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 is longest in the Northern Hemisphere 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 °.

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

Observing the daily motion of the Sun throughout the year, one can easily notice a number of features in its motion that differ from the daily motion of stars. The most characteristic of them are as follows.

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

Stars always rise and set at the same points on the horizon.

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

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

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

We will get the most visual representation of this movement of the Sun if we daily determine its equatorial coordinates - right ascension a and declination b. Then, using the found coordinate values, we plot points on the auxiliary celestial sphere and connect them with a smooth curve. As a result, we get a large circle on the sphere, which will indicate the path of the apparent 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 \u003d \u003d 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 with the celestial equator at two points, which are called the equinoxes. The point at which the Sun moves from the southern hemisphere to the northern, and therefore changes the name of the declination from south to north (i.e., from bS to bN), is called the point spring equinox and is indicated by the Y icon. This icon indicates the constellation Aries, in which this point was once located. Therefore, sometimes it is called the point of Aries. Point T is currently in the constellation Pisces.

The opposite point at which the Sun moves 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 sign of the constellation Libra O, in which it was once located. The autumnal equinox is currently in the constellation Virgo.

The point L is called summer point, and point L" - point winter solstices.

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

The sun arrives at the vernal equinox on March 21st. Right ascension a and solar declination b are zero. Throughout the globe, the Sun rises at point O st and sets at point W, and day equals night. Since March 21, the Sun moves along the ecliptic towards the point of the summer solstice. The right ascension and declination of the Sun are constantly increasing. Astronomical spring is coming in the northern hemisphere, and autumn is coming in the southern hemisphere.

On June 22, after about 3 months, the Sun comes to the point of the summer solstice L. Right ascension of the Sun a \u003d 90 °, a declination b \u003d 23 ° 27 "N. Astronomical summer begins in the northern hemisphere (the longest days and short nights), and in the south - winter (the longest nights and shortest days)... As the Sun moves further, its northern declination begins to decrease, while right ascension continues to increase.

Approximately three months later, on September 23, the Sun comes to the point of the autumnal equinox Q. Right ascension of the Sun a=180°, declination b=0°. Since b \u003d 0 ° (like March 21), then for all points on the 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. Astronomical autumn comes in the northern hemisphere, and spring in the southern hemisphere. With further movement of the Sun along the ecliptic to the point of the winter solstice U, declination 6 and right ascension aO increase.

On December 22, the Sun comes to the point of the winter solstice L ". Right ascension a \u003d 270 ° and declination b \u003d 23 ° 27" S. In the northern hemisphere, astronomical winter sets in, and in the southern hemisphere, summer.

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

Changes in the right ascension and declination of the Sun during the year do not remain constant. 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 equal to 0°.4 for one month before the equinox and one month after, and the change of 0°.1 for one month before the solstices and one month after the solstices; the rest of the time, the change in the declination of the Sun is taken equal to 0 °.3.

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

The vernal equinox 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 50 "3. For the Sun to pass the indicated path, 20 m m 24 s will be needed. For this reason, spring

It comes before the Sun finishes and its apparent annual movement is 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. BC e. from the observations of the stars he made on the island of Rhodes. He called this phenomenon the precession of the equinoxes, or precession.

The phenomenon of the movement of the vernal equinox necessitated the introduction of the concepts of tropical and sidereal years. A tropical year is a period of time during which the Sun makes a complete revolution in the celestial sphere relative to the vernal equinox point T. "The duration of a tropical year is 365.2422 days. A tropical year is consistent with natural phenomena and accurately contains the full cycle of the seasons of the year: spring, summer, autumn and winter.

A sidereal year is a period of time during which the Sun makes a complete revolution in the celestial sphere relative to the stars. The duration 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 zodiac.

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

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

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

In the joint motion of the Sun, which occurs along the ecliptic with the simultaneous rotation of the celestial sphere, there are a number of features: the length of the daily parallel above the horizon and below the horizon changes (and, consequently, the length of day and night), the meridional heights of the Sun, the points of sunrise and sunset, etc. All these phenomena depend on the relationship between the geographic latitude of a place and the declination of the Sun. Therefore, for an observer located at different latitudes, they will be different.

Consider these phenomena in 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 daily parallels of the Sun are parallel to the first vertical, so 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 - March 21 and September 23.

Rice. 83.

2. The observer is in latitude φ
3. The observer is in latitude 23°27"
4. The observer is in latitude φ\u003e 66 ° 33 "N or S (Fig. 83). The belt is polar. Parallels φ \u003d 66 ° 33" N or S are called polar circles. Polar days and nights can be observed in the polar belt, i.e., 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 position of the observer's meridian 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 its greatest values. The altitude of the Sun is always equal to its declination. Polar day and polar night last for 6 months.

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

tropical belt the part of the earth's surface is called (between the latitudes φ \u003d 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 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 belts. The northern polar belt extends from latitude φ \u003d 66 ° 33 "N to the north pole, and the southern - from φ \u003d 66 ° 33" S to the south pole. They occupy 10% of the earth's surface.

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

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 a change of day and night. Its movement around the Sun causes the change of seasons. From the joint rotation of the Earth around its axis and movement around the Sun, the apparent movement of the Sun in the celestial sphere occurs.

To explain the apparent annual motion of the Sun in the celestial sphere, we use Fig. 84. In the center is the Sun S, around which the Earth moves counterclockwise. The earth's axis maintains an unchanged position in space and makes an angle equal to 66 ° 33 with the ecliptic plane. Therefore, the equatorial 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 constellations of the Zodiac inscribed on it in their current location.

The Earth comes into position I on March 21st. Seen from Earth, the Sun is projected onto the celestial sphere at point T, currently in the constellation Pisces. Declination of the Sun be=0°. An observer at the Earth's equator sees the Sun at noon at its zenith. All terrestrial parallels are illuminated by half, therefore, 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. Sun declination 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. The northern polar belt is illuminated and the southern one is not illuminated. The polar day lasts in the northern, and in the south - 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 sets in in the northern hemisphere, and winter in the southern hemisphere.

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

December 22 Earth comes to position IV The sun is projected into the constellation Sagittarius. Sun declination 6=23°,5S. In the southern hemisphere, more of the daily parallels are illuminated than in the northern, so in the southern hemisphere the day is longer than the night, and in the northern hemisphere it is vice versa. The rays of the sun fall almost vertically into the southern hemisphere, and at an angle into the northern hemisphere. Therefore, astronomical summer comes in the southern hemisphere, and winter in the northern hemisphere. The sun illuminates the southern polar belt and does not illuminate the northern one. The polar day is observed in the southern polar belt, and the night is observed in the northern one.

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

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Daily path of the Sun. Every day, as it rises from the horizon in the eastern side of the sky, the Sun passes through 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. During 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 annual path of the Sun 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 their northern hemisphere to the south. 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 measured - 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 point. The tropical year determines the change of seasons on our planet. Since the spring point equinox slowly moves among the stars due to the precession of the earth's axis, the duration of the tropical about a year less than the duration of the sidereal. 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 designated 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 equinox (from March 21 to September 23) the Sun takes 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 summer, the Earth receives less heat from the Sun, but summer in the Northern Hemisphere is longer than winter. Therefore, the Northern Hemisphere is warmer than the Southern Hemisphere.

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.

Place a chair in the middle of the room and, turning to face it, make several circles around it. And it does not 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 items of room furnishings.

In the same way, the Earth revolves around the Sun, and it seems to us, the inhabitants of the Earth, that the Sun moves against the background of the stars, making a complete revolution across the sky in one year. This movement of the Sun is called annual. In addition, the Sun, like all other celestial bodies, is involved 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 complete revolution along the ecliptic in a year, i.e. in about 365 days, so the Sun moves 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 map of the starry sky:

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 it is the equatorial part of the southern hemisphere.

The thick wavy line depicts 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 region 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 the 12 zodiac constellations and one more - in Ophiuchus (from November 29 to December 17),

There are four special points on the ecliptic.

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

LS - the point of the summer solstice, - the point of the ecliptic, located in the northern hemisphere of the sky and the most distant from the celestial equator.

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

ZS - the point of the winter solstice, - the point of the ecliptic, located in the southern hemisphere of the sky and the most distant from the celestial equator.

ecliptic point	The sun is at a given point on the ecliptic	Start of the astronomical season
spring equinox
Summer Solstice
autumnal equinox
winter solstice

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

Currently, this is not a problem at all, because. the brightest 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 one's 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 that are 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.