The moon is gradually moving away from the earth. Indeed, geological data show that in the Jurassic period (190-130 million years ago), the tides were much higher, and the day was shorter. It should be noted that when the distance to the Moon decreases by a factor of 2, the height of the tide increases by a factor of 8. Currently, the day is increasing by 0.00017 s per year. So in about 1.5 billion years their length will increase to 40 modern days. The month will be the same length. As a result, the Earth and the Moon will always face each other with the same side. After that, the Moon will begin to gradually approach the Earth and in another 2-3 billion years it will be torn apart by tidal forces (if, of course, the Solar System still exists by that time).

The influence of the moon on the tide

Consider, following Newton, in more detail the tides caused by the attraction of the Moon, since the influence of the Sun is significantly (2.2 times) less.

Let us write down the expressions for the accelerations caused by the attraction of the Moon for different points of the Earth, taking into account that these accelerations are the same for all bodies at a given point in space. In the inertial frame of reference associated with the center of mass of the system, the acceleration values ​​will be:

A A \u003d -GM / (R - r) 2, a B \u003d GM / (R + r) 2, a O \u003d -GM / R 2,

where a A, aO, a B are the accelerations caused by the attraction of the Moon at the points A, O, B(Fig. 37); M is the mass of the moon; r is the radius of the Earth; R- the distance between the centers of the Earth and the Moon (for calculations, it can be taken equal to 60 r); G is the gravitational constant.

But we live on the Earth and all observations are carried out in a reference system associated with the center of the Earth, and not with the Earth-Moon center of mass. To pass to this system, it is necessary to subtract the acceleration of the center of the Earth from all accelerations. Then

A’ A = -GM ☾ / (R - r) 2 + GM ☾ / R 2 , a’ B = -GM ☾ / (R + r) 2 + GM / R 2 .

Let's do the parentheses and take into account that r little compared to R and can be neglected in sums and differences. Then

A’ A \u003d -GM / (R - r) 2 + GM ☾ / R 2 \u003d GM ☾ (-2Rr + r 2) / R 2 (R - r) 2 \u003d -2GM ☾ r / R 3.

Accelerations a’A and a’B identical in modulus, opposite in direction, each directed from the center of the Earth. They're called tidal accelerations. At points C and D tidal accelerations, smaller in magnitude and directed towards the center of the Earth.

Tidal accelerations are called accelerations arising in the frame of reference associated with the body due to the fact that, due to the finite dimensions of this body, its different parts are attracted differently by the perturbing body. At points A and B the acceleration of gravity is less than at the points C and D(Fig. 37). Therefore, in order for the pressure at the same depth to be the same (as in communicating vessels) at these points, the water must rise, forming the so-called tidal hump. The calculation shows that the rise of water or the tide in the open ocean is about 40 cm. In coastal waters it is much larger, and the record is about 18 m. The Newtonian theory cannot explain this.

On the coast of many outer seas one can see a curious picture: fishing nets are stretched along the coast not far from the water. Moreover, these nets were set up not for drying, but for catching fish. If you stay on the shore and watch the sea, then everything will become clear. Now the water begins to rise, and where only a few hours ago there was a sandbank, waves splashed. When the water receded, nets appeared in which the entangled fish sparkled with scales. The fishermen, bypassing the nets, took off the catch. material from the site

Here is how an eyewitness describes the onset of the tide: “We got to the sea,” a fellow traveler told me. I looked around in bewilderment. There really was a shore in front of me: a trail of ripples, a half-buried skeleton of a seal, rare pieces of a fin, fragments of shells. And beyond that stretched a flat expanse... and no sea. But three hours later, the motionless line of the horizon began to breathe, became agitated. And now the sea swell sparkled behind her. A wave of tide rolled uncontrollably forward across the gray surface. Overtaking each other, the waves ran ashore. One after another, distant rocks sank - and all around you can see only water. She throws salt spray in my face. Instead of a dead plain, the water surface lives and breathes in front of me.

When a tidal wave enters a funnel-shaped bay, the shores of the bay seem to compress it, which causes the height of the tide to increase several times. So, in the Bay of Fundy off the eastern coast of North America, the tide height reaches 18 m. In Europe, the highest tides (up to 13.5 meters) occur in Brittany near the city of Saint-Malo.

Very often the tidal wave comes into the mouth

Ebb and flow

high tide and low tide- periodic vertical fluctuations in the level of the ocean or sea, which are the result of changes in the positions of the Moon and the Sun relative to the Earth, coupled with the effects of the Earth's rotation and the features of this relief, and manifested in a periodic horizontal displacement of water masses. Tides cause changes in sea level and periodic currents, known as tidal currents, making tide prediction important for coastal navigation.

The intensity of these phenomena depends on many factors, but the most important of them is the degree of connection of water bodies with the oceans. The more closed the reservoir, the less the degree of manifestation of tidal phenomena.

The yearly recurring tidal cycle remains unchanged due to the exact compensation of the forces of attraction between the Sun and the center of mass of the planetary pair and the forces of inertia applied to this center.

Since the position of the Moon and the Sun in relation to the Earth periodically changes, the intensity of the resulting tidal phenomena also changes.

Low tide at Saint Malo

Story

Ebb tides played a significant role in supplying the coastal population with seafood, allowing them to collect on the exposed seabed food suitable for eating.

Terminology

Low water (Brittany, France)

The maximum level of the water surface at high tide is called full water, and the minimum at low tide - low water. In the ocean, where the bottom is even, and the land is far away, high water manifests itself as two “bloatings” of the water surface: one of them is located on the side of the moon, and the other is at the opposite end of the globe. There may also be two more smaller swellings on the side directed towards the Sun and opposite to it. An explanation of this effect can be found below, in the section tide physics.

Since the Moon and the Sun move relative to the Earth, water humps move with them, forming tidal waves and tidal currents. In the open sea, tidal currents are rotational in nature, and near the coast and in narrow bays and straits, they are reciprocating.

If the whole Earth were covered with water, we would observe two regular high and low tides daily. But since the unimpeded propagation of tidal waves is prevented by land areas: islands and continents, and also due to the action of the Coriolis force on moving water, instead of two tidal waves, there are many small waves that slowly (in most cases with a period of 12 h 25.2 min ) run around a point called amphidromic, where the tide amplitude is zero. The dominant component of the tide (the lunar tide M2) forms about a dozen amphidromic points on the surface of the World Ocean with wave motion clockwise and about the same counterclockwise (see map). All this makes it impossible to predict the time of the tide only on the basis of the positions of the Moon and the Sun relative to the Earth. Instead, use the "yearbook of the tides" - reference guide to calculate the time of the onset of tides and their height at various points on the globe. Tide tables are also used, with data on the moments and heights of low and high waters, calculated a year ahead for major tidal ports.

Tide component M2

If we connect points on the map with the same tide phases, we get the so-called cotidal lines radiating from the amphidromic point. Typically, cotidal lines characterize the position of the crest of the tidal wave for each hour. In fact, the cotidal lines reflect the speed of propagation of the tidal wave in 1 hour. Maps that show lines of equal amplitudes and phases of tidal waves are called cotidal cards.

high tide- difference between highest level water at high tide (high tide) and its lowest level at low tide (low tide). The height of the tide is a variable value, however, its average indicator is given when characterizing each section of the coast.

Depending on the relative position Moon and Sun small and large tidal waves can reinforce each other. For such tides, special names have historically developed:

• Quadrature tide- the smallest tide, when the tide-forming forces of the Moon and the Sun act at right angles to each other (this position of the luminaries is called quadrature).
• spring tide- the greatest tide, when the tide-forming forces of the Moon and the Sun act along the same direction (this position of the luminaries is called syzygy).

The smaller or larger the tide, the smaller or, respectively, the greater the ebb.

The highest tides in the world

It can be observed in the Bay of Fundy (15.6-18 m), which is located on the east coast of Canada between New Brunswick and Nova Scotia.

On the European continent, the highest tides (up to 13.5 m) are observed in Brittany near the city of Saint Malo. Here the tidal wave is focused by the coastline of the Cornwall (England) and Cotentin (France) peninsulas.

Tide physics

Modern wording

With regard to the planet Earth, the cause of tides is the presence of the planet in a gravitational field, created by the sun and the moon. Since the effects they create are independent, the impact of these celestial bodies on the Earth can be considered separately. In this case, for each pair of bodies, we can assume that each of them revolves around a common center of gravity. For the Earth-Sun pair, this center is located in the depths of the Sun at a distance of 451 km from its center. For the Earth-Moon pair, it is located deep in the Earth at a distance of 2/3 of its radius.

Each of these bodies experiences the action of tidal forces, the source of which is the gravitational force and internal forces that ensure the integrity of the celestial body, in the role of which is the force of its own attraction, hereinafter referred to as self-gravity. The emergence of tidal forces is most clearly seen in the example of the Earth-Sun system.

The tidal force is the result of the competing interaction of the gravitational force directed towards the center of gravity and decreasing inversely with the square of the distance from it, and the fictitious centrifugal force of inertia due to the rotation of a celestial body around this center. These forces, being opposite in direction, coincide in magnitude only at the center of mass of each of the celestial bodies. Due to the action of internal forces, the Earth revolves around the center of the Sun as a whole with a constant angular velocity for each element of its mass. Therefore, as this element of mass moves away from the center of gravity, the centrifugal force acting on it grows in proportion to the square of the distance. A more detailed distribution of tidal forces in their projection onto a plane perpendicular to the plane of the ecliptic is shown in Fig.1.

Fig.1 Scheme of the distribution of tidal forces in the projection onto a plane perpendicular to the Ecliptic. A gravitating body is either on the right or on the left.

According to the Newtonian paradigm, the reproduction of changes in the shape of the bodies subjected to their action, achieved as a result of the action of tidal forces, can be achieved only if these forces are fully compensated by other forces, which may include the force of universal gravitation.

Fig.2 Deformation of the Earth's water shell as a result of the balance of tidal force, self-gravity force and the force of water reaction to the compressive force

As a result of the addition of these forces, tidal forces arise symmetrically on both sides of the globe, directed in different sides From him. The tidal force directed towards the Sun is of a gravitational nature, while that directed away from the Sun is a consequence of a fictitious inertial force.

These forces are extremely weak and cannot be compared with the forces of self-gravity (the acceleration they create is 10 million times less than the acceleration free fall). However, they cause a shift in the particles of water in the oceans (resistance to shear in water at low speeds is practically zero, while compression is extremely high), until the tangent to the surface of the water becomes perpendicular to the resulting force.

As a result, a wave arises on the surface of the oceans, occupying a constant position in systems of mutually gravitating bodies, but running along the surface of the ocean together with the daily movement of its bottom and coasts. Thus (neglecting ocean currents) each particle of water makes an oscillatory movement up and down twice during the day.

The horizontal movement of water is observed only near the coast as a result of the rise in its level. The speed of movement is greater, the more gently the seabed is located.

Tidal potential

(the concept of acad. Shuleikin)

Neglecting the size, structure and shape of the Moon, we write down the specific force of attraction of a test body located on the Earth. Let be the radius vector directed from the test body towards the Moon, be the length of this vector. In this case, the force of attraction of this body by the Moon will be equal to

where is the selenometric gravitational constant. We place the test body at the point . The force of attraction of a test body placed at the center of mass of the Earth will be equal to

Here, and are understood as the radius vector connecting the centers of mass of the Earth and the Moon, and their absolute values. We will call the tidal force the difference between these two gravitational forces

In formulas (1) and (2), the Moon is considered to be a ball with a spherically symmetric mass distribution. The force function of the attraction of the test body by the Moon is no different from the force function of the attraction of the ball and is equal to The second force is applied to the center of mass of the Earth and is a strictly constant value. To obtain the force function for this force, we introduce a time coordinate system. We draw the axis from the center of the Earth and direct it towards the Moon. We leave the directions of the other two axes arbitrary. Then the force function of the force will be equal to . Tidal potential will be equal to the difference of these two force functions. Let's designate it , we will receive Constant we will define from a condition of normalization according to which the tidal potential in the center of the Earth is equal to zero. At the center of the Earth , It follows that . Therefore, we obtain the final formula for the tidal potential in the form (4)

Insofar as

For small values ​​of , , the last expression can be represented in the following form

Substituting (5) into (4), we obtain

Deformation of the surface of the planet under the influence of ebbs and flows

The perturbing effect of the tidal potential deforms the level surface of the planet. Let us evaluate this effect, assuming that the Earth is a sphere with a spherically symmetric mass distribution. The unperturbed gravitational potential of the Earth on the surface will be equal to . For a dot. , located at a distance from the center of the sphere, the gravitational potential of the Earth is . Reducing by the gravitational constant, we get . Here the variables are and . Let us denote the ratio of the masses of the gravitating body to the mass of the planet Greek letter and solve the resulting expression for :

Since with the same degree of accuracy we get

Given the smallness of the ratio, the last expressions can be written as

Thus, we have obtained the equation of a biaxial ellipsoid, in which the axis of rotation coincides with the axis, i.e. with a straight line connecting the gravitating body with the center of the Earth. The semiaxes of this ellipsoid are obviously equal

We give a small numerical illustration at the end. this effect. Let's calculate the tidal "hump" on the Earth, caused by the attraction of the Moon. The radius of the Earth is km, the distance between the centers of the Earth and the Moon, taking into account the instability of the lunar orbit, is km, the ratio of the mass of the Earth to the mass of the Moon is 81:1. Obviously, when substituting into the formula, we get a value approximately equal to 36 cm.

see also

Notes

Literature

• Frish S. A. and Timoreva A. V. Course of General Physics, Textbook for the Physics and Mathematics and Physics and Technology Departments of State Universities, Volume I. M .: GITTL, 1957
• Shchuleykin V.V. Physics of the sea. M.: Publishing House "Nauka", Department of Earth Sciences of the Academy of Sciences of the USSR 1967
• Voight S.S. What are tides. Editorial Board of Popular Science Literature of the Academy of Sciences of the USSR

Links

• WXTide32 is a free tide charting program.

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