What is a tide in the sea? Sea tides

The content of the article

Ebbs and flows, periodic fluctuations in water levels (rises and falls) in water areas on Earth, which are caused by the gravitational attraction of the Moon and 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 in lakes.

Reversible waterfall

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

Greatest tidal amplitudes.

The world's highest tide is generated by strong currents in Minas Bay in the Bay of Fundy. Tidal fluctuations here are characterized by a normal course with a semi-diurnal 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 effect of spring tide, the position of the Moon at perigee and the maximum declination of the Moon occur on the same day, the tide level can reach 15 m. This exceptionally large amplitude of tidal fluctuations is partly due to the funnel-shaped shape of the Bay of Fundy, where the depths decrease and the shores move closer together towards top of the bay.

Wind and weather.

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

Due to the increase in atmospheric pressure over a vast area of ​​water, the water level decreases, as the superimposed weight of the atmosphere is added. When atmospheric pressure increases by 25 mmHg. Art., the water level drops by approximately 33 cm. The decrease in atmospheric pressure causes a corresponding increase in the water level. Consequently, a sharp drop in atmospheric pressure combined with hurricane-force winds can cause a noticeable rise in water levels. Such waves, although called tidal, 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).

Using tidal energy.

Four methods have been developed to harness tidal energy, but the most practical is to create a tidal pool system. At the same time, fluctuations in water levels associated with tidal phenomena are used in the lock system so that a level difference is constantly maintained, which allows energy to be generated. 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 tidal fluctuations. The achievable level difference is by far the most important for power generation, although the cost of the structures depends on the area of ​​the basins. Currently, large tidal power plants operate in Russia on the Kola Peninsula and in Primorye, in France in the Rance River estuary, in China near Shanghai, as well as in other areas globe.

The water surface level in the seas and oceans of our planet changes periodically and fluctuates in certain intervals. These periodic oscillations are sea ​​tides.

Picture of sea tides

To visualize picture of sea ebbs and flows, imagine that you are standing on the sloping shore of the ocean, in some bay, 200–300 meters from the water. There are many different objects on the sand - an old anchor, a little closer big pile white stone.

Now, not far away, lies the iron hull of a small boat, fallen on its side. The bottom of its hull in the bow is badly damaged. Obviously, once this ship, being not far from the shore, hit an anchor. This accident occurred, in all likelihood, during low tide, and, apparently, the ship had been lying in this place for many years, since almost its entire hull had become covered with brown rust. You are inclined to consider the careless captain to be the culprit of the ship's accident.

Apparently, the anchor was the sharp weapon that the ship that had fallen on its side struck. You are looking for this anchor and cannot find it. Where could he have gone? Then you notice that the water is already approaching a pile of white stones, and then you realize that the anchor you saw has long been flooded by a tidal wave. The water “steps” onto the shore, it continues to rise further and further upward. Now the pile of white stones turned out to be almost all hidden under water.

Phenomena of sea tides

Phenomena of sea tides people have long been associated with the movement of the Moon, but this connection remained a mystery until the brilliant mathematician Isaac Newton did not explain on the basis of the law of gravity he discovered. The cause of these phenomena is the effect of the Moon’s gravity on the Earth’s water shell.

Still famous Galileo Galilei connected the ebb and flow of the tides with the rotation of the Earth and saw in this one of the most substantiated and true proofs of the validity of the teachings of Nicolaus Copernicus (more details:). The Paris Academy of Sciences in 1738 announced a prize to the one who would give the most substantiated presentation of the theory of tides.

The award was then received Euler, Maclaurin, D. Bernoulli and Cavalieri. The first three took Newton's law of gravitation as the basis for their work, and the Jesuit Cavalieri explained tides based on Descartes' vortex hypothesis. However, the most outstanding works in this area belong to Newton and Laplace, and all subsequent research is based on the findings of these great scientists.

How to explain the phenomenon of ebb and flow

How most clearly explain the phenomenon of ebb and flow. If, for simplicity, we assume that the earth’s surface is completely covered with water, and we look at the globe from one of its poles, then the picture of sea ebbs and flows can be presented as follows.

Lunar attraction

That part of the surface of our planet that faces the Moon is closest to it; as a result, it is exposed to greater force lunar gravity than, for example, central part our planet and, therefore, is pulled towards the Moon more than the rest of the Earth. Because of this, a tidal hump is formed on the side facing the Moon.

At the same time, on the opposite side of the Earth, which is least subject to the gravity of the Moon, the same tidal hump appears. The Earth therefore takes the form of a figure somewhat elongated along a straight line connecting the centers of our planet and the Moon.

Thus, on two opposite sides of the Earth, located on the same straight line, which passes through the centers of the Earth and the Moon, two large humps are formed, two huge water swellings.

At the same time, on the other two sides of our planet, located at an angle of ninety degrees from the above points of maximum tide, the greatest low tides occur. Here the water drops more than anywhere else on the surface of the globe. The line connecting these points at low tide shortens somewhat, and thus creates the impression of an increase in the elongation of the Earth in the direction of the maximum high tide points.

Due to lunar gravity, these points of maximum tide constantly maintain their position relative to the Moon, but since the Earth rotates around its axis, during the day they seem to move across the entire surface of the globe. That's why in each area there are two high and two low tides during the day.

Solar ebbs and flows

The Sun, like the Moon, produces ebbs and flows by the force of its gravity. But it is much further away greater distance from our planet compared to the Moon, and the solar tides that occur on Earth are almost two and a half times less than the lunar ones. That's why solar tides, are not observed separately, but only their influence on the magnitude of lunar tides is considered.

For example, The highest sea tides occur during full and new moons, since at this time the Earth, Moon and Sun are on the same straight line, and our daylight increases the attraction of the Moon with its attraction.

On the contrary, when we observe the Moon in the first or last quarter (phase), there are lowest sea tides. This is explained by the fact that in this case the lunar tide coincides with solar ebb. The effect of lunar gravity is reduced by the amount of gravity of the Sun.

Tidal friction

« Tidal friction", existing on our planet, in turn affects the lunar orbit, since the tidal wave caused by lunar gravity has a reverse effect on the Moon, creating a tendency to accelerate its movement. As a result, the Moon gradually moves away from the Earth, its period of revolution increases, and it, in all likelihood, lags a little behind in its movement.

The magnitude of sea tides

In addition to the relative position in space of the Sun, Earth and Moon, on the magnitude of the sea tides In each individual area, the shape of the seabed and the nature of the shoreline influence. It is also known that in closed seas, such as the Aral, Caspian, Azov and Black seas, ebbs and flows are almost never observed.

It is difficult to detect them in the open oceans; here the tides barely reach one meter, the water level rises very little. But in some bays there are tides of such colossal magnitude that the water rises to a height of more than ten meters and in some places floods colossal spaces.

Ebbs and flows in the air and solid shells of the Earth

Ebbs and flows also happen in the air and solid shells of the Earth. These phenomena in lower strata We hardly notice the atmosphere. For comparison, we point out that ebbs and flows are not observed at the bottom of the oceans. This circumstance is explained by the fact that mainly the upper layers of the water shell are involved in tidal processes. Ebbs and flows in the air envelope can only be detected by very long-term observation of changes in atmospheric pressure.

As for the earth’s crust, each part of it, due to the tidal action of the Moon, rises twice during the day and falls twice by about several decimeters. In other words, fluctuations in the solid shell of our planet are approximately three times smaller in magnitude than fluctuations in the surface level of the oceans. Thus, our planet seems to be breathing all the time, taking deep breaths and exhalations, and its outer shell, like the chest of a great miracle hero, either rises or falls a little.

These processes occurring in the solid shell of the Earth can only be detected with the help of instruments used to record earthquakes.

It should be noted that ebbs and flows occur on other world bodies and have a huge impact on their development.

If the Moon were motionless in relation to the Earth, then in the absence of other factors influencing the delay of the tidal wave, two high tides and two low tides would occur every 6 hours in any place on the globe every 6 hours.

But since the Moon continuously revolves around the Earth and, moreover, in the same direction in which our planet rotates around its axis, there is some delay: the Earth manages to turn towards the Moon with each part not within 24 hours, but in approximately 24 hours and 50 minutes. Therefore, in each area, the ebb or flow of the tide does not last exactly 6 hours, but about 6 hours and 12.5 minutes.

Alternating tides

In addition, it should be noted that the correctness alternating tides is violated depending on the nature of the location of the continents on our planet and the continuous friction of water on the surface of the Earth. These irregularities in alternation sometimes reach several hours.

Thus, the “highest” water occurs not at the moment of the Moon’s culmination, as it should be according to theory, but several hours later than the Moon’s passage through the meridian; this delay is called the port applied clock and sometimes reaches 12 hours.

Previously, it was widely believed that the ebb and flow of sea tides were related to sea currents. Now everyone knows that these are phenomena different order. A tide is a type of wave movement, similar to that caused by wind.

Ebb and flow

Tide And low tide- periodic vertical fluctuations in ocean or sea level, resulting from 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 a given relief and manifested in periodic horizontal displacement of water masses. Tides cause changes in sea level height, as well as 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 world ocean. The more closed the body of water, the less the degree of manifestation of tidal phenomena.

The annually repeated tidal cycle remains unchanged due to the precise 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.

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

Low tide at Saint-Malo

Story

Low tides played a significant role in the supply of seafood to coastal populations, allowing edible food to be collected from the exposed seabed.

Terminology

Low Water (Brittany, France)

The maximum surface level of the water at high tide is called full of water, and the minimum during low tide is low water. In the ocean, where the bottom is flat and the land is far away, full water manifests itself as two “swells” 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 Sun move relative to the Earth, water humps also move with them, forming tidal waves And tidal currents. In the open sea, tidal currents have a rotational character, and near the coast and in narrow bays and straits they are reciprocating.

If the entire Earth were covered with water, we would experience two regular high and low tides every day. But since the unimpeded propagation of tidal waves is hampered 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 hours 25.2 minutes ) run around a point called amphidromic, in which the tidal amplitude is zero. The dominant component of the tide (lunar tide M2) forms about a dozen amphidromic points on the surface of the World Ocean with the wave moving clockwise and about the same number counterclockwise (see map). All this makes it impossible to predict the time of tide only based on the positions of the Moon and Sun relative to the Earth. Instead, they use a "tide yearbook" - a reference guide for calculating the time of the onset of tides and their heights in various points of the globe. Tide tables are also used, with data on the moments and heights of low and high waters, calculated a year in advance for main tidal ports.

Tide component M2

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

Tide height- difference between highest level water at high tide (high water) and its lowest level at low tide (low water). The height of the tide is not a constant value, but its average 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. Special names have historically been developed for such tides:

• Quadrature tide- the lowest tide, when the tidal 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 highest tide, when the tidal forces of the Moon and the Sun act along the same direction (this position of the luminaries is called syzygy).

The lower or higher the tide, the lower or higher the ebb.

Highest tides in the world

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 peninsulas of Cornwall (England) and Cotentin (France).

Physics of the tide

Modern formulation

In relation to planet Earth, the cause of tides is the presence of the planet in the gravitational field created by the Sun and Moon. Since the effects they create are independent, the impact of these celestial bodies on 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 deep in 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 tidal forces, the source of which is the force of gravity and internal forces that ensure the integrity of the celestial body, in the role of which is the force of its own attraction, hereinafter called self-gravity. The emergence of tidal forces can be most clearly seen in 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 in inverse proportion to the square of the distance from it, and the fictitious centrifugal force of inertia caused by the rotation of the 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. Thanks to the action of internal forces, the Earth rotates around the center of the Sun as a whole with a constant angular velocity for each element of its constituent mass. Therefore, as this element of mass moves away from the center of gravity, the centrifugal force acting on it increases in proportion to the square of the distance. A more detailed distribution of tidal forces in their projection onto the plane, perpendicular to the plane ecliptic, are shown in Fig. 1.

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

The reproduction of changes in the shape of bodies exposed to them, achieved as a result of the action of tidal forces, can, in accordance with the Newtonian paradigm, be achieved only if these forces are completely compensated by other forces, which may include the force of universal gravity.

Fig. 2 Deformation of the Earth’s water shell as a consequence of the balance of tidal force, self-gravitational force and the force of reaction of water to compression force

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

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 of gravity). However, they cause a shift in the water particles of the World Ocean (the resistance to shear in water at low speeds is practically zero, while to compression it is extremely high), until the tangent to the surface of the water becomes perpendicular to the resulting force.

As a result, a wave appears on the surface of the world's 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 shores. Thus (ignoring ocean currents) each particle of water performs twice during the day oscillatory motion up down.

Horizontal movement of water is observed only near the coast as a consequence of a rise in its level. The more shallow the seabed is, the greater the speed of movement.

Tidal potential

(concept of acad. Shuleikina)

Neglecting the size, structure and shape of the Moon, we write down the specific gravitational force of the test body located on Earth. Let be the radius vector directed from the test body towards the Moon, and let 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. Let's place the test body at point . The force of attraction of a test body placed at the center of mass of the Earth will be equal to

Here, and refers to 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 a ball with a spherically symmetrical mass distribution. The force function of attraction of a test body by the Moon is no different from the force function of attraction of a 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. Let's draw the axis from the center of the Earth and direct it towards the Moon. The directions of the other two axes will be left 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. We denote it , we obtain The constant is determined from the normalization condition, according to which the tidal potential in the center of the Earth is equal to zero. In the center of the Earth, It follows that. Consequently, we obtain the final formula for the tidal potential in the form (4)

Because the

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

Substituting (5) into (4), we get

Deformation of the planet's surface under the influence of tides

The disturbing influence of the tidal potential deforms the leveled surface of the planet. Let us evaluate this impact, assuming that the Earth is a ball with a spherically symmetrical mass distribution. The unperturbed gravitational potential of the Earth on the surface will be equal to . For point . , located at a distance from the center of the sphere, the gravitational potential of the Earth is equal to . 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 by a Greek letter and solve the resulting expression for:

Since with the same degree of accuracy we obtain

Considering the smallness of the ratio, the last expressions can be written as follows

We have thus obtained the equation of a biaxial ellipsoid, whose axis of rotation coincides with the axis, that is, with the straight line connecting the gravitating body with the center of the Earth. The semi-axes of this ellipsoid are obviously equal

At the end we give a small numerical illustration of this effect. Let's calculate the tidal hump on Earth caused by the attraction of the Moon. The radius of the Earth is equal to 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 Earth's mass to the Moon's mass is 81:1. Obviously, when substituting into the formula, we get a value approximately equal to 36 cm.

see also

Notes

Literature

• Frisch S. A. and Timoreva A. V. Course of general physics, Textbook for physics-mathematics and physics-technical faculties of state universities, Volume I. M.: GITTL, 1957
• Shchuleykin V.V. Physics of the sea. M.: Publishing house "Science", Department of Earth Sciences of the USSR Academy of Sciences 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 freeware tide table program

Moon
Peculiarities

The ebb and flow of the tides is currently believed to be caused by the gravitational pull of the Moon. So, the Earth turns to the satellite in one direction or another, the Moon attracts this water to itself - these are the tides. In the area where the water leaves there are low tides. The earth rotates, ebbs and flows change each other. This is the lunar theory, in which everything is good except for a number of unexplained facts.

For example, did you know that the Mediterranean Sea is considered tidal, but near Venice and on the Eurekos Strait in eastern Greece, the tides are up to one meter or more. This is considered one of the mysteries of nature. However, Italian physicists discovered in the eastern Mediterranean Sea, at a depth of more than three kilometers, a chain of underwater whirlpools, each ten kilometers in diameter. Interesting coincidence of abnormal tides and whirlpools, isn't it?

A pattern has been noticed: where there are whirlpools, in oceans, seas and lakes, there are ebbs and flows, and where there are no whirlpools, there are no ebbs and flows... The vastness of the world's oceans is completely covered with whirlpools, and whirlpools have the property of a gyroscope to maintain the position of the axis in space, regardless of the rotation of the earth.

If you look at the earth from the side of the Sun, the whirlpools, rotating with the Earth, overturn twice a day, as a result of which the axis of the whirlpools precesses (1-2 degrees) and creates a tidal wave, which is the cause of ebbs and flows, and the vertical movement of ocean waters .

Precession of a top

Giant ocean whirlpool

The Mediterranean Sea is considered tidal, but near Venice and on the Eurekos Strait in eastern Greece, the tides are up to one meter or more. And this is considered one of the mysteries of nature, but at the same time, Italian physicists discovered in the east of the Mediterranean Sea, at a depth of more than three kilometers, a chain of underwater whirlpools, each ten kilometers in diameter. From this we can conclude that along the coast of Venice, at a depth of several kilometers, there is a chain of underwater whirlpools.

If in the Black Sea the water rotated like in the White Sea, then the ebb and flow of the tides would be more significant. If a bay is flooded by a tidal wave and the wave swirls there, then the ebbs and flows in this case are higher... The place of whirlpools, and atmospheric cyclones and anticyclones in science, at the intersection of oceanology, meteorology, and celestial mechanics studying gyroscopes. The behavior of atmospheric cyclones and anticyclones, I believe, is similar to the behavior of whirlpools in the oceans.

To test this idea, I mounted a fan on the globe, where the whirlpool is located, and instead of blades I inserted metal balls on springs. I turned on the fan (whirlpool), simultaneously rotating the globe both around its axis and around the Sun, and got an imitation of the ebb and flow of the tides.

The attractiveness of this hypothesis is that it can be quite convincingly tested using a whirlpool fan attached to the globe. The sensitivity of the whirlpool gyroscope is so high that the globe has to be rotated extremely slowly (one revolution every 5 minutes). And if a whirlpool gyroscope is installed on a globe at the mouth of the Amazon River, then without a doubt, it will show the exact mechanics of the ebb and flow of the Amazon River. When only the globe rotates around its axis, the gyroscope-whirlpool tilts in one direction and stands motionless, and if the globe is moved in orbit, the whirlpool-horoscope begins to oscillate (precess) and gives two ebbs and flows per day.

Doubts about the presence of precession in whirlpools, as a result of slow rotation, are removed by the high speed of overturning of whirlpools, in 12 hours.. And we must not forget that the orbital speed of the earth is thirty times greater than the orbital speed of the moon.

The experience with the globe is more convincing than the theoretical description of the hypothesis. The drift of whirlpools is also associated with the effect of a gyroscope - a whirlpool, and depending on which hemisphere the whirlpool is located, and in which direction the whirlpool rotates around its axis, the direction of the whirlpool drift depends.

floppy disk

Tilting gyroscope

Experience with a gyroscope

Oceanographers in the middle of the ocean are not actually measuring the height of the tidal wave, but the wave created by the gyroscopic effect of the whirlpool created by precession, the axis of rotation of the whirlpool. And only whirlpools can explain the presence of a tidal hump on the opposite side of the earth. There is no fuss in nature, and if whirlpools exist, then they have a purpose in nature, and this purpose, I believe, is the vertical and horizontal mixing of ocean waters to equalize the temperature and oxygen content in the world's oceans.

And even if lunar tides existed, they would not mix ocean waters. Whirlpools, to some extent, prevent the oceans from silting up. If a couple of billion years ago, the earth actually rotated faster, then the whirlpools were more active. Mariana Trench and the Mariana Islands, I believe the result of the whirlpool.

The tide calendar existed long before the discovery of the tidal wave. Just as there was a regular calendar, before Ptolemy, and after Ptolemy, and before Copernicus, and after Copernicus. Today there are also unclear questions about the characteristics of the tides. So, in some places (South China Sea, Persian Gulf, Gulf of Mexico and Gulf of Thailand) there is only one tide per day. In a number of regions of the Earth (for example, in Indian Ocean) there are sometimes one or two hot tides per day.

500 years ago, when the idea of ​​ebb and flow of tides was formed, thinkers did not have enough technical means to test this idea, and little was known about eddies in the oceans. And today, this idea, with its attractiveness and plausibility, is so rooted in the consciousness of the public and thinkers that it will not be easy to abandon it.

Why, every year and every decade, on the same calendar day (for example, the first of May) at the mouths of rivers and bays, there is not the same tidal wave? I believe the whirlpools that are located at the mouths of rivers and bays drift and change their size.

And if the cause of the tidal wave was the gravity of the moon, the height of the tides would not change for millennia. There is an opinion that a tidal wave moving from east to west is created by the gravity of the moon, and the wave floods bays and river mouths. But why, the mouth of the Amazon floods well, but the Bay of La Plata, which is located south of the Amazon, does not flood very well, although by all measures the Bay of La Plata should flood more than the Amazon.

I believe that a tidal wave at the mouth of the Amazon is created by one whirlpool, and for the La Plata neck of the river a tidal wave is created by another whirlpool, less powerful (diameter, height, revolutions).

Amazon Maelstrom

The tidal wave crashes into the Amazon at a speed of about 20 kilometers per hour, the height of the wave is about five meters, the width of the wave is ten kilometers. These parameters are more suitable for a tidal wave created by the precession of an eddy. And if it were a lunar tidal wave, it would hit at a speed of several hundred kilometers per hour, and the width of the wave would be about a thousand kilometers.

It is believed that if the depth of the ocean was 20 kilometers, then the lunar wave would move as expected at 1600 km.hour, they say that the shallow ocean interferes with it. And now it is crashing into the Amazon at a speed of 20 km.h., and into the Fuchunjiang River at a speed of 40 km.h. I think the math is dubious.

And if the Moon wave moves so slowly, then why in pictures and animations the tidal hump is always directed towards the Moon, the Moon rotates much faster. And it is not clear why, the water pressure does not change, under the tidal hump, at the bottom of the ocean... There are zones in the oceans where there are no ebbs and flows at all (amphidromic points).

Amphidromic point

M2 tide, tide height shown in color. White lines are cotidal lines with a phase interval of 30°. Amphidromic points are dark blue areas where white lines converge. Arrows around these points indicate the direction of the “run around”.An amphidromic point is a point in the ocean where the tidal wave amplitude is zero. The height of the tide increases with distance from the amphidromic point. Sometimes these points are called tide nodes: the tidal wave “runs” around this point clockwise or counterclockwise. The cotidal lines converge at these points. Amphidromic points arise due to the interference of the primary tidal wave and its reflections from the coastline and underwater obstacles. The Coriolis force also contributes.

Although for a tidal wave they are in a convenient zone, I believe in these zones the whirlpools rotate extremely slowly. It is believed that the maximum tides occur during the new moon, due to the fact that the Moon and the Sun exert gravity on the Earth in the same direction.

For reference: a gyroscope is a device that, due to rotation, reacts differently to external forces than a stationary object. The simplest gyroscope is a spinning top. By untwisting the spinning top on a horizontal surface and tilting the surface, you will notice that the spinning top maintains horizontal torsion.

But on the other hand, on a new moon the earth’s orbital speed is maximum, and on a full moon it is minimum, and the question arises which of the reasons is the key. The distance from the earth to the moon is 30 diameters of the earth, the approach and distance of the moon from the earth is 10 percent, this can be compared by holding a cobblestone and a pebble with outstretched arms, and bringing them closer and further away by 10 percent, are ebbs and flows possible with such mathematics. It is believed that at the new moon, the continents run into a tidal hump, at a speed of about 1600 kilometers per hour, is this possible?

It is believed that tidal forces have stopped the rotation of the moon, and now it rotates synchronously. But there are more than three hundred known satellites, and why did they all stop at the same time, and where did the force that rotated the satellites go... The gravitational force between the Sun and the Earth does not depend on the orbital speed of the Earth, and the centrifugal force depends on the orbital speed of the Earth, and this fact cannot be the cause of the lunar ebbs and flows.

Calling tides, the phenomenon of horizontal and vertical movement of ocean waters, is not entirely true, for the reason that most whirlpools are not in contact with the ocean coastline... If you look at the Earth from the side of the Sun, whirlpools that are located on the midnight and noon side of the earth are more active because they are in the zone of relative movement.

And when the whirlpool enters the zone of sunset and dawn and becomes edge-on to the Sun, the whirlpool falls into the power of Coriolis forces and subsides. During the new moon, the tides increase and decrease due to the fact that the orbital speed of the earth is at its maximum...

Let's continue the conversation about the forces acting on celestial bodies and the effects caused by this. Today I will talk about tides and non-gravitational disturbances.

What does this mean – “non-gravitational disturbances”? Perturbations are usually called small corrections to a large, main force. That is, we will talk about some forces, the influence of which on an object is much less than gravitational ones

What other forces exist in nature besides gravity? Let us leave aside strong and weak nuclear interactions; they are local in nature (act at extremely short distances). But electromagnetism, as we know, is much stronger than gravity and extends just as far - infinitely. But since electric charges of opposite signs are usually balanced, and the gravitational “charge” (the role of which is played by mass) is always of the same sign, then with sufficiently large masses, of course, gravity comes to the fore. So in reality we will talk about disturbances in the movement of celestial bodies under the influence electromagnetic field. There are no more options, although there is still dark energy, but we will talk about it later, when we talk about cosmology.

As I explained on , Newton's simple law of gravity F = G∙M∙m/R² is very convenient to use in astronomy, because most bodies have a close to spherical shape and are sufficiently distant from each other, so that when calculating they can be replaced by points - point objects containing their entire mass. But a body of finite size, comparable to the distance between neighboring bodies, nevertheless experiences different force influences in its different parts, because these parts are located differently from the sources of gravity, and this must be taken into account.

Attraction crushes and tears apart

To feel the tidal effect, let's do a thought experiment popular among physicists: imagine ourselves in a freely falling elevator. We cut off the rope holding the cabin and begin to fall. Before we fall, we can watch what is happening around us. We hang free masses and observe how they behave. At first they fall synchronously, and we say this is weightlessness, because all the objects in this cabin and it itself feel approximately the same acceleration of free fall.

But over time our material points will begin to change their configuration. Why? Because the lower one at the beginning was a little closer to the center of attraction than the upper one, so the lower one, being attracted stronger, begins to outstrip the upper one. And the side points always remain at the same distance from the center of gravity, but as they approach it they begin to approach each other, because accelerations of equal magnitude are not parallel. As a result, the system of unrelated objects is deformed. This is called the tidal effect.

From the point of view of an observer who has scattered grains around him and watches how individual grains move while the entire system falls onto a massive object, one can introduce such a concept as a field of tidal forces. Let us define these forces at each point as the vector difference between the gravitational acceleration at this point and the acceleration of the observer or the center of mass, and if we take only the first term of the expansion in the Taylor series for relative distance, we will get a symmetrical picture: the nearest grains will be ahead of the observer, the distant ones will lag behind him, i.e. the system will stretch along the axis directed towards the gravitating object, and along directions perpendicular to it the particles will be pressed towards the observer.

What do you think will happen when a planet is pulled into a black hole? Those who have not listened to lectures on astronomy usually think that black hole Only from the surface facing itself will the substance be torn off. They do not know that an almost equally strong effect occurs on back side freely falling body. Those. it is torn in two diametrically opposite directions, not in one at all.

The Dangers of Outer Space

To show how important it is to take into account the tidal effect, take the International space station. It, like all Earth satellites, falls freely in a gravitational field (if the engines are not turned on). And the field of tidal forces around it is a quite tangible thing, so when an astronaut works on outside station, he definitely ties himself to it, and, as a rule, with two cables - just in case, you never know what might happen. And if he finds himself untethered in those conditions where tidal forces pull him away from the center of the station, he can easily lose contact with it. This often happens with tools, because you can’t link them all. If something falls out of an astronaut’s hands, then this object goes into the distance and becomes an independent satellite of the Earth.

The work plan for the ISS includes tests in outer space of a personal jetpack. And when his engine fails, tidal forces carry the astronaut away, and we lose him. The names of the missing are classified.

This is, of course, a joke: fortunately, such an incident has not happened yet. But this could very well happen! And maybe someday it will happen.

Planet-ocean

Let's return to Earth. This is the most interesting object for us, and the tidal forces acting on it are felt quite noticeably. From which celestial bodies do they act? The main one is the Moon, because it is close. The next largest impact is the Sun, because it is massive. The other planets also have some influence on the Earth, but it is barely noticeable.

To analyze external gravitational influences on the Earth, it is usually represented as a solid ball covered with a liquid shell. This is a good model, since our planet actually has a mobile shell in the form of ocean and atmosphere, and everything else is quite solid. Although Earth's crust and the inner layers have limited rigidity and are slightly susceptible to tidal influence, their elastic deformation can be neglected when calculating the effect on the ocean.

If we draw tidal force vectors in the Earth’s center of mass system, we get the following picture: the field of tidal forces pulls the ocean along the Earth-Moon axis, and in a plane perpendicular to it presses it to the center of the Earth. Thus, the planet (at least its moving shell) tends to take the shape of an ellipsoid. In this case, two bulges appear (they are called tidal humps) on opposite sides of the globe: one faces the Moon, the other faces away from the Moon, and in the strip between them, a corresponding “bulge” appears (more precisely, the surface of the ocean there has less curvature).

A more interesting thing happens in the gap - where the tidal force vector tries to move the liquid shell along the earth's surface. And this is natural: if you want to raise the sea in one place, and lower it in another place, then you need to move the water from there to here. And between them, tidal forces drive water to the “sublunar point” and to the “anti-lunar point.”

Quantifying the tidal effect is very simple. The Earth's gravity tries to make the ocean spherical, and the tidal part of the lunar and solar influence– pull it along the axis. If we left the Earth alone and allowed it to fall freely onto the Moon, the height of the bulge would reach about half a meter, i.e. The ocean rises only 50 cm above its average level. If you are sailing on a ship on the open sea or ocean, half a meter is not noticeable. This is called static tide.

But in order to create a half-meter bulge at the sublunar point, you need to distill a large amount of water here. But the surface of the Earth does not remain motionless, it rotates quickly in relation to the direction to the Moon and the Sun, making full turn per day (and the Moon moves slowly in orbit - one revolution around the Earth in almost a month). Therefore, the tidal hump constantly runs along the surface of the ocean, so that the solid surface of the Earth is under the tidal hump 2 times per day and 2 times under the tidal drop in ocean level. Let's estimate: 40 thousand kilometers (the length of the earth's equator) per day, that's 463 meters per second. This means that this half-meter wave, like a mini-tsunami, hits the eastern coasts of the continents in the equator region at supersonic speed. At our latitudes, the speed reaches 250-300 m/s - also quite a lot: although the wave is not very high, due to inertia it can create a great effect.

The second object in terms of influence on the Earth is the Sun. It is 400 times farther from us than the Moon, but 27 million times more massive. Therefore, the effects from the Moon and from the Sun are comparable in magnitude, although the Moon still acts a little stronger: the gravitational tidal effect from the Sun is about half as weak as from the Moon. Sometimes their influence is combined: this happens on a new moon, when the Moon passes against the background of the Sun, and on a full moon, when the Moon is on the opposite side from the Sun. On these days - when the Earth, Moon and Sun line up, and this happens every two weeks - the total tidal effect is one and a half times greater than from the Moon alone. And after a week, the Moon passes a quarter of its orbit and finds itself in quadrature with the Sun (a right angle between the directions on them), and then their influence weakens each other. On average, the height of tides in the open sea varies from a quarter of a meter to 75 centimeters.

Sailors have known tides for a long time. What does the captain do when the ship runs aground? If you have read sea adventure novels, then you know that he immediately looks at what phase the Moon is in and waits for the next full moon or new moon. Then the maximum tide can lift the ship and refloat it.

Coastal problems and features

Tides are especially important for port workers and for sailors who are about to bring their ship into or out of port. As a rule, the problem of shallow water arises near the coast, and to prevent it from interfering with the movement of ships, underwater channels - artificial fairways - are dug to enter the bay. Their depth should take into account the height of the maximum low tide.

If we look at the height of the tides at some point in time and draw lines of equal heights of water on the map, we will get concentric circles with centers at two points (sublunar and anti-lunar), in which the tide is maximum. If the orbital plane of the Moon coincided with the plane of the Earth’s equator, then these points would always move along the equator and would make a full revolution per day (more precisely, in 24ʰ 50ᵐ 28ˢ). However, the Moon does not move in this plane, but near the ecliptic plane, in relation to which the equator is inclined by 23.5 degrees. Therefore, the sublunar point also “walks” along latitude. Thus, in the same port (i.e., at the same latitude), the height of the maximum tide, which repeats every 12.5 hours, changes during the day depending on the orientation of the Moon relative to the Earth's equator.

This “trifle” is important for the theory of tides. Let's look again: the Earth rotates around its axis, and the plane of the lunar orbit is inclined towards it. Therefore, each seaport “runs” around the Earth’s pole during the day, once falling into the region of the highest tide, and after 12.5 hours - again into the region of the tide, but less high. Those. two tides during the day are not equivalent in height. One is always larger than the other, because the plane of the lunar orbit does not lie in the plane of the earth's equator.

For coastal residents, the tidal effect is vital. For example, in France there is one that is connected to the mainland by an asphalt road laid along the bottom of the strait. There are many people living on the island, but they cannot use this road while the sea level is high. This road can only be driven twice a day. People drive up and wait for low tide, when the water level drops and the road becomes accessible. People travel to and from work on the coast using a special tide table that is published for each settlement coast. If this phenomenon is not taken into account, water may overwhelm a pedestrian along the way. Tourists simply come there and walk around to look at the bottom of the sea when there is no water. A local residents At the same time, something is collected from the bottom, sometimes even for food, i.e. in essence, this effect feeds people.

Life came out of the ocean thanks to the ebb and flow of the tides. As a result of the low tide, some coastal animals found themselves on the sand and were forced to learn to breathe oxygen directly from the atmosphere. If there were no Moon, then life might not have come out of the ocean so actively, because it is good there in all respects - a thermostatic environment, weightlessness. But if you suddenly found yourself on the shore, you had to somehow survive.

The coast, especially if it is flat, is greatly exposed at low tide. And for some time people lose the opportunity to use their watercraft, lying helplessly like whales on the shore. But there is something useful in this, because the low tide period can be used to repair ships, especially in some bay: the ships sailed, then the water went away, and they can be repaired at this time.

For example, there is the Bay of Fundy on the east coast of Canada, which is said to have the highest tides in the world: the water level drop can reach 16 meters, which is considered a record for a sea tide on Earth. Sailors have adapted to this property: during high tide they bring the ship to the shore, strengthen it, and when the water goes away, the ship hangs, and the bottom can be caulked.

People have long begun to monitor and regularly record the moments and characteristics of high tides in order to learn how to predict this phenomenon. Soon invented tide gauge- a device in which a float moves up and down depending on sea level, and the readings are automatically drawn on paper in the form of a graph. By the way, the means of measurement have hardly changed since the first observations to the present day.

Based on a large number of hydrograph records, mathematicians are trying to create a theory of tides. If you have a long-term record of a periodic process, you can decompose it into elementary harmonics - sinusoids of different amplitudes with multiple periods. And then, having determined the parameters of the harmonics, extend the total curve into the future and make tide tables on this basis. Now such tables are published for every port on Earth, and any captain about to enter a port takes a table for him and looks at when there will be sufficient water level for his ship.

The most famous story, associated with prognostic calculations, occurred in the Second world war: in 1944, our allies - the British and Americans - were going to open a second front against Nazi Germany, for this it was necessary to land on the French coast. The northern coast of France is very unpleasant in this regard: the coast is steep, 25-30 meters high, and the ocean bottom is quite shallow, so ships can only approach the coast at times of maximum tide. If they ran aground, they would simply be shot from cannons. To avoid this, a special mechanical one was created (there were no electronic ones yet) Calculating machine. She performed Fourier analysis of sea-level time series using drums rotating at their own speed, through which a metal cable passed, which summed up all the terms of the Fourier series, and a feather connected to the cable plotted a graph of tide height versus time. This was top secret work that greatly advanced the theory of tides because it was possible to predict with sufficient accuracy the moment of the highest tide, thanks to which heavy military transport ships swam across the English Channel and landed troops ashore. This is how mathematicians and geophysicists saved the lives of many people.

Some mathematicians are trying to generalize the data on a planetary scale, trying to create a unified theory of tides, but comparing records made in different places is difficult because the Earth is so irregular. It is only in the zero approximation that a single ocean covers the entire surface of the planet, but in reality there are continents and several weakly connected oceans, and each ocean has its own frequency of natural oscillations.

Previous discussions about sea level fluctuations under the influence of the Moon and the Sun concerned open ocean spaces, where tidal acceleration varies greatly from one coast to another. And in local bodies of water - for example, lakes - can the tide create a noticeable effect?

It would seem that it should not be, because at all points of the lake the tidal acceleration is approximately the same, the difference is small. For example, in the center of Europe there is Lake Geneva, it is only about 70 km long and is in no way connected with the oceans, but people have long noticed that there are significant daily fluctuations in water there. Why do they arise?

Yes, the tidal force is extremely small. But the main thing is that it is regular, i.e. operates periodically. All physicists know the effect that, when a force is periodically applied, sometimes causes an increased amplitude of oscillations. For example, you take a bowl of soup from the cafeteria and... This means that the frequency of your steps is in resonance with the natural vibrations of the liquid in the plate. Noticing this, we sharply change the pace of walking - and the soup “calms down.” Each body of water has its own basic resonant frequency. And what larger size reservoir, the lower the frequency of natural vibrations of the liquid in it. So, Lake Geneva’s own resonant frequency turned out to be a multiple of the frequency of the tides, and a small tidal influence “looses” Lake Geneva so that the level on its shores changes quite noticeably. These long-period standing waves that occur in closed bodies of water are called seiches.

Tidal Energy

Nowadays, they are trying to connect one of the alternative energy sources with the tidal effect. As I said, the main effect of tides is not that the water rises and falls. The main effect is a tidal current that moves water around the entire planet in a day.

In shallow places this effect is very important. In the New Zealand area, captains do not even risk guiding ships through some straits. Sailboats have never been able to get through there, and even modern ships have difficulty getting through there, because the bottom is shallow and tidal currents have enormous speed.

But since the water is flowing, this kinetic energy can be used. And power plants have already been built, in which turbines rotate back and forth due to tidal currents. They are quite functional. The first tidal power plant (TPP) was made in France, it is still the largest in the world, with a capacity of 240 MW. Compared to a hydroelectric power station, it’s not so great, of course, but it serves the nearest rural areas.

The closer to the pole, the lower the speed of the tidal wave, therefore in Russia there are no coasts that would have very powerful tides. In general, we have few outlets to the sea, and the coast of the Arctic Ocean is not particularly profitable for using tidal energy, also because the tide drives water from east to west. But there are still places suitable for PES, for example, Kislaya Bay.

The fact is that in bays the tide always creates a greater effect: the wave runs up, rushes into the bay, and it narrows, narrows - and the amplitude increases. A similar process occurs as if a whip was cracked: at first the long wave travels slowly along the whip, but then the mass of the part of the whip involved in the movement decreases, so the speed increases (impulse mv is preserved!) and reaches supersonic at the narrow end, as a result of which we hear a click.

By creating the experimental Kislogubskaya TPP of low power, power engineers tried to understand how effectively tides at circumpolar latitudes can be used to produce electricity. It doesn't make much economic sense. However, now there is a project for a very powerful Russian TPP (Mezenskaya) – for 8 gigawatts. In order to achieve this colossal power, it is necessary to block off a large bay, separating the White Sea from the Barents Sea with a dam. True, it is highly doubtful that this will be done as long as we have oil and gas.

The past and future of tides

By the way, where does tidal energy come from? The turbine spins, electricity is generated, and what object loses energy?

Since the source of tidal energy is the rotation of the Earth, if we draw from it, it means that the rotation must slow down. It would seem that the Earth has internal sources energy (heat from the depths comes from geochemical processes and the decay of radioactive elements), there is something to compensate for the loss of kinetic energy. This is true, but the energy flow, spreading on average almost evenly in all directions, can hardly significantly affect the angular momentum and change the rotation.

If the Earth did not rotate, the tidal humps would point exactly in the direction of the Moon and the opposite direction. But, as it rotates, the Earth’s body carries them forward in the direction of its rotation - and a constant divergence of the tidal peak and the sublunar point of 3-4 degrees arises. What does this lead to? The hump that is closer to the Moon is attracted to it more strongly. This gravitational force tends to slow down the Earth's rotation. And the opposite hump is further from the Moon, it tries to speed up the rotation, but is attracted weaker, so the resultant moment of force has a braking effect on the rotation of the Earth.

So, our planet is constantly decreasing its rotation speed (though not quite regularly, in jumps, which is due to the peculiarities of mass transfer in the oceans and atmosphere). What effect do Earth's tides have on the Moon? The near tidal bulge pulls the Moon along with it, while the distant one, on the contrary, slows it down. The first force is greater, as a result the Moon accelerates. Now remember from the previous lecture, what happens to a satellite that is forcibly pulled forward in motion? As its energy increases, it moves away from the planet and its angular velocity decreases because the orbital radius increases. By the way, an increase in the period of revolution of the Moon around the Earth was noticed back in the time of Newton.

Speaking in numbers, the Moon moves away from us by about 3.5 cm per year, and the length of the Earth’s day increases by a hundredth of a second every hundred years. It seems like nonsense, but remember that the Earth has existed for billions of years. It is easy to calculate that in the time of dinosaurs there were about 18 hours in a day (the current hours, of course).

As the Moon moves away, tidal forces become smaller. But it was always moving away, and if we look into the past, we will see that before the Moon was closer to the Earth, which means the tides were higher. You can appreciate, for example, that in the Archean era, 3 billion years ago, the tides were kilometer high.

Tidal phenomena on other planets

Of course, the same phenomena occur in the systems of other planets with satellites. Jupiter, for example, is a very massive planet with big number satellites. Its four largest satellites (they are called Galilean because Galileo discovered them) are quite significantly influenced by Jupiter. The nearest of them, Io, is entirely covered with volcanoes, among which there are more than fifty active ones, and they emit “extra” matter 250-300 km upward. This discovery was quite unexpected: on Earth there are such powerful volcanoes no, but here is a small body the size of the Moon, which should have cooled down long ago, but instead it is bursting with heat in all directions. Where is the source of this energy?

Io's volcanic activity was not a surprise to everyone: six months before the first probe approached Jupiter, two American geophysicists published a paper in which they calculated Jupiter's tidal influence on this moon. It turned out to be so large that it could deform the satellite’s body. And during deformation, heat is always released. When we take a piece of cold plasticine and begin to knead it in our hands, after several compressions it becomes soft and pliable. This happens not because the hand heated it with its heat (the same thing will happen if you squish it in a cold vice), but because the deformation put mechanical energy into it, which was converted into thermal energy.

But why on earth does the shape of the satellite change under the influence of tides from Jupiter? It would seem that, moving in a circular orbit and rotating synchronously, like our Moon, it once became an ellipsoid - and there is no reason for subsequent distortions of the shape? However, there are also other satellites near Io; all of them cause its (Io) orbit to shift slightly back and forth: it either approaches Jupiter or moves away. This means that the tidal influence either weakens or intensifies, and the shape of the body changes all the time. By the way, I haven’t talked about tides yet solid body Earth: they, of course, also exist, they are not so high, about a decimeter. If you sit in your place for six hours, then, thanks to the tides, you will “walk” about twenty centimeters relative to the center of the Earth. This vibration is imperceptible to humans, of course, but geophysical instruments register it.

Unlike the solid earth, the surface of Io fluctuates with an amplitude of many kilometers during each orbital period. A large number of the deformation energy is dissipated in the form of heat and heats the subsoil. By the way, meteorite craters are not visible on it, because volcanoes constantly bombard the entire surface with fresh matter. As soon as an impact crater is formed, a hundred years later it is covered with products of eruptions of neighboring volcanoes. They work continuously and very powerfully, and to this are added fractures in the planet’s crust, through which a melt of various minerals, mainly sulfur, flows from the depths. At high temperature it darkens, so the stream from the crater looks black. And the light rim of the volcano is the cooled substance that falls around the volcano. On our planet, matter ejected from a volcano is usually decelerated by air and falls close to the vent, forming a cone, but on Io there is no atmosphere, and it flies along a ballistic trajectory far in all directions. Perhaps this is an example of the most powerful tidal effect in the solar system.

The second satellite of Jupiter, Europa, all looks like our Antarctica, it is covered with a continuous ice crust, cracked in some places, because something is constantly deforming it too. Since this satellite is further away from Jupiter, the tidal effect here is not so strong, but still quite noticeable. Beneath this icy crust is a liquid ocean: the photographs show fountains gushing out of some of the cracks that have opened up. Under the influence of tidal forces, the ocean rages, and ice fields float and collide on its surface, almost like ours in the North Arctic Ocean and off the coast of Antarctica. The measured electrical conductivity of Europa's ocean fluid suggests that it salty water. Why shouldn't there be life there? It would be tempting to lower a device into one of the cracks and see who lives there.

In fact, not all planets meet ends meet. For example, Enceladus, a moon of Saturn, also has an icy crust and an ocean underneath. But calculations show that tidal energy is not enough to maintain the subglacial ocean in a liquid state. Of course, in addition to tides, any celestial body has other sources of energy - for example, decaying radioactive elements (uranium, thorium, potassium), but on small planets they can hardly play a significant role. This means there is something we don’t understand yet.

The tidal effect is extremely important for stars. Why - more on this in the next lecture.