Chapter Seventeen ASTRONOMY AND PHYSICS Objects of study and methods of obtaining scientific information The fruitful, mutually stimulating and harmonious interaction of such important sciences as mathematics, astronomy and physics is obvious. Subject of mathematical research

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Astronomy Leonardo Records of observations of the Moon date back to 1508. Leonardo explained why the waxing Moon is visible in its entirety in the evening, and yet most of it has a grayish tint. He also showed that at this time the Moon glows with reflected light from the Earth. About the last one

1. Vanga and entertaining mathematics In no case will I argue with a person who will prove that Vanga is a phenomenon. But what phenomenon? Human, paranormal, psychological, supersensual? Or is it a social phenomenon? What is one prophet worth without

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Yakov Isidorovich Perelman
FUN ASTRONOMY

EDITOR'S FOREWORD

After the release in 1966 of the next edition of the book by Ya.I. Perelman's “Entertaining Astronomy” more than forty years have passed. During this time, a lot has changed. People's knowledge of outer space has expanded to the same extent that objects in near and far space have become accessible to science. New opportunities in observational astronomy, the development of astrophysics and cosmology, successes in manned space exploration, information from more and more advanced automatic interplanetary stations, launching powerful telescopes into low-Earth orbit, “probing” the universal spaces with radio waves - all this constantly enriches astronomical knowledge. Of course, new astronomical information was also included in the upcoming edition of the book by Ya.I. Perelman.

In particular, the book was supplemented with new results from studies of the Moon and updated data on the planet Mercury. The dates of the nearest solar and lunar eclipses, as well as oppositions of Mars, are brought into line with modern knowledge.

The new information obtained with the help of telescopes and automatic interplanetary stations about the giant planets Jupiter, Saturn, Uranus and Neptune is very impressive - in particular, about the number of their satellites and the presence of planetary rings not only on Saturn. This information was also included in the text of the new edition, where the structure of the book allows it. New data about the planets of the Solar System are included in the table “Planetary System in Numbers”.

The new edition also takes into account changes in geographical and political-administrative names that appeared as a result of changes in power and economic system in the country. The changes also affected the sphere of science and education: for example, astronomy is gradually being removed from the list of subjects studied in secondary schools and is being removed from compulsory school curricula. And the fact that the ACT publishing group continues to publish popular books on astronomy, including a new edition of the book by the great popularizer of science Ya.I. Perelman, gives hope that young people of new generations will still know something about their native planet Earth, the Solar system, our Galaxy and other objects of the Universe.

N.Ya. Dorozhkin

EDITOR'S FOREWORD TO THE 1966 EDITION

Preparing for publication the 10th edition of “Entertaining Astronomy” by Ya.I. Perelman, the editor and the publishing house believed that this was the last edition of this book. The rapid development of celestial science and successes in the exploration of outer space have awakened interest in astronomy among numerous new readers, who have the right to expect to receive a new book of this kind, reflecting the events, ideas and dreams of our time. However, numerous persistent requests for the republication of “Entertaining Astronomy” showed that the book by Ya.I. Perelman - an outstanding master of popularizing science in an easy, accessible, entertaining, but at the same time quite strict form - has become, in a certain sense, classic. And classics, as you know, are republished countless times, introducing new and new generations of readers to them.

In preparing the new edition, we did not strive to bring its content closer to our “space age”. We hope that new books dedicated to the new stage in the development of science will appear, which a grateful reader will expect. We have made only the most necessary changes to the text. Basically, this is updated information about celestial bodies, indications of new discoveries and achievements, and links to books published in recent years. As a book that can significantly expand the horizons of readers interested in celestial science, we can recommend “Essays on the Universe” by B.A. Vorontsov-Velyaminov, which, perhaps, also became classic and have already gone through five editions. The reader will find a lot of new and interesting things in the popular science magazine of the USSR Academy of Sciences, “Earth and the Universe,” dedicated to the problems of astronomy, geophysics and space exploration. This magazine began publication in 1965 by the Nauka publishing house.

P. Kulikovsky

FOREWORD BY THE AUTHOR

Astronomy is a happy science: it, in the words of the French scientist Arago, does not need decoration. Her achievements are so exciting that she doesn’t have to put much effort into attracting attention to them. However, the science of the sky consists not only of amazing revelations and bold theories. It is based on everyday facts that are repeated day after day. People who are not sky lovers are in most cases rather vaguely familiar with this prosaic side of astronomy and show little interest in it, since it is difficult to concentrate on what is always before their eyes.

The everyday part of the science of the sky, its first, and not the last pages, constitutes mainly (but not exclusively) the content of “Entertaining Astronomy”. It seeks first of all to help the reader understand basic astronomical facts. This does not mean that the book is some kind of elementary textbook. The way the material is processed significantly distinguishes it from a textbook. Semi-familiar everyday facts are presented here in an unusual, often paradoxical form, shown from a new, unexpected side in order to sharpen attention to them and refresh interest. The presentation is whenever possible freed from special terms and from that technical apparatus, which often becomes a barrier between an astronomical book and the reader.

Popular books are often reproached with the fact that one cannot seriously learn anything from them. The reproach is to a certain extent fair and is supported (if we have in mind works in the field of exact natural science) by the custom of avoiding any numerical calculations in popular books. Meanwhile, the reader only really masters the material of the book when he learns, at least to an elementary extent, to operate with it numerically. Therefore, in “Entertaining Astronomy,” as in his other books of the same series, the compiler does not avoid the simplest calculations and only cares that they are presented in a dissected form and are quite feasible for those familiar with school mathematics. Such exercises not only reinforce the acquired information more firmly, but also prepare for reading more serious essays.

The proposed collection includes chapters related to the Earth, the Moon, planets, stars and gravity, and the compiler chose mainly such material that is usually not considered in popular works. The author hopes to cover topics not presented in this collection over time in the second book of Entertaining Astronomy. However, a work of this type does not at all set itself the task of uniformly exhausting all the rich content of modern astronomy.

Chapter first
THE EARTH, ITS FORM AND MOVEMENT

The shortest path on Earth and on the map

Having marked two points on the blackboard with chalk, the teacher offers the young schoolboy a task: to draw the shortest path between both points.

The student, after thinking, carefully draws a winding line between them.

- That's the shortest way! – the teacher is surprised. -Who taught you that?

- My dad. He is a taxi driver.

The drawing of a naive schoolboy is, of course, anecdotal, but wouldn’t you smile if you were told that the dotted arc in Fig. 1 - the shortest route from the Cape of Good Hope to the southern tip of Australia!

Even more striking is the following statement: shown in Fig. 2 the roundabout route from Japan to the Panama Canal is shorter than the straight line drawn between them on the same map!

Rice. 1. On a sea map, the shortest route from the Cape of Good Hope to the southern tip of Australia is indicated not by a straight line (“loxodrome”), but by a curve (“orthodrome”)

All this looks like a joke, and yet in front of you are indisputable truths, well known to cartographers.

Rice. 2. It seems incredible that the curved path connecting Yokohama to the Panama Canal on a sea map is shorter than a straight line drawn between the same points

To clarify the issue, we will have to say a few words about maps in general and sea maps in particular. Depicting parts of the earth's surface on paper is not an easy task, even in principle, because the earth is a ball, and it is known that no part of a spherical surface can be unfolded on a plane without folds and tears. One inevitably has to put up with inevitable distortions on maps. Many ways of drawing maps have been invented, but all maps are not free from shortcomings: some have distortions of one kind, others of another kind, but there are no maps without distortions at all.

Sailors use maps drawn according to the method of an ancient Dutch cartographer and mathematician of the 16th century. Mercator. This method is called “Mercatorian projection”. It is easy to recognize a sea map by its rectangular grid: the meridians are depicted on it as a series of parallel straight lines; circles of latitude are also straight lines, perpendicular to the first ones (see Fig. 5).

Imagine now that you need to find the shortest path from one ocean port to another, lying on the same parallel. On the ocean, all paths are accessible, and traveling there along the shortest path is always possible if you know how it runs. In our case, it is natural to think that the shortest path goes along the parallel on which both ports lie: after all, on the map it is a straight line, and what could be shorter than a straight path! But we are mistaken: the parallel path is not the shortest at all.

Indeed: on the surface of a ball, the shortest distance between two points is the great circle arc connecting them. 1
Big circle on the surface of a ball any circle whose center coincides with the center of this ball is called. All other circles on the ball are called small.

But the circle of parallels - small circle. The arc of a large circle is less curved than the arc of any small circle drawn through the same two points: a larger radius corresponds to a smaller curvature. Stretch a thread on the globe between our two points (cf. Fig. 3); you will be convinced that it will not lie along the parallel at all. A stretched thread is an indisputable indicator of the shortest path, and if it does not coincide with a parallel on the globe, then on a sea map the shortest path is not indicated by a straight line: remember that circles of parallels are depicted on such a map as straight lines, but any line that does not coincide with a straight line , There is curve .

Rice. 3. A simple way to find the truly shortest path between two points: you need to pull a thread on a globe between these points

After what has been said, it becomes clear why the shortest path on a sea map is depicted not as a straight line, but as a curved line.

They say that when choosing the direction for the Nikolaevskaya (now Oktyabrskaya) railway, there were endless debates about which route to lay it on. The controversy was put to an end by the intervention of Tsar Nicholas I, who solved the problem literally “straightforward”: he connected St. Petersburg with Moscow along a line. If this had been done on a Mercator map, the result would have been an embarrassing surprise: instead of a straight road, the road would have turned out crooked.

Anyone who does not avoid calculations can make sure with a simple calculation that the path that seems crooked to us on the map is actually shorter than the one that we are ready to consider straight. Let our two harbors lie on the 60th parallel and are separated by a distance of 60°. (Whether such two harbors actually exist is, of course, immaterial to the calculation.)

Rice. 4. To calculate the distances between points A and B on a ball along a parallel arc and along a great circle arc

In Fig. 4 point ABOUT - center of the globe, AB – arc of the circle of latitude on which the harbors lie A and B; V it's 60°. The center of the circle of latitude is at the point WITH Let's imagine that from the center ABOUT the globe is drawn through the same harbors by an arc of a great circle: its radius OB = OA = R; it will pass close to the drawn arc AB, but will not coincide with it.

Let's calculate the length of each arc. Since the points A And IN lie at latitude 60°, then the radii OA And OB amount to OS(the axis of the globe) an angle of 30°. In a right triangle ASO leg AC (=r), lying opposite an angle of 30°, equal to half the hypotenuse JSC;

Means, r=R/2 Arc length AB is one-sixth the length of the circle of latitude, and since this circle has half the length of the large circle (corresponding to half the radius), then the arc length of the small circle

To now determine the length of the arc of a great circle drawn between the same points (i.e., the shortest path between them), we need to find out the magnitude of the angle AOB. Chord AS, subtending an arc of 60° (of a small circle), is the side of a regular hexagon inscribed in the same small circle; That's why AB = r=R/2

Having drawn a straight line O.D. connecting the center ABOUT globe with middle D chords AB, we get a right triangle ODA, where is the angle D – straight:

DA=½AB and OA = R.

sinAOD=AD: AO=R/4:R=0.25

From here we find (from the tables):

ﮮAOD=14°28′.5

and therefore

ﮮAOB= 28°57′.

Now it is not difficult to find the required length of the shortest path in kilometers. The calculation can be simplified if we remember that the length of a minute of the great circle of the globe is a nautical mile, i.e. about 1.85 km. Therefore, 28°57′ = 1737" ≈ 3213 km.

We learn that the path along the circle of latitude, depicted on the sea map as a straight line, is 3333 km, and the path along the great circle - along the curve on the map - is 3213 km, i.e. 120 km shorter.

Armed with a thread and having a globe at hand, you can easily check the correctness of our drawings and make sure that the arcs of great circles really lie as shown in the drawings. Shown in Fig. 1 allegedly the “straight” sea route from Africa to Australia is 6020 miles, and the “curve” one is 5450 miles, i.e. shorter by 570 miles, or 1050 km. The “direct” air route from London to Shanghai on the sea map cuts the Caspian Sea, while in fact the shortest route runs north of St. Petersburg. It is clear what role these issues play in saving time and fuel.

If in the era of sailing navigation time was not always valued - then “time” was not yet considered “money” - then with the advent of steam ships one has to pay for every ton of coal that is excessively consumed. That is why nowadays ships are guided along the truly shortest route, often using maps made not in the Mercator projection, but in the so-called “central” projection: on these maps, the arcs of great circles are depicted as straight lines.

Why did earlier navigators use such deceptive maps and choose unfavorable routes? It is a mistake to think that in the old days they did not know about the now indicated feature of sea charts. The matter is explained, of course, not by this, but by the fact that maps drawn according to Mercator’s method have, along with inconveniences, benefits that are very valuable for sailors. Such a map, firstly, depicts individual small parts of the earth's surface without distortion, maintaining the angles of the contour. This is not contradicted by the fact that with distance from the equator, all contours noticeably stretch. In high latitudes, the stretching is so significant that a nautical map gives a person unfamiliar with its features a completely false idea of ​​the true size of the continents: Greenland seems the same size as Africa, Alaska is larger than Australia, although Greenland is 15 times smaller than Africa, and Alaska together with Greenland half the size of Australia. But a sailor who is well acquainted with these features of the map cannot be misled by them. He puts up with them, especially since within small areas the sea chart gives an exact resemblance to nature (Fig. 5).

But a nautical chart greatly facilitates solving navigational practice problems. This is the only type of map on which the path of a ship moving on a constant course is depicted as a straight line. To walk on a “constant course” means to consistently adhere to one direction, one specific “point of reference,” in other words, to walk in such a way as to intersect all meridians at an equal angle. But this path (“loxodrome”) can be depicted as a straight line only on a map on which all meridians are straight lines parallel to each other. 2
In reality, a rhoxodrome is a spiral line that winds around the globe in a helical manner.

And since on the globe the circles of latitude intersect with the meridians at right angles, then on such a map the circles of latitude should be straight lines perpendicular to the lines of the meridians. In short, we arrive at precisely the coordinate grid that constitutes a characteristic feature of a sea map.

Rice. 5. Nautical or Mercator map of the globe. Such maps greatly exaggerate the size of contours distant from the equator. What, for example, is bigger: Greenland or Australia? (Answer in text)

The predilection of sailors for Mercator's maps is now understandable. Wanting to determine the course to follow when going to the designated port, the navigator applies a ruler to the end points of the path and measures the angle it makes with the meridians. Keeping in the open sea all the time in this direction, the navigator will accurately bring the ship to the target. You see that the “loxodrome” is, although not the shortest and not the most economical, but in a certain respect a very convenient route for a sailor. To get, for example, from the Cape of Good Hope to the southern tip of Australia (see Fig. 1), you must always stay on the same course S 87°.50′. Meanwhile, in order to bring the ship to the same final point by the shortest route (according to the “orthodrome”), it is necessary, as can be seen from the figure, to continuously change the ship’s course: start with the course S 42°,50′, and end with the course N 53°,50 ′ (in this case the shortest path is not even feasible - it runs into the ice wall of the Antarctic).

Both paths - along the “loxodrome” and along the “orthodrome” - coincide only when the path along a great circle is depicted on a sea chart as a straight line: when moving along the equator or along the meridian. In all other cases, these paths are different.

Degree of longitude and degree of latitude

Readers, no doubt, have a sufficient understanding of geographical longitude and latitude. But I'm sure not everyone will give the correct answer to the following question:

Are degrees of latitude always longer than degrees of longitude?

Most people believe that each parallel circle is smaller than the meridian circle. And since degrees of longitude are measured along parallel circles, while degrees of latitude are measured along meridians, they conclude that the former can nowhere exceed the length of the latter. At the same time, they forget that the Earth is not a regular sphere, but an ellipsoid, slightly inflated at the equator. On the earth's ellipsoid, not only is the equator longer than the meridian circle, but also the parallel circles closest to the equator are also longer than the meridian circles. The calculation shows that up to approximately 5° latitude, the degrees of parallel circles (i.e. longitude) are longer than the degrees of the meridian (i.e. latitude).

Where did Amundsen fly?

Which direction of the horizon did Amundsen go to when returning from the North Pole, and which direction did he go when returning from the South Pole?

Give the answer without looking at the diaries of the great traveler.

The North Pole is the northernmost point on the globe.

Wherever we went from there, we would always go south.

Returning from the North Pole, Amundsen could only head south; there was no other direction from there. Here is an extract from the diary of his flight to the North Pole on the airship "Norway":

“Norway described a circle near the North Pole. Then we continued on our way... The course was taken south for the first time since the airship left Rome.” In the same way, from the south pole Amundsen could only go to north .

Kozma Prutkov has a comic story about a Turk who ended up in the “easternmost” country. “And in front is the east, and on the sides is the east. And the west? Do you think, perhaps, that he is still visible, like some dot, barely moving in the distance?.. Not true! And behind is the east. In short: endless east everywhere.”

Such a country, surrounded on all sides by the east, cannot exist on the globe. But there is a place on Earth surrounded everywhere by the south, as well as a point covered on all sides by the “endless” north. At the North Pole it would be possible to build a house with all four walls facing south. And our glorious Soviet polar explorers who visited the North Pole could actually do this.

Five kinds of time counting

We are so accustomed to using pocket and wall clocks that we are not even aware of the meaning of their readings. Among the readers, I am convinced, only a few will be able to explain what they actually want to say when they say:

- It’s seven o’clock in the evening now.

Is it really just that the small hand of the clock shows the number seven? What does this number mean? It shows that 7/24 days passed after noon. But after what noon and above all 7/24 what days?

What is a day? Those days, which are referred to by the well-known saying “day and night - a day away,” represent the period of time during which the globe manages to turn once around its axis in relation to the Sun. In practice, it is measured as follows: two successive passages of the Sun (or rather its center) are observed through that line in the sky that connects the point above the observer’s head (“zenith”) with the point of the south on the horizon. This interval is not always the same: the Sun comes to the indicated line sometimes a little earlier, sometimes later. It is impossible to adjust the clock according to this “true noon”; the most skilled craftsman is not able to adjust the clock so that it runs strictly according to the Sun: for this it is too sloppy. “The sun shows time deceivingly,” Parisian watchmakers wrote on their coat of arms a hundred years ago.

Our clocks are not regulated by the real Sun, but by some imaginary sun that does not shine, does not warm, but was invented only for the correct calculation of time. Imagine that in nature there is a celestial body that moves uniformly throughout the year, circling the Earth in exactly the same amount of time as it takes our truly existing Sun to circle the Earth - of course, in an apparent way. This luminary created by the imagination is called in astronomy the “middle sun.” The moment of its passage through the zenith-south line is called “middle noon”; the interval between two average noons is the “average solar day,” and the time so calculated is called “average solar time.” Pocket and wall clocks follow exactly this mean solar time, while a sundial, in which the shadow of the rod serves as the arrow, shows the true solar time for a given place. After what has been said, the reader probably has the idea that the inequality of true solar days is caused by the uneven rotation of the Earth around its axis. The Earth does indeed rotate unevenly, but the inequality of the day is due to the unevenness of another movement of the Earth, namely, its movement in orbit around the Sun. We will now understand how this can affect the length of the day. In Fig. 6 you see two consecutive positions of the globe. Let's look at the left position. The arrows below show in which direction the Earth rotates on its axis: counterclockwise when looking at the north pole. At the point A it is now noon: this point lies exactly opposite the Sun. Imagine now that the Earth has made one full revolution around its axis; During this time, she managed to move in orbit to the right and took another place. Radius of the Earth drawn at a point A, has the same direction as a day ago, but the point A turns out to no longer lie directly opposite the Sun. For the person standing at the point A, noon has not yet arrived: the Sun is to the left of the drawn line. The earth needs to rotate for a few more minutes so that at the point A a new afternoon has arrived.

Rice. 6. Why are solar days longer than sidereal days? (Details in the text)

What follows from this? That the interval between two true solar noons longer the time it takes for the Earth to completely rotate around its axis. If the Earth moved uniformly around the Sun circle , in the center of which the Sun would be located, then the difference between the actual duration of rotation around the axis and the apparent one, which we establish from the Sun, would be the same from day to day. It is easy to determine if we take into account that these small additions should add up to a whole day over the course of a year (the Earth, moving in orbit, makes one extra revolution around its axis per year); This means that the actual duration of each revolution is equal to

Let us note, by the way, that the “real” length of a day is nothing more than the period of rotation of the Earth in relation to any star; That is why such days are called “stellar”.

So, sidereal day average shorter than the sun by 3 m. 56 s, in round - by 4 m. The difference does not remain constant, because: 1) The Earth goes around the Sun not in a uniform motion in a circular orbit, but in an ellipse, in some parts of which (closer to the Sun ) it moves faster, in others (more distant) it moves slower, and 2) the Earth’s rotation axis is inclined to the plane of its orbit. Both of these reasons determine that the true and mean solar time on different days diverge from each other by a different number of minutes, reaching up to 16 on some days. Only four times a year do both times coincide:

On the contrary, on days

the difference between true and average time reaches its greatest value - about a quarter of an hour. Curve in Fig. 7 shows how large this discrepancy is on different days of the year.

Until 1919, citizens of the USSR lived according to local solar time. For each meridian of the globe, average noon occurs at a different time (“local” noon), so each city lived according to to his local time; only the arrival and departure of trains were scheduled according to the common time for the entire country: Petrograd time. Citizens distinguished between “city” and “station” time; the first - local mean solar time - was shown by the city clock, and the second - Petrograd mean solar time - was shown by the railway station clock. Currently, all railway traffic in Russia operates according to Moscow time.

Rice. 7. This graph, called the “equation of time graph,” shows how large the discrepancy between true and mean noon (left scale) is on a given day. For example, on April 1 at true noon, a faithful mechanical watch should show 12:50; in other words, the curve gives the average time at true noon (right scale)

Since 1919, we have used non-local time as the basis for calculating the time of day, called “zone” time. The globe is divided by meridians into 24 identical “zones”, and all points of one zone calculate the same time, namely the average solar time that corresponds to the time of the average meridian of a given zone. On the entire globe, at every moment, there “exist,” therefore, only 24 different times, and not many times, as was the case before the introduction of zone time.

To these three types of time counting - 1) true solar, 2) average local solar and 3) zone - we must add a fourth, used only by astronomers. This is 4) “sidereal” time, calculated according to the previously mentioned sidereal days, which, as we already know, are shorter than the average solar day by about 4 minutes. On September 22, both time accounts coincide, but with each subsequent day, sidereal time is ahead of the average solar time by 4 minutes.

Finally, there is also a fifth type of time - 5) the so-called maternity leave time - the one by which the entire population of Russia and most Western countries live during the summer season.

Maternity time is exactly one hour ahead of standard time. The purpose of this event is as follows: during the daytime of the year - from spring to autumn - it is important to start and end the work day early in order to reduce energy consumption for artificial lighting. This is achieved by officially moving the clock hand forward. Such a translation in Western countries is done every spring (at one in the morning the hand is moved to number 2), and every autumn the clocks are moved back again.

Maternity time was first introduced in our country in 1917; 3
At the initiative of Ya.I. Perelman, who proposed this bill. (Editor's note)

For some period the clock hand was moved forward two and even three hours; after a several-year break, it was reintroduced into the USSR in the spring of 1930 and differs from the zone time by one hour.

Length of day

The exact length of the day for each place and any date of the year can be calculated from the tables of the astronomical yearbook. Our reader, however, is unlikely to need such precision for everyday purposes; if he is ready to be content with a relatively rough approximation, then the attached drawing will serve him well (Fig. 8). Along its left edge is shown in hours duration day. The angular distance of the Sun from the celestial equator is plotted along the bottom edge. This distance, measured in degrees, is called the “declination” of the Sun. Finally, oblique lines correspond to different latitudes of observation sites.

To use the drawing, you need to know how great the angular distance (“declination”) of the Sun from the equator in one direction or another for different days of the year. The relevant data is shown on the plate on page 28.

Rice. 8. Drawing for graphically determining the length of the day (Details in the text)

Let's show with examples how to use this drawing.

1. Find the length of the day in mid-April at latitude 60°.

We find in the tablet the declination of the Sun in mid-April, i.e. its angular distance these days from the celestial equator: +10°. At the bottom edge of the drawing we find the number 10° and draw a straight line from it at right angles to the bottom edge until it intersects with an oblique line corresponding to the 60th parallel. On left edge, the intersection point corresponds to the number 14 ½, i.e., the desired length of the day is approximately 14 hours 30 minutes.

When drawing up this drawing, the influence of the so-called “atmospheric refraction” was taken into account (see page 49, Fig. 15).

The declination of the Sun on November 10 is -17°. (Sun in southern hemispheres of the sky.) Doing as before, we find 14 ½ hours. But since this time the declination is negative, the resulting number means the length of the night, not the day. The desired length of the day is 24–14 ½ = 9 ½ hours.

We can also calculate the moment of sunrise. Dividing 9 ½ in half, we get 4 hours 45 meters. Knowing from Fig. 7, that on November 10 the clock at true noon shows 11:43 am, we find out the moment of sunrise. 11:43 am – 4:45 am = 6:58 am. Sunset on this day will occur at 11:43 am + 4:45 am = 16:28 am, i.e. e. at 4:28 pm. Thus, both drawings (Figs. 7 and 8), when used properly, can replace the corresponding tables of the astronomical yearbook.

Rice. 9. Chart of sunrise and sunset during the year for the 50th parallel

You can, using the technique outlined now, draw up a schedule of sunrise and sunset for the entire year for the latitude of your place of permanent residence, as well as the length of the day. You can see an example of such a graph for the 50th parallel in Fig. 9 (it is compiled according to local, not maternity time). Having examined it carefully, you will understand how to draw such graphs. And having drawn it once for the latitude where you live, you can, glancing at your drawing, immediately say at what time the Sun will rise or set on this or that day of the year.