The apparent annual movement of the sun on the celestial sphere. Astrological roots in modern astronomy The sun is at a given point on the ecliptic

Due to the annual revolution of the Earth around the Sun in the direction from West to East, it seems to us that the Sun moves among the stars from West to East along a large circle of the celestial sphere, which is called ecliptic, with a period of 1 year . The plane of the ecliptic (the plane of the earth's orbit) is inclined to the plane of the celestial (as well as the earth's) equator at an angle. This angle is called ecliptic inclination.

The position of the ecliptic on the celestial sphere, that is, the equatorial coordinates of the points of the ecliptic and its inclination to the celestial equator are determined from daily observations of the Sun. By measuring the zenith distance (or height) of the Sun at the moment of its upper culmination at the same geographical latitude,

,	(6.1)
,	(6.2)

It can be established that the declination of the Sun throughout the year varies from to . In this case, the direct ascension of the Sun varies throughout the year from to, or from to.

Let's take a closer look at the change in the coordinates of the Sun.

At the point spring equinox^, which the Sun passes annually on March 21, the right ascension and declination of the Sun are zero. Then, every day the right ascension and declination of the Sun increase.

At the point summer solstice a, where the Sun falls on June 22, its right ascension is 6 h, and the declination reaches its maximum value + . After this, the declination of the Sun decreases, but the right ascension continues to increase.

When the Sun comes to point on September 23 autumn equinox d, its right ascension will become equal to , and its declination will again become zero.

Further, right ascension, continuing to increase, at the point winter solstice g, where the Sun hits on December 22, becomes equal, and the declination reaches its minimum value - . After this, the declination increases, and after three months the Sun comes again to the point of the vernal equinox.

Let's consider the change in the location of the Sun in the sky throughout the year for observers located in different places on the Earth's surface.

Earth's north pole, on the day of the vernal equinox (21.03) the Sun circles the horizon. (Recall that at the North Pole of the earth there are no phenomena of rising and setting of luminaries, that is, any luminary moves parallel to the horizon without crossing it). This marks the beginning of polar day at the North Pole. The next day, the Sun, having risen slightly along the ecliptic, will describe a circle parallel to the horizon at a slightly higher altitude. Every day it will rise higher and higher. The Sun will reach its maximum height on the day of the summer solstice (June 22) – . After this, a slow decrease in altitude will begin. On the day of the autumn equinox (September 23), the Sun will again be on the celestial equator, which coincides with the horizon at the North Pole. Having made a farewell circle along the horizon on this day, the Sun descends below the horizon (under the celestial equator) for six months. The polar day, which lasted six months, is over. The polar night begins.

For an observer located on Arctic Circle greatest height The sun reaches at noon on the summer solstice - . The midnight altitude of the Sun on this day is 0°, that is, the Sun does not set on this day. This phenomenon is usually called polar day.

On the day of the winter solstice, its midday height is minimal - that is, the Sun does not rise. It is called polar night. The latitude of the Arctic Circle is the smallest in the northern hemisphere of the Earth, where the phenomena of polar day and night are observed.

For an observer located on northern tropics, The sun rises and sets every day. The Sun reaches its maximum midday height above the horizon on the day of the summer solstice - on this day it passes the zenith point (). The Tropic of the North is the northernmost parallel where the Sun is at its zenith. The minimum midday altitude, , occurs on the winter solstice.

For an observer located on equator, absolutely all the luminaries set and rise. Moreover, any luminary, including the Sun, spends exactly 12 hours above the horizon and 12 hours below the horizon. This means that the length of the day is always equal to the length of the night - 12 hours each. Twice a year - on the days of the equinoxes - the midday altitude of the Sun becomes 90°, that is, it passes through the zenith point.

For an observer located on latitude of Sterlitamak, that is, in the temperate zone, the Sun is never at its zenith. It reaches its greatest height at noon on June 22, on the day of the summer solstice. On the day of the winter solstice, December 22, its height is minimal - .

So, let us formulate the following astronomical signs of thermal belts:

1. In cold zones (from the polar circles to the poles of the Earth) the Sun can be both a non-setting and non-rising luminary. The polar day and polar night can last from 24 hours (at the northern and southern polar circles) to six months (at the northern and southern poles of the Earth).

2. In temperate zones (from the northern and southern tropics to the northern and southern polar circles) the Sun rises and sets every day, but is never at its zenith. In summer, the day is longer than the night, and in winter, the opposite is true.

3. In the hot zone (from the northern tropic to the southern tropic) the Sun is always rising and setting. The Sun is at its zenith from once - in the northern and southern tropics, to twice - at other latitudes of the belt.

The regular change of seasons on Earth is a consequence of three reasons: the annual revolution of the Earth around the Sun, the inclination of the Earth's axis to the plane of the Earth's orbit (the ecliptic plane), and the Earth's axis maintaining its direction in space over long periods of time. Thanks to the combined action of these three causes, the apparent annual movement of the Sun occurs along the ecliptic, inclined to the celestial equator, and therefore the position of the daily path of the Sun above the horizon of various places earth's surface changes throughout the year, and consequently, the conditions of their illumination and heating by the Sun change.

The unequal heating by the Sun of areas of the earth's surface with different geographic latitudes (or the same areas at different times of the year) is easily determined by simple calculation. Let us denote by the amount of heat transferred to a unit area of ​​the earth's surface by vertically falling solar rays (Sun at zenith). Then, at a different zenith distance of the Sun, the same unit of area will receive the amount of heat

(6.3)

By substituting the values ​​of the Sun at true noon on different days of the year into this formula and dividing the resulting equalities by each other, you can find the ratio of the amount of heat received from the Sun at noon on these days of the year.

Tasks:

1. Calculate the inclination of the ecliptic and determine the equatorial and ecliptic coordinates of its main points from the measured zenith distance. The Sun at its highest culmination on the days of the solstices:

№	22nd of June	December 22
1)	29〫48ʹ south	76〫42ʹ south
№	22nd of June	December 22
2)	19〫23ʹ south	66〫17ʹyu
3)	34〫57ʹ south	81〫51ʹ south
4)	32〫21ʹ south	79〫15ʹ south
5)	14〫18ʹ south	61〫12ʹ south
6)	28〫12ʹ south	75〫06ʹ south
7)	17〫51ʹ south	64〫45ʹ south
8)	26〫44ʹ south	73〫38ʹ south

2. Determine the inclination of the apparent annual path of the Sun to the celestial equator on the planets Mars, Jupiter and Uranus.

3. Determine the inclination of the ecliptic about 3000 years ago, if, according to observations at that time in some place in the northern hemisphere of the Earth, the midday altitude of the Sun on the day of the summer solstice was +63〫48ʹ, and on the day of the winter solstice +16〫00ʹ south of the zenith.

4. According to the maps of the star atlas of Academician A.A. Mikhailov to establish the names and boundaries of the zodiacal constellations, indicate those of them in which the main points of the ecliptic are located, and determine the average duration of the movement of the Sun against the background of each zodiacal constellation.

5. Using a moving map of the starry sky, determine the azimuths of points and the times of sunrise and sunset, as well as the approximate duration of day and night at the geographic latitude of Sterlitamak on the days of the equinoxes and solstices.

6. Calculate the noon and midnight heights of the Sun for the days of the equinoxes and solstices in: 1) Moscow; 2) Tver; 3) Kazan; 4) Omsk; 5) Novosibirsk; 6) Smolensk; 7) Krasnoyarsk; 8) Volgograd.

7. Calculate the ratio of the amounts of heat received at noon from the Sun on the days of the solstices by identical sites at two points on the earth’s surface located at latitude: 1) +60〫30ʹ and in Maykop; 2) +70〫00ʹ and in Grozny; 3) +66〫30ʹ and in Makhachkala; 4) +69〫30ʹ and in Vladivostok; 5) +67〫30ʹ and in Makhachkala; 6) +67〫00ʹ and in Yuzhno-Kurilsk; 7) +68〫00ʹ and in Yuzhno-Sakhalinsk; 8) +69〫00ʹ and in Rostov-on-Don.

Kepler's laws and planetary configurations

Under the influence of gravitational attraction to the Sun, the planets revolve around it in slightly elongated elliptical orbits. The Sun is located at one of the foci of the planet's elliptical orbit. This movement obeys Kepler's laws.

The magnitude of the semimajor axis of a planet's elliptical orbit is also the average distance from the planet to the Sun. Due to minor eccentricities and small inclinations of the orbits major planets, when solving many problems, it is possible to approximately assume that these orbits are circular with a radius and lie practically in the same plane - in the ecliptic plane (the plane of the Earth's orbit).

According to Kepler’s third law, if and are, respectively, the sidereal periods of revolution of a certain planet and the Earth around the Sun, and and are the semimajor axes of their orbits, then

.

(7.1)

Here, the periods of revolution of the planet and the Earth can be expressed in any units, but the dimensions must be the same. A similar statement is true for the semimajor axes and.

If we take 1 tropical year ( – the period of revolution of the Earth around the Sun) as a unit of measurement of time, and 1 astronomical unit () as a unit of measurement of distance, then Kepler’s third law (7.1) can be rewritten as

where is the sidereal period of the planet’s revolution around the Sun, expressed in average solar days.

Obviously, for the Earth the average angular velocity is determined by the formula

If we take the angular velocities of the planet and the Earth as the unit of measurement, and the orbital periods are measured in tropical years, then formula (7.5) can be written as

The average linear speed of the planet in orbit can be calculated using the formula

The average value of the Earth's orbital speed is known and is . Dividing (7.8) by (7.9) and using Kepler’s third law (7.2), we find the dependence on

The "-" sign corresponds to internal or the lower planets (Mercury, Venus), and “+” – external or upper (Mars, Jupiter, Saturn, Uranus, Neptune). In this formula they are expressed in years. If necessary, the found values ​​can always be expressed in days.

The relative position of the planets is easily determined by their heliocentric ecliptic spherical coordinates, the values ​​of which for various days of the year are published in astronomical yearbooks, in a table called “heliocentric longitudes of the planets.”

The center of this coordinate system (Fig. 7.1) is the center of the Sun, and the main circle is the ecliptic, the poles of which are spaced 90º from it.

Great circles drawn through the poles of the ecliptic are called circles of ecliptic latitude, according to them is measured from the ecliptic heliocentric ecliptic latitude, which is considered positive in the northern ecliptic hemisphere and negative in the southern ecliptic hemisphere of the celestial sphere. Heliocentric ecliptic longitude is measured along the ecliptic from the point of the vernal equinox ¡ counterclockwise to the base of the circle of latitude of the luminary and has values ​​ranging from 0º to 360º.

Due to the small inclination of the orbits of large planets to the ecliptic plane, these orbits are always located near the ecliptic, and as a first approximation, their heliocentric longitude can be considered, determining the position of the planet relative to the Sun only by its heliocentric ecliptic longitude.

Rice. 7.1. Ecliptic celestial coordinate system

Consider the orbits of the Earth and some inner planet (Fig. 7.2), using heliocentric ecliptic coordinate system. In it, the main circle is the ecliptic, and the zero point is the vernal equinox point ^. The ecliptic heliocentric longitude of the planet is counted from the direction “Sun – vernal equinox ^” to the direction “Sun – planet” counterclockwise. For simplicity, we will assume that the orbital planes of the Earth and the planet are coincident, and the orbits themselves are circular. The position of the planet in its orbit is then given by its ecliptic heliocentric longitude.

If the center of the ecliptic coordinate system is aligned with the center of the Earth, then this will be geocentric ecliptic coordinate system. Then the angle between the directions “center of the Earth - point of the vernal equinox ^” and “center of the Earth - planet” is called ecliptic geocentric longitude planets Heliocentric ecliptic longitude of the Earth and geocentric ecliptic longitude of the Sun, as can be seen from Fig. 7.2 are related by the relation:

.

(7.12)

We will call configuration planets are some fixed relative positions of the planet, the Earth and the Sun.

Let us consider separately the configurations of the inner and outer planets.

Rice. 7.2. Helio- and geocentric system
ecliptic coordinates

There are four configurations of the inner planets: bottom connection(n.s.), top connection(v.s.), greatest western elongation(n.s.e.) and greatest eastern elongation(n.v.e.).

In inferior conjunction (NC), the inner planet is on the line connecting the Sun and the Earth, between the Sun and the Earth (Fig. 7.3). For an earthly observer, at this moment the inner planet “connects” with the Sun, that is, it is visible against the background of the Sun. In this case, the ecliptic geocentric longitudes of the Sun and the inner planet are equal, that is: .

Near the inferior conjunction, the planet moves in the sky in a retrograde motion near the Sun; it is above the horizon during the day, near the Sun, and it is impossible to observe it by looking at anything on its surface. It's very rare to see something unique astronomical phenomenon– passage of the inner planet (Mercury or Venus) across the disk of the Sun.

Rice. 7.3. Configurations of the inner planets

Since the angular velocity of the inner planet is greater than the angular velocity of the Earth, after some time the planet will shift to a position where the “planet-Sun” and “planet-Earth” directions differ by (Fig. 7.3). For an observer on Earth, the planet is removed from the solar disk at its maximum angle, or they say that the planet at this moment is at its greatest elongation (distance from the Sun). There are two greatest elongations of the inner planet - western(n.s.e.) and eastern(n.v.e.). At greatest western elongation (), the planet sets below the horizon and rises earlier than the Sun. This means that it can be observed in the morning, before sunrise, in the eastern sky. It is called morning visibility planets.

After passing through the greatest western elongation, the disk of the planet begins to approach the disk of the Sun on the celestial sphere until the planet disappears behind the disk of the Sun. This configuration, when the Earth, the Sun and the planet lie on the same straight line, and the planet is behind the Sun, is called top connection(v.s.) planets. Observations of the inner planet cannot be carried out at this moment.

After superior conjunction, the angular distance between the planet and the Sun begins to increase, reaching its maximum value at greatest eastern elongation (CE). At the same time, the heliocentric ecliptic longitude of the planet is greater than that of the Sun (and the geocentric one, on the contrary, is less, that is). The planet in this configuration rises and sets later than the Sun, which makes it possible to observe it in the evening after sunset ( evening visibility).

Due to the ellipticity of the orbits of the planets and the Earth, the angle between the directions to the Sun and to the planet at greatest elongation is not constant, but varies within certain limits, for Mercury - from to , for Venus - from to .

The greatest elongations are the most convenient moments for observing the inner planets. But since even in these configurations Mercury and Venus do not move far from the Sun on the celestial sphere, they cannot be observed throughout the night. The duration of evening (and morning) visibility for Venus does not exceed 4 hours, and for Mercury - no more than 1.5 hours. We can say that Mercury is always “bathed” in the sun’s rays - it must be observed either immediately before sunrise or immediately after sunset, in a bright sky. The apparent brightness (magnitude) of Mercury varies over time, ranging from to . The apparent magnitude of Venus varies from to . Venus is the brightest object in the sky after the Sun and Moon.

The outer planets also have four configurations (Fig. 7.4): compound(With.), confrontation(P.), eastern And western quadrature(Z.Q. and Q.Q.).

Rice. 7.4. Outer planet configurations

In the conjunction configuration, the outer planet is located on the line connecting the Sun and Earth, behind the Sun. At this moment it cannot be observed.

Since the angular velocity of the outer planet is less than that of the Earth, the further relative motion of the planet on the celestial sphere will be retrograde. At the same time, it will gradually shift west of the Sun. When the angular distance of the outer planet from the Sun reaches , it will fall into the “western quadrature” configuration. In this case, the planet will be visible in the eastern sky throughout the second half of the night until sunrise.

In the “opposition” configuration, sometimes also called “opposition”, the planet is located in the sky from the Sun by , then

The planet located in the eastern quadrature can be observed from evening to midnight.

The most favorable conditions for observing the outer planets are during the era of their opposition. At this time, the planet is available for observation throughout the night. At the same time, it is closest to the Earth and has the greatest angular diameter and maximum shine. It is important for observers that all the upper planets reach their greatest height above the horizon during winter oppositions, when they move across the sky in the same constellations where the Sun is in the summer. Summer oppositions at northern latitudes occur low above the horizon, which can make observations very difficult.

When calculating the date of a particular configuration of a planet, its location relative to the Sun is depicted in a drawing, the plane of which is taken to be the plane of the ecliptic. The direction to the vernal equinox point ^ is chosen arbitrarily. If a day of the year is given on which the heliocentric ecliptic longitude of the Earth has a certain value, then the location of the Earth should first be noted on the drawing.

The approximate value of the Earth's heliocentric ecliptic longitude is very easy to find from the date of observation. It is easy to see (Fig. 7.5) that, for example, on March 21, looking from the Earth towards the Sun, we are looking at the vernal equinox point ^, that is, the direction “Sun - vernal equinox point” differs from the direction “Sun - Earth” by , which means that the heliocentric ecliptic longitude of the Earth is . Looking at the Sun on the day of the autumnal equinox (September 23), we see it in the direction of the autumnal equinox point (in the drawing it is diametrically opposite to point ^). At the same time, the ecliptic longitude of the Earth is . From Fig. 7.5 it is clear that on the day of the winter solstice (December 22) the ecliptic longitude of the Earth is , and on the day of the summer solstice (June 22) - .

Rice. 7.5. Earth's ecliptic heliocentric longitudes
on different days of the year, since the Sun and Earth are always at opposite ends of the same radius vector. But geocentric longitude and by difference

,

(7.16)

determine the conditions for their visibility from Earth, assuming that on average a planet becomes visible when it moves away from the Sun at an angle of about 15º.

In reality, the conditions for the visibility of planets depend not only on their distance from the Sun, but also on their declination and on the geographic latitude of the observation site, which affects the duration of twilight and the altitude of the planets above the horizon.

Since the position of the Sun on the ecliptic is well known for each day of the year, using the star chart and the values ​​it is easy to indicate the constellation in which the planet is located on the same day of the year. The solution to this problem is made easier by the fact that on the lower edge of the maps of the Small Star Atlas A.A. Mikhailov, red numbers indicate the dates on which the declination circles marked by them culminate at the middle midnight. These same dates show the approximate position of the Earth in its orbit according to observations from the Sun. Therefore, having determined from the map the equatorial coordinates and the points of the ecliptic culminating at the middle midnight of a given date, it is easy to find the equatorial coordinates of the Sun for the same date

(7.17)

and using them to show its position on the ecliptic.

Using the heliocentric longitude of the planets, it is easy to calculate the days (dates) of the onset of their various configurations. To do this, it is enough to go to the reference system associated with the planet. This assumes that ultimately we will consider the planet stationary, and the Earth moving in its orbit, but with a relative angular velocity.

Let us obtain the necessary formulas for studying the motion of the upper planet. Suppose that on some day of the year the heliocentric longitude of the upper planet is , and the heliocentric longitude of the Earth is . The upper planet moves slower than the Earth (), which is catching up with the planet, and on some day of the year. Therefore, to calculate the distance the lower planet travels from one configuration to another, assuming a stationary Earth.

All the problems discussed above should be solved approximately, rounding the values ​​to 0.01 astronomical units, and to 0.01 years, and to a whole day.

Modern scientific thought defines the Zodiac as twelve constellations located in a strip 18 degrees wide along the visible annual path of the Sun among the stars, called the Ecliptic, within which all the planets of the Solar System move.
Thus, it does not distinguish between the NATURAL Zodiac that exists in the sky and its ASTROLOGICAL concept, which astrologers operate with in their calculations.
On the first pages scientific works in Astrology you will find the following graphic images Zodiac (Fig. 1-4).

No one explains why it is possible to twist the Zodiac left and right and even “convert” it. Unless, of course, we take into account the following explanations: the right-sided Zodiac is a tribute to ancient traditions that cannot be violated; the left side is also a tribute, but to achievements modern science, which proved that it is not the Sun that revolves around the Earth, but the Earth that revolves around the Sun.
Further, after endowing each Zodiac sign and planet with certain qualitative characteristics, you, in fact, get the right to start an independent game of Astrology, which is best started by predicting your own destiny. And already during the course of the game, it is proposed to observe some non-rigid rules, the acceptance and observance of which depends mainly on the taste of the player, who is free to interpret these rules quite freely, to make his own additions and amendments to them, which are significant for him, since “the end justifies the means.”

Therefore, if we put together bit by bit from different sources the basic principles inherent in the concept of the Zodiac, we will get the following, rather motley picture.
1. The apparent annual path of the Sun among the stars, or the Ecliptic, is a circle. That is, the movement of the Sun around the Earth is a cyclical process, and if only for this reason, the Astrological Zodiac should be round and not rectangular.
2. The zodiac circle is divided into 12 equal parts according to the number of Zodiac constellations, named exactly the same, in the same sequence as the Natural ones: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces.
3. Each Zodiac sign has its own natural energy, the quality of which is determined by the group of stars or constellations that is located in it.
4. The energy of each planet has its own specific natural color, reflecting its individuality.
5. All processes occurring on Earth are brought to life by planetary energy, which is necessarily associated with it, and their course of development depends on the movement and relative position of the planets relative to each other.
6. The original quality of the energy of planets and zodiac signs does not change over time.
7. A planet, passing through the signs of the Zodiac, is additionally “colored” in the energy of the Sign through which it passes. (We are not yet considering the question of harmony and disharmony of this color.) Therefore, the quality of energy coming from the planet to Earth is constantly changing depending on which Zodiac sign it is in at the moment.
8. The beginning and end of the annual process of the movement of the Sun around the Earth is taken to be a natural rhythm, namely: The Vernal Equinox point is the equality of the length of day and night on March 21. It is believed that it is at this moment that the Sun enters the beginning of Aries, its zero degree, from which all the coordinates of the planets on the Zodiac circle for a given year are then calculated.

The equinox on Earth occurs at the moment when the Sun, in its movement, hits the point of intersection of the Ecliptic with the Celestial Equator. In turn, the position of the Celestial Equator is necessarily related to the angle of inclination of the constantly precessing Earth's axis to the plane of the Ecliptic. Consequently, the Vernal Equinox Point is not stationary, but mobile. Indeed, it moves along the Ecliptic at a speed of 1° in 72 years. Currently, this point is not in the zero degree of Aries, but in the first degree of Pisces. Thus, it turns out that the Natural and Astrological Zodiac are completely different things, and the entire modern scientific astrological basis is falling apart at the seams.
True, some astrologers involved in karmic Astrology believe that there are no contradictions here, but simply when constructing horoscopes it is necessary to make corrections to the coordinates of the planets, taking into account precession, and then everything will fall into place.
And let Aries become Pisces, Gemini Taurus, and so on, but this will not be considered a mistake; on the contrary, it will be a correction of the mistakes of those astrologers who are still mistaken in their calculations.
To confirm their correctness, they cite the horoscopes of two famous figures of our time: Vladimir Lenin and Adolf Hitler, who, according to ordinary Astrology, were born Taurus, but, according to the internal conviction of karmists, Taurus, supposedly, are not able to do what they did, and only transformation them in Aries makes their actions understandable, like two and two are four.
In order to understand this scientific chaos and determine specific guidelines in it, we will use the keys already known to us and first answer the main question: why modern scientific astrology fails?
The whole point is that modern astrologers, paying tribute to the achievements of modern science, and most importantly, so as not to be branded profane, in their theoretical reasoning proceed mainly from the HELIOCENTRIC picture of the World, but in their practical work use the achievements of ancient astrologers, who were guided by the ideas of GEOCENTRISM. The result is a mess.
We will be guided by the Canons of the Universe, but we will project them onto our planetary body. Therefore, for us, planet Earth will become the center of the Universe, that is, that specific focal point at which we will consider the manifestation of these laws and their individual coloring.

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 am 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+ λ h

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. The main prime meridian is 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 in 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 a celestial object, before entering 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 refractive 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.

Every day, rising from the horizon in the eastern sky, the Sun passes across the sky and disappears again in the west. For residents of the Northern Hemisphere, this movement occurs from left to right, for 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 one - at midnight. At our mid-latitudes, the lower culmination of the Sun is not visible, since it occurs below the horizon. But beyond the Arctic Circle, where the Sun sometimes does not set in the summer, you can observe both the upper and lower climaxes.

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?). The next quarter of the year, until the autumn equinox, the Sun descends. It's a polar day. Then the polar night comes for six months. In mid-latitudes, the apparent daily path of the Sun alternates between shortening and increasing throughout the year. It is the smallest on the day of the winter solstice, the largest on the day of the summer solstice. On the days of the equinoxes

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

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

Then the sunrise and sunset locations shift back to the south. On the day of the winter solstice, the Sun rises in the southeast, crosses the celestial meridian at its minimum altitude and sets in the southwest. It should be taken into account 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 sun rises earlier and sunset later than it would 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, throughout the year the Sun moves relative to the celestial equator, either north or south. The day and night parts of his journey are not the same. They are equal only on the days of the equinoxes, when the Sun is at the celestial equator.

The expression “the path of the Sun among the stars” 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 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 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 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 passes from the southern hemisphere of the sky to the northern. At the second - on September 23, when it passes from the 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 a 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 - from the constellation Libra to the constellation Virgo. But according to tradition, the equinox points are designated by the previous signs of the previous “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

There is 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.

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 full turn 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 per day the Sun moves by 360°/365≈1°.

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... 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 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.