What is the average radius of the earth. Figure of the earth

The earth is round - this is common knowledge. What else do we know about its shape and size? Which of us can remember from memory how many kilometers the circumference of the Earth is at the equator? What about the meridian? Who knows when and how the circumference of the earth was first measured? Meanwhile, these facts are extremely interesting.

The circumference of the Earth was first measured by Eratosthenes, who lived in the city of Siena. At that time, scientists already knew that the Earth is spherical in shape. Observing the celestial body at different times of the day, Eratosthenes noticed that at the same time the sun, being observed from Syene, is located exactly at the zenith, while in Alexandria on the same day and hour it deviates by a certain angle.

Observations were carried out annually. Having measured this angle using astronomical instruments, the scientist found that it was 1/50 of the full circle.

As you know, a complete circle is equal to 360 degrees. Thus, it is enough to know the chord of an angle of 1 degree (i.e., the distance between points on the Earth’s surface lying on rays with an angular distance between them of 1 degree). Then the resulting value should be multiplied by 360.

Taking the distance between the cities of Alexandria and Syene (5 thousand Egyptian stadia) as the length of the chord and assuming that these cities lie on the same meridian, Eratosthenes made the necessary calculations and named the figure that equaled the circumference of the Earth - 252 thousand Egyptian stadia.

For that time, this measurement was quite accurate, because there were no reliable methods for measuring the distance between cities, and the path from Siena to Alexandria was measured by the speed of the camel caravan.

Subsequently, scientists from different countries repeatedly measured and clarified the value that is the circumference of the Earth. In the 17th century, a Dutch scientist named Sibelius came up with a way to measure distances using the first theodolites - special geodetic instruments. This method was called triangulation and is based on constructing a large number of triangles and measuring the basis of each of them.

The triangulation method is still used today; the entire earth's surface is virtually divided and lined into large triangles.

Russian scientists also contributed to these studies. In the 19th century, the circumference of the Earth was measured by V. Ya. Struve, who led the research.

Until the mid-17th century, the Earth was considered a sphere of regular shape. But later, some facts were accumulated indicating a decrease in the force of gravity from the equator to the pole. Scientists fiercely debated the reasons for this; the most plausible theory was considered to be the compression of the Earth from the poles.

To test this hypothesis, the French Academy organized two independent expeditions (in 1735 and 1736), which measured the length of the equatorial and polar degrees, respectively, in Peru and Lapland. At the equator, the degree, as it turns out, is shorter!

Subsequently, other, more accurate measurements confirmed that the polar circle of the Earth is 21.4 km shorter than the equatorial one.

Currently, high-precision measurements have been made using the latest research methods and modern instruments. In our country, the data obtained by Soviet scientists A. A. Izotov and F. N. Krasovsky have been officially approved. According to these studies, the circumference of our planet along the equator is 40075.7 kilometers, along the meridian - 40008.55 km. The equatorial radius of the globe (the so-called semi-major axis) is equal to 6378245 meters, the polar (semi-minor axis) is 6356863 meters.

510 million sq. kilometers, of which only 29% belongs to land. The volume of the earth's "ball" is 1083 billion cubic meters. kilometers. The mass of our planet is characterized by the figure 6X10^21 tons. Of this, about 7% comes from water resources.

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

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

It is unknown which stage Eratosthenes used. Only if it is 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.

Radius of the earth in m. What is the radius of the earth?

The polar radius of the Earth is the semiminor axis of the Krasovsky ellipsoid, equal to 6,356,863 m.

The equatorial radius of the Earth is the semimajor axis of the Krasovsky ellipsoid, equal to 6,378,245 m.

The average radius of the Earth is 6,371,302 m.

History of measuring the radius of the Earth

Eratorsthenes. Even the ancient Egyptians noticed that during the summer solstice the Sun illuminates the bottom of deep wells in Siena (now Aswan), but not in Alexandria. Eratosthenes of Cyrene (276 BC - 194 BC) had 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 was in the sky.
So, after measuring the angle turned out to be 7 degrees 12 minutes, that is, 1/50 of a circle. Therefore, Siena is 1/50 of the circumference of the Earth from Alexandria. The distance between cities was considered equal to 5 thousand stadia, therefore the circumference of the Earth was 250 thousand stadia, and the radius was then 39.8 thousand stadia.
It is unknown which stage Eratosthenes used. If Greek (178 meters), then its radius of the Earth was 7.08 thousand km, if Egyptian, then 6.3 thousand 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.

are determined by more than one numerical characteristic. Scientists indicate its size using several parameters. The first parameter is the radius. Its size is 3,389.5 kilometers. The second is a circle, which is numerically equal to 21,344 kilometers. Next comes the volume – 6.083·1010 km³. The last parameter is the mass of Mars, which is equal to 3.33022·1023 kg.

For comparison, the diameter is 53% of the Earth's diameter. At first glance, this is not much, but its value is comparable to the total land area on. The volume of Mars is 15% of the volume of the Earth, and the mass is 11%. From the given data it is clear that Mars is a small planet, it is 2 times smaller than the Earth and is the 7th planet in size.

Comparison of the sizes of the Earth, Mars and the Moon

Despite its small size and lack of life on it, Mars has many interesting features. The highest mountain in the Solar System is located on the Red Planet. Martian is the deepest. Hundreds of thousands of craters cover the surface of the Red Planet. The North Polar Basin is the largest known plain, and the Hellas Plain, which measures 2,100 km, is the deepest on the planet and the third largest in the solar system.

The extreme topographical features of the Red Planet are complemented by equally extreme weather conditions. Mars is a cold planet. The average surface temperature is 470C below zero. In summer, near the equator, the temperature during the day can rise to +200C, and at night drop to -900C. Such temperature changes of 1100C cause severe hurricanes reaching the speed of a tornado. They raise dust from the surface of Mars, and then a dust storm begins. Astronomers have observed storms on Mars that engulfed the entire planet in just a few days.

According to scientists, Mars was much larger at the beginning of the development of the solar system. The size of the planet decreased as a result of external influences, for example, a collision with some kind of cosmic body, which caused the formation of the North Polar Basin. Pieces of the surface destroyed by the explosion, overcoming the gravitational field of Mars, were thrown into cosmic space.

So, not only the size of Mars may be of interest. You can learn a lot more interesting things about the Red Planet, it all depends on our desires. You can learn a lot of interesting things about other planets - and

How Eratosthenes measured the radius of the earth. Greek astronomer Eratosthenes was the first to calculate the radius of the Earth: interesting facts

The accuracy of Eratosthenes' measurements was simply amazing for those times.

Eratosthenes of Cyrene (276 BC - 194 BC) - Greek mathematician, astronomer, geographer and poet.

June 19, 240 BC Eratosthenes used a scaphis (a bowl with a long needle), with which it was possible to determine at what angle the Sun was in the sky. It was the summer solstice in Alexandria.

Dissatisfied with the knowledge acquired in Alexandria, Eratosthenes went to Athens, where he became so close to the school of Plato that he usually called himself a Platonist.

The result of the study of sciences in both of these centers of ancient Greek enlightenment was the very versatile, almost encyclopedic erudition of Eratosthenes; In addition to works on mathematics, astronomy, geodesy, geography and chronology, he also wrote treatises “on good and evil”, on comedy, etc.

King Ptolemy III Euergetes, immediately after the death of Callimachus, summoned Eratosthenes from Athens and entrusted him with the management of the great library of Alexandria. Erastofen is the author of many works on mathematics, astronomy, geodesy, and geography. One of the interesting facts of the life of Eratosthenes is the calculation of the radius of the Earth.

The ancient Egyptians noticed that during the summer solstice the Sun illuminated the bottom of deep wells in Siena (now Aswan), but not in Alexandria. Eratosthenes used this fact to measure the circumference and radius of the Earth.

After measurement, the angle turned out to be 7 degrees 12 minutes, that is, 1/50 of a circle. Therefore, Siena lags behind Alexandria by 1/50 of the circumference of the Earth. The distance between the cities was 5,000 stadia, therefore the circumference of the Earth was 250,000 stadia, and the radius was then 39,790 stadia.

It is unknown what stages Eratosthenes used. If in Greek (178 meters), then its radius of the earth is 7.082 km, and if in Egyptian - 6.287 km.

Modern measurements give the average radius of the Earth as 6.371 km.

In any case, the measurement accuracy was simply amazing for those times!

Eratosthenes lived an amazing, eventful and long life. For several decades he remained the permanent archivist of the Library of Alexandria. He idolized and loved books more than anything in the world, a source of knowledge and the brightest discoveries. In old age, removed from office, blind and infirm, he reduced himself to extreme poverty and starved himself to death in 194 BC.

As the portal “Know.ua” reported, astronomers have discovered a system in which there are three Earth-like planets at once. Moreover, scientists have discovered a system with two super-Earths.

Astronomers already know about 500 Earth-like planets. The problem is that most of them are either too hot or, on the contrary, too cold, so scientists continue to search for planets similar to Earth.

How to measure the radius of the earth message 7th grade. How the ancient Greek measured the radius of the Earth (3 photos)

The ancient Greeks, observing lunar eclipses, discovered that the Earth casts a circular shadow on the Moon. Thus they realized that our planet is round. At the same time, the Egyptians made an observation that during the summer solstice, the Sun illuminates the bottom of even the deepest wells.

In those days (240 BC) there lived a famous Greek mathematician, astronomer, geographer and poet - Eratosthenes of Cyrene. He received his education in Alexandria, but unsatisfied with that education, he went to Athens, where he studied at the Platonic school, and subsequently began to call himself a Platonist.
After receiving his education, having almost encyclopedic knowledge, Eratosthenes began his scientific activity, subsequently becoming famous thanks to his work. So, at one fine moment, King Ptolemy III invited Eratosthenes from Athens to Alexandria to manage the great Library of Alexandria.

One of Eratosthenes' greatest discoveries was the calculation of the radius of the Earth. He calculated the radius thanks to wells and the knowledge that the Earth is round. During the solstice in Alexandria, Eratosthenes measured, using a bowl with a long needle, at what angle the Sun was in relation to the Earth in Syene. After measurement, the angle turned out to be 7 degrees 12 minutes, that is, 1/50 of a circle. Therefore, Siena is located 1/50 of the circumference of the Earth from Alexandria, that is, 5000 stadia, therefore the circumference of the Earth was 250,000 stadia, and the radius was then 39,790 stadia.
According to calculations, Eratosthenes received a value of 6287 km, which differs from the true value by only less than 100 km.

Video Refutation of Eratosthenes' calculations of the Earth's radius

Each of us studied many subjects at school: physics, chemistry, biology, mathematics and others. Astronomy was often included in this list. This is an interesting science that tells us about various cosmic quantities (the distance from our planet to the Sun, the diameter of the Earth, the mass of the moon, etc.), universal phenomena (black holes, star falls, eclipses, etc.).

Agree that all this is very important and informative information about what surrounds us. But if someone asks us what the diameter of planet Earth is, we are unlikely to be able to answer correctly. Unfortunately, everything we learned at school tends to be gradually forgotten if the knowledge is not maintained. This article will help to renew some “cosmic” information.

Earth diameter

It is believed that this indicator of our planet began to be studied even before our era. The famous ancient astronomer Eratosthenes, using the distance between cities and the angle of incidence of the sun's rays, was able to calculate the circumference of our planet, and then the radius and diameter of the Earth. So, the average of this value is approximately 12,756 kilometers. Agree that this is quite a lot. The word “average” is used here because the Earth is not spherical (but it is not an ellipse, which was talked about so much at one time).

This is a peculiar shape elongated towards the poles, which is currently called a geoid. Because of this “deformation,” the diameter of the Earth at the equator differs from the corresponding indicator at the prime meridian (the second value is slightly larger).

Other important parameters of the blue planet

The earth has a very large and rich history, most of which it keeps within itself and which, unfortunately, we are unlikely to learn about. Our planet is already more than four and a half billion years old. During this time, she has undergone a large number of changes. The Earth is part of the Solar System and rotates in orbit around its center - our star. The distance to it from the third planet is approximately one hundred and fifty million kilometers. The Earth has only one natural satellite - the well-known Moon, which has a significant influence on the tides on the blue planet. The length of the equator is approximately 40,076 kilometers, which is almost 44 kilometers longer than the length of the meridian (which is why the diameter of the Earth changes depending on the place of measurement).

Living Planet

Indeed, the Earth is currently the only place in the Universe studied (by local scientists) where there are living organisms that appeared here almost four billion years ago. They live both on land and in water. And water on our planet occupies more than seventy percent. In addition to the presence of organisms, the Earth also has its own life. It manifests itself in the movement of tectonic plates: volcanic eruptions, strong and weak earthquakes occur. This confirms the fact that our Earth does not stop in its development even now. Nobody knows what other surprises the home of people - the living blue planet - has prepared for us.

Distance from Earth to Moon

The Moon became the first celestial body to which it was possible to calculate the distance from the Earth. It is believed that astronomers in Ancient Greece were the first to do this.

People have been trying to measure the distance to the Moon since time immemorial - Aristarchus of Samos was the first to try. He estimated the angle between the Moon and the Sun to be 87 degrees, so it turned out that the Moon is 20 times closer to the Sun (the cosine of an angle of 87 degrees is 1/20). The angle measurement error resulted in a 20-fold error; today it is known that this ratio is actually 1 to 400 (the angle is approximately 89.8 degrees). The large error was caused by the difficulty of estimating the exact angular distance between the Sun and Moon using the primitive astronomical instruments of the ancient world. Regular solar eclipses by this time had already allowed ancient Greek astronomers to conclude that the angular diameters of the Moon and the Sun were approximately the same. In this regard, Aristarchus concluded that the Moon is 20 times smaller than the Sun (in fact, about 400 times).

To calculate the sizes of the Sun and Moon relative to the Earth, Aristarchus used a different method. We are talking about observations of lunar eclipses. By this time, ancient astronomers had already guessed the reasons for these phenomena: the Moon was eclipsed by the Earth's shadow.


The diagram above clearly shows that the difference in distances from the Earth to the Sun and to the Moon is proportional to the difference between the radii of the Earth and the Sun and the radii of the Earth and its shadow to the distance of the Moon. At the time of Aristarchus, it was already possible to estimate that the radius of the Moon is approximately 15 arc minutes, and the radius of the earth's shadow is 40 arc minutes. That is, the size of the Moon was approximately 3 times smaller than the size of the Earth. From here, knowing the angular radius of the Moon, one could easily estimate that the Moon is located about 40 Earth diameters from the Earth. The ancient Greeks could only approximately estimate the size of the Earth. Thus, Eratosthenes of Cyrene (276 - 195 BC), based on differences in the maximum height of the Sun above the horizon in Aswan and Alexandria during the summer solstice, determined that the radius of the Earth is close to 6287 km (modern value 6371 km). If we substitute this value into Aristarchus’ estimate of the distance to the Moon, it will correspond to approximately 502 thousand km (the modern value of the average distance from the Earth to the Moon is 384 thousand km).

The sun is a colossal hot ball, in the center of which energy is released from hydrogen. Hydrogen is transformed into helium, and the radiated energy is released into outer space. It was not for nothing that people in ancient times deified the luminary. It is its energy that ensures the existence of life on Earth.

Dimensions of the Sun

Diameter

The Sun (Helios) is the closest star to our planet. It belongs to the category of “Yellow Dwarfs”. Like other luminaries, Helios does not have a solid surface. Its primary layer is considered to be the photosphere, which emits energy. Therefore, the diameter of the Sun is nothing more than the diameter of its photosphere.

You can measure the scale of the luminary in a simple, accessible way. The experiment requires a dark room where a ray of sunlight penetrates through a small hole. It is enough to place thick white paper opposite the beam, and a tiny image of the Sun will appear on the surface of the sheet. The further the paper is from the hole, the larger the stain will be. At a distance of 107 cm, its diameter will be 1 cm. At a distance of 214 cm, it will increase to 2 cm. That is, the diameter of the real star is 107 times less than the distance to the Earth and is 1,400,000 km.

Scientists were able to determine the exact diameter of the Sun in kilometers based on an effect called the Bailey's rosary. Rosaries are red dots around the circumference of the solar disk that become visible during an eclipse. With their help, astronomers accurately identified the position of the star and were able to measure its size.

Analysis of historical data, supplemented by regular modern monitoring, has shown that the diameter of the Sun is subject to change. So, in the 17th century the star was 2 thousand kilometers wider than it is today. Astronomers have found that the star expands and contracts over the course of 160 minutes. During the same period, the amount of energy released changes.

Radius

Measuring the duration of solar eclipses and observing the movement of Mercury and Venus against the background of the solar disk allowed scientists to calculate the approximate radius of the star. It is equal to 695990 km.

Instruments on board space stations made it possible to refine the calculations. The studies were carried out using helioseismology methods. In this case, the movement of so-called f-waves on the surface of the Sun was considered. This method of calculation gave a slightly different result - 300 km less (695,700 km). The identified error could have serious consequences for the study of the Sun, its composition and activity.

The radius will have the same value in all directions, since Helios has a regular spherical shape.

Comparison of the sizes of celestial bodies

The value of the solar radius in astronomy is used as a measure of the dimensions of other space objects:

  • The North Star has 30 solar radii. Consequently, it is 30 times higher than the parameters of the Sun.
  • Our planet looks like a small dot against the background of the main star. It is 109 times smaller in size than the star.
  • But the largest planet in the solar system, Jupiter, is only 9.7 times smaller than the Sun.

In the Universe you can find stars - giants that are many times larger than our luminary. The largest star, VY Canis Majoris, according to scientists, has 2100 Helios diameters.

Mass of the Sun, its measurement and comparison

The Sun is the largest celestial body in our star system (99.86% of the total mass). It took almost 5 billion years for the mass of the sun to form.

Three scientific methods have been developed to measure the mass of celestial bodies:

  1. Gravimetric. This method uses parameters for measuring gravity, which characterizes the surface of the body being measured.
  2. Kepler's third law. It is practiced if the planet has at least one satellite. Calculations are carried out taking into account the distance between the planet and its satellite, as well as the period of its orbit. In this way, the ratio of the masses of the planet and the star is determined.
  3. Analysis of noticeable impacts caused by the movement of some celestial bodies relative to the movement of others.

First of all, using the geodetic method, we found out the mass of our planet. She was estimated to be 6*1024kg. Then, based on Kepler's Third Law, the mass of the Moon was calculated - 73477 * 1022 kg. And in conclusion, we found out what the mass of the Sun is - 19891 * 1030 kg.

Solar mass became an abstract metric unit. Astronomers use it to describe various space objects. The largest known star, Eta Carinae, is estimated to be 150 Helios masses.

Scientists have made a forecast of solar activity for the future. Based on observations of other stars, they came to the conclusion that the star is gradually using up the energy of the photosphere. Its dimensions will expand unprecedentedly. The nearest planets - Mercury and Venus will be absorbed. It is possible that the same fate will befall the Earth. The Sun transforms into a Red Giant. The period of growth will be followed by a catastrophic contraction. The star will shrink to approximately the current parameters of the Earth and will be called a White Dwarf.

People have long guessed that the Earth they live on is like a ball. One of the first to express the idea that the Earth was spherical was the ancient Greek mathematician and philosopher Pythagoras (c. 570-500 BC). 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 confidently judge that our Earth is spherical. Now, thanks to the achievements of space technology, we all (more than once) had the opportunity to admire the beauty of the globe from photographs taken from space.

A reduced likeness of the Earth, its miniature model is a globe. To find out the circumference of a globe, just wrap it in drink and then determine the length of this thread. You cannot walk around the vast Earth with a measured contribution along the meridian or equator. And no matter in what direction we begin to measure it, insurmountable obstacles will certainly appear along the way - high mountains, impassable swamps, deep seas and oceans...

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

It is known 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 measurement result 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 shores of the Mediterranean Sea.

Camel caravans came to Alexandria from the south. 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 was overhead on the same day. Objects at this time do not provide any shadow, 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 circumference. (In fact: 360: 7.2 = 50.) Now, in order to find out what the circumference of the Earth is, all that remained was to measure the distance between the cities and multiply it by 50. But Eratosthenes was not able to measure this distance running through the desert. The guides of the trade caravans could not measure it either. They only knew how much time their camels spent on one journey, and believed that from Siena to Alexandria there were 5,000 Egyptian stadia. This means the entire circumference of the Earth: 5000 x 50 = 250,000 stadia.

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

According to modern data, the average radius of the Earth is 6371 km. Why average? After all, if the Earth is a sphere, then in theory 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).

Let's imagine that it is necessary to measure the distance between points A and B, hundreds of kilometers away from each other. The solution to this problem should begin with the construction of a so-called reference geodetic network on the ground. In its simplest form, it is created in the form of a chain of triangles. Their tops are chosen in elevated places, where so-called geodetic signs are built in the form of special pyramids, and always so that from each point the directions to all neighboring points are visible. And these pyramids should also be convenient for work: for installing a goniometer instrument - a theodolite - and measuring all the angles in the triangles of this network. In addition, one side of one of the triangles 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 begins with a triangle containing the basis. Using the side and angles, the other two sides of the first triangle are calculated. But one of its sides is also a side of the 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 required distance is calculated - the arc of the meridian AB.

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

Now that the length of the arc of the AB meridian is known, as well as its expression in degrees (as the difference in 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 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 study of the size of our planet and the shape of its surface is the science of geodesy, which translated from Greek means “earth measurement.” Its origins should be attributed to Eratosthesnus. But scientific geodesy itself began with triangulation, first proposed by Siellius.

The most ambitious degree measurement of the 19th century was headed by the founder of the Pulkovo Observatory, V. Ya. Struve. Under the leadership of Struve, Russian surveyors, together with Norwegian ones, measured an arc stretching 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 arc”. In the post-war years, the author of this book had the opportunity to work on observations (measurements of angles) at state triangulation points adjacent directly to the famous “arc”.

Degree measurements showed that our Earth is not exactly a sphere, but is similar to 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 the radius of the Earth can be calculated and its compression determined.

Domestic surveyors measured the state triangulation network over 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 ellipsoid: equatorial radius - 6378.245 km, polar radius - 6356.863 km. The compression of the planet is 1/298.3, that is, by this part the polar radius of the Earth is shorter than the equatorial radius (in linear measure - 21.382 km).

Let's imagine that on a globe with a diameter of 30 cm we 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 appears completely round from a great distance. This is how the astronauts observe it.

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 that 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 is absolutely 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, there is almost three times less land than water. What, then, should we mean by the underground surface?

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

What to do in continental areas? What is considered the surface of the Earth? Also the surface of the World Ocean, mentally continued under all the continents and islands.

This figure, limited by the surface of the average level of the World Ocean, was called the geoid. All known “heights above sea level” are measured from the surface of the geoid. The word "geoid", or "Earth-like", was specifically coined to name the shape of the Earth. In geometry, such a figure does not exist. A geometrically regular ellipsoid is close in shape to the geoid.

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.”

As you know, the classic method for studying the geometric characteristics of the Earth is triangulation. But previously, geodetic networks were developed only within continents, and they were not connected to each other. 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 was reduced.

With the launch of the satellites, surveyors immediately realized that “sighting targets” had appeared at high altitudes. Now it will be possible to measure large distances.

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 their geodetic coordinates to a single system. This is how triangulations built on different continents were linked together, and at the same time the dimensions of the Earth were clarified: equatorial radius - 6378.160 km, polar radius - 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 sphere, and the masses inside it were distributed evenly, then the satellite could move around the Earth in a circular orbit. But the deviation of the Earth’s shape from spherical and the heterogeneity of its interior lead to the fact that the force of attraction over different points of the earth’s surface is not the same. The force of gravity of the Earth changes - the orbit of the satellite changes. And everything, even the slightest change in the movement of a low-orbit satellite, is 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 approximately the same amount (as if pressed in). So it turns out that in a 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 polar asymmetry: This hemisphere is not identical to the Southern one. Thus, based on satellite data, the most accurate idea of ​​the true shape of the Earth was obtained. As we 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.

To understand the movements of the earth's crust and volcanism, the formation of minerals, rocks and processes occurring on the surface of the Earth (weathering, the influence of climatic factors, the cycle of substances in nature, soil formation, etc.), it is necessary to have an idea of ​​the size, structure and physical state of the Earth.

Earth, the third planet from the Sun in the solar system, rotating around it in an elliptical orbit (close to circular) with an average speed of 29.765 km/s, at an average distance of 149.6 million km over a period equal to 365.24 average solar days, has a satellite - the Moon, revolving around the Earth at an average distance of 384,000 km.

Measurements using various methods have shown that the Earth is not completely round - it is slightly flattened towards the poles. The shape of the Earth is a geoid, approximately a triaxial ellipsoid, a spheroid.

Equatorial radius of the Earth(distance from the center of the Earth to the equator) is 6378.160 km, and the polar radius (distance from the center of the Earth to the pole) is 6356.777 km. The average radius of the Earth is taken to be 6371.032 km. The difference between these radii is 21.383 km. The Earth's surface area is 510.2 million km2, volume - 1.083-1012 km2, density - 5518 kg/cm3, mass -5976-1021 kg.

The earth has magnetic and closely related electric fields. The Earth's gravitational field determines the spherical shape of the Earth and the existence of an atmosphere.

The composition of the Earth is dominated by iron (34.6%), oxygen (29.5%), silicon (15.2%), magnesium (12.7%). From the surface of the Earth towards the center, pressure, density and temperature increase; the pressure in the center of the Earth is 3.6-10 N/m2, density is about 12.5-103 kg/m3, temperature is 4000-5000 °C. The main types of the earth's crust are continental and oceanic; In the transition zone from the continent to the ocean, a crust of intermediate structure is developed.

Most of the Earth's surface is occupied by the World Ocean(361.1 million km2, or 70.8%). The average depth of the ocean is about 3800 m, the greatest is 11022 m (Mariana Trench in the Pacific Ocean), the volume of water is 1370 million km3, the average salinity is 35 g/l.

The land area is 149.1 million km2 (29.2%) and forms 6 continents and islands. It rises above the level of the World Ocean by an average of 875 m (the highest height is Mount Chomolungma (Everest) 8848 m); mountains occupy over 1/3 of the land surface. Deserts cover about 20% of the land surface, savannas and woodlands - about 20, forests - about 30, glaciers - over 10%. Over 10% of the land is occupied by agricultural land.

For a long time, processes of transformation and movement of matter took place on Earth, as a result of which it was divided into a number of shells, or geospheres, successively replacing one another. The following geospheres of the Earth are distinguished:: atmosphere, hydrosphere and lithosphere, behind which there is an intermediate shell and core. In addition to the listed spheres, the biosphere is also distinguished.

The Earth's geospheres differ greatly in chemical composition and physical properties (temperature, density, pressure).

Atmosphere surrounds the Earth with a thick gas shell up to 3 thousand km high, which, depending on the chemical composition and density of chemical elements, is divided into the troposphere, stratosphere, and ionosphere.

The troposphere is located above the Earth's surface at an altitude of 10-15 km. The composition of the air in the troposphere includes nitrogen (78%), oxygen (21%), carbon dioxide (0.03%), argon, neon, xenon, etc. The troposphere is characterized by the fact that the air pressure in it decreases with increasing altitude, and the temperature decreases and at a distance of 10-12 km from the Earth reaches 55 ° C. The air in the troposphere is very saturated; this is where the greatest movement of air masses occurs.

The stratosphere is located at an altitude of 50-100 km. It is characterized by thin air.

The ionosphere is located above the stratosphere. The air in it is very rarefied and under the influence of ultraviolet rays from the Sun, ions are formed that are scattered in space.

Hydrosphere- these are seas, oceans, lakes, rivers, groundwater, glaciers and snow covers. It occupies up to 71% of the Earth's surface. The hydrosphere contains over 40 chemical elements, including 85.45% oxygen, 10.63% hydrogen, 2.06% chlorine, 1.14% sodium and 0.72% other elements. The hydrosphere has the most active effect on the redistribution of chemical compounds in nature.

Biosphere- this is the space occupied by living organisms (in the air - up to a height of 10 km, in the oceans - up to a depth of 11 km) inhabiting the lithosphere, hydrosphere and atmosphere. According to V.I. Vernadsky, the biosphere is a zone of life.

Throughout all geological periods, the biosphere has developed and changed. The living substance of the biosphere contains up to 75% water, almost 25% dry matter and 2% ash (non-combustible or mineral) substances. Organic matter contains 50% carbon assimilated from air and water.

A new factor that has a powerful influence on the biosphere is the production activity of man, who appeared on Earth at least 3 million years ago.

The climatic conditions of different zones of the Earth have a significant impact on the biosphere.. The maximum temperature of the land surface in the tropical deserts of Africa and North Africa is 57-58 °C, and the minimum in the central regions of Antarctica is about 90 °C. The distribution of solar energy entering the Earth by latitude and altitude above sea level caused a natural change in climate, vegetation, soil, and fauna within the geographic envelope, resulting in the formation of physical-geographical zones, physical-geographical zones, and altitudinal zones.

The formation of the Earth and the initial stage of its development belong to pre-geological history. The absolute age of the most ancient rocks is over 3.5 billion years. The geological history of the Earth is divided into two unequal stages: the Precambrian, which occupies about 5/6 of the entire geological chronology (about 3 billion years), and the Phanerozoic, covering the last 570 million years.

Of the geospheres, the most interesting for soil science are the zone of sedimentary rocks, the biosphere, the weathering crust and a significant part of the atmosphere (troposphere) with an average thickness of 8-18 km depending on latitude.

The troposphere, biosphere and weathering crust have a direct and collateral influence on the cycle of substances in nature, on parent rocks, soils that cover a significant part of the Earth's continents, on the development of plants, animals and human activities.

Lithosphere- the outer sphere of the “solid” Earth, including the earth’s crust and part of the upper mantle, has a thickness according to Fersman of up to 1200 km. Its deepest part, the peredotite shell, consists primarily of olivine and hornblende minerals. Its specific gravity reaches 3.6-4, and its temperature is 1200-1500 °C. Of the chemical elements, oxygen, silicon, iron, magnesium, calcium, chromium, aluminum, and vanadium predominate in it.

The intermediate shell, or mantle, is located between the lithosphere and the core and extends to a depth of 2900 km. This shell is divided into two parts - the upper, which is dominated by oxygen, silicon and, obviously, magnesium, and the lower, which consists mainly of oxygen, silicon, iron, magnesium and nickel. The boundary between these two layers passes at a depth of 900 km.

The Earth's core is located from a depth of 2900 km from the Earth's surface to its center. Scientists have differing opinions regarding the composition of the nucleus. Some believe that the core consists mainly of iron and nickel, others believe that the composition of the core is slightly different from the composition of the lower mantle, but the substance there is in a highly compacted, so-called metallized state.

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I periodically have the feeling that many simple things are deliberately presented in such a way that the reader does not understand anything and stupidly memorizes it, or feels his insignificance in front of the sophistication of science. This entirely refers to the enchanting method known from school textbooks. Eratosthenes measurements circumference of the globe. Maybe he actually calculated in such a perverted way, but why replicate this nonsense from school?

Let's look at how you can confuse your brain with a simple question using the example of calculating the circumference of the Earth in nautical miles, which is a special case of measuring the latitude of an area and the length of the path traveled along the meridian.

If a modern person is given the task of calculating the circumference of the Earth in nautical miles, in the vast majority of cases he will look at the Internet/reference books and decide something like this: the circumference of the Earth, for example along the Parisian meridian, 40,000 km, using a calculator, divide by a modern nautical mile 1,852 km and get 21,598 .3 nautical miles, which will be close to reality.

Now I will show you how to calculate the circumference of the Earth in my mind and absolutely. To do this, you need to know only one thing: “The nautical mile is a unit of measurement of distance used in navigation and aviation. Initially, the nautical mile was defined as the length of the arc of a great circle on the surface of the globe measuring one minute of arc.” via

There are 60 minutes in one angular degree, 360 degrees in a circle, that is, in a circle 360x60 = 21,600 angular minutes, which in this case corresponds to the circumference of the globe in 21.600 nautical miles. And this is absolutely accurate, since the circumference of the globe along the meridian is the standard, and the arc minute-mile is a derived unit. Since the Earth is not a perfect spheroid, but slightly curved, the miles on different meridians will differ slightly from each other, but this is completely unimportant for navigation, because an arc minute is also an arc minute in Africa.

The latitude of the area can be measured accurately to the nearest degree even with primitive devices like a protractor with a plumb line, which is not very different from the quadrant actually used by sailors and is essentially the same as an astrolabe:

For more accurate measurements of angles, a sextant was subsequently invented (Marine argo - sextant):

Modern people have little idea what it is analog computers and how to use them. In order to calculate the distance between two points in the meridional direction, you just need to measure the latitudes of the points, and the difference in latitude expressed in arc minutes and will be the distance between them in nautical miles. Everything is simple, convenient and practically applicable.

If you really want to find out how many stages, fathoms, arshins, or Egyptian cubits there are in a nautical mile, you need to carefully use your knees to measure the distance between points with a known distance in nautical miles-arcminutes. But why? How is this practically applicable?

Eratosthenes allegedly measured angles with an accuracy of arc seconds and the difference in latitudes of Alexandria was 7° 6.7", that is, 7x60 = 420 + 6.7 = 426.7 nautical miles (arc minutes). It seems that what else is needed? But for some reason it takes days of camel travel and stages.There is a feeling of something far-fetched - a fake or a hoax.

Eratosthenes' method according to V. A. Bronstein, Claudius Ptolemy, Chapter 12. Ptolemy's works in the field of geography:

“As is known, Eratosthenes’ method was to determine the arc of the meridian between Alexandria and Syene on the day of the summer solstice. On this day, according to the stories of people who visited Syene, the Sun at noon illuminated the bottom of the deepest wells and, therefore, passed through the zenith. Consequently, the latitude Siene was equal to the angle of inclination of the ecliptic to the equator, which Eratosthenes determined at 23°51"20". Same day and time in Alexandria the shadow from the vertical column of the gnomon covered 1/50 of the circle, the center of which was the tip of the gnomon. This means that the Sun was 1/50th of a circle away from the zenith at noon, or 7° 12". Taking the distance between Alexandria and Siena to be 5000 stadia Eratosthenes found that the circumference of the globe was 250,000 stadia. The exact length of the stage adopted by Eratosthenes has long been a subject of debate, since there were stages ranging from 148 to 210 m in length<60>. Most researchers accepted the length of the stage 157.5 m(“Egyptian” stages). Then the circumference of the Earth is, according to Eratosthenes, 250,000-0.1575 = 39,375 km, which is very close to the actual value 40,008 km. If Eratosthenes used the Greek (“Olympic”) stage of length 185.2 m, then the circumference of the Earth was already 46,300 km.

According to modern measurements<97>latitude of the Museum in Alexandria 31°11.7" latitude of Aswan (Siena) 24° 5.0", latitude difference 7° 6.7", what is the distance between these cities 788 km. Dividing this distance by 5000, we obtain the length of the stage used by Eratosthenes, 157.6 m. Does this mean he used the Egyptian stadion?

This question is more complicated than it might seem. The mere fact that Eratosthenes gave a clearly rounded number - 5000 stadia (and not, say, 5150 or 4890) does not inspire confidence in him. And if Eratosthenes’ estimate was overestimated by at least 15%, we find that he used the Egyptian stade in 185 m. This issue cannot be resolved yet." via

Let us now pay attention to the following circumstances:

Aswan (Siena) and Alexandria are not located on the same meridian, the difference in longitude is 3 °, that is, about 300 kilometers.

Eratosthenes did not measure the distance, butacceptedbased on the days of travel of the camels, which clearly did not walk in a straight line.

Completely unclear what device Eratosthenes measured angles to the nearest second

Unclear what stage used by Eratosthenes to measure distances, etc.

But at the same time he seemed to get a fairly accurate result! Or have historians made adjustments to the result?

From Wikipedia: “Eratosthenes says that Syene and Alexandria lie on the same meridian. And since the meridians in space are large circles, the meridians on Earth will certainly be the same large circles. And since this is the solar circle between Siena and Alexandria, then the path between them on Earth necessarily goes in a large circle. Now he says that Siena lies on the circle of the summer tropic. And if the summer solstice in the constellation Cancer occurred exactly at noon, then the sundial at this moment in time would necessarily not cast a shadow, since the Sun would be exactly at its zenith; things are indeed this way in [a strip of width] 300 stadia. And in Alexandria at the same hour the sundial casts a shadow, since this city lies south of Siena. These cities lie on the same meridian and on a great circle. On the sundial in Alexandria we draw an arc passing through the end of the shadow of the gnomon and the base of the gnomon, and this segment of the arc will produce a large circle on the bowl, since the sundial bowl is located on the large circle. Next, imagine two straight lines descending underground from each gnomon and meeting in the center of the Earth. The sundial at Siena is perpendicular to the Sun, and an imaginary straight line runs from the Sun through the top of the sundial gnomon, producing one straight line from the Sun to the center of the Earth. Let us imagine another straight line drawn from the end of the shadow of the gnomon through the top of the gnomon to the Sun on the bowl in Alexandria; and it will be parallel to the already named straight line, since it has already been said that straight lines from different parts of the Sun to different parts of the Earth are parallel (and how does he know this?). A straight line drawn from the center of the Earth to the gnomon in Alexandria forms equal opposite angles with these parallel ones. One of them is with the vertex in the center of the Earth, when meeting the straight lines drawn from the sundial to the center of the Earth, and the other is with the vertex at the end of the gnomon in Alexandria, when meeting with the straight line going from this end to the end of its shadow from the Sun, where these lines meet at the top. The first angle rests on an arc from the end of the shadow of the gnomon to its base, and the second on an arc with its center at the center of the Earth, drawn from Siena to Alexandria. These arcs are similar to each other because they have equal angles. And what relation does the arc on the cup have to its circle, the same relation does the arc from Siena to Alexandria have [to its circle]. But it was found that on the cup it makes up a fiftieth of its circle. Therefore, the distance from Syene to Alexandria will necessarily be a fiftieth of the great circle of the Earth. But it is equal to 5,000 stadia. Therefore the whole circle will be equal to 250,000 stadia. This is the method of Eratosthenes."

The number obtained by Eratosthenes was later increased to 252,000 stades. It is difficult to determine how close these estimates are to reality, since it is not known exactly what stage Eratosthenes used. But if we assume that we are talking about Greek (178 meters), then its radius of the earth was 7,082 km, if Egyptian (157.5), then 6,287 km. Modern measurements give the average radius of the Earth a value of 6,371 km, which makes the above calculation an outstanding achievement and the first sufficiently accurate calculation of the size of our planet." via

I would like to draw your attention to the fact that in Wikipedia, in addition to adjusting the results, it also first talks about Eratosthenes’ measurement of the circumference of the Earth, and ultimately draws a conclusion about the accuracy of calculating the radius of the Earth. In general, there is an elderberry in the garden, and a man in Kyiv, although they are interconnected.

The diagnosis is very simple: in textbooks they will continue to replicate the method of Eratosthenes, which does not provide anything for understanding the essence and practical applicability, but they will not mention a word of the connection “nautical mile - arc minute” as an example of the proportional thinking of the ancients, because the modern trend is tailored to discrete computers, and about analog computers of antiquity I have to tell it again.