Jesus second coming. Yearly path of the sun Mean solar time

The movement of the sun among the stars

(lesson - lecture)

This lesson is for studentsXItextbook classesG.Ya. Myakisheva, B.B. Bukhovtseva "Physics. Grade 11 "(profile classes)

The educational goal of the lesson: study the motion of the sun relative to distant stars.

Educational objectives of the lesson:

Determine the main types of celestial motion of the Sun and correlate them with such phenomena as changing the length of day and night, changing seasons, the presence of climatic zones;

To form the ability of students to find and determine the main planes, lines, points of the celestial sphere associated with the movement of the Sun;

To form the ability of students to determine the horizontal coordinates of the Sun;

General remarks

The information in the lecture is presented in a concise manner, so a short phrase may require a lot of thought. The development of the need for reflection, and, consequently, for the understanding of the content of a particular topic by students, is correlated with the performance of tasks:

Practical tips for working with information:

having received new information, think it over and clearly formulate the answer to the question: “What is it about and why was it told to you?”;

get into the habit of asking yourself “why?” and independently find answers on his way, thinking, talking with comrades, a teacher;

when checking a formula, solving a problem, etc., perform mathematical operations gradually, writing down all intermediate calculations;

Main questions of the lecture

The movement of heavenly bodies.

The movement of the sun among the stars.

Ecliptic. Ecliptic coordinate system.

Ecliptic- a large circle of the celestial sphere, along which the apparent annual movement of the Sun occurs. The direction of this movement (about 1 per day) is opposite to the direction of the daily rotation of the Earth. The word "ecliptic" comes from the Greek word "eclipsis" - an eclipse.

The axis of rotation of the Earth has a constant angle of inclination to the plane of revolution of the Earth around the Sun, equal to approximately 66 ° 34 "(see Fig. 1). As a result, the angle ε between the plane of the ecliptic and the plane of the celestial equator is 23°26".

Figure 1. Ecliptic and celestial equator

Based on Figure 1, fill in the gaps in the definitions below.

Axis of the ecliptic (PP") - ………………

………………………………………….. .

North ecliptic pole (P) - ……………………………………………. .

South ecliptic pole (P") - ………………………………………………………………………….. .

The ecliptic passes through 13 constellations. Ophiuchus does not belong to the zodiac constellations.

The points of the spring (γ) and autumn (Ω) equinoxes are the points of intersection of the ecliptic and the celestial equator. The vernal equinox is located in the constellation of Pisces (until recently - in the constellation of Aries). The date of the spring equinox is March 20 (21). The point of the autumnal equinox is in the constellation of Virgo (until recently - in the constellation of Libra). The date of the autumn equinox is September 22 (23).

Summer Solstice and Winter Solstice points 90° away from the equinoxes. The summer solstice lies in the northern hemisphere, falls on June 22. The winter solstice lies in the southern hemisphere and falls on December 22nd.

Ecliptic coordinate system.

Figure 2. Ecliptic coordinate system

The plane of the ecliptic is chosen as the main plane of the ecliptic coordinate system (Fig. 2). The ecliptic coordinates are:

The latitude and longitude of a star do not change as a result of the daily movement of the celestial sphere. The ecliptic coordinate system is used mainly in the study of the motion of the planets. This is convenient because the planets move relative to the stars approximately in the plane of the ecliptic. Due to the smallness β formulas containing cos β and sin β can be simplified.

The ratio between degrees, hours and minutes is as follows: 360 =24, 15=1, 1=4.

Movement of heavenly bodies

Daily movement of the luminaries. per diem the paths of the luminaries on the celestial sphere are circles whose planes are parallel to the celestial equator. These circles are called celestial parallels. The daily movement of the luminaries is a consequence of the rotation of the Earth around its axis. The visibility of the luminaries depends on their celestial coordinates, the position of the observer on the Earth's surface (see Fig. 3).

Figure 3. Daily paths of the luminaries relative to the horizon, for an observer located: a - in middle geographical latitudes; b - at the equator; c - at the pole of the Earth.

1. Formulate a theorem about the height of the world pole.

2. Describe how you can explain the properties of the daily movement of the luminaries, due to the rotation of the Earth around its axis at different latitudes?

How does the daily movement of its luminary change: a) height; b) right ascension; c) declination?

Does the height, right ascension and declination of the main points of the celestial sphere change during the day: Z, Z ׳ , P, P ׳ , N, S, E, W?

3. The movement of the Sun among the stars.

climax- the phenomenon of crossing the heavenly meridian by the luminary. In the upper climax, the luminary has the greatest height. The azimuth of the luminary in the upper climax is equal to ……. And at the bottom - the smallest. The azimuth of the star at the lower culmination is ...... The moment of the upper culmination of the center of the Sun is called true noon, and the bottom - true midnight.

AT luminary height ( h) or zenith distance ( z) at the moment of culmination depends on the declination of the star ( δ) and latitude of the observation site ( φ )

Figure 4. Projection of the celestial sphere onto the plane of the celestial meridian

Table 3 shows the formulas for determining the height of the luminary in the upper and lower culminations. The type of expression for the height of the luminary at the climax is determined based on Figure 4.

Table 3

The height of the luminary at the climax

Sun declination

The height of the luminary at the upper climax

The height of the luminary at the lower climax

δ < φ

h \u003d 90˚-φ + δ

h=90˚-φ-δ

δ = φ

h=90˚

h=0˚

δ > φ

h=90˚+φ-δ

h= φ+δ-90˚

There are three categories of luminaries, for places on earth for which 0<φ <90˚:

If the declination of the star δ< -(90˚- φ ), то оно будет невосходящим. Если склонение светила δ >(90˚- φ ), it will be non-setting.

The conditions for the visibility of the Sun and the change of seasons depend on the position of the observer on the surface of the Earth and on the position of the Earth in orbit.

Annual motion of the Sun- the phenomenon of the movement of the Sun relative to the stars in the direction opposite to the daily rotation of the celestial sphere. This phenomenon is a consequence of the movement of the Earth around the Sun in an elliptical orbit in the direction of the Earth's rotation around its axis, i.e. counterclockwise when viewed from the north pole to the south (see Fig. 5).

Figure 5. Tilt of the Earth's axis of rotation and seasons

Figure 6. Scheme of the positions of the Earth during the summer and winter solstices

During the annual movement of the Sun, the following phenomena occur: a change in the noon height, the position of the points of sunrise and sunset, the length of day and night, the appearance of the starry sky at the same hour after sunset.

The rotation of the Earth around the Sun, as well as the fact that the axis of the Earth's daily rotation is always parallel to itself at any point in the Earth's orbit, are the main reasons for the change of seasons. These factors determine the different inclination of the sun's rays with respect to the Earth's surface and the different degree of illumination of the hemisphere on which it shines (see Fig. 5, 6). The higher the Sun is above the horizon, the stronger its ability to heat the earth's surface. In turn, a change in the distance from the Earth to the Sun during the year does not affect the change of seasons: the Earth, running its elliptical orbit, is at its closest point in January, and at its most distant point in July.

Using the lecture material, complete table 4.

Table 4

Daily movement of the Sun at different times of the year at middle latitudes

position on the ecliptic

declination

midday height

Minimum Height

sunrise point

entry point

Day length

20(21) .03

22.06

22(23).09

22.12

Astronomical signs of thermal zones:

Changing the appearance of the starry sky. Each subsequent night, compared to the previous one, the stars appear before us slightly shifted to the west. From evening to evening the same star rises 4 minutes earlier. A year later, the view of the starry sky is repeated.

If a certain star is at its zenith at 9 pm on September 1st, what time will it be at its zenith on March 1st? Can you see her? Justify the answer.

Precession - cone-shaped rotation of the earth's axis with a period of 26,000 years under the influence of gravitational forces from the Sun and Moon. The precessional movement of the Earth causes the north and south poles of the world to describe circles in the sky: the axis of the world describes a cone around the axis of the ecliptic, with a radius of about 23˚26", remaining all the time inclined to the plane of the Earth's motion at an angle of about 66˚34" clockwise for the observer northern hemisphere (Fig. 7).

Precession changes the position of the celestial poles. 2700 years ago, the star α Draconis was located near the North Pole of the world, called the Royal Star by Chinese astronomers. Currently, the North Star is α Ursa Minor. By the year 10,000, the North Pole of the world will approach the star Deneb (α Cygnus). In 13600, Vega (α Lyrae) will become the polar star.

Figure 7. Precessional motion of the earth's axis

As a result of precession, the points of the spring and autumn equinoxes, summer and winter solstices slowly move through the zodiac constellations. 5000 years ago, the vernal equinox was in the constellation of Taurus, then moved to the constellation of Aries, and is now in the constellation of Pisces (see Fig. 8). This offset is
= 50",2 per year.

Figure 8. Precession and nutation on the celestial sphere

The attraction of the planets is too small to cause changes in the position of the Earth's axis of rotation, but it acts on the movement of the Earth around the Sun, changing the position in space of the plane of the Earth's orbit, i.e. plane of the ecliptic: the inclination of the ecliptic to the equator changes periodically, which is currently decreasing by 0.47 per year. 2 * cos ε ), secondly, the curves described by the poles of the world do not close (Fig. 9).

Figure 9. Precessional movement of the north celestial pole. The dots in the center show the positions of the celestial pole

Nutation of the earth's axis small various fluctuations of the Earth's axis of rotation around its average position. Nutational oscillations arise because the precessional forces of the Sun and Moon continuously change their magnitude and direction; they are equal to zero when the Sun and Moon are in the plane of the Earth's equator and reach a maximum at the greatest distance from these luminaries.

As a result of the precession and nutation of the earth's axis, the celestial poles actually describe complex wavy lines in the sky (see Fig. 8).

It should be noted that the effects of precession and nutation are generated by external forces that change the orientation of the Earth's axis of rotation in space. The body Earth remains in this case, so to speak, fixed with respect to the changing axis. Therefore, the flag set today at the North Pole will also mark the North Pole in 13,000 years, and the latitude a of the point will remain equal to 90 °. Since neither precession nor nutation leads to any changes in latitude on Earth, these phenomena do not cause climatic changes either. However, they still create a shift in the seasons relative to some ideal calendar.

What can you say about the changes in ecliptic longitude, ecliptic latitude, right ascension and declination of all stars, as a result of the precessional movement of the earth's axis?

Assignments for independent homework

Name the main planes, lines and points of the celestial sphere.

Where do the heavenly bodies rise and set for an observer located in the northern (southern) hemisphere of the Earth?

How are astronomical coordinate systems constructed?

What is called the height and azimuth of the sun?

What are equatorial and ecliptic coordinates called?

How are right ascension and hour angle related?

How are the declination and the height of the luminary at the moment of the upper culmination related?

What is precession and nutation?

Why do stars always rise and set at the same points on the horizon, while the Sun and Moon do not?

How is the apparent motion of the Sun across the celestial sphere related to the motion of the Earth around the Sun?

What is the ecliptic?

What points are called equinoxes and why?

What is a solstice?

At what angle is the ecliptic inclined to the horizon and why does this angle change during the day?

How can the ecliptic coincide with the horizon?

Draw with a pen on a circle depicting a model of the celestial sphere the points where the Sun is located:

Mark the position of the ecliptic using the marked points. Indicate on the ecliptic (approximately) the position of the Sun on April 21, October 23 and your birthday. Find the points listed in the previous paragraphs on the model of the celestial sphere.

Literature

Levitan, E.P. Methods of teaching astronomy in secondary school / E.P. Levitan. - M.: Enlightenment, 1965. - 227 p.

Malakhov A.A. Physics and astronomy (competence-based approach): textbook-method. allowance / A.A. Malakhov; Shadr. state ped. in-t. - Shadrinsk: Shadr. House of the Press, 2010. - 163 p.

Mayorov, V.F. How to know that the earth is rotating? / V.F. Mayorov // Physics. - 2010. - No. 2. - S. 45-47.

Myakishev G.Ya., Bukhovtsev B.B., Sotsky N.N. Physics: Proc. For 10 cells. educational institutions. – M.: Enlightenment, 2010.

Pinsky A.A., Razumovsky V.G., Bugaev A.I. etc. Physics and Astronomy: Textbook for 9th grade. general education Institutions / Ed. A.A. Pinsky, V.G. Razumovsky.- M.: Enlightenment, 2001. - S. 202-212

Ranzini, D. Cosmos / D. Ranzini; Per. from Italian. N. Lebedeva. - M .: LLC Astrel Publishing House, 2004. - 320 p.

Every day, as it rises from the horizon in the eastern side of the sky, the Sun passes across the sky and hides again in the west. For the inhabitants of the Northern Hemisphere, this movement occurs from left to right, for the southerners from right to left. At noon, the Sun reaches its greatest height, or, as astronomers say, culminates. Noon is the upper climax, and there is also a lower climax - at midnight. At our mid-latitudes, the lower culmination of the Sun is not visible, as it occurs below the horizon. But beyond the Arctic Circle, where the Sun sometimes does not set in summer, you can observe both the upper and lower culminations.

At the geographic pole, the daily path of the Sun is almost parallel to the horizon. Appearing on the day of the vernal equinox, the Sun rises higher and higher for a quarter of the year, describing circles above the horizon. On the day of the summer solstice, it reaches its maximum height (23.5?). For the next quarter of the year, before the autumnal equinox, the Sun descends. This is a polar day. Then the polar night sets in for half a year. At mid-latitudes, the visible daily path of the Sun either shortens or increases throughout the year. It is lowest on the winter solstice and highest on the summer solstice. On the days of the equinoxes

The sun is at the celestial equator. At the same time, it rises at the point of the east and sets at the point of the west.

In the period from the spring equinox to the summer solstice, the place of sunrise shifts slightly from the sunrise point to the left, to the north. And the place of entry moves away from the west point to the right, although also to the north. On the day of the summer solstice, the Sun appears in the northeast, and at noon it culminates at the highest altitude of the year. The sun sets in the northwest.

Then the places of sunrise and sunset shift back to the south. On the winter solstice, the Sun rises in the southeast, crosses the celestial meridian at its lowest point, and sets in the southwest. It should be borne in mind that due to refraction (that is, the refraction of light rays in the earth's atmosphere), the apparent height of the luminary is always greater than the true one.

Therefore, the sunrise occurs earlier and the sunset later than it would be in the absence of an atmosphere.

So, the daily path of the Sun is a small circle of the celestial sphere, parallel to the celestial equator. At the same time, during the year, the Sun moves relative to the celestial equator either to the north or to the south. The daytime and nighttime parts of his journey are not the same. They are equal only on the days of the equinoxes, when the Sun is at the celestial equator.

The expression "the path of the Sun among the stars" will seem strange to someone. You can't see the stars during the day. Therefore, it is not easy to notice that the Sun is slow, by about 1? per day, moves among the stars from right to left. But you can see how the appearance of the starry sky changes during the year. All this is a consequence of the revolution of the Earth around the Sun.

The path of the visible annual movement of the Sun against the background of stars is called the ecliptic (from the Greek "eclipsis" - "eclipse"), and the period of revolution along the ecliptic is called a stellar year. It is equal to 265 days 6 hours 9 minutes 10 seconds, or 365.2564 mean solar days.

The ecliptic and the celestial equator intersect at an angle of 23? 26 "at the points of the spring and autumn equinoxes. At the first of these points, the Sun usually happens on March 21, when it passes from the southern hemisphere of the sky to the northern one. In the second, on September 23, when they pass from the northern hemisphere At the farthest point of the ecliptic to the north, the Sun is June 22 (summer solstice), and to the south - December 22 (winter solstice).In a leap year, these dates are shifted by one day.

Of the four points on the ecliptic, the main point is the vernal equinox. It is from her that one of the celestial coordinates is counted - right ascension. It also serves to count sidereal time and the tropical year - the time interval between two successive passages of the center of the Sun through the vernal equinox. The tropical year determines the change of seasons on our planet.

Since the vernal equinox slowly moves among the stars due to the precession of the earth's axis, the duration of the tropical year is less than the duration of the sidereal one. It is 365.2422 mean solar days. About 2 thousand years ago, when Hipparchus compiled his star catalog (the first to have come down to us in its entirety), the vernal equinox was in the constellation Aries. By our time, it has moved almost 30?, into the constellation Pisces, and the autumn equinox point has moved from the constellation Libra to the constellation Virgo. But according to tradition, the points of the equinoxes are indicated by the former signs of the former "equinoctial" constellations - Aries and Libra. The same happened with the solstice points: the summer in the constellation Taurus is marked by the sign of Cancer, and the winter in the constellation of Sagittarius is marked by the sign of Capricorn.

And finally, the last thing is connected with the apparent annual movement of the Sun. Half of the ecliptic from the spring equinox to the autumn (from March 21 to September 23) the Sun passes in 186 days. The second half, from the autumn equinox to the spring equinox, takes 179 days (180 in a leap year). But after all, the halves of the ecliptic are equal: each is 180?. Therefore, the Sun moves along the ecliptic unevenly. This unevenness is explained by a change in the speed of the Earth's movement in an elliptical orbit around the Sun. The uneven movement of the Sun along the ecliptic leads to different lengths of the seasons. For residents of the northern hemisphere, for example, spring and summer are six days longer than autumn and winter. The Earth on June 2-4 is located from the Sun 5 million kilometers longer than on January 2-3, and moves in its orbit more slowly in accordance with Kepler's second law. In the summer the earth receives from

The sun is less warm, but summer in the Northern Hemisphere is longer than winter. Therefore, the Northern Hemisphere is warmer than the Southern Hemisphere.

True motion of the Earth - Apparent annual motion of the Sun on the celestial sphere - Celestial equator and ecliptic plane - Equatorial coordinates of the Sun during the year

True motion of the earth

To understand the principle of the apparent motion of the Sun and other luminaries in the celestial sphere, we first consider the true motion of the earth. Earth is one of the planets. It continuously rotates around its axis.

Its rotation period is equal to one day, therefore, to an observer located on Earth, it seems that all celestial bodies revolve around the Earth from east to west with the same period.

But the Earth not only rotates around its axis, but also revolves around the Sun in an elliptical orbit. It completes one revolution around the Sun in one year. The axis of rotation of the Earth is inclined to the plane of the orbit at an angle of 66°33′. The position of the axis in space during the movement of the Earth around the Sun remains almost unchanged all the time. Therefore, the Northern and Southern hemispheres are alternately turned towards the Sun, as a result of which the seasons change on Earth.

When observing the sky, one can notice that the stars for many years invariably retain their relative position.

The stars are “fixed” only because they are very far away from us. The distance to them is so great that from any point of the earth's orbit they are equally visible.

But the bodies of the solar system - the Sun, the Moon and the planets, which are relatively close to the Earth, and we can easily notice the change in their positions. Thus, the Sun, along with all the luminaries, participates in the daily movement and at the same time has its own visible movement (it is called annual movement) due to the motion of the earth around the sun.

Apparent annual motion of the Sun on the celestial sphere

The most simple annual motion of the Sun can be explained by the figure below. From this figure it can be seen that, depending on the position of the Earth in orbit, an observer from the Earth will see the Sun against the background of different . It will seem to him that it is constantly moving around the celestial sphere. This movement is a reflection of the revolution of the Earth around the Sun. In a year, the Sun will make a complete revolution.

The large circle on the celestial sphere, along which the apparent annual movement of the Sun occurs, is called ecliptic. Ecliptic is a Greek word and means eclipse. This circle was named so because eclipses of the Sun and Moon occur only when both luminaries are on this circle.

It should be noted that the plane of the ecliptic coincides with the plane of the Earth's orbit.

The apparent annual movement of the Sun along the ecliptic occurs in the same direction in which the Earth moves in orbit around the Sun, i.e., it moves to the east. During the year, the Sun successively passes through the ecliptic 12 constellations, which form a belt and are called zodiacal.

The Zodiac belt is formed by the following constellations: Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn and Aquarius. Due to the fact that the plane of the earth's equator is inclined to the plane of the earth's orbit by 23°27', plane of the celestial equator also inclined to the plane of the ecliptic at an angle e=23°27′.

The inclination of the ecliptic to the equator does not remain constant (due to the influence of the forces of attraction of the Sun and the Moon on the Earth), therefore, in 1896, when approving astronomical constants, it was decided to consider the inclination of the ecliptic to the equator to be on average equal to 23 ° 27'8 "26.

Celestial equator and ecliptic plane

The ecliptic intersects the celestial equator at two points called points of spring and autumn equinoxes. The point of the vernal equinox is usually denoted by the sign of the constellation Aries T, and the point of the autumnal equinox - by the sign of the constellation Libra -. The sun at these points, respectively, is on March 21 and September 23. These days on Earth, day is equal to night, the Sun exactly rises in the east point and sets in the west point.

The points of the spring and autumn equinoxes are the points of intersection of the equator and the plane of the ecliptic

The points on the ecliptic that are 90° from the equinoxes are called solstice points. Point E on the ecliptic, at which the Sun is at its highest position relative to the celestial equator, is called summer solstice point, and the point E' at which it occupies the lowest position is called winter solstice point.

At the point of the summer solstice, the Sun occurs on June 22, and at the point of the winter solstice - on December 22. For several days close to the dates of the solstices, the midday height of the Sun remains almost unchanged, in connection with which these points got their name. When the Sun is at the summer solstice, the day in the Northern Hemisphere is longest and the night is shortest, and when it is at the winter solstice, the opposite is true.

On the day of the summer solstice, the points of sunrise and sunset are as far as possible north of the points of east and west on the horizon, and on the day of the winter solstice they are at the greatest distance to the south.

The movement of the Sun along the ecliptic leads to a continuous change in its equatorial coordinates, a daily change in the noon height and a movement of the points of sunrise and sunset along the horizon.

It is known that the declination of the Sun is measured from the plane of the celestial equator, and right ascension - from the point of the vernal equinox. Therefore, when the Sun is at the vernal equinox, its declination and right ascension are zero. During the year, the declination of the Sun in the present period varies from +23°26′ to -23°26′, passing through zero twice a year, and right ascension from 0 to 360°.

Equatorial coordinates of the Sun during the year

The equatorial coordinates of the Sun during the year change unevenly. This happens due to the uneven motion of the Sun along the ecliptic and the motion of the Sun along the ecliptic and the inclination of the ecliptic to the equator. The Sun covers half of its apparent annual path in 186 days from March 21 to September 23, and the other half in 179 days from September 23 to March 21.

The uneven movement of the Sun along the ecliptic is due to the fact that the Earth during the entire period of revolution around the Sun does not move in orbit at the same speed. The Sun is at one of the foci of the Earth's elliptical orbit.

From Kepler's second law It is known that the line connecting the Sun and the planet covers equal areas in equal periods of time. According to this law, the Earth, being closest to the Sun, i.e. in perihelion, moves faster, and being farthest from the Sun, i.e. in aphelion- slower.

Earth is closer to the Sun in winter, and further away in summer. Therefore, on winter days, it moves in orbit faster than on summer days. As a result, the daily change in the right ascension of the Sun on the day of the winter solstice is 1°07', while on the day of the summer solstice it is only 1°02'.

The difference in the velocities of the Earth's motion at each point of the orbit causes an uneven change in not only the right ascension, but also the declination of the Sun. However, due to the inclination of the ecliptic to the equator, its change has a different character. The declination of the Sun changes most rapidly near the equinoxes, and at the solstices it almost does not change.

Knowing the nature of the change in the equatorial coordinates of the Sun allows us to make an approximate calculation of the right ascension and declination of the Sun.

To perform such a calculation, take the nearest date with known equatorial coordinates of the Sun. Then it is taken into account that the right ascension of the Sun per day changes by an average of 1 °, and the declination of the Sun during the month before and after the passage of the equinoxes changes by 0.4 ° per day; during the month before and after the solstices - by 0.1 ° per day, and during the intermediate months between the indicated ones - by 0.3 °.

The day is one of the basic units of time measurement. The rotation of the Earth and the apparent movement of the starry sky.

The main quantity for measuring time is related to the period of a complete revolution of the globe around its axis.

Until recently, it was believed that the rotation of the Earth is completely uniform. However, some irregularities have now been found in this rotation, but they are so small that they do not matter for the construction of the calendar.

Being on the surface of the Earth and participating together with it in its rotational motion, we do not feel it.

We judge the rotation of the globe around its axis only by those visible phenomena that are associated with it. The consequence of the daily rotation of the Earth is, for example, the apparent movement of the firmament with all the luminaries located on it: stars, planets, the Sun, the Moon, etc.

Nowadays, to determine the duration of one revolution of the globe, you can use - a special telescope - a transit instrument, the optical axis of the tube of which rotates strictly in one plane - the plane of the meridian of a given place, passing through the points of south and north. The crossing of a meridian by a star is called the upper climax. The time interval between two consecutive upper climaxes of a star is called a sidereal day.

A more precise definition of a sidereal day is as follows: it is the interval of time between two successive upper climaxes of the vernal equinox. They are one of the basic units of time measurement, since their duration remains unchanged. A sidereal day is divided into 24 sidereal hours, each hour into 60 sidereal minutes, and each minute into 60 sidereal seconds.

Sidereal hours, minutes and seconds are counted on sidereal clocks, which are available in every astronomical observatory and always show sidereal time. It is inconvenient to use such watches in everyday life, since the same high point during the year falls on different times of the sunny day. The life of nature, and with it all the life of people, is connected not with the movement of the stars, but with the change of day and night, that is, with the daily movement of the Sun. Therefore, in everyday life we do not use sidereal time, but solar time. The concept of solar time is much more complicated than the concept of sidereal time. First of all, we must clearly imagine the apparent movement of the Sun.

Apparent annual motion of the Sun. Ecliptic.

Watching the starry sky from night to night, you can see that at each subsequent midnight more and more stars culminate. This is explained by the fact that due to the annual movement of the globe in orbit, the movement of the Sun among the stars occurs. It takes place in the same direction in which the Earth rotates, that is, from west to east.

The path of the apparent movement of the Sun among the stars is called the ecliptic. . It is a large circle on the celestial sphere, the plane of which is inclined to the plane of the celestial equator at an angle of 23 ° 27 "and intersects with the celestial equator at two points. These are the points of the spring and autumn equinoxes. In the first of them, the Sun is around March 21, when it passes from the southern celestial hemisphere to the northern.The second point it is about September 23, when it passes from the northern hemisphere to the southern.Zodiac constellations.Moving along the ecliptic, the Sun sequentially moves during the year among the following 12 constellations located along the ecliptic and making up the belt zodiac .

The apparent movement of the Sun through the zodiac constellations: Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn and Aquarius. (Strictly speaking, the Sun also passes through the 13th constellation - Ophiuchus. It would be even more correct to consider this constellation of the zodiac than such a constellation as Scorpio, in which the Sun is less than a long time than in each of the other constellations.) These constellations , called zodiac, got their common name from the Greek word "zoon" - an animal, since many of them were named after animals in ancient times. In each of the zodiac constellations, the Sun is on average about a month. Therefore, even in ancient times, each month corresponded to a certain sign of the zodiac. March, for example, was designated by the sign of Aries, since the vernal equinox was located in this constellation about two thousand years ago and, therefore, the Sun passed this constellation in March. When the Earth moves in its orbit and moves from position III (March) to position IV (April), the Sun will move from the constellation Aries to the constellation Taurus, and when the Earth is in position V (May), the Sun will move from the constellation Taurus to the constellation Gemini, etc.

Movement of the north pole of the world among the stars in 26,000 years.

However, the vernal equinox does not remain unchanged in the celestial sphere. Its movement, discovered in the II century. BC e. the Greek scientist Hipparchus, was called the precession, i.e., the precession of the equinox. It is caused by the following reason. The earth is not a sphere, but a spheroid, flattened at the poles. Attractive forces from the Sun and the Moon act differently on different parts of the spheroidal Earth. These forces lead to the fact that during the simultaneous rotation of the Earth and its movement around the Sun, the axis of rotation of the Earth describes a cone near the perpendicular to the plane of the orbit. As a result, the celestial poles move among the stars in a small circle centered on the ecliptic pole, being at a distance of about 231/2° from it. Due to precession, the vernal equinox moves along the ecliptic to the west, i.e., towards the visible movement of the Sun, by 50 "3 per year. Therefore, it will make a full circle in about 26,000 years. For the same reason, the north pole of the world, located in our time near the North Star, 4000 years ago was near the Dragon, and in 12,000 years it will be near Vega (a Lyra).

Sunny day and solar time.

True sunny day. If, with the help of a transit instrument, we observe not the stars, but the Sun and daily mark the time of passage of the center of the solar disk through the meridian, i.e., the moment of its upper climax, then we can find that the time interval between the two upper culminations of the center of the solar disk, which is called true solar days, always turns out to be longer than a sidereal day by an average of 3 minutes. 56 seconds, or approximately 4 minutes. This comes from the fact that the Earth, revolving around the Sun, makes a complete revolution around it during the year, i.e., approximately in 365 and a quarter days. Reflecting this movement of the Earth, the Sun in one day moves about 1/365 of its annual path, or about one degree, which corresponds to four minutes of time. However, unlike the sidereal day, the true solar day periodically changes its duration.

This is due to two reasons: firstly, the inclination of the ecliptic plane to the plane of the celestial equator, and secondly, the elliptical shape of the Earth's orbit. When the Earth is on the part of the ellipse closest to the Sun, it moves faster; in half a year, the Earth will be in the opposite part of the ellipse and will move in orbit more slowly. The uneven movement of the Earth in its orbit causes uneven apparent movement of the Sun in the celestial sphere: at different times of the year, the Sun moves at different speeds. Therefore, the length of a true solar day is constantly changing. So, for example, on December 23, when the true day is the longest, they are 51 seconds. longer than September 16, when they are the shortest. Mean solar day. Due to the non-uniformity of true solar days, it is inconvenient to use them as a unit for measuring time. About three hundred years ago, Parisian watchmakers knew this well when they wrote on their guild coat of arms: "The sun shows time deceptively."

All our clocks - wrist, wall, pocket and others - are adjusted not according to the movement of the true Sun, but according to the movement of an imaginary point, which during the year makes one complete revolution around the Earth in the same time as the Sun, but at the same time moves along the celestial equator and perfectly evenly. This point is called the middle sun. The moment of passage of the average sun through the meridian is called the average noon, and the time interval between two successive average noons is the average solar day. Their duration is always the same. They are divided into 24 hours, each hour of mean solar time is in turn divided into 60 minutes, and each minute is divided into 60 seconds of mean solar time. It is the average solar day, and not the sidereal day, that is one of the main units of time measurement, which is the basis of the modern calendar. The difference between mean solar time and true time at the same moment is called the equation of time.

Astronomical basis of the calendar.

We know that every calendar is based on astronomical phenomena: the change of day and night, the change of lunar phases and the change of seasons. These phenomena provide the three basic units of time that underlie any calendar system, namely the solar day, the lunar month, and the solar year. Taking the average solar day as a constant value, we establish the duration of the lunar month and the solar year. Throughout the history of astronomy, the duration of these units of time has been continually refined.

synodic month.

The basis of the lunar calendars is the synodic month - the time interval between two successive identical phases of the moon. Initially, as already known, it was determined at 30 days. Later it was found that the lunar month has 29.5 days. At present, the average duration of a synodic month is taken to be 29.530588 mean solar days, or 29 days 12 hours 44 minutes 2.8 seconds of mean solar time.

tropical year.

Of exceptional importance was the gradual refinement of the duration of the solar year. In the first calendar systems, the year contained 360 days. The ancient Egyptians and Chinese about five thousand years ago determined the length of the solar year at 365 days, and a few centuries before our era, both in Egypt and China, the length of the year was set at 365.25 days. The modern calendar is based on the tropical year - the time interval between two successive passages of the center of the Sun through the vernal equinox.

Such outstanding scientists as P. Laplace (1749-1827) in 1802, F. Bessel (1784-1846) in 1828, P. Hansen (1795-1874) in 1853 were engaged in determining the exact value of the tropical year. , W. Le Verrier (1811-1877) in 1858, and some others.

To determine the length of the tropical year, S. Newcomb proposed a general formula: T == 365.24219879 - 0.0000000614 (t - 1900), where t is the ordinal number of the year.

In October 1960, the XI General Conference on Weights and Measures was held in Paris, at which a unified international system of units (SI) was adopted and a new definition of the second as the basic unit of time recommended by the IX Congress of the International Astronomical Union (Dublin, 1955) was approved. . In accordance with the adopted decision, the ephemeris second is defined as 1/31556925.9747 part of the tropical year for the beginning of 1900. From here it is easy to determine the value of the tropical year: T ==- 365 days 5 hours. 48 min. 45.9747 sec. or T = 365.242199 days.

For calendar purposes, such high accuracy is not required. Therefore, rounding up to the fifth decimal place, we get T == 365.24220 days. This rounding of the tropical year gives an error of one day per 100,000 years. Therefore, the value we have adopted may well be the basis of all calendar calculations. So, neither the synodic month nor the tropical year contains an integer number of mean solar days and, consequently, all these three quantities are incommensurable. This means that it is impossible to simply express one of these quantities in terms of the other, i.e., it is impossible to choose some integer number of solar years that would contain an integer number of lunar months and an integer number of mean solar days. This explains the whole complexity of the calendar problem and all the confusion that has reigned for many millennia in the issue of calculating large periods of time.

Three kinds of calendars.

The desire to at least to some extent coordinate the day, month and year among themselves led to the fact that in different eras three types of calendars were created: solar, based on the movement of the Sun, in which they sought to coordinate the day and year; lunar (based on the motion of the moon), the purpose of which was to coordinate the day and the lunar month; finally, lunisolar, in which attempts were made to harmonize all three units of time.

At present, almost all countries of the world use the solar calendar. The lunar calendar played a big role in ancient religions. It has survived to this day in some eastern countries that profess the Muslim religion. In it, the months have 29 and 30 days each, and the number of days changes so that the first day of each next month coincides with the appearance of the “new month” in the sky. Years of the lunar calendar contain alternately 354 and 355 days.

Thus, the lunar year is 10-12 days shorter than the solar year. The lunisolar calendar is used in the Jewish religion to calculate religious holidays, as well as in the State of Israel. It is of particular complexity. The year in it contains 12 lunar months, consisting of either 29 or 30 days, but to take into account the movement of the Sun, "leap years" are periodically introduced, containing an additional, thirteenth month. Simple, i.e., twelve-month years, consist of 353, 354, or 355 days, and leap years, i.e., thirteen-month years, have 383, 384, or 385 days each. This achieves that the first day of each month coincides almost exactly with the new moon.

1 Annual motion of the Sun and the ecliptic coordinate system

The sun, along with daily rotation, slowly moves throughout the celestial sphere in the opposite direction along a large circle during the year, called the ecliptic. The ecliptic is inclined to the celestial equator at an angle Ƹ, whose value is currently close to 23 26´. The ecliptic intersects with the celestial equator at the point of spring ♈ (March 21) and autumn Ω (September 23) equinoxes. The points of the ecliptic, 90 from the equinoxes, are the points of the summer (June 22) and winter (December 22) solstices. The equatorial coordinates of the center of the solar disk continuously change during the year from 0h to 24h (right ascension) - ecliptic longitude ϒm, counted from the vernal equinox to the circle of latitude. And from 23 26´ to -23 26´ (declination) - ecliptic latitude, measured from 0 to +90 to the north pole and 0 to -90 to the south pole. The zodiac constellations are the constellations that lie on the line of the ecliptic. It is located on the ecliptic line of 13 constellations: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces and Ophiuchus. But the constellation Ophiuchus is not mentioned, although the Sun is in it most of the time of the constellations of Sagittarius and Scorpio. This is done for convenience. When the Sun is under the horizon at heights from 0 to -6 - civil twilight lasts, and from -6 to -18 - astronomical twilight.

2 Measuring time

The measurement of time is based on observations of the daily rotation of the dome and the annual motion of the Sun, i.e. rotation of the earth on its axis and on the revolution of the earth around the sun.

The length of the basic unit of time, called a day, depends on a chosen point in the sky. In astronomy, such points are taken:

The vernal equinox ♈ ( sidereal time);

The center of the visible disk of the Sun ( true sun, true solar time);

- mean sun - a fictitious point whose position in the sky can be calculated theoretically for any moment in time ( mean solar time)

The tropical year is used to measure long periods of time, based on the movement of the Earth around the Sun.

tropical year- the time interval between two successive passages of the center of the true center of the Sun through the vernal equinox. It contains 365.2422 mean solar days.

Due to the slow movement of the dot spring equinox towards the sun, caused precession, relative to the stars, the Sun is at the same point in the sky after a time interval of 20 minutes. 24 sec. longer than the tropical year. It is called star year and contains 365.2564 mean solar days.

3 sidereal time

The time interval between two successive climaxes of the vernal equinox on the same geographic meridian is called sidereal days.

Sidereal time is measured by the hour angle of the vernal equinox: S=t ♈ , and is equal to the sum of the right ascension and the hour angle of any star: S = α + t.

Sidereal time at any moment is equal to the right ascension of any luminary plus its hour angle.

At the moment of the upper culmination of the sun its hour angle t=0, and S = α.

4 True solar time

The time interval between two successive climaxes of the Sun (the center of the solar disk) on the same geographic meridian is called I am true sunny days.

The beginning of a true solar day on a given meridian is taken as the moment of the lower culmination of the Sun ( true midnight).

The time from the lower culmination of the Sun to any other position, expressed in fractions of a true solar day, is called true solar time Tʘ

True solar time expressed in terms of the hour angle of the Sun, increased by 12 hours: Т ʘ = t ʘ + 12 h

5 Mean solar time

In order for the day to have a constant duration and at the same time be associated with the movement of the Sun, the concepts of two fictitious points are introduced in astronomy:

Mean Ecliptic and Mean Equatorial Sun.

The mean ecliptic Sun (cf. eclip. S.) moves uniformly along the ecliptic at an average speed.

The mean equatorial Sun moves along the equator at a constant speed of the mean ecliptic Sun and simultaneously passes the vernal equinox.

The time interval between two successive climaxes of the mean equatorial Sun on the same geographic meridian is called average solar day.

The time elapsed from the lower culmination of the mean equatorial Sun to any other of its positions, expressed in fractions of a mean solar day, is called mean solar timeTm.

mean solar time Tm on a given meridian at any moment is numerically equal to the hour angle of the Sun: Tm= t m+ 12h

The average time differs from the true one by the value equations of time: Tm= Tʘ +n .

6 Universal, standard and standard time

World:

The local mean solar time of the Greenwich meridian is called universal or universal time T 0 .

The local mean solar time of any point on Earth is determined by: Tm= T 0+λh

standard time:

Time is kept on 24 main geographic meridians located from each other at longitude exactly 15 (or 1 hour) approximately in the middle of each time zone. The main zero meridian is considered Greenwich. Standard time is universal time plus the time zone number: T P \u003d T 0+n

Maternity:

In Russia, in practical life, until March 2011, maternity time was used:

T D \u003d T P+ 1 h .

Decree time of the second time zone in which Moscow is located is called Moscow time. In the summer period (April-October), the clock hands were moved forward an hour, and in the winter they returned an hour ago.

7 Refraction

The apparent position of the luminaries above the horizon differs from that calculated by the formulas. Rays from a celestial object, before entering the observer's eye, pass through the Earth's atmosphere and are refracted in it. And since the density increases towards the surface of the Earth, the beam of light deviates more and more in the same direction along a curved line, so that the direction OM 1, along which the observer sees the star, turns out to be deflected towards the zenith and does not coincide with the direction OM 2, by which he would see the luminary in the absence of an atmosphere.

The phenomenon of refraction of light rays during the passage of the earth's atmosphere is called astronomical refraction. Angle M 1 OM 2 is called refractive angle or refraction ρ.

The angle ZOM 1 is called the apparent zenith distance of the star zʹ, and the angle ZOM 2 is called the true zenith distance z: z - zʹ = ρ, i.e. the true distance of the luminary is greater than the visible one by a value ρ.

On the horizon line refraction is on average equal to 35ʹ.

Due to refraction, changes in the shape of the disks of the Sun and Moon are observed when they rise or set.