How Eratosthenes calculated the circumference of the earth. The area of land plots for individual housing construction, private household plots is usually indicated in acres

Eratosthenes' contribution to the development of geography, the great Greek mathematician, astronomer, geographer and poet is outlined in this article.

Eratosthenes' contribution to geography. What did Eratosthenes discover?

The scientist was a contemporary of Aristarchus of Samos and Archimedes, who lived in the 3rd century BC. e. He was an encyclopedic scholar, library keeper in Alexandria, philosopher, correspondent and friend of Archimedes. He also became famous as a surveyor and geographer. It is logical that he should summarize his knowledge in one work. And what book did Eratosthenes write? They would not have known about it if it were not for Strabo's Geography, who mentioned it and its author, who measured the circumference of the Earth's globe. And this is the book "Geography" in 3 volumes. In it, he outlined the foundations of systematic geography. In addition, the following treatises belong to his hand - “Chronography”, “Platonist”, “On Averages”, “On Ancient Comedy” in 12 books, “Revenge, or Hesiod”, “On Elevation”. Unfortunately, they came to us in small snatches.

What did Eratosthenes discover in geography?

The Greek scientist is rightfully considered the father of geography. So what did Eratosthenes do to earn this honorary title? First of all, it is worth noting that it was he who introduced the term “geography” in its modern sense into scientific circulation.

He owns the creation of mathematical and physical geography. The scientist suggested the following assumption: if you sail west from Gibraltar, then you can reach India. In addition, he tried to calculate the size of the Sun and Moon, studied eclipses and showed how the length of daylight hours depends on geographical latitude.

How did Eratosthenes measure the radius of the earth?

In order to measure the radius, Eratosthenes used calculations made at two points - Alexandria and Syene. He knew that on June 22 the day summer solstice, the heavenly body illuminates the bottom of the wells at exactly noon. When the Sun is at its zenith in Syene, it is 7.2° behind in Alexandria. To get the result, he needed to change the zenith distance of the Sun. And what tool did Eratosthenes + use to determine the size? It was a skafis - a vertical pole, fixed at the bottom of a hemisphere. Putting it in a vertical position, the scientist was able to measure the distance from Syene to Alexandria. It is equal to 800 km. Comparing the zenith difference between the two cities with the generally accepted circle of 360 °, and the zenith distance with the circumference of the earth, Erastosthenes made up a proportion and calculated the radius - 39,690 km. He was mistaken by just a little, modern scientists have calculated that it is 40,120 km.

The ancient Egyptians noticed that during the summer solstice the sun illuminates the bottom of deep wells in Syene (now Aswan), but not in Alexandria. Eratosthenes of Cyrene (276 BC -194 BC)

) came up with a brilliant idea - to use this fact to measure the circumference and radius of the earth. On the day of the summer solstice in Alexandria, he used a scaphis - a bowl with a long needle, with which it was possible to determine at what angle the sun is in the sky.

So, after the measurement, the angle turned out to be 7 degrees 12 minutes, that is, 1/50 of the circle. Therefore, Siena is separated from Alexandria by 1/50 of the circumference of the earth. The distance between cities was considered to be 5,000 stadia, hence the circumference of the earth was 250,000 stadia, and the radius was then 39,790 stadia.

It is not known what stage Eratosthenes used. Only if Greek (178 meters), then its radius of the earth was 7, 082 km, if Egyptian, then 6, 287 km. Modern measurements give a value of 6.371 km for the average radius of the earth. In any case, the accuracy for those times is amazing.

People have long guessed that the Earth they live on is like a ball. The ancient Greek mathematician and philosopher Pythagoras (ca. 570-500 BC) was one of the first to express the idea of the sphericity of the Earth. The Greatest Thinker antiquity Aristotle, observing lunar eclipses, noticed that the edge of the earth's shadow falling on the moon always has round shape. This allowed him to judge with confidence that our Earth is spherical. Now, thanks to the achievements space technology, all of us (and more than once) had the opportunity to admire the beauty of the globe from images taken from space.

A reduced likeness of the Earth, its miniature model is a globe. To find out the circumference of a globe, it is enough to wrap it with a drink, and then determine the length of this thread. By vast earth with a measured mite you can’t get around the meridian or the equator. And in whatever direction we begin to measure it, insurmountable obstacles will surely appear on the way - high mountains, impenetrable swamps, deep seas and oceans ...

Is it possible to know the size of the Earth without measuring its entire circumference? Of course you can.

We know that there are 360 degrees in a circle. Therefore, in order to find out the circumference, in principle it is enough to measure exactly the length of one degree and multiply the result of the measurement by 360.

The first measurement of the Earth in this way was made by the ancient Greek scientist Eratosthenes (c. 276-194 BC), who lived in the Egyptian city of Alexandria, on the coast of the Mediterranean Sea.

Camel caravans came from the south to Alexandria. From the people accompanying them, Eratosthenes learned that in the city of Syene (present-day Aswan) on the day of the summer solstice, the Sun is overhead on yol-day. Objects at this time do not give any shade, and the sun's rays penetrate even into the most deep wells. Therefore, the Sun reaches its zenith.

way astronomical observations Eratosthenes established that on the same day in Alexandria, the Sun is 7.2 degrees from the zenith, which is exactly 1/50 of the circle. (Indeed: 360: 7.2 = 50.) Now, in order to find out what the circumference of the Earth is, it remained to measure the distance between cities and multiply it by 50. But Eratosthenes could not measure this distance, which runs through the desert. Nor could the guides of trade caravans measure it. They only knew how much time their camels spend on one crossing, and they believed that from Syene to Alexandria there were 5,000 Egyptian stadia. So the whole circumference of the earth: 5,000 x 50 = 250,000 stadia.

Unfortunately, we do not know the exact length of the Egyptian stage. According to some reports, it is equal to 174.5 m, which gives 43,625 km for the earth's circumference. It is known that the radius is 6.28 times less than the circumference. It turned out that Earth radius, but Eratosthenes - 6943 km. This is how, more than twenty-two centuries ago, the dimensions of the globe were first determined.

According to modern data, average radius Earth is 6371 km. Why average? After all, if the Earth is a sphere, then the idea of the earth's radii should be the same. We will talk about this further.

A method for accurately measuring large distances was first proposed by the Dutch geographer and mathematician Wildebrord Siellius (1580-1626).

Imagine that it is necessary to measure the distance between points A and B, hundreds of kilometers apart from each other. The solution of this problem should begin with the construction of the so-called reference geodetic network on the ground. In the simplest version, it is created in the form of a chain of triangles. Their peaks are chosen on elevated places, where so-called geodesic signs are constructed in the form of special pyramids, and it is necessary so that directions to all neighboring points are visible from each point. And these pyramids should also be convenient for work: for installing a goniometric tool - a theodolite - and measuring all the angles in the triangles of this network. In addition, in one of the triangles, one side is measured, which lies on a flat and open area, convenient for linear measurements. The result is a network of triangles with known angles and the original side - the basis. Then comes the calculations.

The solution is drawn from the triangle containing the basis. Based on the side and angles, the other two sides of the first triangle are calculated. But one of its sides is at the same time a side of a triangle adjacent to it. It serves as the starting point for calculating the sides of the second triangle, and so on. In the end, the sides of the last triangle are found and the desired distance is calculated - the arc of the meridian AB.

The geodetic network is necessarily based on astronomical points A and B. The method of astronomical observations of stars determines their geographical coordinates(latitudes and longitudes) and azimuths (directions to local objects).

Now that the length of the arc of the meridian AB is known, as well as its expression in degree measure (as the difference between the latitudes of astropoints A and B), it will not be difficult to calculate the length of the arc of 1 degree of the meridian by simply dividing the first value by the second.

This method of measuring large distances on earth's surface is called triangulation Latin word"triapgulum", which means "triangle". It turned out to be convenient for determining the size of the Earth.

The study of the size of our planet and the shape of its surface is the science of geodesy, which in Greek means "land measurement". Its origin should be attributed to Eratosfsnus. But proper scientific geodesy began with triangulation, first proposed by Siellius.

The grandest degree measurement XIX century was headed by the founder of the Pulkovo Observatory V. Ya. Struve.

Under the leadership of Struve, Russian geodesists, together with Norwegian ones, measured the arc "stretching from the Danube through the western regions of Russia to Finland and Norway to the coast of the Northern Arctic Ocean. Total length this arc exceeded 2800 km! It contained more than 25 degrees, which is almost 1/14 of the earth's circumference. It entered the history of science under the name "Struve arcs". The author of this book in post-war years I had a chance to work on observations (angle measurements) at state triangulation points adjacent directly to the famous "arc".

Degree measurements have shown that the Earth is not exactly a ball, but looks like an ellipsoid, that is, it is compressed at the poles. In an ellipsoid, all meridians are ellipses, and the equator and parallels are circles.

The longer the measured arcs of meridians and parallels, the more accurately you can calculate the radius of the Earth and determine its compression.

Domestic surveyors measured the state triangulation network in almost half of the territory of the USSR. This allowed the Soviet scientist F. N. Krasovsky (1878-1948) to more accurately determine the size and shape of the Earth. Krasovsky's ellipsoid: equatorial radius - 6378.245 km, polar radius - 6356.863 km. The compression of the planet is 1/298.3, that is, the polar radius of the Earth is shorter than the equatorial one by such a part (in a linear measure - 21.382 km).

Imagine that on a globe with a diameter of 30 cm, they decided to depict the compression of the globe. Then the polar axis of the globe would have to be shortened by 1 mm. It is so small that it is completely invisible to the eye. This is how the Earth looks perfectly round from a distance. This is how the astronauts see it.

By studying the shape of the Earth, scientists come to the conclusion that it is compressed not only along the axis of rotation. The equatorial section of the globe in projection onto a plane gives a curve, which also differs from a regular circle, although quite a bit - by hundreds of meters. All this indicates that the figure of our planet is more complex than it seemed before.

Now it's quite clear that the earth is not right geometric body, that is, an ellipsoid. In addition, the surface of our planet is far from smooth. It has hills and high mountain ranges. True, land is almost three times less than water. What, then, should we mean by the underground surface?

As you know, oceans and seas, communicating with each other, form a vast water surface on Earth. Therefore, scientists agreed to take the surface of the World Ocean, which is in a calm state, for the surface of the planet.

And what about the regions of the continents? What is considered the surface of the Earth? It is also the surface of the World Ocean, mentally extended under all the continents and islands.

This figure, bounded by the surface of the middle level of the World Ocean, was called the geoid. From the surface of the geoid, all known "altitudes above sea level" are measured. The word "geoid", or "earth-like", was specially invented for the name of the figure of the Earth. There is no such figure in geometry. Close in shape to the geoid is a geometrically regular ellipsoid.

October 4, 1957 with the launch in our country of the first artificial satellite Earth humanity has entered the space age. 11started active research near-earth space. At the same time, it turned out that satellites are very useful for understanding the Earth itself. Even in the field of geodesy, they said their "weighty word".

As you know, the classic method for studying the geometric characteristics of the Earth is triangulation. But earlier geodetic networks were developed only within the continents, and they were not interconnected. After all, you cannot build triangulation on the seas and oceans. Therefore, the distances between the continents were determined less accurately. Due to this, the accuracy of determining the size of the Earth itself decreased.

With the launch of the satellites, surveyors immediately realized that “sight targets” appeared at high altitude. Now long distances can be measured.

The idea of the space triangulation method is simple. Synchronous (simultaneous) satellite observations from several distant points on the earth's surface make it possible to bring them geodetic coordinates to unified system. Thus, triangulations built on different continents were connected together, and at the same time the dimensions of the Earth were clarified: the equatorial radius is 6378.160 km, the polar radius is 6356.777 km. The compression value is 1/298.25, that is, almost the same as that of the Krasovsky ellipsoid. The difference between the equatorial and polar diameters of the Earth reaches 42 km 766 m.

If our planet were a regular ball, and the masses inside it were evenly distributed, then the satellite could move around the Earth in a circular orbit. But the deviation of the shape of the Earth from a spherical one and the heterogeneity of its interior lead to the fact that over different points the earth's surface, the force of attraction is not the same. The force of gravity of the Earth changes - the orbit of the satellite changes. And all, even the slightest changes in the motion of a satellite with a low orbit are the result of the gravitational influence on it of one or another earthly bulge or depression over which it flies.

It turned out that our planet also has a slightly pear-shaped shape. Her North Pole raised above the plane of the equator by 16 m, and the South one is lowered by about the same amount (as if depressed). So it turns out that in cross section along the meridian, the figure of the Earth resembles a pear. It is slightly elongated to the north and flattened at South Pole. There is a polar asymmetry: The northern hemisphere is not identical to the southern one. Thus, on the basis of satellite data, the most accurate idea of the true shape of the Earth was obtained. As you can see, the figure of our planet noticeably deviates from geometrically correct form ball, as well as from the figure of an ellipsoid of revolution.

The sphericity of the Earth allows you to determine its size in a way that was first used by the Greek scientist Eratosthenes. The idea of Eratosthenes is as follows. Let's choose two points \(O_(1)\) and \(O_(2)\) on the same geographic meridian of the globe. Let us denote the length of the meridian arc \(O_(1)O_(2)\) as \(l\), and its angular value as \(n\) (in degrees). Then the length of the 1° arc of the meridian \(l_(0)\) will be equal to: \ and the length of the entire circumference of the meridian: \ where \(R\) is the radius of the globe. Hence \(R = \frac(180° l)(πn)\).

The length of the meridian arc between the points \(O_(1)\) and \(O_(2)\) selected on the earth's surface in degrees is equal to the difference geographical latitudes these points, i.e. \(n = Δφ = φ_(1) - φ_(2)\).

To determine the value \(n\), Eratosthenes used the fact that the cities of Siena and Alexandria are located on the same meridian and the distance between them is known. With the help of a simple device, which the scientist called "skafis", it was found that if in Siena at noon on the day of the summer solstice the Sun illuminates the bottom of deep wells (it is at the zenith), then at the same time in Alexandria the Sun is separated from the vertical by \ (\ frac(1)(50)\) fraction of a circle (7.2°). Thus, having determined the length of the arc \(l\) and the angle \(n\), Eratosthenes calculated that the length of the earth's circumference is 252 thousand stadia (the stages are approximately equal to 180 m). Considering the roughness of the measuring instruments of that time and the unreliability of the initial data, the measurement result was very satisfactory (the actual average length of the Earth's meridian is 40,008 km).

Accurate measurement of the distance \(l\) between the points \(O_(1)\) and \(O_(2)\) is difficult due to natural obstacles (mountains, rivers, forests, etc.).

Therefore, the length of the arc \(l\) is determined by calculations requiring only a relatively small distance to be measured - basis and a number of corners. This method was developed in geodesy and is called triangulation(lat. triangulum - triangle).

Its essence is as follows. On both sides of the arc \(O_(1)O_(2)\), the length of which is to be determined, select several points \(A\), \(B\), \(C\), ... on mutual distances up to 50 km, so that at least two other points are visible from each point.

At all points, geodetic signals are installed in the form of pyramidal towers with a height of 6 to 55 m, depending on the terrain conditions. At the top of each tower there is a platform for placing an observer and installing a goniometric instrument - a theodolite. The distance between any two neighboring points, for example \(O_(1)\) and \(A\), is chosen on a completely flat surface and is taken as the basis of the triangulation network. The length of the basis is very carefully measured with special measuring tapes.

The measured angles in triangles and the length of the basis allow trigonometric formulas calculate the sides of the triangles, and from them the length of the arc \(O_(1)O_(2)\) taking into account its curvature.

In Russia, from 1816 to 1855, under the leadership of V. Ya. Struve, a meridian arc 2800 km long was measured. In the 30s. In the 20th century, high-precision degree measurements were carried out in the USSR under the guidance of Professor F. N. Krasovsky. The length of the base at that time was chosen to be small, from 6 to 10 km. Later, thanks to the use of light and radar, the length of the base was increased to 30 km. The measurement accuracy of the meridian arc has increased to +2 mm for every 10 km of length.

Triangulation measurements have shown that the length of the 1° meridian arc is not the same at different latitudes: near the equator it is 110.6 km, and near the poles it is 111.7 km, i.e., it increases towards the poles.

The true shape of the Earth cannot be represented by any of the known geometric bodies. Therefore, in geodesy and gravimetry, the shape of the Earth is considered geoid, i.e., a body with a surface close to the surface of a calm ocean and extended under the continents.

At present, triangulation networks have been created with complex radar equipment installed at ground stations and with reflectors on geodetic artificial satellites of the Earth, which makes it possible to accurately calculate the distances between points. A well-known geodesist, hydrographer and astronomer ID Zhongolovich, a native of Belarus, made a significant contribution to the development of space geodesy. Based on the study of the dynamics of the movement of artificial satellites of the Earth, ID Zhongolovich specified the compression of our planet and the asymmetry of the Northern and Southern hemispheres.

Traveling from the city of Alexandria to the south, to the city of Siena (now Aswan), people noticed that there in the summer on the day when the sun is highest in the sky (the day of the summer solstice - June 21 or 22), at noon it illuminates the bottom of deep wells, that is, it happens just above your head, at the zenith. Vertically standing pillars at this moment do not give a shadow. In Alexandria, even on this day, the sun does not reach its zenith at noon, does not illuminate the bottom of the wells, objects give a shadow.

Eratosthenes measured how far the midday sun in Alexandria was deviated from the zenith, and received a value equal to 7 ° 12 ′, which is 1/50 of a circle. He managed to do this with the help of a device called a scaphis. Skafis was a bowl in the shape of a hemisphere. In its center was sheerly strengthened

On the left - determination of the height of the sun with a skafis. In the center - a diagram of the direction of the sun's rays: in Siena they fall vertically, in Alexandria - at an angle of 7 ° 12 ′. On the right - the direction of the sunbeam in Siena at the time of the summer solstice.

Skafis - an ancient device for determining the height of the sun above the horizon (in section).

needle. The shadow of the needle fell on inner surface skafis. To measure the deviation of the sun from the zenith (in degrees), circles marked with numbers were drawn on the inner surface of the skafis. If, for example, the shadow reached the circle marked 50, the sun was 50° below the zenith. Having built a drawing, Eratosthenes quite correctly concluded that Alexandria is 1/50 of the circumference of the Earth from Syene. To find out the circumference of the Earth, it remained to measure the distance between Alexandria and Siena and multiply it by 50. This distance was determined by the number of days that camel caravans spent on the transition between cities. In the units of that time, it was equal to 5 thousand stages. If 1/50 of the circumference of the earth is 5000 stadia, then the whole circumference of the earth is 5000 x 50 = 250,000 stadia. In terms of our measures, this distance is approximately equal to 39,500 km. Knowing the circumference, you can calculate the radius of the Earth. The radius of any circle is 6.283 times less than its length. Therefore, the average radius of the Earth, according to Eratosthenes, turned out to be equal to a round number - 6290 km, and the diameter is 12 580 km. So Eratosthenes found approximately the dimensions of the Earth, close to those determined by precise instruments in our time.

How information about the shape and size of the earth was checked

After Eratosthenes of Cyrene, for many centuries, none of the scientists tried to measure the earth's circumference again. In the 17th century a reliable method for measuring large distances on the surface of the Earth was invented - the method of triangulation (so named from the Latin word "triangulum" - a triangle). This method is convenient because the obstacles encountered on the way - forests, rivers, swamps, etc. - do not interfere with the accurate measurement of large distances. The measurement is made as follows: directly on the surface of the Earth, the distance between two closely spaced points is very accurately measured BUT and AT, from which distant tall objects are visible - hills, towers, bell towers, etc. If from BUT and AT through a telescope, you can see an object located at a point WITH, then it is easy to measure at the point BUT angle between directions AB and AU, and at the point AT- angle between VA and Sun.

After the side is measured AB the first triangle (basis), the whole thing comes down to measuring the angles between the two directions. Having built a network of triangles, it is possible to calculate, according to the rules of trigonometry, the distance from the vertex of one triangle to the vertex of any other, no matter how far apart they may be. This solves the problem of measuring large distances on the surface of the Earth. Practical use triangulation is not an easy task. This work can only be done by experienced observers armed with very precise goniometric instruments. Usually for observations it is necessary to build special towers. Work of this kind is entrusted to special expeditions, which last for several months and even years.

The triangulation method helped scientists refine their knowledge of the shape and size of the Earth. This happened under the following circumstances.

Famous English scientist Newton(1643-1727) expressed the opinion that the Earth cannot be an exact ball because it rotates on its axis. All particles of the Earth are under the influence of centrifugal force (force of inertia), which is especially strong

If we need to measure the distance from A to D (while point B is not visible from point A), then we measure the basis AB and in the triangle ABC we measure the angles adjacent to the basis (a and b). On one side and two corners adjacent to it, we determine the distance AC and BC. Further, from point C, we use the telescope of the measuring instrument to find point D, visible from point C and point B. In the triangle CUB, we know the side CB. It remains to measure the angles adjacent to it, and then determine the distance DB. Knowing the distances DB u AB and the angle between these lines, you can determine the distance from A to D.

Triangulation scheme: AB - basis; BE - measured distance.

at the equator and absent at the poles. The centrifugal force at the equator acts against the force of gravity and weakens it. The balance between gravity and centrifugal force was achieved when the globe at the equator "inflated", and at the poles "flattened" and gradually acquired the shape of a tangerine, or, to put it scientific language, spheroid. Interesting discovery, made at the same time, confirmed Newton's assumption.

In 1672, a French astronomer established that if accurate clock transport from Paris to Cayenne (in South America, near the equator), they begin to lag behind by 2.5 minutes per day. This lag occurs because the clock pendulum swings more slowly near the equator. It became obvious that the force of gravity, which makes the pendulum swing, is less in Cayenne than in Paris. Newton explained this by the fact that at the equator the surface of the Earth is farther from its center than in Paris.

The French Academy of Sciences decided to test the correctness of Newton's reasoning. If the Earth is shaped like a tangerine, then the 1° meridian arc should lengthen as it approaches the poles. It remained to measure the length of an arc of 1 ° using triangulation at different distances from the equator. The director of the Paris Observatory, Giovanni Cassini, was assigned to measure the arc in the north and south of France. However, his southern arc turned out to be longer than the northern one. It seemed that Newton was wrong: the Earth is not flattened like a tangerine, but elongated like a lemon.

But Newton did not abandon his conclusions and assured that Cassini made a mistake in the measurements. Between supporters of the theory of "tangerine" and "lemon" a scientific dispute broke out, which lasted 50 years. After the death of Giovanni Cassini, his son Jacques, also director of the Paris Observatory, wrote a book in order to defend his father's opinion, where he argued that, according to the laws of mechanics, the Earth should be stretched like a lemon. In order to finally resolve this dispute, the French Academy of Sciences equipped in 1735 one expedition to the equator, the other to the Arctic Circle.

The southern expedition carried out measurements in Peru. A meridian arc with a length of about 3° (330 km). She crossed the equator and passed through a series mountain valleys and the highest mountain ranges of America.

The work of the expedition lasted eight years and was fraught with great difficulties and dangers. However, scientists completed their task: the degree of the meridian at the equator was measured with very high accuracy.

The northern expedition worked in Lapland (until the beginning of the 20th century, this was the name given to the northern part of the Scandinavian and the western part of the Kola Peninsula).

After comparing the results of the work of the expeditions, it turned out that the polar degree is longer than the equatorial one. Therefore, Cassini was indeed wrong, and Newton was right when he said that the Earth was shaped like a tangerine. Thus ended this protracted dispute, and scientists recognized the correctness of Newton's statements.

Nowadays there is special science- geodesy, which deals with determining the size of the Earth using the most accurate measurements of its surface. The data of these measurements made it possible to accurately determine the actual figure of the Earth.

Geodetic work on measuring the Earth was carried out and is being carried out in various countries. Such work has been carried out in our country. As early as the last century, Russian geodesists carried out very precise work to measure the "Russian-Scandinavian arc of the meridian" with a length of more than 25 °, i.e., a length of almost 3 thousand meters. km. It was called the "Struve arc" in honor of the founder of the Pulkovo Observatory (near Leningrad) Vasily Yakovlevich Struve, who conceived and supervised this huge work.

Degree measurements have a large practical value primarily for compiling accurate maps. Both on the map and on the globe, you see a network of meridians - circles going through the poles, and parallels - circles, parallel to the plane earth's equator. A map of the Earth could not be drawn up without the long and painstaking work of geodesists, who determined step by step over many years the position of different places on the earth's surface and then plotted the results on a network of meridians and parallels. To have accurate maps, it was necessary to know the actual shape of the Earth.

The measurement results of Struve and his collaborators turned out to be a very important contribution to this work.

Subsequently, other geodesists measured with great accuracy the lengths of the arcs of the meridians and parallels in different places on the earth's surface. Using these arcs, with the help of calculations, it was possible to determine the length of the Earth's diameters in the equatorial plane (equatorial diameter) and in the direction earth's axis(polar diameter). It turned out that the equatorial diameter is longer than the polar one by about 42.8 km. This once again confirmed that the Earth is compressed from the poles. According to the latest data from Soviet scientists, the polar axis is 1/298.3 shorter than the equatorial one.

Let's say we would like to depict the deviation of the Earth's shape from a sphere on a globe with a diameter of 1 m. If a sphere at the equator has a diameter of exactly 1 m, then its polar axis should be only 3.35 mm shorter! This is such a small value that it cannot be detected by the eye. The shape of the earth, therefore, differs very little from a sphere.

You might think that the unevenness of the earth's surface, and especially the mountain peaks, the highest of which Chomolungma (Everest) reaches almost 9 km, must strongly distort the shape of the Earth. However, it is not. On the scale of a globe with a diameter of 1 m a nine-kilometer mountain will be depicted as a grain of sand adhering to it with a diameter of about 3/4 mm. Is it only by touch, and even then with difficulty, that this protrusion can be detected. And from the height at which our satellite ships fly, it can only be distinguished by the black speck of the shadow cast by it when the Sun is low.

In our time, the dimensions and shape of the Earth are very accurately determined by the scientists F. N. Krasovsky, A. A. Izotov and others. Here are the numbers showing the size of the globe according to the measurements of these scientists: the length of the equatorial diameter is 12,756.5 km, length of polar diameter - 12 713.7 km.

The study of the path traveled by artificial satellites of the Earth will make it possible to determine the magnitude of the force of gravity at different places above the surface of the globe with an accuracy that could not be achieved by any other method. This, in turn, will allow us to further refine our knowledge of the size and shape of the Earth.

Gradual change in the shape of the earth

However, as it was possible to find out with the help of all the same space observations and special calculations made on their basis, the geoid has a complex shape due to the rotation of the Earth and the uneven distribution of masses in earth's crust, but quite well (with an accuracy of several hundred meters) is represented by an ellipsoid of revolution with a polar oblateness of 1:293.3 (Krasovsky's ellipsoid).

Nevertheless, until very recently, it was considered a well-established fact that this small defect is slowly but surely leveled out due to the so-called process of restoring gravitational (isostatic) equilibrium, which began about eighteen thousand years ago. But more recently, the Earth began to flatten again.

Geomagnetic measurements, which since the late 1970s have become an integral attribute of satellite observation research programs, have consistently recorded the alignment of the planet's gravitational field. In general, from the point of view of mainstream geophysical theories, the gravitational dynamics of the Earth seemed quite predictable, although, of course, both within the mainstream and outside it, there were numerous hypotheses that interpreted the medium and long-term prospects of this process in different ways, as well as what happened in past life our planet. Quite popular today is, say, the so-called pulsation hypothesis, according to which the Earth periodically contracts and expands; There are also supporters of the "contract" hypothesis, which postulates that in the long run the size of the Earth will decrease. There is no unity among geophysicists in terms of what phase the process of post-glacial restoration of gravitational equilibrium is in today: most experts believe that it is quite close to completion, but there are also theories stating that it is still far from its end or that it has already stopped.

Nevertheless, despite the abundance of discrepancies, until the end of the 90s of the last century, scientists still did not have any good reasons doubt that the process of post-glacial gravitational alignment is alive and well. The end of scientific complacency came rather abruptly: after spending several years checking and rechecking the results obtained from nine different satellites, two American scientists, Christopher Cox of Raytheon and Benjamin Chao, a geophysicist at NASA's Goddard Space Flight Control Center, came to a surprising conclusion: since 1998, the "equatorial coverage" of the Earth (or, as many Western media dubbed this dimension, its "thickness") began to increase again.
The sinister role of ocean currents.

Thanks to this "mysterious adversary", the Earth again, as in the last "epoch of the Great Icing", began to flatten, that is, since 1998, an increase in the mass of matter has been taking place in the equator region, while its outflow has been going on from the polar zones.

Earth geophysicists do not yet have direct measuring methods to detect this phenomenon, so in their work they have to use indirect data, primarily the results of ultra-precise laser measurements of changes in satellite orbit trajectories occurring under the influence of fluctuations in the Earth's gravitational field. Accordingly, speaking of "observed displacements of the masses of the terrestrial matter", scientists proceed from the assumption that they are responsible for these local gravitational fluctuations. The first attempts to explain this strange phenomenon were undertaken by Cox and Chao.

The version of any underground phenomena, for example, the flow of matter in the earth's magma or core, looks, according to the authors of the article, rather doubtful: in order for such processes to have any significant gravitational effect, much more long time than a ridiculous four years by scientific standards. As possible causes, which caused the thickening of the Earth along the equator, they name three main ones: oceanic influence, melting of polar and high-mountain ice, and certain "processes in the atmosphere." However, the latter group of factors is also immediately swept aside by them - regular measurements of the weight of the atmospheric column do not give any grounds for suspicion of the involvement of certain air phenomena in the occurrence of the discovered gravitational phenomenon.

Far from being so unambiguous seems to Cox and Chao the hypothesis of the possible influence on the equatorial swelling of the process of ice melting in the Arctic and Antarctic zones. This process is like essential element notorious global warming world climate, of course, to one degree or another can be responsible for the transfer of significant masses of matter (primarily water) from the poles to the equator, but the theoretical calculations made by American researchers show that in order for it to turn out to be a determining factor (in particular, "blocked "consequences of the thousand-year "growth of the positive relief"), the dimension of the "virtual block of ice" annually melted since 1997 should have been 10x10x5 kilometers! There is no empirical evidence that the process of ice melting in the Arctic and Antarctic last years could take on such a scale, geophysicists and meteorologists do not have. According to the most optimistic estimates, the total volume of melted ice floes is at least an order of magnitude smaller than this "super iceberg", therefore, even if it had some effect on the increase in the Earth's equatorial mass, this effect could hardly be so significant.

As the most probable reason for the sudden change in the Earth's gravitational field, Cox and Chao consider today the oceanic impact, that is, the same transfer of large volumes of the World Ocean's water mass from the poles to the equator, which, however, is associated not so much with the rapid melting of ice, how many with some not quite explainable sharp fluctuations ocean currents occurring in recent years. Moreover, as experts believe, the main candidate for the role of a disturber of gravitational calm is the Pacific Ocean, more precisely, the cyclic movements of huge water masses from its northern regions to its southern regions.

If a this hypothesis turns out to be true, humanity in the very near future may face very serious changes in the global climate: the sinister role of ocean currents is well known to everyone who is more or less familiar with the basics of modern meteorology (which is worth one El Niño). True, the assumption that the sudden swelling of the Earth along the equator is a consequence of the climate revolution already in full swing looks quite logical. But, by and large, it is still hardly possible to really understand this tangle of cause-and-effect relationships on the basis of fresh traces.

The obvious lack of understanding of the ongoing "gravitational outrages" is perfectly illustrated by a small fragment of an interview by Christopher Cox himself with the correspondent of the Nature magazine news service Tom Clarke: one: Our planet's 'weight problems' are likely temporary and not a direct result of human activity". However, continuing this verbal balancing act, the American scientist immediately once again prudently stipulates: "Apparently, sooner or later everything will return to 'normal', but perhaps we are mistaken on this score."

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Units of land area measurement

The system adopted in Russia for measuring land areas

1 weave = 10 meters x 10 meters = 100 sq.m
1 hectare \u003d 1 ha \u003d 100 meters x 100 meters \u003d 10,000 square meters \u003d 100 acres
1 square kilometer\u003d 1 sq. km \u003d 1000 meters x 1000 meters \u003d 1 million square meters \u003d 100 hectares \u003d 10,000 acres

Inverse units

1 sq. m = 0.01 acres = 0.0001 ha = 0.000001 sq. km
1 weave \u003d 0.01 ha \u003d 0.0001 sq. km

Area units conversion table

Area units	1 sq. km.	1 hectare	1 acre	1 weave	1 sq.m.
1 sq. km.	1	100	247.1	10.000	1.000.000
1 hectare	0.01	1	2.47	100	10.000
1 acre	0.004	0.405	1	40.47	4046.9
1 weave	0.0001	0.01	0.025	1	100
1 sq.m.	0.000001	0.0001	0.00025	0.01	1

a unit of area in the metric system of measures used to measure land.

Abbreviated designation: Russian ha, international ha.

1 ha equal to area square with a side of 100 m.

The name "hectares" is formed by adding the prefix "hecto..." to the name of the area unit "ar":

1 ha = 100 are = 100 m x 100 m = 10,000 m2

a unit of area in the metric system of measures, equal to the area of a square with a side of 10 m, that is:

1 ar \u003d 10 m x 10 m \u003d 100 m2.
1 tithe = 1.09254 ha.

land measure applied in a number of countries using English system measures (Great Britain, USA, Canada, Australia, etc.).

1 acre = 4840 sq. yards = 4046.86 m2

The most commonly used land measure in practice is hectare - the abbreviation ha:

1 ha = 100 are = 10,000 m2

In Russia, a hectare is the main unit for measuring land area, especially agricultural land.

On the territory of Russia, the unit "hectare" was put into practice after October revolution, instead of a tithe.

Old Russian units of area measurement

1 sq. verst = 250,000 sq.
fathoms = 1.1381 km²
1 tithe = 2400 sq. fathoms = 10,925.4 m² = 1.0925 ha
1 quarter = 1/2 tithe = 1200 sq. fathoms = 5462.7 m² = 0.54627 ha
1 octopus \u003d 1/8 tithe \u003d 300 square sazhens \u003d 1365.675 m² ≈ 0.137 ha.

The area of land plots for individual housing construction, private household plots is usually indicated in acres

One hundred- this is the area of \u200b\u200ba plot measuring 10 x 10 meters, which is 100 square meters, and therefore is called a hundred.

Here are some typical examples of the sizes that a land plot of 15 acres can have:

In the future, if you suddenly forget how to find the area of a rectangular plot of land, then remember a very old joke when a grandfather asks a fifth grader how to find Lenin Square, and he answers: "You need to multiply Lenin's width by Lenin's length")))

It is useful to know this

For those who are interested in the possibility of increasing the area of land plots for individual housing construction, private household plots, gardening, horticulture, which are owned, it is useful to familiarize yourself with the procedure for registration of cuts.

From January 1, 2018, the exact boundaries of the plot must be recorded in the cadastral passport, since buying, selling, mortgaging or donating land without accurate description borders will be simply impossible. This is regulated by amendments to the Land Code. A total revision of the borders at the initiative of the municipalities began on June 1, 2015.

On March 1, 2015, a new the federal law"On Amendments to the Land Code of the Russian Federation and Certain Legislative Acts of the Russian Federation" (N 171-FZ "dated 06/23/2014), in accordance with which, in particular, the procedure for purchasing land plots from municipalities is simplified& You can familiarize yourself with the main provisions of the law here.

With regard to the registration of houses, baths, garages and other buildings on land owned by citizens, the situation will improve with a new dacha amnesty.

Eratosthenes measured how far the midday sun in Alexandria deviated from the zenith, and received a value equal to 7 ° 12 ", which is 1/50 of the circle. He managed to do this using an instrument called a scaphis. The scaphis was a bowl in the shape of a hemisphere. In the center she was sheerly strengthened

On the left - determination of the height of the sun with a skafis. In the center - a diagram of the direction of the sun's rays: in Siena they fall vertically, in Alexandria - at an angle of 7 ° 12 ". On the right - the direction of the sun's beam in Siena at the time of the summer solstice.

Skafis - an ancient device for determining the height of the sun above the horizon (in section).

needle. The shadow from the needle fell on the inner surface of the scaphi. To measure the deviation of the sun from the zenith (in degrees), circles marked with numbers were drawn on the inner surface of the skafis. If, for example, the shadow reached the circle marked 50, the sun was 50° below the zenith. Having built a drawing, Eratosthenes correctly concluded that Alexandria is 1/50 of the Earth's circumference from Syene. To find out the circumference of the Earth, it remained to measure the distance between Alexandria and Siena and multiply it by 50. This distance was determined by the number of days that camel caravans spent on the transition between cities. In the units of that time, it was equal to 5 thousand stages. If 1/50 of the circumference of the earth is 5,000 stadia, then the whole circumference of the earth is 5,000 x 50 = 250,000 stadia. In terms of our measures, this distance is approximately equal to 39,500 km. Knowing the circumference, you can calculate the radius of the Earth. The radius of any circle is 6.283 times less than its length. Therefore, the average radius of the Earth, according to Eratosthenes, turned out to be equal to a round number - 6290 km, and the diameter is 12 580 km. So Eratosthenes found approximately the dimensions of the Earth, close to those determined by precise instruments in our time.

How information about the shape and size of the earth was checked

After that, on the measured side AB and two corners at the vertices BUT and AT you can build a triangle ABC and hence find the lengths of the sides AC and sun, i.e. distances from BUT before With and from AT before WITH. Such a construction can be performed on paper, reducing all dimensions by several times or using a calculation according to the rules of trigonometry. Knowing the distance from AT before With and directing from these points the telescope of the measuring instrument (theodolite) to the object at some new point D, measure the distance from AT before D and from With before D. Continuing the measurements, as if covering part of the Earth's surface with a network of triangles: ABC, BCD etc. In each of them, you can consistently determine all the sides and angles (see Fig.). After the side is measured AB the first triangle (basis), the whole thing comes down to measuring the angles between the two directions. Having built a network of triangles, it is possible to calculate, according to the rules of trigonometry, the distance from the vertex of one triangle to the vertex of any other, no matter how far apart they may be. This solves the problem of measuring large distances on the surface of the Earth. The practical application of the triangulation method is far from simple. This work can only be done by experienced observers armed with very precise goniometric instruments. Usually for observations it is necessary to build special towers. Work of this kind is entrusted to special expeditions, which last for several months and even years.

The triangulation method helped scientists refine their knowledge of the shape and size of the Earth. This happened under the following circumstances.

The famous English scientist Newton (1643-1727) expressed the opinion that the Earth cannot have the shape of an exact ball, because it rotates around its axis. All particles of the Earth are under the influence of centrifugal force (force of inertia), which is especially strong

Triangulation scheme: AB - basis; BE - measured distance.

at the equator and absent at the poles. The centrifugal force at the equator acts against the force of gravity and weakens it. The balance between gravity and centrifugal force was achieved when the globe at the equator "inflated" and at the poles "flattened" and gradually acquired the shape of a tangerine, or, in scientific terms, a spheroid. An interesting discovery made at the same time confirmed Newton's assumption.

In 1672, a French astronomer found that if accurate clocks were transported from Paris to Cayenne (in South America, near the equator), they begin to fall behind by 2.5 minutes per day. This lag occurs because the clock pendulum swings more slowly near the equator. It became obvious that the force of gravity, which makes the pendulum swing, is less in Cayenne than in Paris. Newton explained this by the fact that at the equator the surface of the Earth is farther from its center than in Paris.

The southern expedition carried out measurements in Peru. A meridian arc with a length of about 3° (330 km). It crossed the equator and passed through a series of mountain valleys and the highest mountain ranges in America.

The northern expedition worked in Lapland (until the beginning of the 20th century, this was the name given to the northern part of the Scandinavian and the western part of the Kola Peninsula).

In our time, there is a special science - geodesy, which deals with determining the size of the Earth using the most accurate measurements of its surface. The data of these measurements made it possible to accurately determine the actual figure of the Earth.

Geodetic work on measuring the Earth has been and is being carried out in various countries. Such work has been carried out in our country. As early as the last century, Russian geodesists carried out very precise work to measure the "Russian-Scandinavian arc of the meridian" with a length of more than 25 °, i.e., a length of almost 3 thousand meters. km. It was called the "Struve arc" in honor of the founder of the Pulkovo Observatory (near Leningrad) Vasily Yakovlevich Struve, who conceived and supervised this huge work.

Degree measurements are of great practical importance, primarily for the preparation of accurate maps. Both on the map and on the globe, you see a network of meridians - circles going through the poles, and parallels - circles parallel to the plane of the earth's equator. A map of the Earth could not be drawn up without the long and painstaking work of geodesists, who determined step by step over many years the position of different places on the earth's surface and then plotted the results on a network of meridians and parallels. To have accurate maps, it was necessary to know the actual shape of the Earth.

The measurement results of Struve and his collaborators turned out to be a very important contribution to this work.

Subsequently, other geodesists measured with great accuracy the lengths of the arcs of the meridians and parallels in different places on the earth's surface. Using these arcs, with the help of calculations, it was possible to determine the length of the Earth's diameters in the equatorial plane (equatorial diameter) and in the direction of the earth's axis (polar diameter). It turned out that the equatorial diameter is longer than the polar one by about 42.8 km. This once again confirmed that the Earth is compressed from the poles. According to the latest data from Soviet scientists, the polar axis is 1/298.3 shorter than the equatorial one.

Gradual change in the shape of the earth

However, as it was possible to find out with the help of all the same space observations and special calculations made on their basis, the geoid has a complex shape due to the rotation of the Earth and the uneven distribution of masses in the earth's crust, but quite well (with an accuracy of several hundred meters) is represented by an ellipsoid of rotation, having a polar contraction of 1:293.3 (Krasovsky's ellipsoid).

Geomagnetic measurements, which since the late 1970s have become an integral attribute of satellite observation research programs, have consistently recorded the alignment of the planet's gravitational field. In general, from the point of view of mainstream geophysical theories, the gravitational dynamics of the Earth seemed quite predictable, although, of course, both within the mainstream and outside it, there were numerous hypotheses that interpreted the medium and long-term prospects of this process in different ways, as well as what happened in the past life of our planet. Quite popular today is, say, the so-called pulsation hypothesis, according to which the Earth periodically contracts and expands; There are also supporters of the "contract" hypothesis, which postulates that in the long run the size of the Earth will decrease. There is no unity among geophysicists in terms of what phase the process of post-glacial restoration of gravitational equilibrium is in today: most experts believe that it is quite close to completion, but there are also theories stating that it is still far from its end or that it has already stopped.

Nevertheless, despite the abundance of discrepancies, until the end of the 90s of the last century, scientists still did not have any good reason to doubt that the process of post-glacial gravitational alignment is alive and well. The end of scientific complacency came rather abruptly: after spending several years checking and rechecking the results obtained from nine different satellites, two American scientists, Christopher Cox of Raytheon and Benjamin Chao, a geophysicist at NASA's Goddard Space Flight Control Center, came to a surprising conclusion: since 1998, the "equatorial coverage" of the Earth (or, as many Western media dubbed this dimension, its "thickness") began to increase again.
The sinister role of ocean currents.

Cox and Chao's paper, which claims "the discovery of a large-scale redistribution of the Earth's mass," was published in the journal Science in early August 2002. As the authors of the study note, "long-term observations of the behavior of the Earth's gravitational field have shown that the post-glacial effect that leveled it in the past few years has suddenly had a more powerful adversary, approximately twice as strong as its gravitational effect." Thanks to this "mysterious adversary", the Earth again, as in the last "epoch of the Great Icing", began to flatten, that is, since 1998, an increase in the mass of matter has been taking place in the equator region, while its outflow has been going on from the polar zones.

The version about any underground phenomena, for example, the flow of matter in the earth's magma or core, looks, according to the authors of the article, rather doubtful: in order for such processes to have any significant gravitational effect, it allegedly takes a much longer time than ludicrous by scientific standards for four years. As possible reasons for the thickening of the Earth along the equator, they name three main ones: oceanic influence, melting of polar and high mountain ice, and certain "processes in the atmosphere." However, they also immediately dismiss the last group of factors - regular measurements of the weight of the atmospheric column do not give any grounds for suspicion of the involvement of certain air phenomena in the occurrence of the discovered gravitational phenomenon.

Far from being so unambiguous seems to Cox and Chao the hypothesis of the possible influence on the equatorial swelling of the process of ice melting in the Arctic and Antarctic zones. This process, as the most important element of the notorious global warming of the world climate, certainly, to one degree or another, can be responsible for the transfer of significant masses of matter (primarily water) from the poles to the equator, but the theoretical calculations made by American researchers show that in order for it to be determining factor (in particular, it "blocked" the consequences of the thousand-year "growth of the positive relief"), the dimension of the "virtual block of ice" annually melted since 1997 should have been 10x10x5 kilometers! Geophysicists and meteorologists have no empirical evidence that the process of ice melting in the Arctic and Antarctic in recent years could take on such a scale. According to the most optimistic estimates, the total volume of melted ice floes is at least an order of magnitude smaller than this "super iceberg", therefore, even if it had some effect on the increase in the Earth's equatorial mass, this effect could hardly be so significant.

As the most probable reason for the sudden change in the Earth's gravitational field, Cox and Chao consider today the oceanic impact, that is, the same transfer of large volumes of the World Ocean's water mass from the poles to the equator, which, however, is associated not so much with the rapid melting of ice, how much with some not quite explainable sharp fluctuations in ocean currents that have occurred in recent years. Moreover, as experts believe, the main candidate for the role of a disturber of gravitational calm is the Pacific Ocean, more precisely, the cyclic movements of huge water masses from its northern regions to the southern ones.

If this hypothesis turns out to be correct, humanity in the very near future may face very serious changes in the global climate: the sinister role of ocean currents is well known to everyone who is more or less familiar with the basics of modern meteorology (which is worth one El Niño). True, the assumption that the sudden swelling of the Earth along the equator is a consequence of the climate revolution already in full swing looks quite logical. But, by and large, it is still hardly possible to really understand this tangle of cause-and-effect relationships on the basis of fresh traces.

The obvious lack of understanding of the ongoing "gravitational outrages" is perfectly illustrated by a small fragment of the interview of Christopher Cox himself to the correspondent of the Nature magazine news service Tom Clark: one thing: Our planet's "weight problems" are likely temporary and not a direct result of human activity." However, continuing this verbal balancing act, the American scientist immediately once again prudently stipulates: "It seems that sooner or later everything will return" to normal ", but perhaps we are mistaken on this score."

Now you know that in the fabulous Universe of our distant ancestors, the Earth did not even resemble a ball. Inhabitants Ancient Babylon imagined it as an island in the ocean. The Egyptians saw it as a valley stretched from north to south, in the center of which was Egypt. And the ancient Chinese at one time depicted the Earth as a rectangle ... You smile, imagining such an Earth, but how often have you thought about how people guessed that the Earth is not an unlimited plane or a disk floating in the ocean? When I asked the guys about this, some said that people learned about the sphericity of the Earth after the first around the world travel, while others recalled that when a ship appears from behind the horizon, we first see the masts, and then the deck. Do such and some similar examples prove that the Earth is a sphere? Unlikely. After all, you can go around and around ... a suitcase, and the upper parts of the ship would appear even if the Earth had the shape of a hemisphere or looked like, say, a ... log. Think about it and try to depict what is said in your drawings. Then you will understand: the examples given show only that The earth is isolated in space and possibly spherical.

How did you know that the Earth is a sphere? It helped, as I already told you, the Moon, or rather, lunar eclipses, during which the round shadow of the Earth is always visible on the Moon. Arrange a small "shadow theater": illuminate objects in a dark room different shapes(triangle, plate, potato, ball, etc.) and notice what kind of shadow they get on the screen or just on the wall. Make sure only the ball always casts a circle shadow on the screen. So, the Moon helped people to know that the Earth is a sphere. To this conclusion, scientists Ancient Greece(For example, great Aristotle) came as early as the 4th century BC. But for a very long time common sense"A person could not come to terms with the fact that people live on the ball. They could not even imagine how it was possible to live on the" other side "of the ball, because the" antipodes " located there would have to walk upside down all the time ... But no matter where there was a person on the globe, everywhere a stone thrown upwards will fall down under the influence of the force of gravity of the Earth, that is, on the earth's surface, and if it were possible, then to the center of the Earth.In fact, people, of course, nowhere, except for circuses and gyms, you don't have to walk upside down and upside down.They walk normally anywhere on the Earth: the earth's surface is under their feet, and the sky is above their heads.

Around 250 BC, a Greek scholar Eratosthenes first accurately measured the globe. Eratosthenes lived in Egypt in the city of Alexandria. He guessed to compare the height of the Sun (or its angular distance from a point overhead, zenith, which is called - zenith distance) at the same time in two cities - Alexandria (in northern Egypt) and Syene (now Aswan, in southern Egypt). Eratosthenes knew that on the day of the summer solstice (June 22) the Sun was at noon illuminates the bottom of deep wells. Therefore, at this time the Sun is at its zenith. But in Alexandria at this moment the Sun is not at its zenith, but is separated from it by 7.2 °. Eratosthenes obtained this result by changing the zenith distance of the Sun with the help of his simple goniometric tool - the scaphis. This is just a vertical pole - a gnomon, fixed at the bottom of a bowl (hemisphere). The skafis is installed in such a way that the gnomon takes a strictly vertical position (directed to the zenith). The pole illuminated by the sun casts a shadow on the inner surface of the skafis divided into degrees. So, at noon on June 22 in Siena, the gnomon does not cast a shadow (the Sun is at its zenith, its zenith distance is 0 °), and in Alexandria, the shadow from the gnomon, as can be seen on the scale of the skafis, marked a division of 7.2 °. At the time of Eratosthenes, the distance from Alexandria to Syene was considered equal to 5000 Greek stadia (about 800 km). Knowing all this, Eratosthenes compared an arc of 7.2 ° with the entire circle of 360 ° degrees, and a distance of 5000 stadia - with the entire circumference of the globe (we denote it by the letter X) in kilometers. Then from the proportion

it turned out that X = 250,000 stages, or about 40,000 km (imagine this is true!).

If you know that the circumference of a circle is 2πR, where R is the radius of the circle (and π ~ 3.14), knowing the circumference of the globe, it is easy to find its radius (R):

It is remarkable that Eratosthenes was able to measure the Earth very accurately (after all, even today it is believed that the average radius of the Earth 6371 km!).

But why is it mentioned here average radius of the earth, Aren't all spheres the same radius? The fact is that the figure of the Earth is different from the ball. Scientists began to guess about this back in the 18th century, but what the Earth really is - is it compressed at the poles or at the equator - it was difficult to find out. To understand this, the French Academy of Sciences had to equip two expeditions. In 1735, one of them went to carry out astronomical and geodetic work in Peru and did this in the equatorial region of the Earth for about 10 years, and the other, Lapland, worked in 1736-1737 near the North polar circle. As a result, it turned out that the length of the arc of one degree of the meridian is not the same at the poles of the Earth and at its equator. The meridian degree turned out to be longer at the equator than at high latitudes (111.9 km and 110.6 km). This can only happen if the Earth is compressed at the poles and is not a ball, but a body close in shape to spheroid. At the spheroid polar radius less equatorial(for the terrestrial spheroid, the polar radius is shorter than the equatorial one by almost 21 km).

It's good to know that great Isaac Newton (1643-1727) anticipated the results of the expeditions: he correctly concluded that the Earth is compressed, because our planet rotates around its axis. In general, the faster the planet rotates, the greater must be its compression. Therefore, for example, the compression of Jupiter is greater than that of the Earth (Jupiter has time to make a revolution around the axis with respect to the stars in 9 hours and 50 minutes, and the Earth only in 23 hours and 56 minutes).

And further. The true figure of the Earth is very complex and differs not only from a ball, but also from a spheroid. rotation. True, in this case we are talking about the difference not in kilometers, but ... meters! Scientists are engaged in such a thorough refinement of the figure of the Earth to this day, using for this purpose specially conducted observations from artificial satellites of the Earth. So it is quite possible that someday you will have to take part in solving the problem that Eratosthenes took up a long time ago. This is very what people need case.

What is the best way to remember the figure of our planet? I think that for now it is enough if you imagine the Earth as a ball with an "additional belt" put on it, a kind of "slap" on the equator region. Such a distortion of the figure of the Earth, turning it from a sphere into a spheroid, has considerable consequences. In particular, due to the attraction of the "additional belt" by the Moon, the earth's axis describes a cone in space in about 26,000 years. This movement of the earth's axis is called precessional. As a result, the role polar star, which now belongs to α Ursa Minor, some other stars alternately play (in the future it will become, for example, α Lyra - Vega). In addition, because of this precessional) movements of the earth's axis Zodiac signs more and more do not coincide with the corresponding constellations. In other words, 2000 years after the era of Ptolemy, the "sign of Cancer", for example, no longer coincides with the "constellation of Cancer", etc. However, modern astrologers try not to pay attention to this ...

People have long guessed that the Earth they live on is like a ball. The ancient Greek mathematician and philosopher Pythagoras (ca. 570-500 BC) was one of the first to express the idea of the sphericity of the Earth. The greatest thinker of antiquity, Aristotle, observing lunar eclipses, noticed that the edge of the earth's shadow falling on the moon always has a round shape. This allowed him to judge with confidence that our Earth is spherical. Now, thanks to the achievements of space technology, all of us (and more than once) have had the opportunity to admire the beauty of the globe from images taken from space.

A reduced likeness of the Earth, its miniature model is a globe. To find out the circumference of a globe, it is enough to wrap it with a drink, and then determine the length of this thread. You can't get around the huge Earth with a measured contribution along the meridian or the equator. And in whatever direction we begin to measure it, insurmountable obstacles will certainly appear on the way - high mountains, impenetrable swamps, deep seas and oceans ...

Is it possible to know the size of the Earth without measuring its entire circumference? Of course you can.

We know that there are 360 degrees in a circle. Therefore, to find out the circumference, in principle, it is enough to measure exactly the length of one degree and multiply the result of the measurement by 360.

Camel caravans came from the south to Alexandria. From the people accompanying them, Eratosthenes learned that in the city of Syene (present-day Aswan) on the day of the summer solstice, the Sun is overhead on yol-day. Objects at this time do not give any shade, and the sun's rays penetrate even the deepest wells. Therefore, the Sun reaches its zenith.

Through astronomical observations, Eratosthenes established that on the same day in Alexandria, the Sun is 7.2 degrees from the zenith, which is exactly 1/50 of the circle. (Indeed: 360: 7.2 = 50.) Now, in order to find out what the circumference of the Earth is, it remained to measure the distance between cities and multiply it by 50. But Eratosthenes could not measure this distance, which runs through the desert. Nor could the guides of trade caravans measure it. They only knew how much time their camels spend on one crossing, and they believed that from Syene to Alexandria there were 5,000 Egyptian stadia. So the whole circumference of the earth: 5,000 x 50 = 250,000 stadia.

Unfortunately, we do not know the exact length of the Egyptian stage. According to some reports, it is equal to 174.5 m, which gives 43,625 km for the earth's circumference. It is known that the radius is 6.28 times less than the circumference. It turned out that the radius of the Earth, but to Eratosthenes, was 6943 km. This is how, more than twenty-two centuries ago, the dimensions of the globe were first determined.

According to modern data, the average radius of the Earth is 6371 km. Why average? After all, if the Earth is a sphere, then the idea of the earth's radii should be the same. We will talk about this further.

A method for accurately measuring large distances was first proposed by the Dutch geographer and mathematician Wildebrord Siellius (1580-1626).

The geodetic network necessarily relies on astronomical points A and B. The method of astronomical observations of stars determines their geographical coordinates (latitudes and longitudes) and azimuths (directions to local objects).

This method of measuring large distances on the earth's surface is called triangulation - from the Latin word "triapgulum", which means "triangle". It turned out to be convenient for determining the size of the Earth.

The most grandiose degree measurement of the 19th century was headed by the founder of the Pulkovo Observatory, V. Ya. Struve. Under the leadership of Struve, Russian geodesists, together with Norwegian ones, measured the arc that stretched from the Danube through the western regions of Russia to Finland and Norway to the coast of the Arctic Ocean. The total length of this arc exceeded 2800 km! It contained more than 25 degrees, which is almost 1/14 of the earth's circumference. It entered the history of science under the name "Struve arcs". In the post-war years, the author of this book happened to work on observations (angle measurements) at state triangulation points adjacent directly to the famous "arc".

The longer the measured arcs of meridians and parallels, the more accurately you can calculate the radius of the Earth and determine its compression.

Now it is quite clear that the Earth is not a regular geometric body, that is, an ellipsoid. In addition, the surface of our planet is far from smooth. It has hills and high mountain ranges. True, land is almost three times less than water. What, then, should we mean by the underground surface?

And what about the regions of the continents? What is considered the surface of the Earth? It is also the surface of the World Ocean, mentally extended under all the continents and islands.

On October 4, 1957, with the launch of the first artificial Earth satellite in our country, humanity entered the space age. Active exploration of near-Earth space began. At the same time, it turned out that satellites are very useful for understanding the Earth itself. Even in the field of geodesy, they said their "weighty word".

With the launch of the satellites, surveyors immediately realized that “sight targets” appeared at high altitude. Now long distances can be measured.

The idea of the space triangulation method is simple. Synchronous (simultaneous) observations of a satellite from several distant points on the earth's surface make it possible to bring their geodetic coordinates to a single system. Thus, triangulations built on different continents were connected together, and at the same time the dimensions of the Earth were clarified: the equatorial radius is 6378.160 km, the polar radius is 6356.777 km. The compression value is 1/298.25, that is, almost the same as that of the Krasovsky ellipsoid. The difference between the equatorial and polar diameters of the Earth reaches 42 km 766 m.

If our planet were a regular ball, and the masses inside it were evenly distributed, then the satellite could move around the Earth in a circular orbit. But the deviation of the shape of the Earth from spherical and the heterogeneity of its bowels lead to the fact that over different points of the earth's surface the force of attraction is not the same. The force of gravity of the Earth changes - the orbit of the satellite changes. And all, even the slightest changes in the motion of a satellite with a low orbit are the result of the gravitational influence on it of one or another earthly bulge or depression over which it flies.

It turned out that our planet also has a slightly pear-shaped shape. Its North Pole is raised above the plane of the equator by 16 m, and the South Pole is lowered by about the same amount (as if depressed). So it turns out that in cross section along the meridian, the figure of the Earth resembles a pear. It is slightly elongated to the north and flattened at the South Pole. There is a polar asymmetry: The northern hemisphere is not identical to the southern one. Thus, on the basis of satellite data, the most accurate idea of the true shape of the Earth was obtained. As you can see, the figure of our planet noticeably deviates from the geometrically correct shape of a ball, as well as from the figure of an ellipsoid of revolution.

How Eratosthenes calculated the circumference of the earth. The area of ​​land plots for individual housing construction, private household plots is usually indicated in acres

Eratosthenes' contribution to geography. What did Eratosthenes discover?

What did Eratosthenes discover in geography?

How did Eratosthenes measure the radius of the earth?

Units of land area measurement

The system adopted in Russia for measuring land areas

Area units conversion table

The area of ​​land plots for individual housing construction, private household plots is usually indicated in acres

It is useful to know this

How Eratosthenes calculated the circumference of the earth. The area of land plots for individual housing construction, private household plots is usually indicated in acres

The area of land plots for individual housing construction, private household plots is usually indicated in acres