The Sun is the central object of our star system. Almost all of its mass is concentrated in it - 99%. The size of a celestial body can be determined using observation, geometric models and precise calculations. Scientists need to not only know the diameter of the Sun in kilometers, as well as its angular dimensions, but also monitor the activity of the star. Its influence on our planet is very great - flows of charged particles have a strong impact on the Earth's magnetosphere.
How to determine the diameter of the Sun in kilometers
Determining the diameter of the Sun has always occupied people interested in astronomy. Since ancient times, man has observed the sky and tried to form an idea of the objects visible on it. With their help, calendars were created and many were predicted. natural phenomena. Celestial bodies have been given mystical significance for thousands of years.
The Moon and the Sun became central objects of study. With the help of the Earth's satellite, it was possible to find out the exact dimensions of the star. The diameter of the Sun was determined using the Bailey's Rosary. This is the name of the optical effect that occurs in the phase of full solar eclipse. When the edges of the solar and lunar disks coincide, light breaks through the irregularities lunar surface, forming red dots. They helped astronomers determine the exact position of the edge of the solar disk.
The most detailed studies of this phenomenon were carried out in Japan in 2015. Data from several observatories were supplemented with information from the Kaguya lunar probe. As a result, it was calculated how much the diameter of the Sun is in kilometers - 1 million 392 thousand 20 km. Other parameters of the luminary are also important for astronomers.
Angular diameter of the Sun
The angular diameter of an object is the angle between lines extending from the observer to diametrically opposed points on its edges. In astronomy it is measured in minutes (′) and seconds (″). It does not mean a flat angle, but a solid angle (the union of all rays emanating from a point). The angular diameter of the star is 31′59″.
During the day, the Sun changes its size (2.5-3.5 times). However, such appearance is only psychological phenomenon. The illusion of perception is that the angle at which the Sun is visible does not change depending on its position in the sky.
However, the sky appears to a person not as a hemisphere, but as a dome, which is adjacent to the horizon at the edges. Therefore, the projection of the star onto its plane appears to be different in size.
There is another explanation. All objects become smaller as they approach the horizon. However, the Sun does not change its size. This makes it appear as if it is getting larger. An interesting psychological effect can be easily verified: it is worth measuring the diameter of the Sun using your little finger. Its dimensions at the zenith and at the horizon will be the same.
Solar Research
Before the invention of the telescope, astronomers had no idea about the structure of the celestial body. In Europe, sunspots were discovered only in the 17th century. They are photospheres that have escaped to the surface. magnetic fields. By interfering with the movement of matter at the ejection sites, they create a decrease in temperature on the surface of the Sun. At the same time, Galileo determined the period of revolution of the Sun around its axis. Its outer layer makes full turn in 25.38 days.
Structure of the Sun:
- hydrogen - 70%;
- helium - 28%;
- other elements - 2%.
In the core of the star occurs nuclear reaction converting hydrogen into helium. Here the temperature reaches 15 billion degrees. On the surface it is equal to 5780 degrees.
After the appearance spacecraft Many attempts have been made to study the celestial body. American satellites launched into space between 1962 and 1975 studied the Sun in the ultraviolet and X-ray wavelengths. The series was called the Orbital Solar Observatory.
In 1976, the West German satellite Helios-2 was launched, which approached the star at a distance of 43.4 million km. It was intended to study the solar wind. For the same purpose, in 1990 I went to space Ulysses solar probe.
NASA plans to launch the Solar Probe Plus satellite in 2018, which will approach the Sun by 6 million kilometers. This distance will be a record in recent decades.
Comparison with other celestial bodies
When determining the size of the Sun, comparison with other celestial objects helps. It's interesting to see the comparison in perspective. For example, the diameter of the Sun is 109 times the diameter of the Earth and 9.7 times the diameter of Jupiter. Gravity on the Sun exceeds Earth's gravity by 28 times. A person here would weigh 2 tons.
The mass of the star is 333 thousand Earth masses. The polar star is 30 times larger than the Sun. Among the celestial bodies, it is of medium size. The Sun is still far from the giants. The largest star, VY Canis Majoris, is 2100 solar diameters.
Impact on Earth
Life on Earth is possible only at a distance of 149.6 million km. from the sun. All living organisms receive the necessary heat from it, and photosynthesis is carried out by plants only with the participation of light. Thanks to this star, weather phenomena such as wind, rain, seasons, etc. are possible.
The answer to the question of what diameter of the Sun is needed for the normal development of life on a planet like Earth is simple - exactly the same as it is now. Our planet's magnetic field often reflects "attacks from the solar wind." Thanks to him, the northern and southern lights appear at the poles. During the period of occurrence solar flares it can appear even near the equator.
The impact of the star on the climate of our planet is also significant. The coldest winters occurred between 1683 and 1989. This was due to a decrease in the star's activity.
A look into the future
The diameter of the Sun is changing. In 5 billion years it will exhaust all its hydrogen fuel and become a red giant. Having increased in size, it will absorb Mercury and Venus. The Sun will then shrink to the size of the Earth, becoming a white dwarf star.
The size of the star that determines life on our planet is one of the most interesting data not only for scientists, but also for ordinary people. The development of astronomy makes it possible to determine the distant future celestial bodies and contributes to the accumulation of information for the weather service. It also becomes possible to explore new planets, and the level of protection of the Earth from collisions with small celestial bodies increases.
Work No. 7. Determination of the angular and linear dimensions of the Sun (or Moon)
I. Using a theodolite.1. Having installed the device and inserted a light filter into the eyepiece of the tube, align the alidade zero with the horizontal limb zero. Secure the alidade and, with the limb detached, point the tube at the Sun so that the vertical thread touches the right edge of the Sun's disk (this is achieved using a micrometer screw of the limb). Then, by quickly rotating the alidade micrometer screw, move vertical thread to the left edge of the Sun image. By taking readings from the horizontal limb, the angular diameter of the Sun is obtained.
2. Calculate the radius of the Sun using the formula:
R = D ∙ sinr
where r is the angular radius of the Sun, D is the distance to the Sun.
3. To calculate the linear dimensions of the Sun, you can use another formula. It is known that the radii of the Sun and the Earth are related to the distance to the Sun by the relation:
R = D ∙ sin r,
R 0 = D ∙ sin p,
where r is the angular radius of the Sun, and p is its parallax.
Dividing these equalities term by term, we get:
Due to the smallness of the angles, the ratio of sines can be replaced by the ratio of arguments.
Then
The values of parallax p and radius of the Earth are taken from the tables.
Calculation example.
| R0 = 6378 km, | 
|
| r = 16" | |
| p = 8",8 |
Attitude 
, i.e. The radius of the Sun is 109 times the radius of the Earth.
The dimensions of the Moon are determined similarly.
II. Based on the time of passage of the luminous disk through the vertical filament of the optical tube
If you look at the Sun (or Moon) through a stationary telescope, then due to the daily rotation of the Earth, the star will constantly move out of the telescope’s field of view. To determine the angular diameter of the Sun, using a stopwatch, measure the time it takes for its disk to pass through the vertical thread of the eyepiece and multiply the found time by cos d, where d is the declination of the luminary. Then the time is converted into angular units, remembering that in 1 minute the Earth rotates by 15", and in 1 second - by 15". Linear diameter D is determined from the relationship:
Where R is the distance to the luminary, a is its angular diameter, expressed in degrees.
If we use the angular diameter expressed in units of time (for example, seconds), then 
where t is the time it takes for the disk to pass through the vertical thread, expressed in seconds.
Calculation example:
Date of observation - October 28, 1959
The time it takes for the disk to pass through the eyepiece thread is t = 131 sec.
The declination of the Sun on October 28 d = - 13њ.
Angular diameter of the Sun a = 131∙ cos 13њ = 131∙0.9744 = 128 sec. or in angular units a = 32 = 0.533њ.
Methodological notes
1. Of the two methods, the second is more accessible. It is simpler in technique and does not require any preliminary training.
2. Carrying out such measurements, it is interesting to note the difference in the apparent diameter of the Sun when it is at perigee and apogee. This difference is about 1" or in time - 4 seconds.
The apparent diameter of the Moon varies within significantly larger limits (from 33",4 to 29",4). This is clearly seen from Fig. 55. There is already a time difference here - about 16 seconds.
Rice. 55. The largest and smallest visible dimensions of the Moon’s disk, located concentrically (left) eccentrically (right).
Such observations will convince students with their own eyes that the orbits of the Earth and the Moon are not circular, but elliptical (illustration of Kepler's laws).
3. Using the second method, you can determine the size of some lunar formations, the length of shadows from mountains, etc.
1 Declension is taken from the Astronomical calendar.
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Task 2. Determining the time of maximum and minimum solar activity
Analyze the data in Table 1P, compare Wolf’s numbers for 2000–2011 (it’s better to do this by building a relationship in EXCEL).
Task 3. Determining the size of sunspots
Determine the angular and linear size of the sunspot (see Fig. A3). Compare the size of this spot with the size of the Earth.
table 2
Task 4. Determination of the temperature of the photosphere in the spot area
Study the bright halos around sunspots in SOHO images of the solar surface. Infer the temperature of the sunspot, the temperature of the bright halo, and the average temperature of the photosphere.
Table 3
Make a conclusion about the differences in the images in the photographs and the temperature values.
Task 5. Study of prominences
Prominences(German) Protuberanzen, from lat. protubero- swell) - dense condensations of relatively cold (compared to the solar corona) matter that rise and are held above the surface of the Sun by a magnetic field.
The following classification of prominences has been adopted, taking into account the nature of the movement of matter in them and their shape, developed at the Crimean Astrophysical Observatory:
· Type I (rare) has the form of a cloud or a stream of smoke. Development begins from the foundation; the substance rises in a spiral to great heights. The speed of matter can reach 700 km/sec. At an altitude of about 100 thousand km, pieces separate from the prominence, then fall back along trajectories resembling magnetic field lines;
· Type II has the shape of curved jets that begin and end on the surface of the Sun. Nodes and jets move as if along magnetic lines of force. The speed of movement of the clumps is from several tens to 100 km/sec. At altitudes of several hundred thousand km, the jets and clumps fade away;
· Type III has the form of a bush or tree; reaches very large sizes. The movements of the clumps (up to tens of km/sec) are disordered.
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| Type I | Type II | III type |
| Rice. eleven |
Using the photographs in Figure 12, study the prominences. Draw a conclusion about their size, estimate the approximate temperature. Try to classify them as one of the three types known to you.
Task 6. Study of solar coronal ejections
Coronal mass ejections(Coronal mass ejections or CME) are gigantic volumes of solar matter ejected into interplanetary space from the solar atmosphere as a result of active processes occurring in it. Apparently, it is the matter of coronal ejections reaching the Earth that is the main cause of the appearance of auroras and magnetic storms.
Coronal holes– these are regions of the solar corona of reduced luminosity. They were discovered after the start of X-ray studies of the Sun using spacecraft from outside the Earth's atmosphere. It is currently believed that the solar wind originates in coronal holes. Coronal holes are sources of solar wind with low temperatures, so they appear dark in images of the Sun.
Task 7. Study of Kreutz comets
Circumsolar comets Kreutz(English) Kreutz Sungrazers) is a family of circumsolar comets named after the German astronomer Heinrich Kreutz (1854–1907), who first showed their relationship. It is believed that they are all parts of one large comet that collapsed several centuries ago.
Kreutz comets can be observed in both the Lasco C2 and LascoC3 systems. Regular observations make it possible to detect new comets and determine their approximate speed.
To determine the speed of comets, a sequence of images with exactly known observation times for each of them is required. Then the coordinates of the comet are determined from the image, and, based on the assumption of their uniform motion, their speed is calculated.
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).
Rice. 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.
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 are 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.
Comparing the circumference of the Earth's shadow on the Moon during a lunar eclipse, Aristarchus found the numbert= 8/3 - the ratio of the radius of the Earth's shadow to the radius of the Moon. In addition, he had already calculated κ = 400 (the ratio of the radius of the Sun to the radius of the Moon, which is almost equal to the ratio of the Sun-Earth distance to the Moon-Earth distance). After rather non-trivial geometric constructions, Aristarchus finds that the ratio of the diameters of the Sun and Earth is equal, and that of the Moon and 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 that it 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.
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. .. 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, in 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 system of the world (“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? The case of Alfonso X (1226-1284), king of Castile and Leon, a state that occupied part of modern Spain, is widely known. 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.
Therefore, it is quite difficult for an ordinary person to estimate the size and shape of the Sun. At the same time, astronomers have established that the Sun is a ball with an almost regular shape. Therefore, to estimate the size of the Sun, you can use standard indicators used to measure the size of a circle.
Thus, the diameter of the Sun is 1.392 million kilometers. For comparison, the diameter of the Earth is only 12,742 kilometers: thus, by this indicator, the size of the Sun is 109 times the size of our planet. Moreover, the circumference of the Sun at the equator reaches 4.37 million kilometers, while for the Earth this figure is only 40,000 kilometers; in this dimension, the size of the Sun turns out to be larger than the size of our planet, by the same amount.
At the same time, thanks to the enormous temperature on the surface of the Sun, which is almost 6 thousand degrees, its size is gradually decreasing. Scientists involved in solar activity research claim that the Sun shrinks in diameter by 1 meter every hour. Thus, they suggest, a hundred years ago the diameter of the Sun was approximately 870 kilometers larger than it is now.
Mass of the Sun
The mass of the Sun differs from the mass of planet Earth even more significantly. Thus, according to astronomers, at the moment the mass of the Sun is about 1.9891*10^30 kilograms. At the same time, the mass of the Earth is only 5.9726 * 10^24 kilograms. Thus, the Sun turns out to be almost 333 thousand times heavier than the Earth.At the same time, due to the high temperature on the surface of the Sun, most of its constituent substances are in a gaseous state, and therefore have a fairly low density. Thus, 73% of the composition of this star is hydrogen, and the remaining part is helium, which occupies about 1/4 of its composition, and other gases. Therefore, despite the fact that the volume of the Sun exceeds the corresponding figure for the Earth by more than 1.3 million times, the density of this star is still lower than that of our planet. Thus, the density of the Earth is about 5.5 g/cm³, while the density of the Sun is about 1.4 g/cm³: thus, these indicators differ by about 4 times.
Newton called mass a quantity of matter. Now it is defined as a measure of the inertia of bodies: the heavier the object, the more difficult it is to give it acceleration. To find inert mass body, compare the pressure it exerts on the surface of the support with the standard, and introduce a measurement scale. To calculate the mass of celestial bodies, the gravimetric method is used.
Instructions
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. At an age of 4.57 billion years, the Sun is capable of remaining as bright a star as long as a lifetime when compared with human life.
