• Change of seasons

    Equinoxes and solstices. Rotating around its axis, the Earth at the same time at a speed of 30 km / s moves around the Sun. In this case, the imaginary axis of the daily rotation of the planet does not change its direction in space, but is transferred parallel to itself. Therefore, the amount of declination of the Sun δ continuously throughout the year( and, at the same time, at different rates!) Changes. Thus, on December 21( 22) it has the smallest value δ = -23 ° 27, after three months, on March 20( 21) δ = 0 °, then on June 21( 22) it reaches the greatest value δ = + 23 ° 27, 22(23) September again becomes equal to zero, after which until December 21 the decline of the Sun is continuously decreasing. But in spring and autumn the rate of change of δ is quite high, whereas in June and December it is much less. Specifically, for five days - from 21 to 26 March( as well as from 16 to 21), the declination of the Sun will increase by 2 °, and in 10 days - by almost 4 °( that is, in ten days the sun "has time" to rise above the heavenlyequator "up" to eight of its angular diameters!), but around June 22( as in December) for five days the decline of the Sun changes by only 5, and by 4 ° only in 35 days. This creates the impression of some "standing" of the Sun in summer and winter at a certain distance from the celestial equator for several days. Therefore, December 21-22 in the northern hemisphere, the height of the Sun above the horizon in its upper culmination is the smallest;This day of the year is the shortest, followed by the longest winter solstice in the year. On the contrary, in the summer, on June 21 or 22, the height of the Sun above the horizon in the upper culmination. The greatest, this day of the summer solstice has the longest duration. On March 20 or 21, the vernal equinox comes( the Sun in its apparent yearly movement passes through the point of the spring equinox from the southern hemisphere to the northern), and on September 22 or 23 is the autumn equinox. In these dates, the length of the day and night is equalized( Fig.).

    Fig. Visible motion of the Sun in the sky on the days of solstices and equinoxes »

    In particular, at a latitude of 50 °, the height of the Sun above the horizon in the upper culmination is: December 22, 16, 5, 21 March and 23 September 40 °, 22 June 63 °, 5.Accordingly, throughout the year, the azimuth of the point of sunrise( and sunset) changes. Thus, at the same latitude, the azimuth of the point of sunrise on December 22, March 21( and September 22) and June 22 are, respectively, -54 °, -92 ° and -129 °.In other words, during the year the point of sunrise( and sunset) of the Sun moves along the horizon to an angle of 129 ° -54 ° = 75 °.

    Under the influence of gravity acting on the Earth from other planets, the parameters of the Earth's orbit, in particular its inclination to the plane of the celestial equator ε, change: the plane of the earth's orbit seems to "stagger" and for millions of years the value of e fluctuates near its mean value. Thus, it follows from the calculations that in 4000 BC.e.the angle e was somewhat larger and reached the value e = 24 ° 13.Therefore, the height of the Sun in the upper climax at the time was 46 more than in our days. In its turn, the point of sunrise on the horizon was then located "to the left", and the point of approach is "to the right", than it is fixed by the observer today. This circumstance, of course, should be taken into account when studying the ancient landmarks, which, it is supposed, could indicate to the ancient inhabitants of the Earth the directions of the azimuths of the sunrises and sunset on the days of solstices.

    And one more thing. The Earth turns around the Sun in an elliptical orbit, and therefore its distance from it varies throughout the year. The closest to the Sun, our planet( currently!) Is 2-5 January, at which time the speed of its orbit is greatest. Therefore, the duration of the seasons is not the same: spring - 92 days, summer - 94 days, autumn - 90 and winter - 89 days for the northern hemisphere. Spring and summer( the number of days elapsed from the moment of the transition of the Sun through the point of the vernal equinox to its crossing through the point of the autumnal equinox) lasts 186 days in the northern hemisphere, while autumn and winter are 179. Several thousand years ago the elongation of the ellipse of the earth's orbit wasTherefore, the difference between the intervals mentioned was also smaller. In addition, for example, in 4000 BC.e.its closest distance to the Sun, the Earth passed a little earlier - around September 24-27.

    In connection with the change in the height of the Sun over the horizon, there is a regular change of the seasons ( Fig.).

    Fig. The movement of the Earth around the Sun and the change of seasons

    Cold winter with its fierce frosts, long nights and short days gives way to blossoming spring, then a generous harvest in summer, followed by autumn with its golden colors and. .. prolonged rains.

    Star year. Comparing the view of the starry sky immediately after the sunset from day to day for several weeks, you can see that the visible position of the sun with respect to the stars is continuously changing: the sun moves from west to east and for every 365.256360 days makes a full skycircle, returning to the same star. This period of time is called the star year.

    Zodiac constellations. For better orientation in the boundless starry ocean, astronomers divided the sky into 88 separate sites - constellations. By the 12 constellations, which are called zodiacal( from the Greek word "zoon" - animal, since ancient people gave them mostly names of animals), and passes the Sun for a year. The duration of the Sun in each of the zodiacal constellations in the modern era according to the Gregorian calendar is indicated in Table.

    Table. Movement of the Sun by the zodiacal constellations



    Length of the sun in the constellation
    Sagittarius December 18-January 19
    Capricorn January 19 - February 16
    Aquarius February 16 - March 12
    Fish March 12-April 18
    Aries April 18 - May 14
    Taurus May 14 - June 21
    Gemini June 21 - July 20
    Cancer July 20 - August 11
    Leo August 11 - September 17
    Virgo September 17 - October 31
    Scale October 31 - November 22
    Scorpio November 22 - November 30

    Note. From November 30 to December 18, the Sun is in the constellation Ophiuchus, which is not included in the zodiacal number.

    «Signs of the Zodiac». In the past, 2000 years ago, and in the Middle Ages for convenience in counting the position of the Sun on the ecliptic, it was divided into 12 equal parts of 30 ° each. Each arc at 30 ° was usually designated as the sign of that zodiacal constellation through which the Sun passed in one or another month. So the "signs of the zodiac" appeared in the sky. The origin of the reference was the point of the vernal equinox, located at the beginning of n.e.in the constellation of Aries. The arc 30 ° from it was designated by the sign ¡( "mutton horns").Further, the Sun passed through the constellation of Taurus, therefore the arc of the ecliptic from 30 to 60 ° was designated by the "sign of Taurus" Ŏ, etc. Calculations of the position of the Sun,

    of the Moon and planets in the "signs of the Zodiac", ie, in fact at certain angular distances fromthe points of the vernal equinox, were held for many centuries for the compilation of horoscopes.

    By our time, due to precession, the vernal equinox point shifted from the constellation of Aries to the constellation Pisces( moving the point on the ¡ 1 ° for every 72 years for 2000 years gives almost 30 °, ie, the value of the arc attributed to one signZodiac!).But, paying tribute to the tradition, here and now they say that the Sun is in the sign of Aries from March 22 to April 20, from April 21 to May 21 - in the sign of Taurus, etc. Actually it is at this timepasses respectively through the constellations of Pisces and Aries.

    This can be an additional proof of the absurdity of calculating horoscopes in our time.

    star or group of stars










    May 12

    May 23

    December 4

    November 14

    Belt of Orion and

    May 12

    July 20

    January 18



    May 14

    August 16

    February 12

    November 15


    June 15

    August 8

    February 5

    December 12

    and Hydra

    June 30

    September 9

    March 7

    December 25


    July 13

    July 20

    January 18

    Jan. 18

    January 5


    August 13

    2. September

    February 27

    January 25

    October 1

    October 26

    April 23

    6 mth of mouth


    November 14

    December 15


    April 22

    P Libra

    November 19

    November 15

    May 15

    April 28


    December 2

    October 13

    10 April

    May 20

    and Sagittarius

    December 21

    January 17

    Aug. 5

    June 15


    January 29

    December 23


    August 4

    and Aquarius

    February 15

    February 3

    September 5

    August 23

    P of China

    4 March

    22 May

    4 December

    6 september

    Characteristic sunrises and sunset of stars. Due to the continuous movement of the Sun's disk in the celestial sphere from west to east, the view of the starry sky from evening to evening, although slowly but continuously, changes. So, if at some time of the year some constellation of the zodiac one hour after sunset is visible in the southern part of the sky( say, passes through the celestial meridian), then due to this movement of the Sun in each subsequent evening this constellation will pass through the meridian four minutes earlier, than in the previous one. By the time the sun sets, it will move more and more to the western part of the sky. After about three months, this zodiacal constellation is already hidden in the rays of the evening dawn, and after 10-20 days it will be visible already in the morning before the sun rises in the eastern part of the sky. About the same way behave and other setting constellations and individual stars. In this case, the change in the conditions for their visibility essentially depends on the geographic latitude of the observer φ and the declination of the light δ, in particular, on its distance from the ecliptic. So, if the stars of the zodiacal constellation are sufficiently far from the ecliptic, then in the morning they are visible even earlier than their evening visibility ceases.

    The first appearance of a star in the rays of the morning dawn( ie, the first morning sunrise of a star) is called its heliacic( from the Greek "helios" - Sun) sunrise. With each subsequent day, this star manages to rise above the horizon higher: the sun continues its yearly movement across the sky. In three months to the moment.the rising of the Sun, this star, along with its "own" constellation, is already passing the meridian( in the upper culmination), and after another three months it will hide behind the horizon in the west.

    Sunset in the rays of the dawn, which occurs only once a year( morning sunset), it is customary to call it cosmic( "space" - "decoration") sunset. Further, the rising of the star above the horizon in the east at sunset( sunrise in the rays of the evening dawn) is called its acronic rise( from the Greek "acros" - the highest, apparently referring to the position most remote from the Sun).And, finally, the setting of a star in the rays of the evening dawn is usually called a heliacal approach.

    The dates of evening and morning sunrises and sunset of some stars for an observer located at latitude φ = 50 ° are given in Table. It should, however, be borne in mind that these dates are only indicative. They correspond to the rising( entering) of the star at the end of the evening( or early morning) civil twilight.

    Table: The dates of sunrise and set of stars at a geographical latitude φ = 50 °

    In fact, the visibility conditions for stars of different magnitude( different brightness) are not the same. Therefore, in astronomy there is the concept of an arc of visibility - the smallest "depth" of the Sun beneath the horizon( its height h <0), from which one or another star becomes noticeable in the sky. In particular, for Sirius, Regulus and Pleiades, the value of h has, respectively, -10 °, -12 ° and -15 °.Therefore, in the last 2-3 days, about the time indicated in Table.the limit of the stars at the end of civil twilight, although they will be above the horizon, it is already extremely difficult to notice them.

    Tropical year. Let us return once more to the question of motion. Sun on the ecliptic. On March 20( or 21) the center of the Sun's disk crosses the celestial equator, moving from the southern hemisphere of the celestial sphere to the northern one. The point of intersection of the celestial equator with the ecliptic - the point of the vernal equinox is in our time in the constellation of Pisces. In the sky, it is not "marked" by any bright star; its location on the celestial sphere is established by astronomers with very high accuracy from the observations of "support" stars close to it.

    The interval between two successive passes of the center of the disk of the Sun through the point of the vernal equinox is called the true, or tropical year. Its duration is 365.2421988 days or 365 days 5 hours 48 minutes and 46 seconds. It is assumed that the average sun returns to the vernal equinox at the same time. Bessilev year. The duration of our calendar year is not the same: it contains 365 or 366 days. Meanwhile, astronomers are counting the tropical years of the same duration. At the suggestion of the German astronomer FV Bessel( 1784-1846), for the beginning of the astronomical( tropical) year, the moment is taken when the direct ascent of the average equatorial sun is 18h40m. For example, in 1980 the Bessel Year began at the time of January 1, 4:32, in 1983-December 31( "January 0") at 21:58 GMT.

    Precession. The duration of the tropical year is 20 min. 24 s shorter than the stellar year. This is due to the fact that the point of the vernal equinox at a speed of 50 ", 2 per year moves along the ecliptic towards the annual movement of the Sun. This phenomenon was discovered by the ancient Greek astronomer Hipparchus in the 2nd century BC and is called precession, or precession of the equinoxes. For 72 years the point of the vernal equinox is displaced by 1 ° in the ecliptic, by 14 ° in 1000 years, etc. In about 26,000 years, it will make a full circle on the celestial sphere. In the past, about 4000 years ago, the point of the vernal equinoxwas in the constellation of Taurus near the starrythe summer Pleistades, the summer solstice at that time came at the time of the passage of the Sun through the constellation of Leo near the star Regulus( Figure)

    Figure of the position of the celestial equator and the point of the vernal equinox among the stars in 4000 BC

    The phenomenon of precessionarises because the shape of the Earth differs from the spherical( our planet is flattened at the poles.) Under the influence of the sun and the moon's various parts of the "flattened" Earth, the axis of its diurnal rotation describes the

    cone around the perpendicular to the plane of the ecliptic. As a result, the poles of the world move among the stars along small circles with radii of about 23 ° 27( Fig.).At the same time, the grid of equatorial coordinates is shifted on the celestial sphere, and with it the point of the vernal equinox.

    Due to precession, the view of the sky on a particular day of the year is slowly but continuously changing. So, 4000 years ago the central place in the southern part of the evening sky at the time of the vernal equinox was occupied by the constellation of Leo, the constellation of Gemini was then low above the horizon near the point of call. The sun. At the same time in spring the constellation of Leo only rises above the horizon in the eastern part of the sky, and the constellation of Gemini flaunts in the south. ..

    The change in the number of days per year. As the culmination of stars has shown over many decades, the rotation of the Earth around its axis gradually slows down, although the magnitude of this effect is still known with insufficient accuracy. It is assumed that over the past two thousand years the duration of the day increased by an average of 0.002 s per century. This seemingly negligible value, accumulating, leads to very noticeable results. Because of this, for example, calculations of solar eclipses and conditions of their visibility in the past( say, 1500-2000 years ago) will be inaccurate, if the current day length is taken as the calculated unit of time. In particular, for a period of -2000 years, a difference of 1/2 *( 0.04 + 0.00) * 365 * 2000 = 14 600 s = 4 hours will accumulate in the time count, since 2000 was a day shorter by 2,000 years ago = 0.002 * 20 = 0, 04 sec.

    Fig.9. Moving the North Pole of the world among the stars for 26,000 years. The discontinuous line shows the offset of the pole of the ecliptic

    . Here it is appropriate to draw an analogy with two runners who reached the finish line simultaneously and at the same speed, but one of them moved evenly, the second gradually slowed down its run. It is clear that this second runner, for the same time interval, ran a longer distance, i.e.started from a more remote point. As this second runner, and our Earth spins with a slowing angular velocity. Compared with some imaginary standard, rotating at a constant speed, for a certain period of time, the Earth turned to a larger angle.

    Therefore, in particular, the eclipse that occurred 2000 years ago was actually observed four hours earlier, and its strip on the Earth's surface was shifted by about 60 ° to the east than it follows from the current calculations, in which, as a unittime is used the duration of today's day. So if, according to the calculation, the eclipse should have occurred in Greenwich at exactly noon, then since the Earth in the past rotated faster, at this point in the fictitious "present" half-day, Greenwich was then still at 60 ° west of the lunar shadow strip, and the eclipse, from the point of view of the then observer, occurred at 8 o'clock in the morning.

    In connection with the effect mentioned here, the amount of days that fall in the tropical year is slowly but steadily decreasing. This effect is described by the approximate formula C. Newcomb

    1 tropical year = 365.24219879 - 0.0000000614( R-1900),

    where R is the ordinal number of the year.

    In particular, the tropical year turns out to be equal to

    in 3000 BC.e.365.242500 days

    1 year olde.365.242316 »

    1900 »365,242199»

    4000 »365,242070»

    In our time, the value of the tropical year decreases every century by 0.54 s. It is estimated that a billion years ago the day was 4 hours shorter than today, and in about 4.5 billion years the Earth will do only nine turns around its axis per year. ..