Diameter of the sun and the earth. The sizes of the planets of the solar system in ascending order and interesting information about the planets. Sizes of planet Earth in comparison

Initially, there was an opinion that the Sun revolves around our planet, thereby illuminating each part of it in turn. But in the process of developing the science of astronomy, scientists nevertheless came to the truth that it is around the Sun that all objects in the solar system, including the Earth, rotate, and not vice versa.

Thanks to the radiation of this star, life is maintained, the process of photosynthesis occurs, during which oxygen is produced, which is so necessary for all living beings on the planet. But I wonder what is bigger: the Sun or the Earth?

Structure of the Sun

By studying the only star in the solar system, scientists came to a conclusion about its structure. The center is occupied by the nucleus. Its radius is approximately 150-175 thousand km. Helium is formed in the core as a result of continuously occurring nuclear reactions. Heat and energy are generated here; the rest of the star is heated due to the phenomenon of thermal exchange with the core. The energy, passing through all layers, is emitted from the photosphere in the form of bright sunlight.

It is by the upper layer of the Sun - the photosphere - that one can judge its size and distance to our planet.

The sun compared to the big stars

Structure of the Earth

The structure of the Earth is similar to that of the sun. The center of our planet is the core, the radius of which is approximately 3.5 thousand km. It is assumed that it consists of two parts, between which a so-called transition zone may periodically arise. In the central part there is a solid core with a radius of 1300 km, from the outside it is enveloped by a liquid outer core.

The mantle is the layer covering the Earth's core. And on top of the mantle there is a solid layer of the Earth - its surface, on which continents and oceans, mountains and depressions, land and water are located. Earth is one of the largest planets in the solar system. In 365 days, it manages to travel around the Sun and turn around its axis the same number of times. It is precisely due to which side our planet is turned to the sun and the angle of inclination of the earth's axis that climate changes and the daily alternation of days and nights are observed. The deviation of the axis from the vertical is 23.5 degrees.

That more

So what is larger: the Earth with an average radius of 6371 km or the Sun, whose core radius alone already exceeds the size of the Earth? Undoubtedly, the Sun is many times larger than our planet. But each of these components plays an important role for life, and for the existence of all humanity as a whole.

Comparison of the sizes of the Earth, the Sun and other celestial bodies

Today we will talk about the fact that the Earth is small and about the sizes of other huge celestial bodies in the Universe. What are the sizes of the Earth compared to other planets and stars of the Universe.

In fact, our planet is very, very small... compared to many other celestial bodies, and even compared to the same Sun, the Earth is a pea (a hundred times smaller in radius and 333 thousand times smaller in mass), and there are stars in times, hundreds, thousands (!!) times more than the Sun... In general, we, people, and each of us especially, are microscopic traces of existence in this Universe, atoms invisible to the eyes of creatures who could live on huge stars (theoretically, but , perhaps practically).

Thoughts from the film on the topic: it seems to us that the Earth is big, it is so - for us, since we ourselves are small and the mass of our body is insignificant in comparison with the scale of the Universe, some have never even been abroad and do not leave for most of their lives They know almost nothing beyond the confines of a house, a room, and even about the Universe. And the ants think that their anthill is huge, but we will step on the ant and not even notice it. If we had the power to reduce the Sun to the size of a white blood cell and reduce the Milky Way in proportion, then it would be equal to the scale of Russia. But there are thousands or even millions and billions of galaxies besides the Milky Way... This cannot possibly fit into people’s consciousness.

Every year, astronomers discover thousands (or more) of new stars, planets, and celestial bodies. Space is an unexplored area, and how many more galaxies, star, planetary systems will be discovered, and it is quite possible that there are many similar solar systems with theoretically existing life. We can judge the sizes of all celestial bodies only approximately, and the number of galaxies, systems, and celestial bodies in the Universe is unknown. However, based on known data, the Earth is not the smallest object, but it is far from the largest; there are stars and planets hundreds, thousands of times larger!!

The largest object, that is, a celestial body, is not defined in the Universe, since human capabilities are limited, with the help of satellites and telescopes we can see only a small part of the Universe, and we do not know what is there, in the unknown distance and beyond the horizons... perhaps even larger ones celestial bodies than those discovered by people.

So, within the Solar System, the largest object is the Sun! Its radius is 1,392,000 km, followed by Jupiter - 139,822 km, Saturn - 116,464 km, Uranus - 50,724 km, Neptune - 49,244 km, Earth - 12,742.0 km, Venus - 12,103.6 km, Mars - 6780.0 km, etc.

Several dozen large objects - planets, satellites, stars and several hundred small ones, these are only those that have been discovered, but there are some that have not been discovered.

The Sun is larger than the Earth in radius - more than 100 times, in mass - 333 thousand times. These are the scales.

Earth is the 6th largest object in the solar system, very close to the scale of Earth, Venus, and Mars is half the size.

The Earth is generally a pea compared to the Sun. And all the other planets, smaller ones, are practically dust for the Sun...

However, the Sun warms us regardless of its size and our planet. Did you know, did you imagine, walking with your feet on mortal soil, that our planet is almost a point in comparison with the Sun? And accordingly, we are microscopic microorganisms on it...

However, people have a lot of pressing problems, and sometimes there is no time to look beyond the ground under their feet.

Jupiter is more than 10 times larger than Earth, it is the fifth planet farthest from the Sun (classified as a gas giant along with Saturn, Uranus, Neptune).

After the gas giants, the Earth is the first largest object in the solar system after the Sun. then come the rest of the terrestrial planets, Mercury after the satellite of Saturn and Jupiter.

Terrestrial planets - Mercury, Earth, Venus, Mars - are planets located in the inner region of the Solar system.

Pluto is about one and a half times smaller than the Moon, today it is classified as a dwarf planet, it is the tenth celestial body in the solar system after 8 planets and Eris (a dwarf planet approximately similar in size to Pluto), consists of ice and rocks, with an area like South America , a small planet, however, it is larger in scale in comparison with the Earth and the Sun, the Earth is still two times smaller in proportions.

For example, Ganymede is a satellite of Jupiter, Titan is a satellite of Saturn - only 1.5 thousand km less than Mars and more than Pluto and large dwarf planets. There are many dwarf planets and satellites discovered recently, and even more so stars, more than several million, or even billions.

There are several dozen objects in the solar system that are slightly smaller than the Earth and half smaller than the Earth, and several hundred of those that are slightly smaller. Can you imagine how many things are flying around our planet? However, to say “flies around our planet” is incorrect, because as a rule, each planet has some relatively fixed place in the solar system.

And if some asteroid is flying towards the Earth, then it is even possible to calculate its approximate trajectory, flight speed, time of approach to the Earth, and with the help of certain technologies and devices (such as hitting the asteroid with the help of super-powerful atomic weapons in order to destroy part of the meteorite and how consequence of a change in speed and flight path) change the direction of flight if the planet is in danger.

However, this is a theory; such measures have not yet been applied in practice, but cases of unexpected falls of celestial bodies to Earth have been recorded - for example, in the case of the same Chelyabinsk meteorite.

In our minds, the Sun is a bright ball in the sky; in the abstract, it is some kind of substance that we know about from satellite images, observations and experiments of scientists. However, all we see with our own eyes is a bright ball in the sky that disappears at night. If you compare the sizes of the Sun and the earth, then it’s about the same as a toy car and a huge jeep; the jeep will crush the car without even noticing it. Likewise, the Sun, if it had at least a little more aggressive characteristics and an unrealistic ability to move, would have absorbed everything in its path, including the Earth. By the way, one of the theories of the death of the planet in the future says that the Sun will engulf the Earth.

We are accustomed, living in a limited world, to believe only what we see and take for granted only what is under our feet and perceive the Sun as a ball in the sky that lives for us, in order to illuminate the path for mere mortals, to warm us, to give we use the Sun to its fullest extent, and the idea that this bright star carries a potential danger seems ridiculous. And only a few people will seriously think that there are other galaxies in which there are celestial objects hundreds and sometimes thousands of times larger than those in the solar system.

People simply cannot comprehend in their minds what the speed of light is, how celestial bodies move in the Universe, these are not the formats of human consciousness...

We talked about the sizes of celestial bodies within the Solar System, about the sizes of large planets, we said that the Earth is the 6th largest object in the Solar System and that the Earth is a hundred times smaller than the Sun (in diameter), and 333 thousand times in mass , however, there are celestial bodies in the Universe MUCH larger than the Sun. And if the comparison of the Sun and the Earth did not fit into the consciousness of mere mortals, then the fact that there are stars in comparison with which the Sun is a ball - is even more impossible to fit into us.

However, according to scientific research, this is true. And this is a fact, based on the data obtained by astronomers. There are other star systems where planetary life exists similar to ours, the Solar one. By “life of the planets” we do not mean earthly life with people or other creatures, but the existence of planets in this system. So, on the question of life in Space - every year, every day, scientists come to the conclusion that life on other planets is more and more possible, but this remains only speculation. In the solar system, the only planet close in conditions to those on Earth is Mars, but the planets of other star systems have not been fully explored.

For example:

“It is believed that Earth-like planets are the most favorable for the emergence of life, so the search for them attracts close public attention. So in December 2005, scientists from the Space Science Institute (Pasadena, California) reported the discovery of a Sun-like star around which rocky planets are believed to be forming.

Subsequently, planets were discovered that were only several times more massive than the Earth and would probably have a solid surface.

An example of terrestrial exoplanets are super-Earths. As of June 2012, more than 50 super-Earths have been found."

These super-Earths are potential carriers of life in the Universe. Although this is a question, since the main criterion for the class of such planets is a mass more than 1 times the mass of the Earth, however, all discovered planets revolve around stars with less thermal radiation compared to the Sun, usually white, red and orange dwarfs.

The first super-Earth discovered in the habitable zone in 2007 was the planet Gliese 581 c near the star Gliese 581, the planet had a mass of about 5 Earth masses, “removed from its star by 0.073 AU.” e. and is located in the “life zone” of the star Gliese 581.” Later, a number of planets were discovered near this star and today they are called a planetary system; the star itself has a low luminosity, several tens of times less than the Sun. It was one of the most sensational discoveries in astronomy.

However, let's return to the topic of big stars.

Below are photos of the largest solar system objects and stars in comparison with the Sun, and then with the last star in the previous photo.

Mercury< Марс < Венера < Земля;

Earth< Нептун < Уран < Сатурн < Юпитер;

Jupiter< < Солнце < Сириус;

Sirius< Поллукс < Арктур < Альдебаран;

Aldebaran< Ригель < Антарес < Бетельгейзе;

Betelgeuse< Мю Цефея < < VY Большого Пса

And this list also includes the smallest stars and planets (the only truly large star on this list is perhaps the VY Canis Majoris).. The largest cannot even be compared with the Sun, since the Sun simply will not be visible.

The equatorial radius of the Sun was used as a unit of measurement for the radius of the star - 695,700 km.

For example, the star VV Cephei is 10 times larger than the Sun, and between the Sun and Jupiter the largest star is considered to be Wolf 359 (a single star in the constellation Leo, a faint red dwarf).

VV Cephei (not to be confused with the star of the same name with the “prefix” A) - “An eclipsing binary star of the Algol type in the constellation Cepheus, which is located at a distance of about 5000 light years from Earth. Component A is the seventh largest star known to science in radius as of 2015 and the second largest star in the Milky Way Galaxy (after VY Canis Majoris)."

“Capella (α Aur / α Auriga / Alpha Aurigae) is the brightest star in the constellation Auriga, the sixth brightest star in the sky and the third brightest in the sky of the Northern Hemisphere.”

The capella is 12.2 times the radius of the Sun.

The polar star is 30 times larger in radius than the Sun. A star in the constellation Ursa Minor, located near the North Pole of the world, a supergiant of spectral class F7I.

Star Y Canes Venatici is larger than the Sun by (!!!) 300 times! (that is, about 3000 times larger than the Earth), a red giant in the constellation Canes Venatici, one of the coolest and reddest stars. And this is far from the largest star.

For example, the star VV Cephei A is 1050-1900 times larger in radius than the Sun! And the star is very interesting for its inconstancy and “leakage”: “luminosity is 275,000-575,000 times greater. The star fills the Roche lobe, and its material flows to the neighboring companion. The speed of gas outflow reaches 200 km/s. It has been established that VV Cephei A is a physical variable pulsating with a period of 150 days.”

Of course, most of us will not understand information in scientific terms, if succinctly - a red-hot star losing matter. Its size, strength, and brightness of luminosity are simply impossible to imagine.

So, the 5 largest stars in the Universe (recognized as those currently known and discovered), in comparison with which our Sun is a pea and a speck of dust:

— VX Sagittarius is 1520 times the diameter of the Sun. A supergiant, hypergiant, variable star in the constellation Sagittarius loses its mass due to stellar wind.

— Star WOH G64 from the constellation Doradus, a red supergiant of spectral type M7.5, is located in the neighboring Large Magellanic Cloud galaxy. The distance to the solar system is approximately 163 thousand light years. years. 1540 times greater than the radius of the Sun.

— NML Cygnus (V1489 Cygnus) is 1183 - 2775 times larger in radius than the Sun, - “the star, a red hypergiant, is located in the constellation Cygnus.”

“UY Scuti is a star (hypergiant) in the constellation Scutum. Located at a distance of 9500 sv. years (2900 pc) from the Sun.

It is one of the largest and brightest stars known. According to scientists, the radius of UY Scuti is equal to 1708 solar radii, the diameter is 2.4 billion km (15.9 AU). At the peak of the pulsations, the radius can reach 2000 solar radii. The volume of the star is approximately 5 billion times the volume of the Sun."

From this list we see that there are about a hundred (90) stars much larger than the Sun (!!!). And there are stars on a scale on which the Sun is a speck, and the Earth is not even dust, but an atom.

The fact is that the places in this list are distributed according to the principle of accuracy in determining parameters, mass, there are approximately larger stars than UY Scuti, but their sizes and other parameters have not been established for certain, however, the parameters of this star may one day come into question. It is clear that stars 1000-2000 times larger than the Sun exist.

And, perhaps, there are or are forming planetary systems around some of them, and who will guarantee that there cannot be life there... or not now? Wasn't there or never will be? Nobody... We know too little about the Universe and Space.

Yes, and even of the stars presented in the pictures - the very last star - VY Canis Majoris has a radius equal to 1420 solar radii, but the star UY Scuti at the peak of pulsation is about 2000 solar radii, and there are stars supposedly larger than 2.5 thousand solar radii. Such a scale is impossible to imagine; these are truly extraterrestrial formats.

Of course, an interesting question is - look at the very first picture in the article and at the last photos, where there are many, many stars - how do so many celestial bodies coexist in the Universe quite calmly? There are no explosions, no collisions of these very supergiants, because the sky, from what is visible to us, is teeming with stars... In fact, this is just the conclusion of mere mortals who do not understand the scale of the Universe - we see a distorted picture, but in fact there is enough room for everyone there , and perhaps there are explosions and collisions, but this simply does not lead to the death of the Universe and even part of the galaxies, because the distance from star to star is enormous.

The sky above is the oldest geometry textbook. The first concepts, such as point and circle, come from there. More likely not even a textbook, but a problem book. In which there is no page with answers. Two circles of the same size - the Sun and the Moon - move across the sky, each at its own speed. The remaining objects - luminous points - move all together, as if they are attached to a sphere rotating at a speed of 1 revolution per 24 hours. True, there are exceptions among them - 5 points move as they please. A special word was chosen for them - “planet”, in Greek - “tramp”. As long as humanity has existed, it has been trying to unravel the laws of this perpetual motion. The first breakthrough occurred in the 3rd century BC, when Greek scientists, using the young science of geometry, were able to obtain the first results about the structure of the Universe. This is what we will talk about.

To have some idea of ​​the complexity of the problem, consider this example. Let's imagine a luminous ball with a diameter of 10 cm, hanging motionless in space. Let's call him S. A small ball revolves around it at a distance of just over 10 meters Z with a diameter of 1 millimeter, and around Z at a distance of 6 cm a very tiny ball turns L, its diameter is a quarter of a millimeter. On the surface of the middle ball Z microscopic creatures live. They have some intelligence, but they cannot leave the confines of their ball. All they can do is look at the other two balls - S And L. The question is, can they find out the diameters of these balls and measure the distances to them? No matter how much you think, the matter seems hopeless. We drew a greatly reduced model of the solar system ( S- Sun, Z- Earth, L- Moon).

This was the task that ancient astronomers faced. And they solved it! More than 22 centuries ago, without using anything other than the most elementary geometry - at the 8th grade level (properties of the line and circle, similar triangles and the Pythagorean theorem). And, of course, watching the Moon and the Sun.

Several scientists worked on the solution. We'll highlight two. These are the mathematician Eratosthenes, who measured the radius of the globe, and the astronomer Aristarchus, who calculated the sizes of the Moon, the Sun and the distance to them. How did they do it?

How the globe was measured

People have known for a long time that the Earth is not flat. Ancient navigators observed how the picture of the starry sky gradually changed: new constellations became visible, while others, on the contrary, went beyond the horizon. Ships sailing into the distance “go under water”; the tops of their masts are the last to disappear from view. It is unknown who first expressed the idea that the Earth is spherical. Most likely - the Pythagoreans, who considered the ball to be the most perfect of figures. A century and a half later, Aristotle provides several proofs that the Earth is a sphere. The main one is: during a lunar eclipse, the shadow of the Earth is clearly visible on the surface of the Moon, and this shadow is round! Since then, constant attempts have been made to measure the radius of the globe. Two simple methods are outlined in exercises 1 and 2. The measurements, however, turned out to be inaccurate. Aristotle, for example, was mistaken by more than one and a half times. It is believed that the first person to do this with high accuracy was the Greek mathematician Eratosthenes of Cyrene (276–194 BC). His name is now known to everyone thanks to sieve of Eratosthenes - a way to find prime numbers (Fig. 1).

If you cross out one from the natural series, then cross out all the even numbers except the first (the number 2 itself), then all the numbers that are multiples of three, except the first of them (the number 3), etc., then the result will be only prime numbers . Among his contemporaries, Eratosthenes was famous as a major encyclopedist who studied not only mathematics, but also geography, cartography and astronomy. For a long time he headed the Library of Alexandria, the center of world science at that time. While working on compiling the first atlas of the Earth (we were, of course, talking about the part of it known by that time), he decided to make an accurate measurement of the globe. The idea was this. In Alexandria, everyone knew that in the south, in the city of Siena (modern Aswan), one day a year, at noon, the Sun reaches its zenith. The shadow from the vertical pole disappears, and the bottom of the well is illuminated for a few minutes. This happens on the day of the summer solstice, June 22 - the day of the highest position of the Sun in the sky. Eratosthenes sends his assistants to Syene, and they establish that at exactly noon (according to the sundial) the Sun is exactly at its zenith. At the same time (as it is written in the original source: “at the same hour”), i.e. at noon according to the sundial, Eratosthenes measures the length of the shadow from a vertical pole in Alexandria. The result is a triangle ABC (AC- pole, AB- shadow, rice. 2).

So, a ray of sunshine in Siena ( N) is perpendicular to the surface of the Earth, which means it passes through its center - the point Z. A beam parallel to it in Alexandria ( A) makes an angle γ = ACB with vertical. Using the equality of crosswise angles for parallel angles, we conclude that AZN= γ. If we denote by l circumference, and through X the length of its arc AN, then we get the proportion . Angle γ in a triangle ABC Eratosthenes measured it and it turned out to be 7.2°. Magnitude X - nothing less than the length of the route from Alexandria to Siena, approximately 800 km. Eratosthenes carefully calculates it based on the average travel time of camel caravans that regularly traveled between the two cities, as well as using data bematists - people of a special profession who measured distances in steps. Now it remains to solve the proportion, obtaining the circumference (i.e. the length of the earth's meridian) l= 40000 km. Then the radius of the Earth R equals l/(2π), this is approximately 6400 km. The fact that the length of the earth's meridian is expressed in such a round number of 40,000 km is not surprising if we remember that the unit of length of 1 meter was introduced (in France at the end of the 18th century) as one forty millionth of the circumference of the Earth (by definition!). Eratosthenes, of course, used a different unit of measurement - stages(about 200 m). There were several stages: Egyptian, Greek, Babylonian, and which of them Eratosthenes used is unknown. Therefore, it is difficult to judge for sure the accuracy of its measurement. In addition, an inevitable error arose due to the geographical location of the two cities. Eratosthenes reasoned this way: if cities are on the same meridian (i.e. Alexandria is located exactly north of Syene), then noon occurs in them at the same time. Therefore, by taking measurements during the highest position of the Sun in each city, we should get the correct result. But in fact, Alexandria and Siena are far from being on the same meridian. Now it’s easy to verify this by looking at the map, but Eratosthenes did not have such an opportunity; he was just working on drawing up the first maps. Therefore, his method (absolutely correct!) led to an error in determining the radius of the Earth. However, many researchers are confident that the accuracy of Eratosthenes' measurements was high and that he was off by less than 2%. Humanity was able to improve this result only 2 thousand years later, in the middle of the 19th century. A group of scientists in France and the expedition of V. Ya. Struve in Russia worked on this. Even during the era of great geographical discoveries, in the 16th century, people were unable to achieve the result of Eratosthenes and used the incorrect value of the earth’s circumference of 37,000 km. Neither Columbus nor Magellan knew the true size of the Earth and what distances they would have to travel. They believed that the length of the equator was 3 thousand km less than it actually was. If they had known, maybe they wouldn’t have sailed.

What is the reason for such a high accuracy of Eratosthenes’ method (of course, if he used the right stage)? Before him, measurements were local, on distances visible to the human eye, i.e. no more than 100 km. These are, for example, the methods in exercises 1 and 2. In this case, errors are inevitable due to the terrain, atmospheric phenomena, etc. To achieve greater accuracy, you need to take measurements globally, at distances comparable to the radius of the Earth. The distance of 800 km between Alexandria and Siena turned out to be quite sufficient.

Exercises
1. How to calculate the radius of the Earth using the following data: from a mountain 500 m high, one can see surroundings at a distance of 80 km?
2. How to calculate the radius of the Earth from the following data: a ship 20 m high, sailing 16 km from the coast, completely disappears from view?
3. Two friends - one in Moscow, the other in Tula, each take a meter-long pole and place them vertically. At the moment during the day when the shadow from the pole reaches its shortest length, each of them measures the length of the shadow. It worked in Moscow A cm, and in Tula - b cm Express the radius of the Earth in terms of A And b. The cities are located on the same meridian at a distance of 185 km.

As can be seen from Exercise 3, Eratosthenes’ experiment can also be done in our latitudes, where the Sun is never at its zenith. True, for this you need two points on the same meridian. If we repeat the experiment of Eratosthenes for Alexandria and Syene, and at the same time make measurements in these cities at the same time (now there are technical possibilities for this), then we will get the correct answer, and it will not matter on which meridian Syene is located (why?).

How the Moon and the Sun were measured. Three steps of Aristarchus

The Greek island of Samos in the Aegean Sea is now a remote province. Forty kilometers long, eight kilometers wide. On this tiny island, three greatest geniuses were born at different times - the mathematician Pythagoras, the philosopher Epicurus and the astronomer Aristarchus. Little is known about the life of Aristarchus of Samos. Dates of life are approximate: born around 310 BC, died around 230 BC. We don’t know what he looked like; not a single image has survived (the modern monument to Aristarchus in the Greek city of Thessaloniki is just a sculptor’s fantasy). He spent many years in Alexandria, where he worked in the library and observatory. His main achievement, the book “On the Magnitudes and Distances of the Sun and the Moon,” is, according to the unanimous opinion of historians, a real scientific feat. In it, he calculates the radius of the Sun, the radius of the Moon and the distances from the Earth to the Moon and to the Sun. He did this alone, using very simple geometry and the well-known results of observations of the Sun and Moon. Aristarchus does not stop there; he makes several important conclusions about the structure of the Universe, which were far ahead of their time. It is no coincidence that he was later called “Copernicus of antiquity.”

Aristarchus' calculation can be roughly divided into three steps. Each step is reduced to a simple geometric problem. The first two steps are quite elementary, the third is a little more difficult. In geometric constructions we will denote by Z, S And L the centers of the Earth, Sun and Moon respectively, and through R, R s And R l- their radii. We will consider all celestial bodies as spheres, and their orbits as circles, as Aristarchus himself believed (although, as we now know, this is not entirely true). We start with the first step, and for this we will observe the Moon a little.

Step 1. How many times further is the Sun than the Moon?

As you know, the Moon shines by reflected sunlight. If you take a ball and shine a large spotlight on it from the side, then in any position exactly half of the surface of the ball will be illuminated. The boundary of an illuminated hemisphere is a circle lying in a plane perpendicular to the rays of light. Thus, the Sun always illuminates exactly half of the Moon's surface. The shape of the Moon we see depends on how this illuminated half is positioned. At new moon, when the Moon is not visible at all in the sky, the Sun illuminates its far side. Then the illuminated hemisphere gradually turns towards the Earth. We begin to see a thin crescent, then a month (“waxing Moon”), then a semicircle (this phase of the Moon is called “quadrature”). Then, day by day (or rather, night by night), the semicircle grows to the full Moon. Then the reverse process begins: the illuminated hemisphere turns away from us. The moon “grows old”, gradually turning into a month, with its left side turned towards us, like the letter “C”, and finally disappears on the night of the new moon. The period from one new moon to the next lasts approximately four weeks. During this time, the Moon makes a full revolution around the Earth. A quarter of the period passes from new moon to half moon, hence the name “quadrature”.

Aristarchus' remarkable guess was that with quadrature, the sun's rays illuminating half of the Moon are perpendicular to the straight line connecting the Moon with the Earth. Thus, in a triangle ZLS apex angle L- straight (Fig. 3). If we now measure the angle LZS, denote it by α, we get that = cos α. For simplicity, we assume that the observer is at the center of the Earth. This will not greatly affect the result, since the distances from the Earth to the Moon and to the Sun significantly exceed the radius of the Earth. So, having measured the angle α between the rays ZL And ZS During the quadrature, Aristarchus calculates the ratio of the distances to the Moon and the Sun. How to catch the Sun and Moon in the sky at the same time? This can be done early in the morning. Difficulty arises for another, unexpected reason. In the time of Aristarchus there were no cosines. The first concepts of trigonometry appear later, in the works of Apollonius and Archimedes. But Aristarchus knew what such triangles were, and that was enough. Drawing a small right triangle Z"L"S" with the same acute angle α = L"Z"S" and measuring its sides, we find that , and this ratio is approximately equal to 1/400.

Step 2. How many times is the Sun larger than the Moon?

In order to find the ratio of the radii of the Sun and the Moon, Aristarchus uses solar eclipses (Fig. 4). They occur when the Moon blocks the Sun. With partial, or, as astronomers say, private During an eclipse, the Moon only passes across the disk of the Sun, without covering it completely. Sometimes such an eclipse cannot even be seen with the naked eye; the Sun shines as on an ordinary day. Only through strong darkness, for example, smoked glass, can one see how part of the solar disk is covered with a black circle. Much less common is a total eclipse, when the Moon completely covers the solar disk for several minutes.

At this time it becomes dark, stars appear in the sky. Eclipses terrified ancient people and were considered harbingers of tragedies. A solar eclipse is observed differently in different parts of the Earth. During a total eclipse, a shadow from the Moon appears on the surface of the Earth - a circle whose diameter does not exceed 270 km. Only in those areas of the globe through which this shadow passes can a total eclipse be observed. Therefore, a total eclipse occurs extremely rarely in the same place - on average once every 200–300 years. Aristarchus was lucky - he was able to observe a total solar eclipse with his own eyes. In the cloudless sky, the Sun gradually began to dim and decrease in size, and twilight set in. For a few moments the Sun disappeared. Then the first ray of light appeared, the solar disk began to grow, and soon the Sun shone in full force. Why does an eclipse last such a short time? Aristarchus answers: the reason is that the Moon has the same apparent dimensions in the sky as the Sun. What does it mean? Let's draw a plane through the centers of the Earth, Sun and Moon. The resulting cross-section is shown in Figure 5 a. Angle between tangents drawn from a point Z to the circumference of the Moon is called angular size Moon, or her angular diameter. The angular size of the Sun is also determined. If the angular diameters of the Sun and Moon coincide, then they have the same apparent sizes in the sky, and during an eclipse, the Moon actually completely blocks the Sun (Fig. 5 b), but only for a moment, when the rays coincide ZL And ZS. The photograph of a total solar eclipse (see Fig. 4) clearly shows the equality of size.

Aristarchus' conclusion turned out to be amazingly accurate! In reality, the average angular diameters of the Sun and Moon differ by only 1.5%. We are forced to talk about average diameters because they change throughout the year, since the planets do not move in circles, but in ellipses.

Connecting the center of the earth Z with the centers of the Sun S and the moon L, as well as with touch points R And Q, we get two right triangles ZSP And ZLQ(see Fig. 5 a). They are similar because they have a pair of equal acute angles β/2. Hence, . Thus, ratio of the radii of the Sun and Moon equal to the ratio of the distances from their centers to the center of the Earth. So, R s/R l= κ = 400. Despite the fact that their apparent sizes are equal, the Sun turned out to be 400 times larger than the Moon!

The equality of the angular sizes of the Moon and the Sun is a happy coincidence. It does not follow from the laws of mechanics. Many planets in the Solar System have satellites: Mars has two, Jupiter has four (and several dozen more small ones), and all of them have different angular sizes that do not coincide with the solar one.

Now we come to the decisive and most difficult step.

Step 3. Calculate the sizes of the Sun and Moon and their distances

So, we know the ratio of the sizes of the Sun and the Moon and the ratio of their distances to the Earth. This information relative: it restores the picture of the surrounding world only to the point of similarity. You can remove the Moon and Sun from the Earth 10 times, increasing their sizes by the same amount, and the picture visible from the Earth will remain the same. To find the real sizes of celestial bodies, you need to correlate them with some known size. But of all the astronomical quantities, Aristarchus still only knows the radius of the globe R= 6400 km. Will this help? Does the radius of the Earth appear in any of the visible phenomena occurring in the sky? It is no coincidence that they say “heaven and earth”, meaning two incompatible things. And yet such a phenomenon exists. This is a lunar eclipse. With its help, using a rather ingenious geometric construction, Aristarchus calculates the ratio of the radius of the Sun to the radius of the Earth, and the circuit is closed: now we simultaneously find the radius of the Moon, the radius of the Sun, and at the same time the distances from the Moon and from the Sun to the Earth.

During a lunar eclipse, the Moon goes into the Earth's shadow. Hiding behind the Earth, the Moon is deprived of sunlight, and thus stops shining. It does not disappear from view completely, since a small part of sunlight is scattered by the earth's atmosphere and reaches the Moon, bypassing the Earth. The moon darkens, acquiring a reddish tint (red and orange rays pass through the atmosphere best). In this case, the shadow of the Earth is clearly visible on the lunar disk (Fig. 6). The round shape of the shadow once again confirms the sphericity of the Earth. Aristarchus was interested in the size of this shadow. In order to determine the radius of the circle of the earth's shadow (we will do this from the photograph in Figure 6), it is enough to solve a simple exercise.

Exercise 4. An arc of a circle is given on a plane. Using a compass and ruler, construct a segment equal to its radius.

Having completed the construction, we find that the radius of the earth's shadow is approximately times larger than the radius of the Moon. Let us now turn to Figure 7. The area of ​​the earth's shadow into which the Moon falls during an eclipse is shaded in gray. Let us assume that the centers of the circles S, Z And L lie on the same straight line. Let's draw the diameter of the Moon M 1 M 2, perpendicular to the line L.S. The extension of this diameter intersects the common tangents of the circles of the Sun and Earth at points D 1 and D 2. Then the segment D 1 D 2 is approximately equal to the diameter of the Earth's shadow. We have arrived at the next problem.

Task 1. Given three circles with centers S, Z And L, lying on the same straight line. Line segment D 1 D 2 passing through L, perpendicular to the line SL, and its ends lie on common external tangents to the first and second circles. It is known that the ratio of the segment D 1 D 2 to the diameter of the third circle is equal to t, and the ratio of the diameters of the first and third circles is equal to ZS/ZL= κ. Find the ratio of the diameters of the first and second circles.

If you solve this problem, you will find the ratio of the radii of the Sun and the Earth. This means that the radius of the Sun will be found, and with it the Moon. But it will not be possible to solve it. You can try - the problem is missing one datum. For example, the angle between common external tangents to the first two circles. But even if this angle were known, the solution would use trigonometry, which Aristarchus did not know (we formulate the corresponding problem in Exercise 6). He finds an easier way out. Let's draw the diameter A 1 A 2 first circles and diameter B 1 B 2 second, both are parallel to the segment D 1 D 2 . Let C 1 and WITH 2 - points of intersection of the segment D 1 D 2 with straight lines A 1 B 1 And A 2 IN 2 accordingly (Fig. 8). Then, as the diameter of the earth's shadow, we take the segment C 1 C 2 instead of a segment D 1 D 2. Stop, stop! What does it mean, “take one segment instead of another”? They are not equal! Line segment C 1 C 2 lies inside the segment D 1 D 2 means C 1 C 2 <D 1 D 2. Yes, the segments are different, but they almost equal. The fact is that the distance from the Earth to the Sun is many times greater than the diameter of the Sun (about 215 times). Therefore the distance ZS between the centers of the first and second circles significantly exceeds their diameters. This means that the angle between the common external tangents to these circles is close to zero (in reality it is approximately 0.5°), i.e. the tangents are “almost parallel”. If they were exactly parallel, then the points A 1 and B 1 would coincide with the points of contact, therefore, the point C 1 would match D 1 , a C 2 s D 2, which means C 1 C 2 =D 1 D 2. Thus, the segments C 1 C 2 and D 1 D 2 are almost equal. Aristarchus’ intuition did not fail here either: in fact, the difference between the lengths of the segments is less than a hundredth of a percent! This is nothing compared to possible measurement errors. Having now removed the extra lines, including circles and their common tangents, we arrive at the following problem.

Task 1". On the sides of the trapezoid A 1 A 2 WITH 2 WITH 1 points taken B 1 and IN 2 so that the segment IN 1 IN 2 is parallel to the bases. Let S, Z u L- midpoints of segments A 1 A 2 , B 1 B 2 and C 1 C 2 respectively. Based C 1 C 2 lies the segment M 1 M 2 with middle L. It is known that And . Find A 1 A 2 /B 1 B 2 .

Solution. Since , then , and therefore triangles A 2 SZ And M 1 LZ similar with coefficient SZ/LZ= κ. Hence, A 2 SZ= M 1 LZ, and therefore the point Z lies on the segment M 1 A 2 . Likewise, Z lies on the segment M 2 A 1 (Fig. 9). Because C 1 C 2 = t·M 1 M 2 And , That .

Hence,

On the other side,

Means, . From this equality we immediately obtain that .

So, the ratio of the diameters of the Sun and the Earth is equal, and the ratio of the Moon and the Earth is equal.

Substituting the known values ​​κ = 400 and t= 8/3, we find that the Moon is approximately 3.66 times smaller than the Earth, and the Sun is 109 times larger than the Earth. Since the radius of the Earth R we know, we find the radius of the Moon R l= R/3.66 and the radius of the Sun R s= 109R.

Now the distances from the Earth to the Moon and to the Sun are calculated in one step, this can be done using the angular diameter. The angular diameter β of the Sun and Moon is approximately half a degree (0.53° to be precise). How ancient astronomers measured it will be discussed later. Dropping the tangent ZQ on the circumference of the Moon, we get a right triangle ZLQ with an acute angle β/2 (Fig. 10).

From it we find , which is approximately equal to 215 R l, or 62 R. Likewise, the distance to the Sun is 215 R s = 23 455R.

All. The sizes of the Sun and Moon and the distances to them have been found.

Exercises
5. Prove that straight lines A 1 B 1 , A 2 B 2 and two common external tangents to the first and second circles (see Fig. 8) intersect at one point.
6. Solve Problem 1 if you additionally know the angle between the tangents between the first and second circles.
7. A solar eclipse may be observed in some parts of the globe and not in others. What about a lunar eclipse?
8. Prove that a solar eclipse can only be observed during a new moon, and a lunar eclipse can only be observed during a full moon.
9. What happens on the Moon when there is a lunar eclipse on Earth?

About the benefits of mistakes

In fact, everything was somewhat more complicated. Geometry was just being formed, and many things that were familiar to us since the eighth grade of school were not at all obvious at that time. It took Aristarchus to write a whole book to convey what we have outlined in three pages. And with experimental measurements, everything was also not easy. Firstly, Aristarchus made a mistake in measuring the diameter of the earth's shadow during a lunar eclipse, obtaining the ratio t= 2 instead of . In addition, he seemed to proceed from the wrong value of the angle β - the angular diameter of the Sun, considering it equal to 2°. But this version is controversial: Archimedes in his treatise “Psammit” writes that, on the contrary, Aristarchus used an almost correct value of 0.5°. However, the most terrible error occurred at the first step, when calculating the parameter κ - the ratio of the distances from the Earth to the Sun and to the Moon. Instead of κ = 400, Aristarchus got κ = 19. How could it be more than 20 times wrong? Let us turn again to step 1, Figure 3. In order to find the ratio κ = ZS/ZL, Aristarchus measured the angle α = SZL, and then κ = 1/cos α. For example, if the angle α were 60°, then we would get κ = 2, and the Sun would be twice as far from the Earth as the Moon. But the measurement result was unexpected: the angle α turned out to be almost straight. This meant that the leg ZS many times superior ZL. Aristarchus got α = 87°, and then cos α =1/19 (remember that all our calculations are approximate). The true value of the angle is , and cos α =1/400. So a measurement error of less than 3° led to an error of 20 times! Having completed the calculations, Aristarchus comes to the conclusion that the radius of the Sun is 6.5 radii of the Earth (instead of 109).

Errors were inevitable, given the imperfect measuring instruments of the time. The more important thing is that the method turned out to be correct. Soon (by historical standards, i.e. after about 100 years), the outstanding astronomer of antiquity Hipparchus (190 - ca. 120 BC) will eliminate all the inaccuracies and, following the method of Aristarchus, calculate the correct sizes of the Sun and Moon. Perhaps Aristarchus' mistake turned out to be useful in the end. Before him, the prevailing opinion was that the Sun and Moon either had the same dimensions (as it seems to an earthly observer), or differed only slightly. Even the 19-fold difference surprised contemporaries. Therefore, it is possible that if Aristarchus had found the correct ratio κ = 400, no one would have believed it, and perhaps the scientist himself would have abandoned his method, considering the result absurd. A well-known principle states that geometry is the art of reasoning well from poorly executed drawings. To paraphrase, we can say that science in general is the art of drawing correct conclusions from inaccurate, or even erroneous, observations. And Aristarchus made this conclusion. 17 centuries before Copernicus, he realized that at the center of the world is not the Earth, but the Sun. This is how the heliocentric model and the concept of the solar system first appeared.

What's in the center?

The prevailing idea in the Ancient World about the structure of the Universe, familiar to us from history lessons, was that in the center of the world there was a stationary Earth, with 7 planets revolving around it in circular orbits, including the Moon and the Sun (which was also considered a planet). Everything ends with a celestial sphere with stars attached to it. The sphere revolves around the Earth, making a full revolution in 24 hours. Over time, corrections were made to this model many times. Thus, they began to believe that the celestial sphere is motionless, and the Earth rotates around its axis. Then they began to correct the trajectories of the planets: the circles were replaced with cycloids, i.e., lines that describe the points of a circle as it moves along another circle (you can read about these wonderful lines in the books of G. N. Berman “Cycloid”, A. I. Markushevich “Remarkable curves”, as well as in “Quantum”: article by S. Verov “Secrets of the Cycloid” No. 8, 1975, and article by S. G. Gindikin “Stellar Age of the Cycloid”, No. 6, 1985). Cycloids were in better agreement with the results of observations, in particular, they explained the “retrograde” movements of the planets. This - geocentric system of the world, at the center of which is the Earth (“gaia”). In the 2nd century, it took its final form in the book “Almagest” by Claudius Ptolemy (87–165), an outstanding Greek astronomer, namesake of the Egyptian kings. Over time, some cycloids became more complex, and more and more intermediate circles were added. But in general, the Ptolemaic system dominated for about one and a half millennia, until the 16th century, before the discoveries of Copernicus and Kepler. At first, Aristarchus also adhered to the geocentric model. However, having calculated that the radius of the Sun is 6.5 times the radius of the Earth, he asked a simple question: why should such a large Sun revolve around such a small Earth? After all, if the radius of the Sun is 6.5 times greater, then its volume is almost 275 times greater! This means that the Sun must be in the center of the world. 6 planets revolve around it, including Earth. And the seventh planet, the Moon, revolves around the Earth. This is how it appeared heliocentric world system (“helios” - the Sun). Aristarchus himself noted that such a model better explains the apparent motion of planets in circular orbits and is in better agreement with observational results. But neither scientists nor official authorities accepted it. Aristarchus was accused of atheism and was persecuted. Of all the astronomers of antiquity, only Seleucus became a supporter of the new model. No one else accepted it, at least historians have no firm information on this matter. Even Archimedes and Hipparchus, who revered Aristarchus and developed many of his ideas, did not dare to place the Sun at the center of the world. Why?

Why didn't the world accept the heliocentric system?

How did it happen that for 17 centuries scientists did not accept the simple and logical system of the world proposed by Aristarchus? And this despite the fact that the officially recognized geocentric system of Ptolemy often failed, not consistent with the results of observations of the planets and stars. We had to add more and more new circles (the so-called nested loops) for the “correct” description of the motion of the planets. Ptolemy himself was not afraid of difficulties; he wrote: “Why be surprised at the complex movement of celestial bodies if their essence is unknown to us?” However, by the 13th century, 75 of these circles had accumulated! The model became so cumbersome that cautious objections began to be heard: is the world really that complicated? A widely known case is that of Alfonso X (1226–1284), king of Castile and Leon, a state that occupied part of modern Spain. He, the patron of sciences and arts, who gathered fifty of the best astronomers in the world at his court, said at one of the scientific conversations that “if, at the creation of the world, the Lord had honored me and asked my advice, many things would have been arranged more simply.” Such insolence was not forgiven even to kings: Alphonse was deposed and sent to a monastery. But doubts remained. Some of them could be resolved by placing the Sun at the center of the Universe and adopting the Aristarchus system. His works were well known. However, for many centuries, none of the scientists dared to take such a step. The reasons were not only fear of the authorities and the official church, which considered Ptolemy’s theory to be the only correct one. And not only in the inertia of human thinking: it is not so easy to admit that our Earth is not the center of the world, but just an ordinary planet. Still, for a real scientist, neither fear nor stereotypes are obstacles on the path to the truth. The heliocentric system was rejected for completely scientific, one might even say geometric, reasons. If we assume that the Earth rotates around the Sun, then its trajectory is a circle with a radius equal to the distance from the Earth to the Sun. As we know, this distance is equal to 23,455 Earth radii, i.e. more than 150 million kilometers. This means that the Earth moves 300 million kilometers within six months. Gigantic size! But the picture of the starry sky for an earthly observer remains the same. The Earth alternately approaches and moves away from the stars by 300 million kilometers, but neither the apparent distances between the stars (for example, the shape of the constellations) nor their brightness change. This means that the distances to the stars should be several thousand times greater, i.e. the celestial sphere should have completely unimaginable dimensions! This, by the way, was realized by Aristarchus himself, who wrote in his book: “The volume of the sphere of fixed stars is as many times greater than the volume of a sphere with the radius of the Earth-Sun, how many times the volume of the latter is greater than the volume of the globe,” i.e. according to Aristarchus it turned out that the distance to the stars was (23,455) 2 R, that's more than 3.5 trillion kilometers. In reality, the distance from the Sun to the nearest star is still about 11 times greater. (In the model we presented at the very beginning, when the distance from the Earth to the Sun is 10 m, the distance to the nearest star is ... 2700 kilometers!) Instead of a compact and cozy world, in which the Earth is at the center and which fits inside a relatively small celestial sphere, Aristarchus drew an abyss. And this abyss scared everyone.

Venus, Mercury and the impossibility of a geocentric system

Meanwhile, the impossibility of a geocentric system of the world, with the circular motions of all planets around the Earth, can be established using a simple geometric problem.

Task 2. A plane is given two circles with a common center ABOUT, two points move uniformly along them: a point M along one circle and a point V on the other. Prove that either they move in the same direction with the same angular velocity, or at some point in time the angle MOV blunt.

Solution. If the points move in the same direction at different speeds, then after some time the rays OM And O.V. will be co-directed. Next angle MOV begins to increase monotonically until the next coincidence, i.e., up to 360°. Therefore, at some moment it is equal to 180°. The case when the points move in different directions is considered in the same way.

Theorem. A situation in which all the planets of the Solar System rotate uniformly around the Earth in circular orbits is impossible.

Proof. Let ABOUT- the center of the Earth, M- the center of Mercury, and V- center of Venus. According to long-term observations, Mercury and Venus have different orbital periods, and the angle MOV never exceeds 76°. By virtue of the result of Problem 2, the theorem is proven.

Of course, the ancient Greeks repeatedly encountered similar paradoxes. That is why, in order to save the geocentric model of the world, they forced the planets to move not in circles, but in cycloids.

The proof of the theorem is not entirely fair, since Mercury and Venus do not rotate in the same plane, as in problem 2, but in different ones. Although the planes of their orbits almost coincide: the angle between them is only a few degrees. In Exercise 10, we invite you to eliminate this drawback and solve an analogue of Problem 2 for points rotating in different planes. Another objection: maybe the angle MOV can be stupid, but we don’t see it because it’s daytime on Earth at that time? We accept this too. In Exercise 11 you need to prove that for three rotating radii, there will always come a point in time when they form obtuse angles with each other. If at the ends of the radii there are Mercury, Venus and the Sun, then at this moment in time Mercury and Venus will be visible in the sky, but the Sun will not, i.e. it will be night on earth. But we must warn you: exercises 10 and 11 are much more difficult than problem 2. Finally, in exercise 12 we ask you, no less, to calculate the distance from Venus to the Sun and from Mercury to the Sun (they, of course, revolve around the Sun, not around Earth). See for yourself how simple it is after we have learned Aristarchus' method.

Exercises
10. Two circles with a common center are given in space ABOUT, two points move along them uniformly with different angular velocities: point M along one circle and a point V on the other. Prove that at some moment the angle MOV blunt.
11. Three circles with a common center are given on a plane ABOUT, three points move uniformly along them with different angular velocities. Prove that at some moment all three angles between the rays with the vertex ABOUT, directed to these points, are obtuse.
12. It is known that the maximum angular distance between Venus and the Sun, i.e. the maximum angle between the rays directed from the Earth to the centers of Venus and the Sun, is 48°. Find the radius of Venus's orbit. The same applies to Mercury, if it is known that the maximum angular distance between Mercury and the Sun is 28°.

The final touch: measuring the angular dimensions of the Sun and Moon

Following Aristarchus' reasoning step by step, we missed only one aspect: how was the angular diameter of the Sun measured? Aristarchus himself did not do this, using the measurements of other astronomers (apparently not entirely correct). Let us recall that he was able to calculate the radii of the Sun and Moon without using their angular diameters. Look again at steps 1, 2 and 3: nowhere is the angular diameter value used! It is only needed to calculate the distances to the Sun and the Moon. Trying to determine the angular size “by eye” does not bring success. If you ask several people to estimate the angular diameter of the Moon, most will name the angle from 3 to 5 degrees, which is many times larger than the true value. This is an optical illusion: the bright white Moon appears massive against the dark sky. The first to carry out a mathematically rigorous measurement of the angular diameter of the Sun and Moon was Archimedes (287-212 BC). He outlined his method in the book “Psammit” (“Calculation of grains of sand”). He was aware of the complexity of the task: “Obtaining the exact value of this angle is not an easy task, because neither the eye, nor the hands, nor the instruments with which the reading is made provide sufficient accuracy.” Therefore, Archimedes does not undertake to calculate the exact value of the angular diameter of the Sun, he only estimates it from above and below. He places a round cylinder at the end of a long ruler, opposite the observer's eye. The ruler is directed towards the Sun, and the cylinder is moved towards the eye until it completely obscures the Sun. Then the observer leaves, and a segment is marked at the end of the ruler MN, equal to the size of the human pupil (Fig. 11).

Then the angle α 1 between the lines MR And NQ less than the angular diameter of the Sun, and angle α 2 = P.O.Q.- more. We designated by PQ the diameter of the base of the cylinder, and through O - the middle of the segment MN. So α 1< β < α 2 (докажите это в упражнении 13). Так Архимед находит, что угловой диаметр Солнца заключен в пределах от 0,45° до 0,55°.

It remains unclear why Archimedes measured the Sun and not the Moon. He was well acquainted with the book of Aristarchus and knew that the angular diameters of the Sun and Moon are the same. It is much more convenient to measure the moon: it does not blind the eyes and its boundaries are more clearly visible.

Some ancient astronomers measured the angular diameter of the Sun based on the duration of a solar or lunar eclipse. (Try to restore this method in Exercise 14.) Or you can do the same without waiting for eclipses, but simply watching the sunset. Let's choose for this the day of the vernal equinox, March 22, when the Sun rises exactly in the east and sets exactly in the west. This means that the sunrise points E and sunset W diametrically opposed. For an observer on earth, the Sun moves in a circle with a diameter E.W.. The plane of this circle makes an angle of 90° with the horizon plane – γ, where γ is the geographic latitude of the point M, in which the observer is located (for example, for Moscow γ = 55.5°, for Alexandria γ = 31°). The proof is given in Figure 12. Direct ZP- the axis of rotation of the Earth, perpendicular to the plane of the equator. Point latitude M- angle between segment ZP and the plane of the equator. Let's pass through the center of the Sun S plane α perpendicular to the axis ZP.

The horizon plane touches the globe at a point M. For an observer located at a point M, The Sun moves in a circle during the day in the α plane with the center R and radius PS. The angle between the plane α and the horizontal plane is equal to the angle MZP, which is equal to 90° – γ, since the plane α is perpendicular ZP, and the horizon plane is perpendicular ZM. So, on the day of the equinox, the Sun sets below the horizon at an angle of 90° - γ. Consequently, during sunset it passes an arc of a circle equal to β/cos γ, where β is the angular diameter of the Sun (Fig. 13). On the other hand, in 24 hours it travels a full circle around this circle, i.e. 360°.

We get the proportion where it is six, not nine, since Uranus, Neptune and Pluto were discovered much later. Most recently, on September 13, 2006, by decision of the International Astronomical Union (IAU), Pluto lost its planetary status. So there are now eight planets in the solar system.
The real reason for the disgrace of King Alphonse was, apparently, the usual struggle for power, but his ironic remark about the structure of the world served as a good reason for his enemies.

We are accustomed to treating the Sun as a given. It appears every morning to shine throughout the day and then disappear over the horizon until the next morning. This continues from century to century. Some worship the Sun, others do not pay attention to it, since they spend most of their time indoors.

Regardless of how we feel about the Sun, it continues to perform its function - giving light and warmth. Everything has its own size and shape. Thus, the Sun has an almost ideal spherical shape. Its diameter is almost the same throughout its entire circumference. The differences can be on the order of 10 km, which is negligible.

Few people think about how far the star is from us and what size it is. And the numbers can surprise. Thus, the distance from the Earth to the Sun is 149.6 million kilometers. Moreover, each individual ray of sunlight reaches the surface of our planet in 8.31 minutes. It is unlikely that in the near future people will learn to fly at the speed of light. Then it would be possible to get to the surface of the star in more than eight minutes.

Dimensions of the Sun

Everything is relative. If we take our planet and compare it in size with the Sun, it will fit on its surface 109 times. The radius of the star is 695,990 km. Moreover, the mass of the Sun is 333,000 times greater than the mass of the Earth! Moreover, in one second it gives off energy equivalent to 4.26 million tons of mass loss, that is, 3.84x10 to the 26th power of J.

Which earthling can boast that he has walked along the equator of the entire planet? There will probably be travelers who crossed the Earth on ships and other vehicles. This took a lot of time. It would take them much longer to go around the Sun. This will take at least 109 times more effort and years.

The sun can visually change its size. Sometimes it seems several times larger than usual. Other times, on the contrary, it decreases. It all depends on the state of the Earth's atmosphere.

What is the Sun

The sun does not have the same dense mass as most planets. A star can be compared to a spark that constantly releases heat into the surrounding space. In addition, explosions and plasma separations periodically occur on the surface of the Sun, which greatly affects people’s well-being.

The temperature on the surface of the star is 5770 K, in the center - 15,600,000 K. With an age of 4.57 billion years, the Sun is capable of remaining the same bright star for an entire

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Comparative sizes of the Sun, Earth and other planets.

Earth is the third planet from the Sun (the proportions of the sizes of all planets and the Sun are observed). So you can complete the circumference of the Sun and you will understand how small the Earth is

The planet Mercury orbits closest to the Sun (at an average distance of 58 million km). It is significantly smaller than Earth. There is no atmosphere on Mercury, which means there can be no life; Mercury always has the same half facing the Sun. Mercury is very difficult to observe from Earth; most often it is lost in the rays of the Sun.
Further than Mercury (at an average distance of 108 million km from the Sun) the planet Venus is the brightest luminary in the sky after the Sun and Moon. Venus is almost equal in size and mass to Earth. Venus is surrounded by an airy atmosphere. Dense clouds hide its surface from us.
The third planet is our Earth. Behind it, at a distance of 228 million km from the Sun, is the planet Mars. This planet is significantly smaller than Earth, but larger than Mercury. Mars is surrounded by an atmosphere, but less dense than the Earth's atmosphere. The transparency of the atmosphere of Mars allowed astronomers to learn a lot about the structure of its surface and find out that Mars has a very harsh climate. Scientists are currently discussing whether certain plant species could exist on Mars. Is there life on Mars and Venus? This is one of the exciting questions of science. It will probably be found out by the field.
you are human on these planets. Probably, such flights will take place in our century.
The planet Jupiter orbits much further from the Sun (5 times further than the Earth). It is the largest of the planets in the solar system, 1312 times larger in volume than Earth. Somewhat smaller than Jupiter, the next planet behind it is Saturn (9 times farther from the Sun than the Earth). Next come two planets: Uranus (19 times farther from the Sun than Earth) and Neptune (30 times farther). Both are smaller than Saturn, but much larger than Earth. These four planets are called "giant planets." They are surrounded by vast atmospheres of poisonous gases. These planets are dominated by cold (temperature 150-220° below zero), and it is clear that there is no need to talk about the possibility of life on them.
And finally, very far away (40 times further than the Earth from the Sun) another planet revolves around the Sun - Pluto, about the nature of which very little is still known.
Whether there are planets even more distant than Pluto, or whether the solar system “ends” with Pluto, we do not yet know.
There are many more small planets in the solar system (most of them orbit the Sun between Mars and Jupiter). Many large planets are orbited by their satellites, similar to the Moon, a satellite of the Earth (for example, Jupiter has 12 known satellites). Comets travel between the planets, also subject to solar gravity.
The Sun is one of the stars closest to us. The closest star after the Sun is 40 trillion kilometers away from Earth. A light beam (travelling 300 thousand km per second) takes 4 1/3 years to travel from the star closest to the Earth, while it takes 8 minutes to arrive from the Sun, and 1.4 seconds from the Moon.
Stars are much more diverse than the planets of the solar system. There are stars many times larger and more massive than the Sun, and stars smaller than it. There are known stars that emit much more heat and light than the Sun, and the stars are relatively “cold”. There is no doubt that many stars have planets orbiting them, and that life exists on some of the planets. But even the most powerful modern telescopes cannot detect planets around nearby stars.
On a clear night, a wide band of the Milky Way is visible in the sky. This is a huge number of stars that are not individually visible to the naked eye due to their distance. The Milky Way and all the other stars visible in the sky form our Galaxy - a huge star system. There are over 150 billion stars in it, and the Sun is only one of them. The Sun (and with it the Earth and other planets) is not in the center of the Galaxy, but closer to its border. A ray of light travels through our entire star system in approximately 100 thousand years.
With powerful telescopes, very small hazy spots can be seen in the sky. These are star systems similar to our Galaxy, some much larger. They are so far from the Earth that the light from them takes millions, hundreds of millions and even billions of years to reach us.
Even in ancient times, people contemplated the starry sky. Even then it was not just admiring the majestic picture of the sky. Changes were noticed in the sky that are closely related to phenomena occurring on Earth.
The sun rises above the horizon every morning, rises above it, reaching its greatest height at noon, and then goes down. This repeats every day. The sun rose and the day began. The sun has set - the day has ended, the night has begun.
It has long been observed that most of the stars appear every evening in the eastern part of the sky, rise above the horizon, reaching their greatest height above it in the southern part of the sky, and then set in the western part of the horizon. The next evening, each star rises again at the same point in the sky as the day before.
However, long and systematic observations of the sky were needed (they were carried out already in ancient times) in order to notice that the Sun moves across the sky from day to day, from month to month, making a full circle in approximately 365 1/4 days, i.e. during the time when the seasons change on Earth. At the same time, the Sun moves across the sky along the same path every time, past the same stars. If at one time or another moment of a given year the Sun is near such and such stars, then it was so at the same time of year many years ago, and it will be so in many years.
The moon appears in the form of a narrow crescent, then “grows”, reaches the full moon and decreases again to a crescent, then becomes invisible at the new moon. And all this happens in 29 days.
“Wandering” luminaries—planets that move across the sky—have long been noticed. People had the opinion that the Earth is motionless, and the entire firmament with countless stars revolves around it every day. The Sun makes a complex movement around the Earth - daily, together with the vault of heaven, and annual, moving among the stars. The Moon revolves around the Earth in 29 days, and the planets at different times.
The erroneous idea that the Earth rests at the center of the Universe, and that the celestial bodies were created only to illuminate and warm the Earth, was supported by the reactionary teaching of the church.

Our Earth is great. Its nature is diverse, the riches of its depths are countless. And at the same time, the huge Earth is only one of the planets revolving around the Sun.
Compared to the Earth, the Sun is a giant hot ball. Its diameter is 109 times greater than the diameter of the Earth, and its volume is 1301 thousand times greater than the volume of the globe. The average distance from the Earth to the Sun is 149,500 thousand km (approximately). Therefore, the Sun appears in the sky as a small disk.
The sun emits a lot of light and heat into space. Only an insignificant part of this heat and light - less than one two-billionth part - is received by the Earth. But this is quite enough to illuminate and warm the Earth and everything living on it for billions of years.
All bodies in nature have the property of attracting each other. This property of bodies is called “gravity”. The greater the mass of the body (i.e., the more substance it contains), the greater the inherent force of attraction.
The mass of the Earth is very large - it is six sextillion tons.
The powerful force of gravity holds everything on Earth. In our time, gigantic advances in science and technology have made it possible for the first time to overcome gravity and launch artificial Earth satellites and spaceships into outer space.
The mass of the Sun is 333 thousand times greater than the mass of the Earth. The gravitational force of the Sun is so great that it subjugates all the planets and makes them move, or, as they say, revolve around the Sun. The planets are the “eternal satellites” of the Sun. Nine planets revolve around the Sun, and among them is the Earth.

And for starters, the ratio of the mass of the Sun to the masses of Black holes in the Galaxy

And an even larger object than the Black Hole, Quasar is a bright object at the center of the galaxy that produces about 10 trillion times more energy per second than our Sun, and whose radiation is highly variable across all wavelengths