The apparent annual path of the sun among the stars is called. Apparent annual movement of the sun

Annual path of the Sun

The expression “the path of the Sun among the stars” may seem strange to some. After all, you can’t see the stars during the day. Therefore, it is not easy to notice that the Sun slowly, 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 throughout the year. All this is a consequence of the Earth’s revolution 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 “eclipse” - “eclipse”), and the period of rotation along the ecliptic is called the sidereal year. It is equal to 265 days 6 hours 9 minutes 10 seconds, or 365.2564 average solar days.

The ecliptic and the celestial equator intersect at an angle of 23˚26" at the points of the spring and autumn equinox. The Sun usually appears at the first of these points on March 21, when it moves from the southern hemisphere of the sky to the northern. At the second - on September 23, when it passes northern hemisphere to the south. At the point of the ecliptic most distant to the north, the Sun occurs on June 22 (summer solstice), and to the south - on December 22 (winter solstice). IN leap year these dates are shifted by one day.

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

Since the point of the vernal equinox moves slowly 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 year. It is 365.2422 average solar days.

About 2 thousand years ago, when Hipparchus compiled his star catalog (the first to come down to us in its entirety), the vernal equinox was located in the constellation Aries. By our time, it has moved almost 30˚ to the constellation Pisces, and the point of the autumnal equinox has moved from the constellation Libra to the constellation Virgo. But according to tradition, the points of the equinoxes are designated by the former signs of the former “equinox” constellations - Aries and Libra. The same thing happened with the solstice points: the summer one in the constellation Taurus is marked by the sign of Cancer, and the winter one in the constellation Sagittarius is marked by the sign of Capricorn.

And finally, the last thing is related to the apparent annual movement of the Sun. The Sun passes half of the ecliptic from the spring equinox to the autumn equinox (from March 21 to September 23) in 186 days. The second half, from the autumn and spring equinox, takes 179 days (180 in a leap year). But the halves of the ecliptic are equal: each is 180˚. Consequently, the Sun moves unevenly along the ecliptic. This unevenness is explained by changes 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 durations 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 5 million kilometers longer from the Sun than on January 2-3, and moves more slowly in its orbit in accordance with Kepler’s second law. In summer, the Earth receives less heat from the Sun, but summer in the Northern Hemisphere is longer than winter. Therefore, the Northern Hemisphere of the Earth is warmer than the Southern Hemisphere.

SOLAR ECLIPSE

At the moment of the lunar new moon, a solar eclipse can occur - after all, it is during the new moon that the Moon passes between the Sun and the Earth. Astronomers know in advance when and where a solar eclipse will be observed, and report this in astronomical calendars.

The Earth got only one satellite, but what a satellite! Moon 400 times smaller than the sun and just 400 times closer to the Earth, so in the sky the Sun and Moon appear to be disks of the same size. So in full solar eclipse The Moon completely obscures the bright surface of the Sun, leaving the entire solar atmosphere exposed.

Exactly at the appointed hour and minute, through the dark glass you can see how something black creeps onto the bright disk of the Sun from the right edge, and how a black hole appears on it. It gradually grows until finally the solar circle takes the form of a narrow sickle. At the same time, daylight quickly weakens. Here the Sun completely hides behind a dark curtain, the last ray of daylight goes out, and the darkness, which seems the deeper the more sudden it is, spreads out around, plunging man and all of nature into silent surprise.

English astronomer Francis Bailey talks about the eclipse of the Sun on July 8, 1842 in the city of Pavia (Italy): “When it came full eclipse And sunlight instantly extinguished, some bright radiance suddenly appeared around the dark body of the Moon, similar to a crown or a halo around the head of a saint. No reports of past eclipses had described anything like this, and I did not at all expect to see the splendor that was now before my eyes. The width of the crown, based on the circumference of the Moon's disk, was equal to approximately half the lunar diameter. It seemed composed of bright rays. Its light was denser near the very edge of the Moon, and as it moved away, the rays of the crown became weaker and thinner. The weakening of the light proceeded completely smoothly along with the increase in distance. The crown was presented in the form of beams of straight weak rays; their outer ends fanned out; the rays were of unequal length. The crown was not reddish, not pearl, it was completely white. Its rays shimmered or flickered like a gas flame. No matter how brilliant this phenomenon was, no matter how much delight it aroused among the spectators, there was still something sinister in this strange, wondrous spectacle, and I fully understand how shocked and frightened people could have been at the time when these phenomena happened completely unexpectedly.

The most surprising detail of the whole picture was the appearance of three large protrusions (prominences) that rose above the edge of the Moon, but obviously formed part of the crown. They looked like mountains of enormous height, like the snowy peaks of the Alps when they are illuminated by the red rays of the setting Sun. Their red color faded into lilac or purple; perhaps a peach blossom shade would be best suited here. The light of the protrusions, in contrast to the rest of the crown, was completely calm, the “mountains” did not sparkle or shimmer. All three protrusions, slightly different in size, were visible until the last moment of the total phase of the eclipse. But as soon as the first ray of the Sun broke through, the prominences, along with the corona, disappeared without a trace, and the bright light of day was immediately restored." This phenomenon, so subtly and colorfully described by Bailey, lasted just over two minutes.

Remember Turgenev's boys on Bezhinsky meadow? Pavlusha talked about how the Sun was no longer visible, about a man with a jug on his head, who was mistaken for the Antichrist Trishka. So this was a story about the same eclipse on July 8, 1842!

But there was no eclipse in Rus' greater than that described in “The Tale of Igor’s Campaign” and the ancient chronicles. In the spring of 1185, the Novgorod-Seversk prince Igor Svyatoslavich and his brother Vsevolod, filled with military spirit, went against the Polovtsians to gain glory for themselves and booty for their squad. On May 1, in the late afternoon, as soon as the regiments of the “Dazhd-God’s grandchildren” (descendants of the Sun) entered the foreign land, it grew dark earlier than expected, the birds fell silent, the horses neighed and did not move, the shadows of the horsemen were unclear and strange, the steppe breathed with cold. Igor looked around and saw that the “sun standing like a moon” was seeing them off. And Igor said to his boyars and his squad: “Do you see? What does this radiance mean??” They looked, and saw, and bowed their heads. And the men said: “Our prince! This radiance does not promise us good!” Igor answered: “Brothers and squad! The secret of God is unknown to anyone. And what God gives us - for our good or for our misfortune - we will see.” On the tenth day of May, Igor’s squad was killed in the Polovtsian steppe, and the wounded prince was captured.

Place a chair in the middle of the room and, facing it, make several circles around it. And it doesn’t matter that the chair is motionless - it will seem to you that it is moving in space, because it will be visible against the background of various objects in the room’s furnishings.

In the same way, the Earth revolves around the Sun, and to us, the inhabitants of the Earth, it seems that the Sun moves against the background of the stars, making a full revolution across the sky in one year. This movement of the Sun is called annual. In addition, the Sun, like all others celestial bodies, participates in the daily movement of the sky.

The path among the stars along which the annual movement of the Sun occurs is called the ecliptic.

The Sun makes a full revolution along the ecliptic in a year, i.e. approximately in 365 days, so the Sun moves by 360°/365≈1° per day.

Since the Sun moves approximately along the same path from year to year, i.e. The position of the ecliptic among the stars changes over time very, very slowly; the ecliptic can be plotted on a star map:

Here the purple line is the celestial equator. Above it is the part of the northern hemisphere of the sky adjacent to the equator, below is the equatorial part of the southern hemisphere.

The thick wavy line represents the annual path of the Sun across the sky, i.e. ecliptic. At the top it is written which season of the year begins in the northern hemisphere of the Earth when the Sun is in the corresponding area of the sky.

The image of the Sun on the map moves along the ecliptic from right to left.

During the year, the Sun manages to visit 12 zodiac constellations and one more - Ophiuchus (from November 29 to December 17),

There are four special points on the ecliptic.

BP is the point of the vernal equinox. The sun, passing through the vernal equinox, falls from the southern hemisphere of the sky to the northern.

LS is the point of the summer solstice, a point on the ecliptic located in the northern hemisphere of the sky and farthest from the celestial equator.

OR is the point of the autumnal equinox. The sun, passing through the autumn equinox, falls from the northern hemisphere of the sky into the southern.

ZS is the winter solstice point, a point on the ecliptic located in the southern hemisphere of the sky and farthest from the celestial equator.

Ecliptic point	The sun is at a given point on the ecliptic	Beginning of the astronomical season
Spring equinox
Summer Solstice
Autumn equinox
Winter Solstice

Finally, how do you know that the Sun is actually moving across the sky among the stars?

Currently this is not a problem at all, because... most bright stars are visible through a telescope even during the day, so the movement of the Sun among the stars with the help of a telescope can, if desired, be seen with your own eyes.

In the pre-telescopic era, astronomers measured the length of the shadow from the gnomon, a vertical pole, which allowed them to determine the angular distance of the Sun from the celestial equator. In addition, they observed not the Sun itself, but stars diametrically opposite to the Sun, i.e. those stars that were highest above the horizon at midnight. As a result, ancient astronomers determined the position of the Sun in the sky and, consequently, the position of the ecliptic among the stars.

1 Annual movement of the Sun and the ecliptic coordinate system

The Sun, along with its daily rotation, slowly moves throughout the celestial sphere in the opposite direction in a large circle throughout the year, called the ecliptic. The ecliptic is inclined to the celestial equator at an angle of Ƹ, the magnitude of which 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, spaced 90 degrees 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 throughout the year from 0h to 24h (right ascension) - ecliptic longitude ϒm, measured from the vernal equinox point 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. Zodiacal constellations are the constellations that are located on the ecliptic line. There are 13 constellations on the ecliptic line: 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 Sagittarius and Scorpio. This is done for convenience. When the Sun is below the horizon at altitudes from 0 to -6, civil twilight lasts, and from -6 to -18, astronomical twilight lasts.

2 Time measurement

The measurement of time is based on observations of the daily rotation of the arch and the annual movement of the Sun, i.e. the rotation of the Earth around its axis and the revolution of the Earth around the Sun.

The duration of the basic unit of time, called a day, depends on the selected point in the sky. In astronomy, such points are taken to be:

Vernal equinox ♈ ( sidereal time);

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

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

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

Tropical year- the period of time 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 point spring equinox towards the Sun, called precession, relative to the stars, the Sun appears at the same point in the sky after a period of time of 20 minutes. 24 sec. greater than a tropical year. It is called sidereal year and contains 365.2564 mean solar days.

3 Sidereal time

The time interval between two successive culminations of the vernal equinox on the same geographical meridian is called sidereal day.

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 star plus its hour angle.

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

4 True solar time

The time interval between two successive culminations of the Sun (the center of the solar disk) on the same geographical meridian is called I'm on true sunny days.

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

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

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

5 Mean solar time

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

Mean ecliptic and mean equatorial Sun.

The average ecliptic Sun (average 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 culminations of the mean equatorial Sun on the same geographic meridian is called average sunny day.

The time elapsed from the lower culmination of the mean equatorial Sun to any other position, expressed in fractions of the 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+ 12 h

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

6 Worldwide, standard and maternity time

Worldwide:

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

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

Standard time :

Time is counted on 24 main geographical meridians, located from each other at longitude exactly 15 (or 1 hour) approximately in the middle of each time zone. Main prime meridian considered Greenwich. Standard time is universal time plus the time zone number: T P = T 0+n

Maternity leave:

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

T D = T P+ 1 h.

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

7 Refraction

The apparent position of the luminaries above the horizon differs from that calculated using the formulas. Rays from celestial object, before hitting the observer's eye, pass through the Earth's atmosphere and are refracted in it. And as the density increases towards the surface of the Earth, the ray of light is increasingly deflected in the same direction along a curved line, so that the direction OM 1, in which the observer sees the body, 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 when passing through the earth's atmosphere is called astronomical refraction. Angle M 1 OM 2 is called refraction angle or refraction ρ.

Angle ZOM 1 is called the apparent zenith distance of the luminary zʹ, and 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 an amount ρ.

On the horizon refraction 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.

Movement of the Sun among the stars

(lesson - lecture)

This lesson is for studentsXIclasses studying according to the textbookG.Ya. Myakisheva, B.B. Bukhovtsev “Physics. 11th grade" (specialized classes)

Educational purpose of the lesson: study the movement of the Sun relative to distant stars.

Educational objectives of the lesson:

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

To develop students’ skills in finding and identifying the main planes, lines, points of the celestial sphere associated with the movement of the Sun;

To develop students’ skills in determining the horizontal coordinates of the Sun;

General remarks

The information in the lecture is presented in a condensed form, so a short phrase may require a lot of thought. The development of the need for reflection, and, consequently, for students to understand the content of a particular topic, is correlated with the completion of tasks:

Practical advice when 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 the question “why?” and independently find the answer along the way, reflecting, talking with comrades, the teacher;

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

Main questions of the lecture

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 visible things occur annual movement Sun. The direction of this movement (about 1 per day) is opposite to the direction of the Earth's daily rotation. The word "ecliptic" comes from the Greek word "eclipse" - eclipse.

The axis of rotation of the Earth has a constant angle of inclination to the plane of rotation 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 blanks in the definitions below.

Ecliptic axis (EA)") - ………………

………………………………………….. .

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

South Pole of the Ecliptic (S") - ………………………………………………………………………….. .

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

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

Summer solstice point and winter solstice point - points spaced 90° from the equinoxes. The summer solstice point lies in the northern hemisphere and falls on June 22. The winter solstice lies in the southern hemisphere and falls on December 22.

Ecliptic coordinate system.

Figure 2. Ecliptic coordinate system

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

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 planetary motion. This is convenient because the planets move relative to the stars approximately in the ecliptic plane. Due to the smallness β formulas containing cos β and sin β can be simplified.

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

Movement of heavenly bodies

Daily movement of the luminaries. Daily allowance 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 stars is a consequence of the rotation of the Earth around its axis. The visibility of luminaries depends on their celestial coordinates and 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 the middle geographical latitudes; b – at the equator; c – at the Earth’s pole.

1. Formulate a theorem about the height of the celestial 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 its luminary change during the daily movement: a) height; b) right ascension; c) declination?

Does the altitude, 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 a luminary crossing the celestial meridian. At the upper culmination the luminary has its greatest height. The azimuth of the star at the upper culmination is ……. And at the bottom - the smallest. The azimuth of the luminary 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.

IN height of the luminary ( h) or zenith distance ( z) at the moment of culmination depends on the declination of the luminary ( 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 formulas for determining the height of the luminary at the upper and lower culmination. The type of expression for the height of the luminary at the culmination is determined based on Figure 4.

Table 3

Height of the luminary at its climax

Declination of the luminary

Height of the luminary at the upper culmination

Height of the luminary at the lower culmination

δ < φ

h =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 is δ< -(90˚- φ ), то оно будет невосходящим. Если склонение светила δ >(90˚-φ), it will be non-setting.

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

Annual movement 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 Earth’s movement around the Sun in an elliptical orbit in the direction of the Earth’s rotation around its axis, i.e. counterclockwise when viewed from north pole to the south (see Fig. 5).

Figure 5. Earth's axis tilt and seasons

Figure 6. Diagram of the Earth’s positions at the summer and winter solstices

During the annual movement of the Sun, the following phenomena occur: changes in midday altitude, the position of the sunrise and sunset points, the duration of day and night, and 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 relative to the Earth's surface and the different degrees 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, the change in the distance from the Earth to the Sun during the year does not affect the change of seasons: the Earth, running through its elliptical orbit, is at its closest point in January, and at its most distant in July.

Using the lecture material, fill out Table 4.

Table 4

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

Position on the ecliptic

Declension

Midday height

Minimum height

sunrise point

Call point

Length of day

20(21) .03

22.06

22(23).09

22.12

Astronomical signs of thermal belts:

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

If a certain star is at its zenith at 9 pm on September 1, at what time will it be at its zenith on March 1? Will you be able to see her? Justify your 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 ecliptic axis, 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, near the North Pole of the world there was a star called α Draco, 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 the polar star will be Vega (α Lyrae).

Figure 7. Precessional movement of the earth's axis

As a result of precession, the points of the spring and autumn equinoxes, summer and winter solstices slowly move along the zodiacal constellations. 5000 years ago, the vernal equinox point was in the constellation Taurus, then moved to the constellation Aries, and is now in the constellation 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 rotation axis, but it acts on the Earth's movement 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. A change in the position of the ecliptic plane introduces a change, firstly, in the value of the speed of movement of the equinox points as a result of precessional movement (v = 50", 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 rotation axis 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 when these luminaries are at their greatest distance from it.

As a result of precession and nutation of the earth's axis, the poles of the world 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 rotation axis in space. The body Earth remains in this case, so to speak, fixed in relation to the changing axis. Therefore, the flag planted today at the North Pole will still mark the North Pole in 13,000 years, and the latitude of the point will remain equal to 90°. Since neither precession nor nutation lead to any changes in latitude on Earth, these phenomena do not cause climate change. 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 celestial bodies rise and set for an observer located in the northern (southern) hemisphere of the Earth?

How are astronomical coordinate systems constructed?

What is the height and azimuth of a star called?

What are the equatorial and ecliptic coordinates called?

How are right ascension and hour angle related?

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

What are precession and nutation?

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

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

What is the ecliptic?

Which points are called equinoxes and why?

What is solstice?

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

In what case can the ecliptic coincide with the horizon?

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

Using the marked points, mark the position of the ecliptic. Indicate on the ecliptic (approximately) the position of the Sun on April 21, October 23 and on 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.: Education, 1965. – 227 p.

Malakhov A.A. Physics and astronomy (competency-based approach): educational method. allowance / A.A. Malakhov; Shadr. state ped. int. – Shadrinsk: Shadr. House of Printing, 2010. – 163 p.

Mayorov, V.F. How do you know that the Earth rotates? / V.F. Mayorov // Physics. - 2010. – No. 2. - P. 45-47.

Myakishev G.Ya., Bukhovtsev B.B., Sotsky N.N. Physics: Textbook. For 10th grade. educational institutions. – M.: Education, 2010.

Pinsky A.A., Razumovsky V.G., Bugaev A.I. and others. Physics and astronomy: Textbook for 9th grade. general education Institutions / Ed. A.A. Pinsky, V.G. Razumovsky.- M.: Education, 2001. – P. 202-212

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§ 52. Apparent annual motion of the Sun and its explanation

Observing the daily movement of the Sun throughout the year, one can easily notice a number of features in its movement that differ from the daily movement of stars. The most typical of them are the following.

1. The place of sunrise and sunset, and therefore its azimuth, changes from day to day. Starting from March 21 (when the Sun rises at the point of the east and sets at the point of the west) to September 23, the sun rises in the north-east quarter, and sunset - in the north-west. At the beginning of this time, the sunrise and sunset points move north and then in the opposite direction. On September 23, just like on March 21, the Sun rises at the east point and sets at the west point. Starting from September 23 to March 21, a similar phenomenon will repeat in the southeast and southwest quarters. The movement of sunrise and sunset points has a one-year period.

The stars always rise and set at the same points on the horizon.

2. The meridional altitude of the Sun changes every day. For example, in Odessa (average = 46°.5 N) on June 22 it will be greatest and equal to 67°, then it will begin to decrease and on December 22 it will reach its lowest value of 20°. After December 22, the meridional altitude of the Sun will begin to increase. This is also a one-year phenomenon. The meridional altitude of stars is always constant. 3. The duration of time between the culminations of any star and the Sun is constantly changing, while the duration of time between two culminations of the same stars remains constant. So, at midnight we see those constellations culminating that are currently located on the opposite side of the sphere from the Sun. Then some constellations give way to others, and over the course of a year at midnight all the constellations will culminate in turn.

4. The length of the day (or night) is not constant throughout the year. This is especially noticeable if you compare the length of summer and winter days in high latitudes, for example in Leningrad. This happens because the time the Sun is above the horizon varies throughout the year. The stars are always above the horizon for the same amount of time.

Thus, the Sun, in addition to the daily movement performed jointly with the stars, also has a visible movement around the sphere with an annual period. This movement is called visible the annual movement of the Sun across the celestial sphere.

We will get the most clear idea of this movement of the Sun if we determine its equatorial coordinates every day - right ascension a and declination b. Then, using the found coordinate values, we plot the points on the auxiliary celestial sphere and connect them with a smooth curve. As a result, we obtain a large circle on the sphere, which will indicate the path of the visible annual movement of the Sun. The circle on the celestial sphere along which the Sun moves is called the ecliptic. The plane of the ecliptic is inclined to the plane of the equator at a constant angle g = =23°27", which is called the angle of inclination ecliptic to equator(Fig. 82).

Rice. 82.

The apparent annual movement of the Sun along the ecliptic occurs in the direction opposite to the rotation of the celestial sphere, that is, from west to east. The ecliptic intersects the celestial equator at two points, which are called the equinox points. The point at which the Sun passes from the southern hemisphere to the northern, and therefore changes the name of the declination from southern to northern (i.e. from bS to bN), is called the point spring equinox and is designated by the Y icon. This icon denotes the constellation Aries, in which this point was once located. Therefore, it is sometimes called the Aries point. Currently, point T is located in the constellation Pisces.

The opposite point at which the Sun passes from the northern hemisphere to the southern and changes the name of its declination from b N to b S is called point of the autumnal equinox. It is designated by the symbol of the constellation Libra O, in which it was once located. Currently, the autumn equinox point is in the constellation Virgo.

Point L is called summer point, and point L" - a point winter solstice.

Let's follow the apparent movement of the Sun along the ecliptic throughout the year.

The Sun arrives at the vernal equinox on March 21st. The right ascension a and declination b of the Sun are zero. Throughout the globe, the Sun rises at point O st and sets at point W, and day is equal to night. Starting March 21, the Sun moves along the ecliptic towards the summer solstice point. The right ascension and declination of the Sun are continuously increasing. It is astronomical spring in the northern hemisphere, and autumn in the southern hemisphere.

On June 22, approximately 3 months later, the Sun comes to the summer solstice point L. The direct ascension of the Sun is a = 90°, a declination b = 23°27"N. In the northern hemisphere, astronomical summer begins (the longest days and shortest nights), and in the south - winter (the longest nights and shortest days). With the further movement of the Sun, its northern declination begins to decrease, and its right ascension continues to increase.

About three more months later, on September 23, the Sun comes to the point of the autumnal equinox Q. The direct ascension of the Sun is a=180°, declination b=0°. Since b = 0 ° (same as March 21), then for all points earth's surface The sun rises at point O st and sets at point W. Day will be equal to night. The name of the declination of the Sun changes from northern 8n to southern - bS. In the northern hemisphere, astronomical autumn begins, and in the southern hemisphere, spring begins. With further movement of the Sun along the ecliptic to the winter solstice point U, declination 6 and right ascension aO increase.

On December 22, the Sun comes to the winter solstice point L". Right ascension a=270° and declination b=23°27"S. Astronomical winter begins in the northern hemisphere, and summer begins in the southern hemisphere.

After December 22, the Sun moves to point T. The name of its declination remains southern, but decreases, and its right ascension increases. Approximately 3 months later, on March 21, the Sun, having completed a full revolution along the ecliptic, returns to the point of Aries.

Changes in the right ascension and declination of the Sun do not remain constant throughout the year. For approximate calculations, the daily change in the right ascension of the Sun is taken equal to 1°. The change in declination per day is taken to be 0°.4 for one month before the equinox and one month after, and the change is 0°.1 for one month before the solstices and one month after the solstices; the rest of the time, the change in solar declination is taken to be 0°.3.

The peculiarity of changes in the right ascension of the Sun plays an important role when choosing the basic units for measuring time.

The vernal equinox point moves along the ecliptic towards the annual movement of the Sun. Its annual movement is 50", 27 or rounded 50",3 (for 1950). Consequently, the Sun does not reach its original place relative to the fixed stars by an amount of 50",3. For the Sun to travel the indicated path, it will take 20 mm 24 s. For this reason, spring

It occurs before the Sun completes its visible annual motion, a full circle of 360° relative to the fixed stars. The shift in the moment of the onset of spring was discovered by Hipparchus in the 2nd century. BC e. from observations of stars that he made on the island of Rhodes. He called this phenomenon the anticipation of the equinoxes, or precession.

The phenomenon of moving the vernal equinox point caused the need to introduce the concepts of tropical and sidereal years. The tropical year is the period of time during which the Sun makes a full revolution across the celestial sphere relative to the point of the vernal equinox T. “The duration of the tropical year is 365.2422 days. The tropical year is consistent with natural phenomena and precisely contains the full cycle of the seasons of the year: spring, summer, autumn and winter.

A sidereal year is the period of time during which the Sun makes a complete revolution across the celestial sphere relative to the stars. The length of a sidereal year is 365.2561 days. The sidereal year is longer than the tropical year.

In its apparent annual movement across the celestial sphere, the Sun passes among various stars located along the ecliptic. Even in ancient times, these stars were divided into 12 constellations, most of which were given the names of animals. The strip of sky along the ecliptic formed by these constellations was called the Zodiac (circle of animals), and the constellations were called zodiacal.

According to the seasons of the year, the Sun passes through the following constellations:

From the joint movement of the annual Sun along the ecliptic and the daily movement due to the rotation of the celestial sphere, the general movement of the Sun along a spiral line is created. The extreme parallels of this line are located on both sides of the equator at distances of = 23°.5.

On June 22, when the Sun describes the extreme diurnal parallel in the northern celestial hemisphere, it is in the constellation Gemini. In the distant past, the Sun was in the constellation Cancer. On December 22, the Sun is in the constellation Sagittarius, and in the past it was in the constellation Capricorn. Therefore, the northernmost celestial parallel was called the Tropic of Cancer, and the southern one was called the Tropic of Capricorn. The corresponding terrestrial parallels with latitudes cp = bemach = 23°27" in the northern hemisphere were called the Tropic of Cancer, or the northern tropic, and in the southern hemisphere - the Tropic of Capricorn, or the southern tropic.

The joint movement of the Sun, which occurs along the ecliptic with the simultaneous rotation of the celestial sphere, has a number of features: the length of the daily parallel above and below the horizon changes (and therefore the duration of day and night), the meridional heights of the Sun, the points of sunrise and sunset, etc. d. All these phenomena depend on the relationship between the geographical latitude of the place and the declination of the Sun. Therefore, for an observer located in different latitudes, they will be different.

Let's consider these phenomena at some latitudes:

1. The observer is at the equator, cp = 0°. The axis of the world lies in the plane of the true horizon. The celestial equator coincides with the first vertical. The diurnal parallels of the Sun are parallel to the first vertical, therefore the Sun in its daily movement never crosses the first vertical. The sun rises and sets daily. Day is always equal to night. The Sun is at its zenith twice a year - on March 21 and September 23.

Rice. 83.

2. The observer is at latitude φ
3. The observer is at latitude 23°27"
4. The observer is at latitude φ > 66°33"N or S (Fig. 83). The belt is polar. Parallels φ = 66°33"N or S are called polar circles. In the polar zone, polar days and nights can be observed, that is, when the Sun is above the horizon for more than a day or below the horizon for more than a day. The longer the polar days and nights, the greater the latitude. The sun rises and sets only on those days when its declination is less than 90°-φ.

5. The observer is at the pole φ=90°N or S. The axis of the world coincides with the plumb line and, therefore, the equator with the plane of the true horizon. The observer's meridian position will be uncertain, so parts of the world are missing. During the day, the Sun moves parallel to the horizon.

On the days of the equinoxes, polar sunrises or sunsets occur. On the days of the solstices, the height of the Sun reaches highest values. The altitude of the Sun is always equal to its declination. The polar day and polar night last for 6 months.

Thus, due to various astronomical phenomena caused by the combined daily and annual movement of the Sun at different latitudes (passage through the zenith, polar day and night phenomena) and the climatic features caused by these phenomena, the earth's surface is divided into tropical, temperate and polar zones.

Tropical zone is the part of the earth's surface (between latitudes φ=23°27"N and 23°27"S) in which the Sun rises and sets every day and is at its zenith twice during the year. The tropical zone occupies 40% of the entire earth's surface.

Temperate zone called the part of the earth's surface in which the Sun rises and sets every day, but is never at its zenith. There are two temperate zones. In the northern hemisphere, between latitudes φ = 23°27"N and φ = 66°33"N, and in the southern hemisphere, between latitudes φ=23°27"S and φ = 66°33"S. Temperate zones occupy 50% of the earth's surface.

Polar belt called the part of the earth's surface in which polar days and nights are observed. There are two polar zones. The northern polar belt extends from latitude φ = 66°33"N to the north pole, and the southern one - from φ = 66°33"S to south pole. They occupy 10% of the earth's surface.

For the first time, the correct explanation of the visible annual movement of the Sun across the celestial sphere was given by Nicolaus Copernicus (1473-1543). He showed that the annual movement of the Sun across the celestial sphere is not its actual movement, but only an apparent one, reflecting the annual movement of the Earth around the Sun. The Copernican world system was called heliocentric. According to this system in the center solar system There is the Sun, around which the planets move, including our Earth.

The Earth simultaneously participates in two movements: it rotates around its axis and moves in an ellipse around the Sun. The rotation of the Earth around its axis causes the cycle of day and night. Its movement around the Sun causes the change of seasons. The combined rotation of the Earth around its axis and the movement around the Sun causes the visible movement of the Sun across the celestial sphere.

To explain the apparent annual movement of the Sun across the celestial sphere, we will use Fig. 84. The Sun S is located in the center, around which the Earth moves counterclockwise. The earth's axis remains unchanged in space and makes an angle with the ecliptic plane equal to 66°33". Therefore, the equator plane is inclined to the ecliptic plane at an angle e=23°27". Next comes the celestial sphere with the ecliptic and the signs of the Zodiac constellations marked on it in their modern location.

The Earth enters position I on March 21. When viewed from the Earth, the Sun is projected onto the celestial sphere at point T, currently located in the constellation Pisces. The declination of the Sun is 0°. An observer located at the Earth's equator sees the Sun at its zenith at noon. All earthly parallels are half illuminated, so at all points on the earth's surface day is equal to night. Astronomical spring begins in the northern hemisphere, and autumn begins in the southern hemisphere.

Rice. 84.

The Earth enters position II on June 22. Declination of the Sun b=23°,5N. When viewed from Earth, the Sun is projected into the constellation Gemini. For an observer located at latitude φ=23°.5N, (The sun passes through the zenith at noon. Most of the daily parallels are illuminated in the northern hemisphere and a smaller part in the southern hemisphere. The northern polar zone is illuminated and the southern one is not illuminated. In the northern, the polar day lasts, and in the southern hemisphere it is polar night. In the northern hemisphere of the Earth, the rays of the Sun fall almost vertically, and in the southern hemisphere - at an angle, so astronomical summer begins in the northern hemisphere, and winter in the southern hemisphere.

The Earth enters position III on September 23. The declination of the Sun is bo = 0 ° and it is projected at the point of Libra, which is now located in the constellation Virgo. An observer located at the equator sees the Sun at its zenith at noon. All earthly parallels are half illuminated by the Sun, so at all points on the Earth day is equal to night. In the northern hemisphere, astronomical autumn begins, and in the southern hemisphere, spring begins.

On December 22, the Earth comes to position IV. The Sun is projected into the constellation Sagittarius. Declination of the Sun 6=23°.5S. The southern hemisphere receives more daylight than the northern hemisphere, so daylight in the southern hemisphere longer than the night, and in the north - vice versa. The sun's rays fall almost vertically into the southern hemisphere, and at an angle into the northern hemisphere. Therefore, astronomical summer begins in the southern hemisphere, and winter begins in the northern hemisphere. The sun illuminates the southern polar zone and does not illuminate the northern one. The southern polar zone experiences polar day, while the northern zone experiences night.

Corresponding explanations can be given for other intermediate positions of the Earth.

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