§ 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 at the point of the east and sets at the point of the west) until 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 passes from the southern hemisphere to the northern, and consequently 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 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 a 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 movement of the Sun in the celestial sphere is not its actual movement, but only the visible one, reflecting the annual movement 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 located 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.