A. OSTAPENKO, Chairman of the Moscow Astronomical Club.

An image of a total solar eclipse that took place in 2001.

Phase sequence during a total solar eclipse (1998).

"Total Solar Eclipse of 1937". Painting by artist D. Stephens. According to some experts, it conveys the view of the sky during the total phase of the eclipse better than photographs.

An engraving by Abbé Moreau depicts a view of the sky, terrain and solar corona during the eclipse of May 28, 1900.

A 19th century engraving showing the appearance of the so-called "running shadows" that are visible on bright surfaces a few seconds before the moment of the total phase of the eclipse.

Time (summer Moscow) of the visibility of individual phases in the band of the upcoming total solar eclipse on the territory of Russia, Georgia, Kazakhstan (h - hours, m - minutes, s - seconds).

Time of visibility of partial phases of the solar eclipse on March 29, 2006 in some cities of Russia and Belarus.

Science and life // Illustrations

View of solar coronas during eclipses of different years.

The dark bar on the globe shows what the path of the moon's shadow will be on the surface of the Earth during the upcoming total solar eclipse. Regions extend to the right and left of this strip for more than 3,500 km, where a partial eclipse of the Sun will be visible.

Very soon, on March 29 of this year, the "insidious demons" will again try to steal the Sun from people. There will be an interesting astronomical phenomenon - a total solar eclipse. The inhabitants of the Earth have been observing it for many thousands of years, and only recently have they learned how to explain the essence of a solar eclipse.

Yet even modern educated person experiences a certain superstitious awe, when before his eyes the whole world plunges into mysterious darkness in broad daylight, and in that place of the sky where the Sun had just shone, a round black "hole" is formed, surrounded by a fantastic, unearthly pearly radiance.

In almost all religions of the world, the description of eclipses was assigned a special role. What was happening was explained, as a rule, as follows: the luminous god of the Sun is fighting dark, evil otherworldly forces - devils, demons, with a terrible dragon. This struggle was of particular importance. And in order to help the Sun defeat the terrible black shadow eating it, our ancestors tried to drive away the evil monster. They raised noise, clamor, beat drums and tambourines, blew horns, rattled rattles, shot demons from weapons at hand ... And the Sun always won!

How eclipses happen

Let's turn to scientific explanations the reasons why they happen.

Every eclipse, both solar and lunar, is just a play of sunlight and shadows cast by celestial bodies. The Moon, moving in its orbit around the Earth, from time to time finds itself on the same straight line connecting the Sun, Moon and Earth (between them). At the same time, an observer on Earth can see how the Moon sometimes partially, and sometimes completely obscures the Sun, a lunar shadow falls on the Earth - a solar eclipse occurs. But not always, much more often the Moon "misses": it passes just above or below the solar disk. This is mainly due to the fact that the plane of the Moon's orbit is slightly (by 5.2 o) inclined to the plane in which the Earth revolves around the Sun. And also with the fact that eclipses can occur only near the so-called nodes of the lunar orbit, that is, those places where it intersects with the plane of the ecliptic. The nodes of the lunar orbit are on the Earth-Sun line once every six months. Therefore, the series of eclipses occur at about a six-month interval.

The shadow cast by the Moon towards the Earth looks like a rather sharp converging cone. The tip of this cone is a little further than our planet. Therefore, when the shadow hits the surface of the Earth, it is not a point, but a relatively small (150-200 km across) black spot. Following the Moon, this spot quickly moves across the surface of our planet and, as it were, draws a line on it, which is called the band of the total eclipse phase.

The Sun is about 400 times farther from the Earth than the Moon, and its diameter is almost 400 times that of the Moon. Therefore, their disks visible from the Earth are approximately the same in size; during an eclipse, the Moon almost perfectly covers the Sun. If it were at least a little smaller, we could never see a total eclipse, and if it were larger, the solar corona during an eclipse could only be seen in parts. The spectacle as a whole would have seemed incomparably less spectacular.

On the strip of the total phase of the eclipse, one can mentally single out the central line, on which the duration of the eclipse is maximum, and towards the edges it quickly decreases.

At the same point on the Earth, total solar eclipses are seen no more than once every 200-300 years, although there are exceptions. We will talk about one of them below.

On the days of solar eclipses for astronomers on expeditions to different parts of the world, it is a common and very important matter, since only in short minutes of the total phase it is possible to study the weak light of the upper layers of the Sun’s atmosphere and its ephemeral corona, which you cannot see at other times, they go out in the powerful glow of the lower , very bright layers of the luminary.

Since the beginning of this century, not a single total solar eclipse has yet been observed on the territory of Russia! And the last one that we saw happened on March 9, 1997, but even then - only in the eastern half of the European part of Russia (only in the northern regions). A total eclipse was observed on July 22, 1990. An eclipse similar to what awaits us now took place a quarter of a century ago - in 1981. The next similar phenomenon in the European part of the country will happen only in 2061.

moon shadow path

It is a narrow strip on the Earth's surface, 150-200 km wide. Only in this band can you see how the Moon completely covers the Sun. In the areas adjacent to the band, a partial eclipse is observed, that is, the Moon hides only part of the solar disk, which looks like a slightly flawed circle somewhere, and somewhere a thin sickle: the degree of coverage decreases with distance from the full phase band.

This time, March 29, 2006, the eclipse will begin at sunrise. The shadow will come to Earth in the rainforests of the easternmost part of Brazil, not far from the Atlantic coast. The speed of its movement at this time is extremely high. The eclipse here will last only one minute. Rapidly crossing the Atlantic, in an hour and a half the shadow will appear off the coast of Africa and enter its coast in Ghana; quickly passing through Togo, Benin and Nigeria, will enter the territory of the Sahara desert. Here, at the junction of the borders of Nigeria, Chad and Libya, the duration of the eclipse will be the longest - 4 min 6 s. In two hours, the shadow will come to the northern coast of Africa, in the area of ​​the Libyan-Egyptian border, not far from the historic El Alamein. Passing over the Mediterranean Sea in 10 minutes, the shadow will appear off the coast of Turkey, in the fertile region of the Anatolian Gulf, the country's most popular resort area. The central line of the shadow will pass right through the cities of Kemer, Antalya, Manavgat, Side, well known to millions of Russian tourists. Here, the duration of the eclipse will already decrease, but it will still reach 3 min 45 s. Having crossed the coastal mountain ranges, the shadow will go deep into Turkish territory - to Cappadocia and further to the Black Sea. Having passed quickly (in 9 minutes) over the eastern part of the sea, it will again come ashore, now in Abkhazia, capturing a strip almost from Gagra to Batumi. In a few minutes it will cover the entire Central Caucasus, pass over Elbrus and reach the plains of southern Russia. Having rushed over Astrakhan, the shadow will go to the territory of Kazakhstan, but will soon return to the territory of Russia, this time in the foothills of Altai. Here the duration of the event will be only 2 minutes. After another 15 minutes, the shadow will be in Mongolia, where the total eclipse (it will be visible already at sunset) will end.

Needless to say, the spectacle is not only rare and unique, but also extremely impressive. Those who have seen the eclipse say that everyone should try to see it at least once in their life.

Where is the best place to see the eclipse?

It is not easy to answer this question. Because the decisive factor in any place will be the weather. An overcast day, thick clouds in the sky will negate all other advantages of any place for observing a solar eclipse.

March in most places northern hemisphere by no means the clearest and most stable month. It is practically impossible to find out in advance a reliable weather forecast for a specific, very small point on the earth, and even for a certain day and hour. So where is the most reliable place to go if someone decides on such a trip? Probably, where, according to long-term statistics, at the end of March, the highest probability of clear weather.

Of course, we are not talking about places like the center of the Sahara in Africa. There, the chance of any significant cloud cover does not exceed 10-15%.

Further, along the route of the shadow - on the Anatolian coast of Turkey, the probability of clear weather drops significantly and is already a little more than 50%. On the Black Sea coast of the Caucasus, the percentage of clear weather is even less, and in the mountains themselves, on both sides of the ridge, the forecast for clear weather is no higher than 25%. On the plains beyond the Caucasus, the probability of the absence of strong cloudiness increases again, in some places it exceeds 40% (in most of Kazakhstan) and even slightly increases as one approaches the zone of action of the Siberian anticyclone (if at that time it will be in its usual place). But, if the anticyclone is absent or shifts far to the side, the possibility of cloudy weather will increase dramatically. In the Astrakhan region, as in the entire Caspian lowland, cloudiness is very likely due to the proximity to the sea; nevertheless, the forecast here is more favorable than in the North Caucasus.

Eclipse in Russia

This time, luck is favorable to us: the strip passes through fairly populated areas of the country with a well-developed transport network, and if you wish, you can easily get to the place of the full phase in your own country. Thus, many Russian astronomy enthusiasts have options for choosing a place for observations.

The lunar shadow will begin to move across the territory of Russia in the mountains of the Caucasus. A few minutes before it appears here, the shadow will pass through the territory of Georgia, namely, through Abkhazia. The eclipse will begin in Gudauta at 15:13:53 Moscow Summer Time (it will be introduced from March 26), then it will cover Sukhumi and nearby settlements, where the duration of the total phase will be almost 3 minutes. Zugdidi and Poti will also be in the full phase zone.

After leaving the territory of Georgia, the shadow of the Moon will enter Russian lands and immediately cover the famous ski resort Dombay and nearby settlements, then the city of Karachaevsk, where the duration of the full phase will be 1 min 23 s. Almost simultaneously, the Sun will go out in Kislovodsk, Essentuki and Mineralnye Vody, where the duration of the full phase will be a little more than 2 minutes. Baksan (the famous mountain resort of Kabardino-Balkaria) will be practically on the central line, and the duration of the full phase there will reach 3 min 17 s. Mount Elbrus will also be in the full phase zone. Vacationers on its slopes will be able to see a fantastic picture of an eclipse surrounded by mountain peaks, if, of course, the weather there is very changeable. At the same time, the shadow will cover Nalchik (phase duration - 3 min 06 s), and a little later the edges will touch Budennovsk (1 min 15 s), Mozdok and Neftekumsk. Then the shadow will glide over the steppes and deserts of Kalmykia to the northeast. In Astrakhan, the duration of the full phase will be about a minute, as the city will be on the very edge of the shadow. However, those who get out 50-70 km to the south or southeast of the city, to the shores of the Caspian Sea, will be able to get almost to the central line of the strip, where the duration of the full phase will reach up to 3 minutes!

After leaving the Astrakhan region and passing through the territory of Kazakhstan, the shadow strip will fall into the Altai Territory, covering the large city of Rubtsovsk along the way, where the duration of the full phase will be 2 min 06 s; soon the shadow will be in Gorno-Altaisk, which lies directly on the central line of the eclipse. It is interesting to note that in less than three years (August 1, 2008) this city will again fall into the band of a total solar eclipse. This usually happens once every 200-300 years. That's really rare luck!

After Gorno-Altaisk, the eclipse will be seen by residents of Kyzyl, where the duration of the total phase will be only 1 min 56 s and the Sun will be visible already at the very horizon, at sunset.

As a result, it can be assumed that the most popular observation sites in the European part of Russia will be the North Caucasus (especially the Mineralnye Vody region) and the Astrakhan region. Both have their advantages and disadvantages. Almost unpredictable weather in the Caucasus, despite a large number of sunny days a year, turns an astronomical expedition into a lottery.

In the Astrakhan region, according to statistics, the probability of cloudiness is close to 60% and, in general, the weather is much more stable than in the Caucasus.

After leaving Kazakhstan, the moon shadow will again be on Russian territory, in the Altai Territory. The weather here at the end of March is quite good, sunny days are frequent, although frosty. Moon shadow, lying not far south of the densely populated areas of Kuzbass and Western Siberia, will attract observers and visitors here, especially, of course, residents of these regions.

partial eclipse

Unfortunately, most of those who would like to see a solar eclipse will not be able, for various reasons, to go for observations where the total phase will be visible. And although, of course, the impressions of observing a partial eclipse cannot be compared with the amazing effect of a total eclipse, one should not refuse the opportunity to observe at least a partial one. It lasts for several hours, and one can slowly sketch or photograph the entire course of the eclipse phase change, imprint in memory the different stages of the defective solar disk and the details of the moon's limb. If spots are visible on the Sun - try to capture the moment of a successful photo composition.

It has long been noticed that animals and birds are very sensitive to changes in nature caused by an eclipse, so it is interesting to follow their behavior.

Spectacular experiments with the shadows cast by the Sun during an eclipse. Visible change geometric shape our luminary also distorts the shape of the most familiar shadows, sometimes in a rather unexpected way. When the Sun takes the form of a crescent, an image of the current Sun will suddenly appear in the shadows - the same crescents, only inverted.

In those places where the phases of the eclipse will be very large, more than 0.95 o, and the sky will noticeably darken, you can try to find bright stars and planets on it.

It is interesting to see through a telescope (at high magnification) the uneven edge of the lunar limb, since almost the entire surface of the Moon is covered with hills and mountains. They are often visible on the edge of the lunar disk.

What will we see

In order not to miss anything during the short minutes of a total eclipse, you need to know in advance what to pay attention to, what is possible to see in these minutes. Sketches and photos taken by eyewitnesses of past solar eclipses will help here. You should remember and clearly imagine what and at what moment (in seconds) you need to find with your eyes. It is good to imagine the course of the eclipse, the appearance of the Sun and the sky in each phase. Make (write down) for yourself the procedure for observing, after which, with a stopwatch in your hands, practice in its implementation.

The beginning of the eclipse, that is, the time of the entry of the Moon onto the disk of the Sun, as well as small partial phases, an unprepared observer cannot detect.

Surprisingly, people usually do not notice a drop in illumination, even when 2/3 of the area of ​​\u200b\u200bthe Sun is covered. Apparently, this is how our brain works, it kind of "enhances" the picture, bringing it to the usual brightness.

Inexperienced observers notice the weakening of sunlight when about 80% or more of the area of ​​\u200b\u200bthe sun is already covered. Then it is clear that a narrow crescent remained from the usual solar circle.

From phase 0.9, the rate of development of events seems to increase sharply. If a little more than an hour passes from the appearance of the first "pocket" on the Sun to a narrow crescent and the phase increases slowly, then this crescent simply becomes thinner before our eyes, turns into a thread, and then abruptly disappears. Along the edge of the lunar disk, an arc of bright sparkling stars (the so-called "Bailey's beads") flashes for a few seconds, after which the sky suddenly darkens sharply, the stars light up, and instead of the Sun, a black circle ("hole") appears in the sky, surrounded by a pearl blue, silvery radiance - this is the solar corona. Depending on the position of the observer, the total phase of the eclipse lasts from a few seconds to three to four minutes. During this time, sharp-sighted observers can see a thin pink ring surrounding the black disk of the Moon - this is the solar chromosphere, top part the atmosphere of our sun.

Large prominences should also be visible - ejections of matter into the chromosphere. They have the appearance of small pinkish-purple tubercles, towering above the chromosphere. Crown, surrounding the sun, flashes brightly, its shape becomes visible, jets and rays are clearly visible.

An observer armed with binoculars, a spyglass or a telescope (of course, always with light-protective filters) will be able to see much more details at this time. For example, the thinnest jets in the solar corona. The shape and size of the corona usually depend on the degree of activity of the Sun. During the years of activity it is wide, "shaggy", during the years of solar minima it is small and relatively calm. The Sun is currently at its cycle minimum, so it is possible that the corona will not be particularly spectacular.

It is very interesting (and even absolutely necessary) during an eclipse to break away from the instruments for at least a few seconds in order to examine the sky and the surrounding area. The sky will appear dark purple. The stars will shine on it. Along the horizon, however, it will be painted in reddish-orange tones - these are the regions of the Earth and the atmosphere that are not hidden from the Sun - where a partial eclipse occurs at this time. An attentive person will also note other phenomena: a change in air temperature, wind direction and strength, a change in the type of cloudiness, etc.

Try to find planets in the sky, especially those that are visible now next to the Sun, and therefore we do not see them at night.

Watching a total solar eclipse, do not limit yourself to visual contemplation. An eclipse can and should be photographed to better capture the magnificent natural phenomenon that you witnessed.

In our time, when modern digital photography technology has stepped incredibly far compared to that used in the recent past, it is much easier to get high-quality pictures. SLR digital cameras are now widespread. With them, the shooting process has been greatly simplified. But to get a really good photo of a solar eclipse, technique alone is not enough. You also need a certain amount of knowledge, skills, some special devices, as well as a fair amount of luck.

We will talk about all this in the next issue of the magazine. Here we want to remind you once again: during the exciting and intense process of shooting, do not forget to just admire the extraordinary spectacle that has opened. Otherwise, you run the risk of replenishing the number of those photographers who say with chagrin that they took good pictures, but did not see the eclipse itself.

Expert advice

EYE SAFETY

The sun is an extremely powerful source of energy and can damage the eyes even for the shortest time looking at it. Therefore, to observe an eclipse - that is, a phenomenon that lasts several hours, is by no means impossible without special precautions. It must be taken as a rule that before the onset of the total phase of the eclipse, that is, until the moment the Sun is completely hidden behind the disk of the Moon, you cannot look at it without protection. To observe partial phases, it is also necessary to use protective equipment - special "eclipse glasses", solar filters (now all this is on sale). At worst, you can use the old proven methods: smoked glass, illuminated and developed film, media from an old computer floppy disk.

Those who plan to observe the Sun with a telescope, be sure to equip the telescope with a special solar filter. Any, even the smallest telescope, collects tens or even hundreds of times more light than the eye. So even a fraction of a second is enough to lose sight forever after looking through a telescope at the Sun.. There are different designs of filters, but it is better that the filter be aperture - put on the lens. You should not use ocular filters, that is, a special black glass that is worn on the eyepiece, which were previously equipped with some models of telescopes, should not be used. With prolonged heating, they often burst and then represent a serious danger. The most popular now are filters made of a special "solar film" - a polymer film with high optical qualities, on which a layer of metal is deposited. It perfectly protects both the eyes of the observer and the telescope, practically without distorting the images.

You should also take care of the safety of others. It happens that, having protected the "main caliber" of the telescope with a filter, they forget about the finder and other devices. Even small telescopes, usually mounted parallel to the main telescope, tend to be of particular interest to children, as well as adults who are not familiar with astronomy. Be sure to cover these devices with covers. And in general, it is better not to leave the telescope unattended.

As you know, the planets and their satellites do not stand still. The earth revolves around the sun and the moon revolves around the earth. And from time to time there are such moments when the Moon in its movement completely or partially obscures the Sun.

Picture 1.

Solar eclipse is the shadow of the moon on the surface of the earth. This shadow is about 200 km in diameter, which is many times smaller than the diameter of the Earth. Therefore, a solar eclipse can be observed simultaneously only in a narrow band along the path of the moon's shadow:

Figure 2. Lunar shadow on the Earth's surface during a solar eclipse

If the observer is in the shadow strip, he sees total solar eclipse, in which the moon completely hides the sun. At the same time, the sky darkens, and stars can become visible on it. It's getting a little cooler. The birds abruptly fall silent, frightened by the sudden darkness, and try to hide. Animals start to get restless. Some plants fold their leaves.

Figure 3 Phase of a total solar eclipse

Observers near the total eclipse can see partial solar eclipse . During a partial eclipse, the Moon passes across the disk of the Sun not exactly in the center, but hides only part of this disk. In this case, the sky darkens much weaker than during a total eclipse, the stars are not visible on it. A partial eclipse can be observed at a distance of about 2 thousand kilometers from the zone of total eclipse.

Figure 4

A solar eclipse always happens on a new moon. At this time, the Moon is not visible on Earth, because the side of the Moon that faces the Earth is not illuminated by the Sun (see Figure 1). Because of this, it seems that during an eclipse, the Sun closes a black spot, taken from nowhere.

The shadow that the Moon casts towards the Earth looks like a converging cone. The tip of this cone is located a little further than our planet (see Figures 1 and 2). Therefore, when the shadow hits the surface of the Earth, it is not a point, but a relatively small (150–270 km across) black spot. Following the Moon, this spot moves across the surface of our planet at a speed of about 1 kilometer per second:

Figure 5
Scheme of the solar eclipse July 22, 2009 from the NASA website

Consequently, the shadow of the Moon moves with great speed over the earth's surface and cannot permanently close any one place on the globe. The maximum possible duration of the full phase is only 7.5 minutes. A partial eclipse lasts about two hours.

Solar eclipses on Earth are a truly unique phenomenon. It is possible because on the celestial sphere the diameters of the Moon and the Sun almost coincide, despite the fact that the diameter of the Sun is almost 400 times the diameter of the Moon. And this happens because the Sun is about 400 times farther from the Earth than the Moon.

But the Moon's orbit is not round, but elliptical. Therefore, at times favorable for the onset of eclipses, the lunar disk can be larger than the solar disk, equal to it or less than it. The first is a total eclipse. In the second case, a total eclipse also occurs, but it lasts only a moment. And in the third case, an annular eclipse occurs: around the dark disk of the Moon, a shining ring of the Sun's surface is visible. Such an eclipse can last up to 12 minutes.

During a total solar eclipse, you can see solar corona - the outer layers of the Sun's atmosphere, which is not visible in normal sunlight. This is a breathtakingly beautiful sight:

Figure 6 Solar eclipse August 11, 1999

In different parts of the Earth, a solar eclipse occurs at different times. Due to the movement of the Moon around the Earth and the rotation of the Earth around its axis, the shadow from the Moon moves along the earth's surface approximately from west to east, forming a strip of shadow several thousand kilometers long and about 200 km wide on average (maximum width 270 km).

Rice.

The cause and types of solar eclipses can be shown by a simple experiment demonstrated in a darkened room.

To do this, you need to put an electric lamp at one end of a long table (preferably in a spherical matte lampshade), at the other end - a geographical globe, and between them you need to hang a small ball on a thread. Illuminated by a lamp, the ball will cast a shadow and penumbra on the globe, i.e. demonstrate total and partial solar eclipses. By shifting the ball a little up and down, you can skip its shadow past the globe, leaving only a penumbra on it, which will show the cause of partial solar eclipses. The displacement of the ball further in the same direction until its penumbra leaves the globe will demonstrate a new moon without solar eclipses.

A solar eclipse begins from the right, western edge of the Sun, on the disk of which a small damage appears, having the shape of a circle of the same radius. Gradually, the phase of the eclipse increases, and the solar disk takes the form of a continuously narrowing crescent, significantly different in shape from crescent-shaped lunar phases, limited not by a circular, but by an elliptical terminator.

If the eclipse is partial, then in the middle of the eclipse its phase reaches a certain the greatest value, and then decreases again, and the eclipse ends on the left, eastern edge of the solar disk. During partial eclipses, the attenuation of sunlight is not noticeable (with the exception of eclipses with the largest phase close to 1), and the phases of the eclipse are visible only when observing through a dark filter.

In the total phase band, a solar eclipse also begins with partial phases, but when the Moon completely covers the Sun, twilight sets in, as in dark twilight, and the brightest stars and planets appear in the darkened sky, and a beautiful radiant pearl-colored radiance is visible around the Sun - the solar corona , which is the outer layers of the solar atmosphere, not visible outside the eclipse due to their low brightness in comparison with the brightness of the daytime sky.

Rice.

A glowing ring flashes over the entire horizon - this is sunlight from neighboring zones where a total eclipse does not occur, but only a partial one is observed in an area covered with a lunar shadow. After all, the radiance and blue rays that enter the sunlight are abundantly scattered by the earth's atmosphere, while the red and orange rays pass through it almost unhindered, and even the dense ground layer of air does not interfere with them.

That is why this layer of air is perceived as reddish-pink.

There are eclipses, annular (Fig. 6), total (Fig. 7) and partial.

A total eclipse is the best time to study the solar atmosphere: the silvery corona and the lower layer - the red chromosphere, above which the fiery fountains of prominences rise.

Rice.

Rice.

Soon, most often after 2 - 3 minutes, the Moon opens the western solar edge, the total phase of the eclipse ends, the glow ring disappears, quickly brightens, stars, planets and the solar corona disappear.

By the way, the appearance of the solar corona changes from year to year, from disheveled in all directions, to elongated along the solar equator. Obviously, the elongated appearance of the crown gave rise to the ancient Egyptians to portray the Sun as winged.

In each area, the eclipse begins and ends at different times and its circumstances, including the duration, depend not only on the speed of the lunar shadow (penumbra), but also on the location of this area in it.

The calculated eclipse circumstances are plotted on geographical map, which in this case is called a solar eclipse map. It depicts lines connecting points on the earth's surface with one or another identical value and therefore called isolines (from the Greek "isos" - equal, the same). Thus, the isochrones of the beginning (end) of a partial eclipse pass through the points at which the partial eclipse begins (ends) at the same moment in a certain time system, for example, Moscow time. Isophases always connect points at which the largest phase of the eclipse is the same (it is more correct to call them isophases of the largest phase).

The duration of the entire eclipse and its total phase on the central line is calculated by the diameters of the lunar penumbra and shadow and by the speed of their movement along the earth's surface. These calculations, as well as calculations of all the circumstances of solar eclipses for different areas of the Earth, are very complex, since the speed of the lunar shadow (and penumbra) on the earth's surface depends on the magnitude and direction of the geocentric velocity of the Moon, on the geographic latitude of the area and on the angle of inclination of the cone of the lunar shadow to surface of this area.

But still, for the sake of clarity, it is possible to show at least an approximate principle for calculating the duration of a total solar eclipse on the central line of the total phase band.

As soon as the movement of the Moon and the rotation of the Earth occur in the forward direction, then the lunar shadow moves along the earth's surface at approximately the speed:

where is the geocentric velocity of the Moon and - line speed points on the earth's surface in the direction of the movement of the moon's shadow.

Obviously, the longest duration of the total eclipse phase is possible only at the maximum diameter of the lunar shadow and only in the equatorial zone of the Earth, where the linear velocity of the points on the earth's surface is the largest and is close to = 0.47 km/sec.

The maximum diameter of the lunar shadow, as we already know, is possible only at the smallest geocentric distance of the Moon, when its speed approaches = 1.08 km/sec. Therefore, the longest duration of the total phase of a solar eclipse

and more accurate calculations lead to the value:

Periodicity of solar eclipses

Partial solar eclipses occur in every locality, naturally more often than total eclipses, since the diameter of the lunar penumbra, as has already been shown, significantly exceeds the diameter of the lunar shadow.

So, for example, in 30 years, from 1952 to 1981, Moscow accounted for 13 partial solar eclipses, i.e. in Moscow they occur on average every 2.3 years.

A similar picture is inherent in many other places on the earth's surface. But since during partial solar eclipses with a small phase, the sunlight almost does not weaken, then they simply do not pay attention to them and refer solar eclipses to a number of very rare events nature.

But partial eclipses with a significant phase are already arousing their interest, since the study of a series of photographs of successive phases of the eclipse makes it possible to refine the motion of the Moon and, if necessary, introduce appropriate corrections into the theory of its motion.

Astronomers observe total solar eclipses without fail, and for this they often have to go on very distant expeditions and install and adjust scientific equipment in advance, three to four weeks before the eclipse.

In addition to refinements for the theory of the motion of the Moon, a comparison of the calculated and observed contacts and phases of the eclipse helps to study insignificant deviations from the uniform rotation of the Earth, well, and the main goal of observing total solar eclipses is, of course, the study of the solar corona, the outer regions and rays of which outside the eclipse do not visible.

In the few minutes that the total phase of the eclipse lasts, astronomers manage to obtain numerous photographs of the corona, taken in different color beams, photographs of its spectrum with their instruments, record changes in the intensity of its radio emission using self-registering equipment, and perform a number of other observations that are essential for studying the physical nature of the Sun and the processes occurring on it.

This study, in turn, helps astronomers to understand the nature of numerous stars, only one of which is our Sun.

In ancient times, a solar eclipse was perceived with horror and admiration at the same time. In our time, when the causes of this phenomenon have become known, people's feelings have not changed much. Some are looking forward to it with impatience in the hope of observing this majestic phenomenon, others - with some anxiety and anxiety. I wonder if there will be a solar eclipse in 2018 in Russia?

A little about the cause and types of solar eclipse

In our age of enlightenment, even a schoolboy knows why an eclipse of the Sun occurs. For those who have forgotten the essence of what is happening, we remind you that a solar eclipse occurs due to the closing of the solar disk by the Moon. The overlap may be complete or partial. Such an event can occur on a full moon and for a very short time. Max Time solar eclipse barely reaches 7.5 minutes. It happens:

1. complete when the lunar disk completely covers the Sun for the human eye on Earth;
2. private when the Moon partially covers the Sun;
3. annular- at this time, the disk of the Moon completely covers the disk of the Sun, but the rays of our luminary are visible along the edges of the lunar disk.

The last kind of eclipse is the most beautiful for all lovers of unusual natural phenomena and the most interesting from the point of view of astrologers and specialists in astronomical science. An annular eclipse is very rare and therefore eagerly awaited. Only a small ring of light remains in the sky for a few minutes.

When is the solar eclipse in 2018

Next year there will be only three such natural phenomena. And only one of them can be observed on the territory of Russia. It is not surprising that Russians are already interested in what time and where the solar eclipse will take place in the Russian Federation, since in order to observe this most beautiful event, which does not last long, you need to know the exact time. This table gives a complete picture of the upcoming events in 2018:

date and time	Where will the solar eclipse
February 15, 2018 at 11:52 p.m.	Partial eclipse can be seen in the south South America and in Antarctica.
07/13/18 at 06-02 a.m.	A partial eclipse will be observed in Antarctica, on the extreme southern coast of Australia, in Tasmania and in the waters indian ocean around Australia and Antarctica.
08/11/18 at 12-47 pm	A partial eclipse will be seen by residents in Greenland, Canada, Scandinavia, northern and central Russia, regions of Siberia and Far East, in the north-eastern part of Kazakhstan, in China and Mongolia.

Impact on all living things

Solar eclipses do not pass without a trace for all living organisms on our planet. Almost all animals become restless and try to hide. Birds stop chirping and singing. Vegetable world and he leads as if it were night. The human body is also going through hard times. Negative processes begin about two weeks before the eclipse. The same period continues after a natural phenomenon. Persons suffering from cardiovascular diseases and hypertension are especially affected. Strong stress older people are also affected. They have exacerbated chronic diseases and a sense of anxiety. People with a weak psyche can become depressed or commit rash acts. Even healthy people become irritable and prone to showdown. These days it is not recommended to sign serious financial or legal documents. Businessmen should not enter into business agreements and contracts.

Scientists do not find an explanation for such changes in the human body. Astrologers who have been observing the influence of planets on a person for a long time do not advise planning anything these days. They recommend taking care of your inner world or reading a book, or listening to calm relaxing music. The ministers of the church are generally advised to pray.

At the same time, life does not stand still these days. Someone dies, others are born. Specialists of astrological science have long noticed that children born on the days of eclipses, as a rule, become outstanding personalities. Very often, nature rewards them with great talent.

Cautions

According to astrologers, all solar eclipses are cyclical. The cycle duration is 18.5 years. Everything that happens to you during the days of eclipses continues for the next eighteen and a half years. In this regard, these critical days are not recommended:

• start something new;
• undergo surgery;
• quarrel, get angry and annoyed over trifles.

What can be done on critical days

In the days of solar eclipse 2018, it is better to say goodbye to the past once and for all. You need to clear your home of trash and old things and let in new energy to transform your life. You can go on a diet if you decide to become slim and beautiful. It is recommended to cleanse your body and forget about bad habits. Some psychics advise you to sort out your thoughts, “sort everything out on the shelves” and make plans for the future. At the same time, you need to clearly imagine your dream and imagine that it has practically already come true. If everything is done meaningfully and correctly, it will give a huge impetus to the implementation of the most incredible decisions. The only thing that needs to be noted is that dreams should be realistically feasible, and not sky-high.

And yet, do not despair if you did not manage to see this miracle of nature. Eclipses will still be in your life, and more than one. The next eclipse that we will see in Russia will take place on 08/12/26.

• The longest eclipse of this century was on July 22, 2009.
• The speed of the shadow of our satellite on the surface of our planet during the eclipse is approximately 2 thousand meters per second.
• The eclipse of the Sun is so beautiful because of an interesting coincidence: the diameter of the planet is four hundred times greater than that of the moon, and at the same time, the distance to the satellite is four hundred times less than to our star. In this regard, only on Earth you can see a total eclipse.

Eclipse- an astronomical situation in which one heavenly body blocks light from another celestial body.

Most famous lunar and solar eclipse. There are also such phenomena as the passage of planets (Mercury and Venus) across the disk of the Sun.

Moon eclipse

A lunar eclipse occurs when the Moon enters the cone of shadow cast by the Earth. The diameter of the spot of the Earth's shadow at a distance of 363,000 km (the minimum distance of the Moon from the Earth) is about 2.5 times the diameter of the Moon, so the entire Moon can be obscured.

Diagram of a lunar eclipse

At each moment of the eclipse, the degree of coverage of the Moon's disk by the Earth's shadow is expressed by the phase of the eclipse F. The phase value is determined by the distance 0 from the center of the Moon to the center of the shadow. In astronomical calendars, the values ​​of Ф and 0 are given for different moments of the eclipse.

When the Moon during an eclipse completely enters the Earth's shadow, they speak of total lunar eclipse, when partially - about partial eclipse. The two necessary and sufficient conditions for the onset of a lunar eclipse are the full moon and the proximity of the Earth to lunar node.

As seen by an observer on Earth, on the imaginary celestial sphere, the Moon crosses the ecliptic twice a month at positions called nodes. The full moon can fall on such a position, on the node, then you can observe a lunar eclipse. (Note: not to scale)

Full eclipse

A lunar eclipse can be observed on half of the Earth's territory (where the Moon is above the horizon at the time of the eclipse). The view of the darkened Moon from any point of observation is negligibly little different from another point, and is the same. The maximum theoretically possible duration of the total phase of a lunar eclipse is 108 minutes; such were, for example, the lunar eclipses of July 26, 1953, July 16, 2000. In this case, the Moon passes through the center of the earth's shadow; total lunar eclipses of this type are called central, they differ from non-central ones in longer duration and lower brightness of the Moon during the total phase of the eclipse.

During an eclipse (even a total one), the Moon does not disappear completely, but becomes dark red. This fact is explained by the fact that the Moon, even in the phase of a total eclipse, continues to be illuminated. The sun's rays passing tangentially to the earth's surface are scattered in the earth's atmosphere and due to this scattering partially reach the moon. Since the earth's atmosphere is most transparent to the rays of the red-orange part of the spectrum, it is these rays that reach the surface of the moon during an eclipse to a greater extent, which explains the color of the lunar disk. In fact, this is the same effect as the orange-red glow of the sky near the horizon (dawn) before sunrise or just after sunset. To estimate the brightness of an eclipse, we use Danjon scale.

An observer on the Moon, at the time of a total (or partial, if he is on the shaded part of the Moon) lunar eclipse, sees a total solar eclipse (an eclipse of the Sun by the Earth).

Danjon scale used to estimate the degree of darkening of the moon during a total lunar eclipse. Proposed by astronomer André Danjon as a result of a study of such a phenomenon as ashen moonlight when the moon is illuminated by light passing through the upper layers of the earth's atmosphere. The brightness of the Moon during an eclipse also depends on how deep the Moon has entered the Earth's shadow.

Two total lunar eclipses. Corresponds to 2 (left) and 4 (right) on the Danjon scale

Ash light of the moon - a phenomenon when we see the entire moon, although only part of it is illuminated by the sun. At the same time, the part of the Moon's surface that is not illuminated by direct sunlight has a characteristic ashy color.

Ash light of the moon

It is observed shortly before and shortly after the new moon (at the beginning of the first quarter and at the end of the last quarter of the phases of the moon).

The glow of the surface of the Moon, which is not illuminated by direct sunlight, is formed by sunlight scattered by the Earth, and then secondarily reflected by the Moon to the Earth. Thus, the route of the Moon's ashen light photons is: Sun → Earth → Moon → observer on Earth.

The route of photons when observing ashen light: Sun → Earth → Moon → Earth

The reason for this phenomenon has been well known since Leonardo da Vinci and Mikhail Mestlin,

Alleged self-portrait of Leonardo da Vinci

Michael Möstlin

teachers Kepler, who for the first time gave a correct explanation of the ashen light.

Johannes Kepler

Crescent moon with ashlight, drawn by Leonardo da Vinci in the Codex Leicester

For the first time, instrumental comparisons of the brightness of the ashen light and the crescent of the moon were made in 1850 by French astronomers. Arago and Lie.

Dominique Francois Jean Arago

The bright crescent is the part that is directly illuminated by the Sun. The rest of the Moon is illuminated by light reflected from the Earth.

Photographic studies of the moon's ashen light at the Pulkovo observatory, carried out by G. A. Tikhov, led him to the conclusion that the Earth from the moon should look like a bluish disk, which was confirmed in 1969 when a man landed on the moon.

Gavriil Adrianovich Tikhov

He considered it important to make systematic observations of the ashen light. Observations of the ashen light of the moon allow us to judge the change in the Earth's climate. The intensity of the ash color depends to some extent on the amount of cloud cover on the currently illuminated side of the Earth; for the European part of Russia, bright ashy light reflected from powerful cyclonic activity in the Atlantic predicts precipitation in 7-10 days.

partial eclipse

If the Moon falls into the total shadow of the Earth only partially, there is partial eclipse. With it, part of the Moon is dark, and part, even in the maximum phase, remains in partial shade and is illuminated by the sun's rays.

View of the moon during a lunar eclipse

penumbral eclipse

Around the cone of the Earth's shadow there is a penumbra - a region of space in which the Earth obscures the Sun only partially. If the Moon passes through the penumbra, but does not enter the shadow, penumbral eclipse. With it, the brightness of the Moon decreases, but only slightly: such a decrease is almost imperceptible to the naked eye and is recorded only by instruments. Only when the Moon in a penumbral eclipse passes near the cone of total shadow, with clear sky you can see a slight darkening from one edge of the lunar disk.

Periodicity

Due to the discrepancy between the planes of the lunar and earth orbits, not every full moon is accompanied by a lunar eclipse, and not every lunar eclipse is complete. The maximum number of lunar eclipses per year is 3, but in some years there is not a single lunar eclipse. Eclipses repeat in the same order every 6585⅓ days (or 18 years 11 days and ~8 hours - a period called saros); knowing where and when a total lunar eclipse was observed, one can accurately determine the time of subsequent and previous eclipses that are clearly visible in this area. This cyclicity often helps to accurately date the events described in the historical annals.

Saros or draconian period, consisting of 223 synodic months(an average of approximately 6585.3213 days or 18.03 tropical years), after which the eclipses of the Moon and the Sun are approximately repeated in the same order.

synodic(from other Greek σύνοδος "connection, rapprochement") month- the time interval between two successive identical phases of the moon (for example, new moons). The duration is not constant; the mean is 29.53058812 mean solar days(29 days 12 hours 44 minutes 2.8 seconds), the actual duration of the synodic month differs from the average within 13 hours.

anomalistic month- the time interval between two successive passages of the Moon through perigee in its movement around the Earth. The duration at the beginning of 1900 was 27.554551 mean solar days (27 days 13 hours 18 minutes 33.16 seconds), decreasing by 0.095 seconds in 100 years.

This period is a consequence of the fact that the 223 synodic months of the Moon (18 calendar years and 10⅓ or 11⅓ days, depending on the number leap years in this period) are almost equal to 242 draconian months (6585.36 days), that is, after 6585⅓ days, the Moon returns to the same syzygy and to the node of the orbit. The second luminary, important for the onset of the eclipse, returns to the same node - the Sun - since almost an integer number of draconian years (19, or 6585.78 days) passes - periods of the passage of the Sun through the same node of the Moon's orbit. In addition, 239 anomalous months The moons are equal to 6585.54 days, so that the corresponding eclipses in each saros occur at the same distance of the Moon from the Earth and have the same duration. During one saros, on average, there are 41 solar eclipses (of which about 10 are total) and 29 lunar eclipses. For the first time, they learned to predict lunar eclipses with the help of saros in ancient Babylon. The best opportunity for predicting eclipses is provided by a period equal to the triple saros - exeligmos A containing an integer number of days that was used in the Antikythera Mechanism.

Beroz calls the calendar period 3600 years saros; smaller periods were named: neros at 600 years and sossos at 60 years.

Solar eclipse

The longest solar eclipse occurred on January 15, 2010 in Southeast Asia and lasted over 11 minutes.

A solar eclipse is an astronomical phenomenon in which the Moon completely or partially obscures the Sun from an observer on Earth. A solar eclipse is possible only on a new moon, when the side of the moon facing the Earth is not illuminated, and the moon itself is not visible. Eclipses are possible only if the new moon occurs near one of the two lunar nodes (the point of intersection of the visible orbits of the Moon and the Sun), no more than about 12 degrees from one of them.

The moon's shadow on the earth's surface does not exceed 270 km in diameter, so a solar eclipse is observed only in a narrow band along the path of the shadow. Since the Moon revolves in an elliptical orbit, the distance between the Earth and the Moon at the time of an eclipse can be different, respectively, the diameter of the lunar shadow spot on the Earth's surface can vary widely from maximum to zero (when the top of the cone of the lunar shadow does not reach the Earth's surface). If the observer is in the shadow strip, he sees total solar eclipse in which the Moon completely hides the Sun, the sky darkens, and planets and bright stars can appear on it. Around the solar disk hidden by the Moon, one can observe sun crown, which is not visible under the normal bright light of the sun.

The elongated shape of the corona during the total solar eclipse of August 1, 2008 (close to a minimum between solar cycles 23 and 24)

When the eclipse is observed by a stationary ground observer, the total phase lasts no more than a few minutes. The minimum speed of the lunar shadow on the earth's surface is just over 1 km/s. During a total solar eclipse, astronauts in orbit can observe the moving shadow of the Moon on the Earth's surface.

Observers close to the total eclipse can see it as partial solar eclipse. During a partial eclipse, the Moon passes across the disk of the Sun not exactly in the center, hiding only part of it. In this case, the sky darkens much weaker than during a total eclipse, the stars do not appear. A partial eclipse can be observed at a distance of about two thousand kilometers from the zone of total eclipse.

The totality of a solar eclipse is also expressed by the phase Φ . The maximum phase of a partial eclipse is usually expressed in hundredths of a unit, where 1 is the total phase of the eclipse. Full phase can be greater than unity, for example 1.01, if the diameter of the visible lunar disk is greater than the diameter of the visible solar disk. Partial phases have a value less than 1. At the edge of the lunar penumbra, the phase is 0.

The moment when the leading / trailing edge of the Moon's disk touches the edge of the Sun is called touch. The first contact is the moment when the Moon enters the disk of the Sun (the beginning of the eclipse, its partial phase). The last touch (the fourth in the case of a total eclipse) is the last moment of the eclipse, when the Moon leaves the disk of the Sun. In the event of a total eclipse, the second touch is the moment when the front of the Moon, having passed all over the Sun, begins to exit the disk. A total solar eclipse occurs between the second and third touches. In 600 million years, tidal drag will push the Moon away from Earth enough to make a total solar eclipse impossible.

Astronomical classification of solar eclipses

According to astronomical classification, if an eclipse at least somewhere on the surface of the Earth can be observed as total, it is called complete.

Diagram of a total solar eclipse

If the eclipse can only be observed as a partial eclipse (this happens when the cone of the moon's shadow passes near the earth's surface, but does not touch it), the eclipse is classified as private. When an observer is in the shadow of the moon, he observes a total solar eclipse. When he is in the penumbra, he can observe a partial solar eclipse. In addition to total and partial solar eclipses, there are annular eclipses.

Animated annular eclipse

Diagram of an annular solar eclipse

An annular eclipse occurs when, at the time of the eclipse, the Moon is at a greater distance from the Earth than during a total eclipse, and the shadow cone passes over the earth's surface without reaching it. Visually, during an annular eclipse, the Moon passes over the disk of the Sun, but it turns out to be smaller than the Sun in diameter, and cannot completely hide it. In the maximum phase of the eclipse, the Sun is covered by the Moon, but a bright ring of the uncovered part of the solar disk is visible around the Moon. The sky during an annular eclipse remains bright, stars do not appear, it is impossible to observe the corona of the Sun. The same eclipse can be seen in different parts of the eclipse band as total or annular. Such an eclipse is sometimes called a total annular (or hybrid) eclipse.

The shadow of the Moon on Earth during an eclipse, photograph from the ISS. The photo shows Cyprus and Turkey

Frequency of solar eclipses

From 2 to 5 solar eclipses can occur on Earth per year, of which no more than two are total or annular. On average, 237 solar eclipses occur in a hundred years, of which 160 are partial, 63 are total, and 14 are annular. At a certain point on the earth's surface, eclipses in a large phase occur quite rarely, and total solar eclipses are even more rare. So, on the territory of Moscow from the 11th to the 18th centuries, 159 solar eclipses with a phase greater than 0.5 could be observed, of which only 3 were total (August 11, 1124, March 20, 1140 and June 7, 1415). Another total solar eclipse occurred on August 19, 1887. An annular eclipse could be observed in Moscow on April 26, 1827. A very strong eclipse with a phase of 0.96 occurred on July 9, 1945. The next total solar eclipse is expected in Moscow only on October 16, 2126.

Mention of eclipses in historical documents

Solar eclipses are often mentioned in ancient sources. More more dated descriptions is contained in Western European medieval chronicles and annals. For example, a solar eclipse is mentioned in the Annals of St. Maximin of Trier: "538 on February 16, from the first to the third hour there was a solar eclipse." Big number descriptions of solar eclipses from ancient times are also contained in the chronicles of East Asia, primarily in the Dynastic histories of China, in Arabic chronicles and Russian chronicles.

Mentions of solar eclipses in historical sources usually provide an opportunity for independent verification or clarification of the chronological connection of the events described in them. If the eclipse is described in the source in insufficient detail, without indicating the place of observation, calendar date, time and phase, such identification is often ambiguous. In such cases, ignoring the time reference of the source over the entire historical interval, it is often possible to select several possible “candidates” for the role of a historical eclipse, which is actively used by some authors of pseudo-historical theories.

Solar eclipse discoveries

Total solar eclipses make it possible to observe the corona and the immediate vicinity of the Sun, which is extremely difficult under normal conditions (although since 1996, astronomers have been able to constantly survey the vicinity of our star thanks to the work SOHO satellite(English) Solarandheliosphericobservatory solar and heliospheric observatory).

SOHO- spacecraft for observing the sun

French scientist Pierre Jansen during a total solar eclipse in India on August 18, 1868, he first explored the chromosphere of the Sun and obtained the spectrum of a new chemical element

Pierre Jules Cesar Jansen

(True, as it turned out later, this spectrum could be obtained without waiting for a solar eclipse, which was done two months later by the English astronomer Norman Lockyer). This element is named after the sun. helium.

In 1882, on May 17, during a solar eclipse, observers from Egypt saw a comet flying near the Sun. She got the name eclipse comets, although it has another name - Comet Tevfik(in honor of khedive Egypt at that time).

1882 eclipse comet(modern official designation: X/1882 K1) is a comet that was discovered by observers in Egypt during the solar eclipse of 1882.Her appearance was a complete surprise, and she was observed during the eclipse on the first and last time. She is a member of the familynear-solar comets Kreutz (Kreutz Sungrazers), and 4 months ahead of the appearance of another member of this family - the great September comet of 1882. Sometimes it is called comet Tevfik in honor of the Khedive of Egypt at that time Tevfik.

Khedive(khediva, khedif) (Persian - lord, sovereign) - the title of the vice-sultan of Egypt, which existed during the period of Egypt's dependence on Turkey (1867-1914). This title was worn by Ismail, Tawfik and Abbas II.

Taufik Pasha

The role of eclipses in the culture and science of mankind

Since ancient times, solar and lunar eclipses, as well as other rare astronomical phenomena, such as the appearance of comets, have been perceived as negative events. People were very afraid of eclipses, as they occur rarely and are unusual and frightening natural phenomena. In many cultures, eclipses were considered harbingers of misfortune and catastrophes (this was especially true of lunar eclipses, apparently due to the red color of the shadowed Moon, associated with blood). In mythology, eclipses were associated with the struggle of higher powers, one of which wants to disrupt the established order in the world (“extinguish” or “eat” the Sun, “kill” or “bleed” the Moon), and the other wants to save it. The beliefs of some peoples demanded complete silence and inaction during eclipses, while others, on the contrary, demanded active witchcraft to help the “light forces”. To some extent, this attitude towards eclipses persisted until modern times, despite the fact that the mechanism of eclipses had long been studied and well known.

Eclipses have provided rich material for science. In ancient times, observations of eclipses helped to study celestial mechanics and understand the structure of solar system. Observation of the shadow of the Earth on the Moon gave the first "cosmic" proof of the fact that our planet is spherical. Aristotle was the first to point out that the shape of the earth's shadow at lunar eclipses always round, which proves the sphericity of the Earth. Solar eclipses made it possible to start studying the corona of the Sun, which cannot be observed at normal times. During solar eclipses, the phenomena of gravitational curvature of the path of light rays near a significant mass were recorded for the first time, which became one of the first experimental proofs of the conclusions of the general theory of relativity. An important role in the study of the inner planets of the solar system was played by observations of their passage through the solar disk. So, Lomonosov, observing the passage of Venus across the solar disk in 1761, for the first time (30 years before Schroeter and Herschel) discovered the Venusian atmosphere, discovering the refraction of the sun's rays during the entry and exit of Venus from the solar disk.

Solar eclipse with the help of Moscow State University

Solar eclipse by Saturn on September 15, 2006. Photo of the Cassini interplanetary station from a distance of 2.2 million km