60 year animal cycle. Eastern lunar calendar

This calendar is a 60-year cyclical system. The current cycle began on February 2, 1984 ( chinese year 4693). This date is Bing Yuin in a 60-day cycle, and the month of Gui Chow in a 60-month cycle. The beginning of the new year ranges from January 20 to February 20 and is tied to the new moon, when the sun enters the constellation Aquarius.

The 60-year cycle is based on the astronomical cycles of the Sun, Earth, Moon, Jupiter and Saturn. The main ones are the 12-year Jupiter and 30-year Saturn cycles. The 12-year period of Jupiter was considered the most important for the life of nomads, and in those days the main peoples of the East were nomadic tribes. The ancient Chinese and Japanese believed that the normal motion of Jupiter brought benefits and virtues.

Dividing the path of Jupiter into twelve equal parts and giving each part the name of a specific animal, the peoples of Asia created a solar-Jupiter 12-year calendar cycle. Legend has it that all the animals were invited by Buddha to celebrate the first New Year. Since only twelve arrived - Rat (Mouse), Ox (Bull), Tiger, Rabbit (Hare), Dragon, Snake, Horse, Sheep, Monkey, Rooster, Dog, Boar (Pig)“The Buddha decided to give their names to the years, so that every person born in the year of a certain animal would acquire the character traits of that animal, both good and bad.

In sixty years, Jupiter makes five revolutions. This number corresponded to the worldview of Chinese natural philosophy. The number five was a symbol of the five elements of nature - wood, fire, metal (gold), water, earth, which correspond to color designations ( Blue, Red, Yellow, White, Black).

Thus, the Chinese sexagenary was formed as a result of the combination of the duodecimal cycle (“earthly shoots”), each year of which was assigned the name of an animal, and the decimal cycle of the “elements” (“heavenly branches”): five elements, each of which corresponded to two cyclic signs , personifying the masculine and feminine principles (Yang and Yin) (therefore, in the Chinese calendar there are consecutive years corresponding to different animals, but one element).

Such a cyclicity divisible by 60 in ancient China was extended to account for the time of day, weeks and months. The day was divided into 12 double hours, each of which corresponded to an animal of the Chinese zodiac (the months were also determined).

Heavenly branches

Jia	Yi	Bing	Ding	Wu	Ji	Geng	Xin	Ren	Gui
Tree		Fire		Metal (Gold)		Water		Earth
Jan	Yin	Jan	Yin	Jan	Yin	Jan	Yin	Jan	Yin

Earthly shoots

Rat (Mouse)	Ox (Bull)	Tiger	Rabbit (Hare)	Dragon	Snake	Horse	Sheep	Monkey	Rooster	Dog	Boar (Pig)
Zi	Chou	Yin	Mao	Chen	Si	Wu	Wei	Shen	You	Xu	Hai
Jan	Yin	Jan	Yin	Jan	Yin	Jan	Yin	Jan	Yin	Jan	Yin

Each of the two components is used sequentially. That is, for next year you need to take the next zodiac sign and the next element.

The Chinese calendar, like the Jewish one, is a combined solar-lunar calendar, so they have a lot in common:

A normal year has 12 months, a leap year has 13.
A regular year has 353, 354 or 355 days, a leap year has 383, 384 or 385 days.

New moon is the first day of the month. In the Chinese calendar, the new moon is determined by full conjunction with the sun, and not when the visible crescent moon appears, as in the Islamic and Jewish ones.

Month numbers are determined as follows: The date is determined when the longitude of the sun is a multiple of 30 degrees (0 - vernal equinox, 90 - summer solstice, 180 - autumn equinox and 270 - winter solstice) These dates are called Principal Terms and are used to determine the number month:

1	2	3	4	5	6	7	8	9	10	11	12
330 o	0 o	30 o	60 o	90 o	120 o	150 o	180 o	210 o	240 o	270 o	300 o

Each month receives the main period number for that month. In cases where a month contains two periods, the numbering is shifted. For example, a month contains period 1 and 2 will be numbered 1, and the next 2. Period 11 (winter solstice) always falls on the 11th month.

To determine a leap year, which has 13 months, the number of new moons between the 11th month of the year and the 11th month of the next year is calculated. If the interval falls within 12 full months, this is leap year. In this case, by at least, one month will not contain a main period. The first of these months is declared a leap month. It is numbered with the same number as the previous one, but with the clarification that this is an additional month.

All astronomical calculations are carried out for the 120th meridian of eastern longitude. This roughly corresponds to the east coast of China.

Dates of the New Year according to the Eastern calendar

Rat (Mouse)	Ox (Bull)	Tiger	Rabbit (Hare)	Dragon	Snake	Horse	Sheep	Monkey	Rooster	Dog	Boar (Pig)
24.01 1936	11.02 1937	31.01 1938	19.02 1939	08.02 1940	27.01 1941	15.02 1942	05.02 1943	25.01 1944	13.02 1945	02.02 1946	22.01 1947
11.02 1948	29.01 1949	17.02 1950	06.02 1951	27.01 1952	14.02 1953	03.02 1954	24.01 1955	12.02 1956	31.01 1957	18.02 1958	08.02 1959
28.01 1960	15.02 1961	05.02 1962	25.01 1963	13.01 1964	02.02 1965	21.01 1966	09.02 1967	30.01 1968	17.02 1969	06.02 1970	27.01 1971
15.01 1972	03.02 1973	23.01 1974	11.02 1975	31.01 1976	18.02 1977	07.02 1978	28.01 1979	16.02 1980	05.02 1981	25.01 1982	13.02 1983
02.02 1984	20.02 1985	09.02 1986	29.01 1987	17.02 1988	06.02 1989	27.01 1990	15.02 1991	04.02 1992	23.01 1993	10.02 1994	31.01 1995
19.02 1996	07.02 1997	28.01 1998	16.02 1999	05.02 2000	24.01 2001	11.02 2002	01.02 2003	20.02 2004	09.02 2005	29.01 2006	17.02 2007
06.02 2008	27.01 2009	15.02 2010	04.02 2011	23.01 2012	10.02 2013	31.01 2014	19.02 2015	07.02 2016	28.01 2017	16.02 2018	05.02 2019
25.01 2020
Rat (Mouse)	Ox (Bull)	Tiger	Rabbit (Hare)	Dragon	Snake	Horse	Sheep	Monkey	Rooster	Dog	Boar (Pig)

60-year cycles according to the eastern calendar

Rat (Mouse)	Ox (Bull)	Tiger	Rabbit (Hare)	Dragon	Snake	Horse	Sheep	Monkey	Rooster	Dog	Boar (Pig)
1864	1865	1866	1867	1868	1869	1870	1871	1872	1873	1874	1875
1876	1877	1878	1879	1880	1881	1882	1883	1884	1885	1886	1887
1888	1889	1890	1891	1892	1893	1894	1895	1896	1897	1898	1899
1900	1901	1902	1903	1904	1905	1906	1907	1908	1909	1910	1911
1912	1913	1914	1915	1916	1917	1918	1919	1920	1921	1922	1923
1924	1925	1926	1927	1928	1929	1930	1931	1932	1933	1934	1935
1936	1937	1938	1939	1940	1941	1942	1943	1944	1945	1946	1947
1948	1949	1950	1951	1952	1953	1954	1955	1956	1957	1958	1959
1960	1961	1962	1963	1964	1965	1966	1967	1968	1969	1970	1971
1972	1973	1974	1975	1976	1977	1978	1979	1980	1981	1982	1983
1984	1985	1986	1987	1988	1989	1990	1991	1992	1993	1994	1995
1996	1997	1998	1999	2000	2001	2002	2003	2004	2005	2006	2007
2008	2009	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019
2020	2021	2022	2023	2024	2025	2026	2027	2028	2029	2030	2031
2032	2033	2034	2035	2036	2037	2038	2039	2040	2041	2042	2043
The day was divided into 12 parts, which, of course, should be equal to our two hours; They divided their “clocks” into parts called ke. Each ke was divided into 100 "minutes", and "minute" into 100 "seconds". The day was divided into two parts: “day” and “night” - each of 6 “hours”. Midnight was considered the beginning of the day. In China, the calendar was a sacred document maintained by the reigning monarch. For more than 2 millennia, the astronomy department made astronomical observations, carried out calculations of astronomical events, and prepared astrological predictions. Besides, lucky calendar contributed not only to practical purposes, but also confirmed the agreement between heaven and the empire. Analyzing the surviving astronomical records on the bones, according to which Ancient China carried out fortune telling and predictions, they discovered in China a lunisolar calendar with intercalation of lunar months, dating back to the Shang Dynasty of the 14th century BC. Were developed various schemes intercalation in earlier versions calendar, including the 19-year and 76-year cycle of moon phases known in the West as the metonic and calliptic cycles. From the earliest records, the beginning of the year occurred at the new moon around the winter solstice. However, the choice of month for the start of the civil year varied over time and geographically. At the end of the second century BC. Calendar reform established a practice that continues to this day, which requires that the winter solstice always fall in the 11th month of the year. This reform also included a system of intercalation, in which new moons were compared to 24 solar periods. However, the calculations were based on averaged motion derived from cyclic relations. Inequalities for calculating the motion of the moon were not used until the 7th century AD, but solar mean longitude was used to calculate solar periods until 1644. Although eras were counted from the beginning of the new emperor's reign, the Emperor could also declare a new era arbitrarily during his reign. This was done to restore the broken connection between heaven and earth, personified by the emperor. New era could indicate the death of an emperor, natural disasters, or the failure of astronomers to predict astronomical events. In the latter case, an era could mark the introduction of a new astronomical or calendar model. Cycles in multiples of 60 were used to count years, months, days and fractions of a day, using a set of celestial branches and terrestrial shoots. Chinese time calculation was later transferred to Japan; it held firm in China until the arrival of European missionaries, that is, until the 17th century. One of them, a Jesuit Father Scholl, was knowledgeable in astronomy and introduced the Chinese to the European reckoning of time. Chinese scientists approved and accepted European system- dividing the day into 24 hours, and the hours into minutes and seconds, 60 each. The Chinese officially recognized the Gregorian calendar in 1911.

Eastern (Chinese) calendar

The Eastern calendar, which has been in effect for several thousand years in Vietnam, Kampuchea, China, Korea, Mongolia, Japan and some other Asian countries, was compiled during the time of the semi-legendary Emperor Huang Di in the middle of the third millennium BC. This calendar is a 60-year cyclical system.

It is based on the astronomical cycles of the Sun, Earth, Moon, Jupiter and Saturn. The 60-year cycle includes the 12-year Jupiter and 30-year Saturn cycles. The 12-year period of Jupiter was considered the most important for the life of nomads, and in those days the main peoples of the East were nomadic tribes. The ancient Chinese and Japanese believed that the normal motion of Jupiter brought benefits and virtues.

By dividing the path of Jupiter into twelve equal parts and giving each part the name of a specific animal, the peoples of Asia created the solar-Jupiter 12-year calendar cycle. Legend has it that all the animals were invited by Buddha to celebrate the first New Year. Since only twelve arrived, the Buddha decided to name their years so that each person born in the year of a particular animal would acquire that animal's character traits, both good and bad.

The Chinese sexagenary was formed as a result of the combination of the duodecimal cycle (“earthly branches”), each year of which was assigned the name of an animal, and the decimal cycle of the “elements” (“heavenly branches”): five elements (wood, fire, earth, metal, water) , each of which corresponded to two cyclic signs, personifying the masculine and feminine principles (therefore, in the Chinese calendar there are consecutive years corresponding to different animals, but one element).

Heavenly branches (untranslatable):

Each of the two components is used sequentially. That is, for next year you need to take the next zodiac sign and the next element.

The Chinese calendar, like the Jewish one, is a combined solar-lunar calendar, so they have a lot in common:

- A normal year has 12 months, a leap year has 13.
- A regular year has 353, 354 or 355 days, a leap year has 383, 384 or 385 days.

The month numbers are determined as follows: The date is determined when the longitude of the sun is a multiple of 30 degrees (0 - spring equinox, 90 - summer solstice, 180 - autumn equinox and 270 - winter solstice) These dates are called main periods (Principal Terms) and are used to determine the month number:

Each month receives the main period number for that month. In cases where a month contains two periods, the numbering shifts. For example, a month contains period 1 and 2 will be numbered 1, and the next 2. Period 11 (winter solstice) always falls on the 11th month.

To determine a leap year, which has 13 months, the number of new moons between the 11th month of the year and the 11th month of the next year is calculated. If the interval includes 12 full months, it is a leap year. In this case, at least one month will not contain a main period. The first of these months is declared a leap month. It is numbered with the same number as the previous one, but with the clarification that this is an additional month.

All astronomical calculations are carried out for the 120th meridian of eastern longitude. This roughly corresponds to the east coast of China.

Methodology for lesson 5
"Time and Calendar"

The purpose of the lesson: to form a system of concepts of practical astrometry about methods and tools for measuring, counting and storing time.

Learning Objectives:
General education: formation of concepts:

Practical astrometry about: 1) astronomical methods, instruments and units of measurement, counting and storing time, calendars and chronology; 2) determining the geographic coordinates (longitude) of the area based on astrometric observations;

About cosmic phenomena: the revolution of the Earth around the Sun, the revolution of the Moon around the Earth and the rotation of the Earth around its axis and about their consequences - celestial phenomena: sunrise, sunset, daily and annual visible movement and culminations of the luminaries (Sun, Moon and stars), changing phases of the Moon .

Educational: the formation of a scientific worldview and atheistic education in the course of acquaintance with the history of human knowledge, with the main types of calendars and chronology systems; debunking superstitions associated with the concepts of “leap year” and the translation of dates of the Julian and Gregorian calendars; polytechnic and labor education in presenting material about instruments for measuring and storing time (clocks), calendars and chronology systems, and practical methods of applying astrometric knowledge.

Developmental: developing skills: solving problems on calculating time and dates and transferring time from one storage and counting system to another; perform exercises to apply the basic formulas of practical astrometry; use a moving star map, reference books and the Astronomical calendar to determine the position and conditions of visibility of celestial bodies and the occurrence of celestial phenomena; determine the geographic coordinates (longitude) of the area based on astronomical observations.

Students must know:

1) the causes of everyday observed celestial phenomena generated by the revolution of the Moon around the Earth (changes in the phases of the Moon, the apparent movement of the Moon across the celestial sphere);
2) the connection between the duration of individual cosmic and celestial phenomena with units and methods of measuring, counting and storing time and calendars;
3) time units: ephemeris second; day (sidereal, true and average solar); week; month (synodic and sidereal); year (stellar and tropical);
4) formulas expressing the connection of times: universal, maternity leave, local, summer;
5) instruments and methods of measuring time: the main types of clocks (solar, water, fire, mechanical, quartz, electronic) and the rules for their use for measuring and storing time;
6) main types of calendars: lunar, lunisolar, solar (Julian and Gregorian) and the basics of chronology;
7) basic concepts of practical astrometry: principles of determining time and geographic coordinates of an area based on astronomical observation data.
8) astronomical quantities: geographical coordinates hometown; time units: ephemeral second; day (sidereal and average solar); month (synodic and sidereal); year (tropical) and length of the year in the main types of calendars (lunar, lunisolar, solar Julian and Gregorian); time zone numbers of Moscow and hometown.

Students must be able to:

1) Use a generalized plan to study cosmic and celestial phenomena.
2) Find your bearings using the Moon.
3) Solve problems related to the conversion of units of time from one counting system to another using formulas expressing the relationship: a) between sidereal and mean solar time; b) World Time, Maternity Time, Local Time, Summer Time and using a time zone map; c) between different chronology systems.
4) Solve problems to determine the geographic coordinates of the place and time of observation.

Visual aids and demonstrations:

Fragments of the film "Practical Applications of Astronomy."

Fragments of filmstrips "Visible movement of celestial bodies"; "Development of ideas about the Universe"; "How astronomy disproved religious ideas about the Universe."

Instruments and instruments: geographical globe; time zone map; gnomon and equatorial sundial, hourglass, water clock (with uniform and uneven scale); candle with divisions as a fire watch model, mechanical, quartz and electronic watches.

Drawings, diagrams, photographs: changes in the phases of the Moon, the internal structure and operating principle of mechanical (pendulum and spring), quartz and electronic watches, the atomic time standard.

Homework:

1. Study textbook material:
B.A. Vorontsov-Velyaminova: §§ 6 (1), 7.
E.P. Levitan: § 6; tasks 1, 4, 7
A.V. Zasova, E.V. Kononovich: §§ 4(1); 6; exercise 6.6 (2.3)

2. Complete tasks from the collection of tasks by Vorontsov-Velyaminov B.A. : 113; 115; 124; 125.

Lesson Plan

Lesson steps		Presentation methods	Time, min
	Knowledge testing and updating	Frontal survey, conversation
	Formation of concepts about time, units of measurement and time counting based on duration cosmic phenomena, connections between different "times" and time zones	Lecture	7-10
	Introducing students to methods for determining the geographic longitude of an area based on astronomical observation data	Conversation, lecture	10-12
	Formation of concepts about instruments for measuring, counting and storing time - clocks and the atomic standard of time	Lecture	7-10
	Formation of concepts about the main types of calendars and chronology systems	Lecture, conversation	7-10
	Problem solving	Work at the board independent decision problems in the notebook
	Summarizing the material covered, summarizing the lesson, homework

Methodology for presenting material

At the beginning of the lesson, you should test the knowledge acquired in the three previous lessons, updating the material intended for study with questions and tasks during a frontal survey and conversation with students. Some students complete programmed tasks, solving problems related to the use of a moving star map (similar to tasks in tasks 1-3).

A series of questions about the causes of celestial phenomena, the main lines and points of the celestial sphere, constellations, conditions of visibility of luminaries, etc. coincides with the questions asked at the beginning of previous lessons. They are supplemented by questions:

1. Define the concepts of “luminosity” and “stellar magnitude”. What do you know about the magnitude scale? What determines the brightness of stars? Write Pogson's formula on the board.

2. What do you know about the horizontal celestial coordinate system? What is it used for? What planes and lines are the main ones in this system? What is the height of the luminary? Zenith distance of the luminary? Azimuth of the luminary? What are the advantages and disadvantages of this celestial coordinate system?

3. What do you know about the I equatorial celestial coordinate system? What is it used for? What planes and lines are the main ones in this system? What is the declination of a luminary? Polar distance? Hour angle of the luminary? What are the advantages and disadvantages of this celestial coordinate system?

4. What do you know about the II equatorial celestial coordinate system? What is it used for? What planes and lines are the main ones in this system? What is the right ascension of the luminary? What are the advantages and disadvantages of this celestial coordinate system?

1) How to navigate the terrain using the Sun? By the North Star?
2) How to determine the geographic latitude of an area from astronomical observations?

Corresponding programmable jobs:

1) Collection of problems by G.P. Subbotina, tasks NN 46-47; 54-56; 71-72.
2) Collection of problems by E.P. Broken, tasks NN 4-1; 5-1; 5-6; 5-7.
3) Strout E.K. : test papers NN 1-2 topics “Practical foundations of astronomy” (transformed into programmable ones as a result of the teacher’s work).

At the first stage of the lesson, in the form of a lecture, the formation of concepts about time, units of measurement and time counting, based on the duration of cosmic phenomena (the rotation of the Earth around its axis, the revolution of the Moon around the Earth and the revolution of the Moon around the Sun), the connection between different “times” and clocks belts We consider it necessary to give students general concept about sidereal time.

Students need to pay attention to:

1. The length of the day and year depends on the reference system in which the Earth’s movement is considered (whether it is connected with the fixed stars, the Sun, etc.). The choice of reference system is reflected in the name of the time unit.

2. The duration of time units is related to the visibility conditions (culminations) of celestial bodies.

3. The introduction of the atomic time standard in science was due to the uneven rotation of the Earth, discovered when the accuracy of clocks increased.

4. The introduction of standard time is due to the need to coordinate economic activities in the territory defined by the boundaries of time zones. A widespread everyday mistake is to equate local time with maternity time.

1. Time. Units of measurement and time counting

Time is the main physical quantity that characterizes the successive change of phenomena and states of matter, the duration of their existence.

Historically, all basic and derivative units of time are determined on the basis of astronomical observations of the course of celestial phenomena caused by: the rotation of the Earth around its axis, the rotation of the Moon around the Earth and the rotation of the Earth around the Sun. To measure and count time in astrometry, different reference systems are used, associated with certain celestial bodies or certain points of the celestial sphere. The most widespread are:

1. "Zvezdnoe"time associated with the movement of stars on the celestial sphere. Measured by the hour angle of the vernal equinox: S = t ^ ; t = S - a

2. "Sunny"time associated: with the visible movement of the center of the Sun's disk along the ecliptic (true solar time) or the movement of the "average Sun" - an imaginary point moving uniformly along the celestial equator in the same period of time as the true Sun (average solar time).

With the introduction of the atomic time standard and the International SI System in 1967, the atomic second has been used in physics.

A second is a physical quantity numerically equal to 9192631770 periods of radiation corresponding to the transition between hyperfine levels of the ground state of the cesium-133 atom.

All the above “times” are consistent with each other through special calculations. In everyday life, mean solar time is used.

Determining the exact time, its storage and transmission by radio constitute the work of the Time Service, which exists in all developed countries of the world, including Russia.

The basic unit of sidereal, true and mean solar time is the day. We obtain sidereal, mean solar and other seconds by dividing the corresponding day by 86400 (24 h´ 60 m´ 60 s).

The day became the first unit of time measurement over 50,000 years ago.

A day is a period of time during which the Earth makes one full revolution around its axis relative to some landmark.

Sidereal day - the period of rotation of the Earth around its axis relative to the fixed stars, is defined as the period of time between two successive upper culminations of the vernal equinox.

A true solar day is the period of rotation of the Earth around its axis relative to the center of the solar disk, defined as the time interval between two successive culminations of the same name at the center of the solar disk.

Due to the fact that the ecliptic is inclined to the celestial equator at an angle of 23º 26¢, and the Earth rotates around the Sun in an elliptical (slightly elongated) orbit, the speed of the apparent movement of the Sun across the celestial sphere and, therefore, the duration of the true solar day will constantly change throughout the year: fastest near the equinoxes (March, September), slowest near the solstices (June, January).

To simplify time calculations in astronomy, the concept of an average solar day was introduced - the period of rotation of the Earth around its axis relative to the “average Sun”.

The average solar day is defined as the time interval between two successive culminations of the same name of the “average Sun”.

The average solar day is 3 m 55.009 s shorter than the sidereal day.

24 h 00 m 00 s sidereal time is equal to 23 h 56 m 4.09 s mean solar time.

For the certainty of theoretical calculations, it was accepted ephemeris (tabular) a second equal to the average solar second on January 0, 1900 at 12 o'clock of equicurrent time not associated with the rotation of the Earth. About 35,000 years ago, people noticed the periodic change in the appearance of the Moon - the change of lunar phases. Phase F celestial body (Moon, planet, etc.) is determined by the ratio of the greatest width of the illuminated part of the disk d¢ to its diameter D: . Line terminator separates the dark and light parts of the luminary's disk.

Rice. 32. Changing phases of the moon

The Moon moves around the Earth in the same direction in which the Earth rotates around its axis: from west to east. This movement is reflected in the visible movement of the Moon against the background of stars towards the rotation of the sky. Every day, the Moon moves east by 13º relative to the stars and completes a full circle in 27.3 days. This is how the second measure of time after the day was established - month(Fig. 32).

Sidereal (sidereal) lunar month- the period of time during which the Moon makes one complete revolution around the Earth relative to the fixed stars. Equal to 27 d 07 h 43 m 11.47 s.

A synodic (calendar) lunar month is the period of time between two successive phases of the same name (usually new moons) of the Moon. Equal to 29 d 12 h 44 m 2.78 s.

Rice. 33. Methods of orientation to
terrain on the moon

The combination of the phenomena of the visible movement of the Moon against the background of stars and the changing phases of the Moon allows one to navigate by the Moon on the ground (Fig. 33). The moon appears as a narrow crescent in the west and disappears in the rays of dawn with the same narrow crescent in the east. Let's mentally draw a straight line to the left of the lunar crescent. We can read in the sky either the letter “R” - “growing”, the “horns” of the month are turned to the left - the month is visible in the west; or the letter “C” - “aging”, the “horns” of the month are turned to the right - the month is visible in the east. During a full moon, the moon is visible in the south at midnight.

As a result of observations of changes in the position of the Sun above the horizon over many months, a third measure of time arose - year.

A year is a period of time during which the Earth makes one full revolution around the Sun relative to some landmark (point).

A sidereal year is the sidereal (stellar) period of the Earth’s revolution around the Sun, equal to 365.256320... average solar day.

An anomalistic year - the time interval between two successive passages of the average Sun through a point in its orbit (usually perihelion) is equal to 365.259641... average solar days.

Tropical year is the time interval between two successive passages of the average Sun through the vernal equinox, equal to 365.2422... average solar days or 365 d 05 h 48 m 46.1 s.

Universal time is defined as the local mean solar time at the prime (Greenwich) meridian.

The Earth's surface is divided into 24 areas bounded by meridians - time zones. The zero time zone is located symmetrically relative to the prime (Greenwich) meridian. The belts are numbered from 0 to 23 from west to east. The real boundaries of the belts are combined with the administrative boundaries of districts, regions or states. The central meridians of time zones are separated from each other by exactly 15 degrees (1 hour), so when moving from one time zone to another, the time changes by an integer number of hours, but the number of minutes and seconds does not change. New calendar day (and New Year) begin with date lines(demarcation line), passing mainly along the meridian of 180°E near the northeastern border Russian Federation. West of the date line, the date of the month is always one more than east of it. When crossing this line from west to east, the calendar number decreases by one, and when crossing the line from east to west, the calendar number increases by one, which eliminates the error in counting time when traveling around the world and moving people from the Eastern to the Western hemispheres of the Earth.

Standard time is determined by the formula:
T n = T 0 + n , Where T 0 - universal time; n- time zone number.

Daylight saving time is standard time changed by an integer number of hours by government decree. For Russia it is equal to zone time, plus 1 hour.

Moscow time - maternity time of the second time zone (plus 1 hour):
Tm = T 0 + 3 (hours).

Daylight saving time is standard standard time, changed by an additional plus 1 hour by government order for the period of summer time in order to save energy resources.

Due to the rotation of the Earth, the difference between the moments of noon or the culmination of stars with known equatorial coordinates at 2 points is equal to the difference in the geographical longitudes of the points, which makes it possible to determine the longitude of a given point from astronomical observations of the Sun and other luminaries and, conversely, local time at any point with a known longitude .

The geographic longitude of the area is measured east of the “zero” (Greenwich) meridian and is numerically equal to the time interval between the same climaxes of the same star on the Greenwich meridian and at the observation point: , where S- sidereal time at a point with a given geographic latitude, S 0 - sidereal time on the prime meridian. Expressed in degrees or hours, minutes and seconds.

To determine the geographic longitude of an area, it is necessary to determine the moment of culmination of a luminary (usually the Sun) with known equatorial coordinates. By converting the observation time from mean solar to sidereal using special tables or a calculator and knowing from the reference book the time of the culmination of this star on the Greenwich meridian, we can easily determine the longitude of the area. The only difficulty in calculations is the exact conversion of time units from one system to another. There is no need to “watch” the moment of culmination: it is enough to determine the height (zenith distance) of the luminary at any precisely recorded moment in time, but the calculations will be quite complicated.

At the second stage of the lesson, students become familiar with instruments for measuring, storing and counting time - clocks. Clock readings serve as a standard against which time intervals can be compared. Students should pay attention to the fact that the need to accurately determine moments and periods of time stimulated the development of astronomy and physics: until the middle of the twentieth century, astronomical methods of measuring, storing time and time standards formed the basis of the world Time Service. The accuracy of the clock was controlled by astronomical observations. Currently, the development of physics has led to the creation of more accurate methods for determining time and standards, which began to be used by astronomers to study the phenomena that underlay previous methods of measuring time.

The material is presented in the form of a lecture, accompanied by demonstrations of the operating principle and internal structure of various types of watches.

2. Instruments for measuring and storing time

Even in Ancient Babylon, the solar day was divided into 24 hours (360њ: 24 = 15њ). Later, each hour was divided into 60 minutes, and each minute into 60 seconds.

The first instruments for measuring time were sundials. The simplest sundial - gnomon- represent a vertical pole in the center horizontal platform with divisions (Fig. 34). The shadow from the gnomon describes a complex curve that depends on the height of the Sun and changes from day to day depending on the position of the Sun on the ecliptic; the speed of the shadow also changes. The sundial does not require winding, does not stop and always runs correctly. By tilting the platform so that the pole from the gnomon is aimed at the celestial pole, we get an equatorial sundial in which the speed of the shadow is uniform (Fig. 35).

Rice. 34. Horizontal sundial. The angles corresponding to each hour have different values and are calculated using the formula: , where a is the angle between the noon line (projection of the celestial meridian onto the horizontal surface) and the direction to the numbers 6, 8, 10..., indicating the hours; j is the latitude of the place; h - hour angle of the Sun (15њ, 30њ, 45њ)

Rice. 35. Equatorial sundial. Each hour on the dial corresponds to an angle of 15º

To measure time at night and in bad weather, sand, fire and water clocks were invented.

Hourglasses are distinguished by their simplicity of design and accuracy, but they are bulky and “wind up” only for a short time.

A fire clock is a spiral or stick made of a flammable substance with marked divisions. In ancient China, mixtures were created that burned for months without constant supervision. The disadvantages of these watches: low accuracy (dependence of the burning rate on the composition of the substance and weather) and complexity of manufacture (Fig. 36).

Water clocks (clepsydra) were used in all countries Ancient world(Fig. 37 a, b).

Mechanical watch with weights and wheels were invented in X-XI centuries. In Russia, the first mechanical tower clock was installed in the Moscow Kremlin in 1404 by the monk Lazar Sorbin. Pendulum clock invented in 1657 by the Dutch physicist and astronomer H. Huygens. Mechanical watches with a spring were invented in the 18th century. In the 30s of our century, quartz watches were invented. In 1954, the idea arose in the USSR to create atomic clock- "State primary standard of time and frequency." They were installed at a research institute near Moscow and gave a random error of 1 second every 500,000 years.

An even more accurate atomic (optical) time standard was created in the USSR in 1978. An error of 1 second occurs once every 10,000,000 years!

With the help of these and many other modern physical instruments, it was possible to determine with very high accuracy the values of the basic and derivative units of time. Many characteristics of the apparent and true motion of cosmic bodies were clarified, new cosmic phenomena were discovered, including changes in the speed of rotation of the Earth around its axis by 0.01-1 second during the year.

3. Calendars. Calculation

The calendar is a continuous number system for large periods of time, based on the periodicity of natural phenomena, especially clearly manifested in celestial phenomena (the movement of celestial bodies). The entire centuries-old history of human culture is inextricably linked with the calendar.

The need for calendars arose in ancient times, when people did not yet know how to read and write. Calendars determined the onset of spring, summer, autumn and winter, periods of flowering of plants, ripening of fruits, collection of medicinal herbs, changes in the behavior and life of animals, weather changes, time of agricultural work and much more. Calendars answer the questions: “What date is today?”, “What day of the week?”, “When did this or that event occur?” and allow you to regulate and plan your life and economic activity people.

There are three main types of calendars:

1. Lunar calendar, which is based on a synodic lunar month with a duration of 29.5 average solar days. Originated over 30,000 years ago. The lunar year of the calendar contains 354 (355) days (11.25 days shorter than the solar one) and is divided into 12 months of 30 (odd) and 29 (even) days each (in the Muslim calendar they are called: Muharram, Safar, Rabi al- Awwal, Rabi al-Sani, Jumada al-Ula, Jumada al-Ahira, Rajab, Sha'ban, Ramadan, Shawwal, Dhul-Qaada, Dhul-Hijra). Since the calendar month is 0.0306 days shorter than the synodic month and over 30 years the difference between them reaches 11 days, in Arabic lunar calendar in each 30-year cycle there are 19 “simple” years of 354 days each and 11 “leap” years of 355 days each (2nd, 5th, 7th, 10th, 13th, 16th, 18th, 21st, 24th, 26th, 29th years of each cycle). Turkish the lunar calendar is less accurate: in its 8-year cycle there are 5 “simple” and 3 “leap” years. New Year's date not fixed (moves slowly from year to year): for example, 1421 Hijri began on April 6, 2000 and will end on March 25, 2001. The lunar calendar is adopted as a religious and state calendar in the Muslim states of Afghanistan, Iraq, Iran, Pakistan, the United Arab Republic and others. Solar and lunisolar calendars are used in parallel for planning and regulating economic activities.

2.Solar calendar, which is based on the tropical year. Originated over 6000 years ago. Currently accepted as the world calendar.

The "old style" Julian solar calendar contains 365.25 days. Developed by the Alexandrian astronomer Sosigenes, introduced by Emperor Julius Caesar into Ancient Rome in 46 BC and then spread throughout the world. In Rus' it was adopted in 988 AD. In the Julian calendar, the length of the year is determined to be 365.25 days; three “simple” years have 365 days each, one leap year has 366 days. There are 12 months in a year of 30 and 31 days each (except February). The Julian year lags behind the tropical year by 11 minutes 13.9 seconds per year. Over 1500 years of its use, an error of 10 days has accumulated.

IN Gregorian According to the “new style” solar calendar, the length of the year is 365.242500 days. In 1582, the Julian calendar, by order of Pope Gregory XIII, was reformed in accordance with the project of the Italian mathematician Luigi Lilio Garalli (1520-1576). The counting of days was moved forward by 10 days and it was agreed that every century that is not divisible by 4 without a remainder: 1700, 1800, 1900, 2100, etc. should not be considered a leap year. This corrects an error of 3 days every 400 years. An error of 1 day “accumulates” in 2735 years. New centuries and millennia begin on January 1 of the “first” year of a given century and millennium: thus, the 21st century and the 3rd millennium AD will begin on January 1, 2001 according to the Gregorian calendar.

In our country, before the revolution, the Julian calendar of the “old style” was used, the error of which by 1917 was 13 days. In 1918, the world-accepted “new style” Gregorian calendar was introduced in the country and all dates moved forward 13 days.

Converting dates from the Julian calendar to the Gregorian calendar is carried out using the formula: , where T G and T Yu– dates in Gregorian and Julian calendar; n – integer number of days, WITH– the number of complete past centuries, WITH 1 is the nearest number of centuries divisible by four.

Other types of solar calendars are:

The Persian calendar, which determined the length of the tropical year at 365.24242 days; The 33-year cycle includes 25 “simple” years and 8 “leap” years. Much more accurate than the Gregorian: an error of 1 year “accumulates” in 4500 years. Developed by Omar Khayyam in 1079; was used on the territory of Persia and a number of other states until mid-19th century.

The Coptic calendar is similar to the Julian: there are 12 months of 30 days in a year; after the 12th month in a “simple” year, 5 are added, in a “leap” year – 6 additional days. Used in Ethiopia and some other states (Egypt, Sudan, Türkiye, etc.) in the territory of Copts.

3.Lunar-solar calendar, in which the movement of the Moon is consistent with the annual movement of the Sun. The year consists of 12 lunar months of 29 and 30 days each, to which “leap” years containing an additional 13th month are periodically added to take into account the movement of the Sun. As a result, “simple” years last 353, 354, 355 days, and “leap” years last 383, 384 or 385 days. It arose at the beginning of the 1st millennium BC and was used in Ancient China, India, Babylon, Judea, Greece, and Rome. Currently accepted in Israel (the beginning of the year falls on different days between September 6 and October 5) and is used, along with the state one, in the countries of Southeast Asia (Vietnam, China, etc.).

In addition to the main types of calendars described above, calendars that take into account the apparent movement of planets on the celestial sphere have been created and are still used in some regions of the Earth.

Eastern lunisolar-planetary 60 year old calendar based on the periodicity of the movement of the Sun, Moon and the planets Jupiter and Saturn. It arose at the beginning of the 2nd millennium BC. in East and Southeast Asia. Currently used in China, Korea, Mongolia, Japan and some other countries in the region.

In the 60-year cycle of the modern eastern calendar there are 21912 days (the first 12 years contain 4371 days; the second and fourth years - 4400 and 4401 days; the third and fifth years - 4370 days). Two 30-year cycles of Saturn fit into this period of time (equal to the sidereal periods of its revolution T Saturn = 29.46 » 30 years), approximately three 19-year lunisolar cycles, five 12-year cycles of Jupiter (equal to the sidereal periods of its revolution T Jupiter= 11.86 » 12 years) and five 12-year lunar cycles. The number of days in a year is not constant and can be 353, 354, 355 days in “simple” years, and 383, 384, 385 days in leap years. The beginning of the year in different countries falls on different dates from January 13 to February 24. The current 60-year cycle began in 1984. Data on the combination of signs of the eastern calendar are given in the Appendix.

The Central American calendar of the Mayan and Aztec cultures was used during the period around 300–1530. AD Based on the periodicity of the movement of the Sun, Moon and the synodic periods of revolution of the planets Venus (584 d) and Mars (780 d). The “long” year, 360 (365) days long, consisted of 18 months of 20 days each and 5 holidays. At the same time, for cultural and religious purposes, a “short year” of 260 days was used (1/3 of the synodic period of the revolution of Mars) divided into 13 months of 20 days each; “numbered” weeks consisted of 13 days, which had their own number and name. The length of the tropical year was determined with the highest accuracy of 365.2420 d (an error of 1 day does not accumulate over 5000 years!); lunar synodic month – 29.53059 d.

By the beginning of the twentieth century, the growth of international scientific, technical, cultural and economic ties necessitated the creation of a single, simple and accurate World Calendar. Existing calendars have numerous disadvantages such as: insufficient correspondence to the length of the tropical year and dates astronomical phenomena, associated with the movement of the Sun across the celestial sphere, unequal and inconsistent lengths of months, inconsistency of the numbers of the month and days of the week, inconsistency of their names with the position in the calendar, etc. The inaccuracies of the modern calendar are revealed

Ideal eternal The calendar has an unchanging structure that allows you to quickly and unambiguously determine the days of the week according to any calendar date. One of the best perpetual calendar projects was recommended for consideration by the UN General Assembly in 1954: although it was similar to the Gregorian calendar, it was simpler and more convenient. The tropical year is divided into 4 quarters of 91 days (13 weeks). Each quarter begins on Sunday and ends on Saturday; consists of 3 months, the first month has 31 days, the second and third – 30 days. Each month has 26 working days. The first day of the year is always Sunday. Data for this project are given in the Appendix. It was not implemented due to religious reasons. The introduction of a unified World Perpetual Calendar remains one of the problems of our time.

The starting date and subsequent chronology system are called era. The starting point of the era is called era.

Since ancient times, the beginning of a certain era (more than 1000 eras are known in various states of various regions of the Earth, including 350 in China and 250 in Japan) and the entire course of chronology have been associated with important legendary, religious or (less often) real events: the reign of certain dynasties and individual emperors, wars, revolutions, Olympics, the founding of cities and states, the “birth” of God (prophet) or the “creation of the world.”

The date of the 1st year of the reign of Emperor Huangdi is taken as the beginning of the Chinese 60-year cyclic era - 2697 BC.

In the Roman Empire, the count was kept from the "foundation of Rome" from April 21, 753 BC. and from the accession of Emperor Diocletian on August 29, 284 AD.

In the Byzantine Empire and later, according to tradition, in Rus' - from the adoption of Christianity by Prince Vladimir Svyatoslavovich (988 AD) to the decree of Peter I (1700 AD), the count of years was carried out “from the creation of the world”: for The starting date was September 1, 5508 BC (the first year of the “Byzantine era”). In Ancient Israel (Palestine), the “creation of the world” occurred later: October 7, 3761 BC (the first year of the “Jewish era”). There were others, different from the most common above-mentioned eras “from the creation of the world.”

The growth of cultural and economic ties and the widespread spread of the Christian religion in Western and Eastern Europe gave rise to the need to unify chronology systems, units of measurement and time counting.

Modern chronology - " AD", "new era" (AD), "era from the Nativity of Christ" ( R.H..), Anno Domeni ( A.D.– “year of the Lord”) – is based on an arbitrarily chosen date of birth of Jesus Christ. Since it is not indicated in any historical document, and the Gospels contradict each other, learned monk Dionysius the Lesser in 278 of the Diocletian era decided to “scientifically”, based on astronomical data, calculate the date of the era. The calculation was based on: a 28-year "solar circle" - a period of time during which the numbers of months fall on exactly the same days of the week, and a 19-year "lunar circle" - a period of time during which the same phases of the Moon fall on the same days. the same days of the month. The product of the cycles of the “solar” and “lunar” circles, adjusted for the 30-year life of Christ (28 ´ 19S + 30 = 572), gave the starting date of modern chronology. Counting years according to the era “from the Nativity of Christ” “took root” very slowly: until the 15th century AD. (i.e. even 1000 years later) in official documents Western Europe 2 dates were indicated: from the creation of the world and from the Nativity of Christ (A.D.).

IN Muslim world The beginning of chronology is July 16, 622 AD - the day of the “Hijra” (the migration of the Prophet Mohammed from Mecca to Medina).

Translation of dates from the "Muslim" chronology system T M to "Christian" (Gregorian) T G can be done using the formula: (years).

For the convenience of astronomical and chronological calculations, the chronology proposed by J. Scaliger has been used since the end of the 16th century. Julian period(J.D.). Continuous counting of days has been carried out since January 1, 4713 BC.

As in previous lessons, students should be instructed to complete the table themselves. 6 information about the cosmic and celestial phenomena studied in the lesson. No more than 3 minutes are allotted for this, then the teacher checks and corrects the students’ work. Table 6 is supplemented with information:

The material is consolidated when solving problems:

Exercise 4:

1. On January 1, the sundial shows 10 am. What time does your watch show at this moment?

2. Determine the difference in readings accurate clock and a chronometer running according to sidereal time, 1 year after their simultaneous launch.

3. Determine the moments of the beginning of the full phase lunar eclipse April 4, 1996 in Chelyabinsk and Novosibirsk, if according to universal time the phenomenon occurred at 23 h 36 m.

4. Determine whether it is possible to observe an eclipse (occultation) of Jupiter by the Moon in Vladivostok if it occurs at 1 h 50 m universal time, and the Moon sets in Vladivostok at 0 h 30 m local summer time.

5. How many days did 1918 last in the RSFSR?

6. What is the greatest number of Sundays there can be in February?

7. How many times a year does the Sun rise?

8. Why does the Moon always face the same side towards the Earth?

9. The captain of the ship measured the zenith distance of the Sun at true noon on December 22 and found it equal to 66º 33". The chronometer running in Greenwich time showed 11:54 am at the moment of observation. Determine the coordinates of the ship and its position on the world map.

10. What are the geographic coordinates of the place where the height of the North Star is 64º 12", and the culmination of the star a Lyrae occurs 4 h 18 m later than at Greenwich Observatory?

11. Determine the geographic coordinates of the place where the star’s upper culmination a - - didactics - tests - task

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Lunar calendars in the East Gidayatkhanova Alisa

The lunar calendar is a type of calendar based on the period of changing phases of the Moon, that is, the synodic month. The changing phases of the Moon are one of the most easily observed celestial phenomena. It is not surprising that many peoples at an early stage of their development used the lunar calendar. However, during the period of formation of a sedentary lifestyle lunar calendar ceased to satisfy the needs of the population, since agricultural work is tied to the change of seasons, that is, the movement of the Sun. Therefore, lunar calendars, with rare exceptions (for example, the Islamic calendar), were inevitably replaced by lunisolar or solar calendars.

Chinese lunar calendar The lunar calendar in China has its roots in ancient times. In China, the traditional way of calculating time is based on the lunar calendar. The basics of the lunar calendar were known to the ancestors of the Chinese already in the middle of the 2nd millennium BC. e. The final design of the Chinese lunar calendar system dates back to the Han era (2nd century BC - 2nd century AD), which, then established, was used until the 20th century.

Changes in the appearance of the moon caused by its position relative to the sun and earth are called phases of the moon. The return of the moon to its previous phases was observed in ancient times and was important for establishing time. The moon rotates around its axis from west to east every 29.530 days, as a result of which the moon always faces the earth with the same side. Even in Ancient China, the phases of the moon were chosen as the main unit of time. In the Chinese lunar calendar, the beginning of the month coincides with the new moon, and the middle with the full moon. The quarter phases of the moon are also distinguished as cardinal points of the lunar month, which have their own characteristics. Twelve lunar months form a year. Almost all traditional holidays of China and neighboring countries are oriented according to the lunar months.

The Chinese calendar today is represented by two types of calendars: lunar (agricultural) and solar-lunar. The second of them is historically known in two versions: the Xia calendar (named after the first semi-mythical dynasty), the most popular in East Asia, counting the year in spring; as well as the Zhuanxu calendar, named after the first ancestor, counting the year in autumn. Since time immemorial, China has been counting days according to the sexagesimal cycle, which became widely known in the West as the eastern calendar. At the turn of our era, the sexagesimal cycle was adapted for counting years. Chinese tradition counted sixty-year cycles from 2637 BC. e., when, according to legend, it was established by Huang Di (Yellow Emperor), who in China had the status of the founder of Chinese civilization. Within the framework of the sixty-year cycle, the twelve-membered series was associated with the already known zodiac animals, and the ten-membered series with the five world primary elements, considered in male and female aspects. In modern China, the Gregorian calendar has also come into use, but the lunar calendar, as before, is widely used to determine the dates of traditional holidays, such as the Spring Festival (Chinese New Year), the Mid-Autumn Festival and to determine the start dates of certain types of agricultural work; By the way, the “Spring Festival” (New Year) according to the lunar calendar is variable, and falls annually on the day of the “First New Moon”. The beginning of the new year is recognized as the second new moon, counting from the winter solstice (December 21–22), which occurs, respectively, no earlier than January 21 and no later than February 20.

The Xia calendar is used for mantic purposes, for example, when choosing the most auspicious days holding weddings, opening institutions - any other events. The personal “fate card”, ming shu, is also calculated using the Xia mantic calendar.

Other eastern calendars either completely identical to Chinese (for example, Korean), or in many ways similar to Chinese, but have some differences (Vietnamese - the Rabbit in the zodiac cycle is replaced by the Cat; Tibetan - the names of animals according to the Zodiac have been slightly changed; Japanese - the principle of calculation has been changed, and therefore there are discrepancies in years compared to other calendars). Elements of the Chinese (Sino-Uyghur) calendar thanks to Mongol conquests became the property of Islamic peoples. In particular, the names of animals, translated from Mongolian into Turkish, began to be used to maintain chronological records, official and historical documents in the territories where Persian and Turkish languages from Asia Minor to India, from the Middle Ages to modern times. In Iran, the lunar calendar was used by peasants and tax collectors until its use was banned in 1925.

Oriental calendar , which has been in effect for several thousand years in Vietnam, Kampuchea, China, Korea, Mongolia, Japan and some other Asian countries, was compiled during the time of the semi-legendary Emperor Huang Di in the middle of the third millennium BC. This calendar is a 60-year cyclical system.

It is based on the astronomical cycles of the Sun, Earth, Moon, Jupiter and Saturn. The 60-year cycle includes the 12-year Jupiter and 30-year Saturn cycles. The 12-year period of Jupiter was considered the most important for the life of nomads, and in those days the main peoples of the East were nomadic tribes. Ancients the Chinese and Japanese believed that the normal movement of Jupiter brings benefits and virtues.

In China calendar was a sacred document, supported by the reigning monarch. For more than 2 millennia, the astronomy department made astronomical observations, carried out calculations of astronomical events, and prepared astrological predictions. Moreover, lucky calendar contributed not only to practical purposes, but also confirmed the agreement between heaven and the empire.

Analyzing the preserved astronomical records on the bones, which were used for fortune-telling and predictions in Ancient China, a lunisolar system is discovered in China. calendar with intercalation of lunar months, dating back to the Shang Dynasty of the 14th century BC. Various intercalation schemes were developed in early versions of the calendar, including the 19-year and 76-year cycles of moon phases known in the West as the metonic and calliptic cycles.

From the earliest records, the beginning of the year occurred at the new moon around the winter solstice. However, the choice of month for the start of the civil year varied over time and geographically. At the end of the second century BC. Calendar reform established a practice that continues to this day, which requires that the winter solstice always fall in the 11th month of the year. This reform also included a system of intercalation, in which new moons were compared to 24 solar periods. However, the calculations were based on averaged motion derived from cyclic relations. Inequalities for calculating the motion of the moon were not used until the 7th century AD, but solar mean longitude was used to calculate solar periods until 1644.

Although eras were counted from the beginning of the reign of the new emperor The Emperor could also declare a new era arbitrarily during his reign. This was done to restore the broken connection between heaven and earth, personified by the emperor. A new era could indicate the death of an emperor, natural disasters, or the failure of astronomers to predict astronomical events. In the latter case, an era could mark the introduction of a new astronomical or calendar model.

Cycles in multiples of 60 were used to count years, months, days and fractions of a day, using a set of celestial branches and terrestrial shoots.

The use of a 60-day cycle is observed in the earliest astronomical records. The 60-year cycle was only introduced in the first century AD. or a little earlier. Although this type of counting of days has ceased to be used nowadays, it is still tabulated in calendars. Western astronomical theories entered China with Jesuit missionaries in the 17th century.