Account of time. Determination of geographic longitude
Lesson 5 methodology
"Time and Calendar"
The purpose of the lesson: the formation of a system of concepts of practical astrometry about the 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 keeping time, calendars and chronology; 2) definition geographical coordinates(longitude) of the area according to 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 their consequences - celestial phenomena: sunrise, sunset, daily and annual visible movement and culminations of the luminaries (Sun, Moon and stars), change of 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 the dates of the Julian and Gregorian calendars; polytechnic and labor education when presenting material on instruments for measuring and storing time (hours), calendars and chronology systems, and on practical ways application of astrometric knowledge.
Developing: the formation of skills: solve problems for calculating the time and dates of the chronology and transferring time from one storage system and account to another; perform exercises on the application of the basic formulas of practical astrometry; use a mobile map of the starry sky, reference books and the Astronomical calendar to determine the position and conditions for the visibility of celestial bodies and the course of celestial phenomena; determine the geographical coordinates (longitude) of the area according to astronomical observations.
Pupils should know:
1) the causes of everyday observed celestial phenomena generated by the revolution of the Moon around the Earth (change of the phases of the Moon, the apparent movement of the Moon in the celestial sphere);
2) the relationship of the duration of individual cosmic and celestial phenomena with units and methods of measurement, calculation and storage of time and calendars;
3) time units: ephemeris second; day (stellar, true and mean solar); a week; month (synodic and sidereal); year (stellar and tropical);
4) formulas expressing the connection of times: universal, decree, local, summer;
5) tools and methods for 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) the main types of calendars: lunar, lunisolar, solar (Julian and Gregorian) and the basics of chronology;
7) the basic concepts of practical astrometry: the principles of determining the time and geographical coordinates of the area according to astronomical observations.
8) astronomical quantities: geographical coordinates hometown; time units: ephemeroid second; day (stellar and mean 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.
Pupils should be able to:
1) Use a generalized plan for the study of cosmic and celestial phenomena.
2) Navigate the terrain by the moon.
3) Solve problems related to the conversion of time units from one counting system to another using formulas expressing the relationship: a) between sidereal and mean solar time; b) World, daylight, local, summer time and using a map of time zones; c) between different systems of reckoning.
4) Solve problems to determine the geographical 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 heavenly bodies"; "Development of ideas about the Universe"; "How Astronomy Refuted Religious Ideas about the Universe".
Devices and tools: geographical globe; map of time zones; gnomon and equatorial sundial, hourglass, water clock (with a uniform and non-uniform scale); a candle with divisions as a model of a fire clock, mechanical, quartz and electronic clocks.
Drawings, diagrams, photographs: changing the phases of the moon, the internal structure and the principle of operation of mechanical (pendulum and spring), quartz and electronic clocks, the atomic time standard.
Homework:
1. Study the material of textbooks:
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 Vorontsov-Velyaminov B.A. : 113; 115; 124; 125.
Lesson Plan
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Lesson stages |
Presentation methods |
Time, min |
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Knowledge check and update |
Frontal survey, conversation |
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Formation of concepts about time, units of measurement and counting of time, based on the duration of space phenomena, the relationship between different "times" and time zones |
Lecture |
7-10 |
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Acquaintance of students with methods for determining the geographical longitude of the area according to astronomical observations |
Conversation, lecture |
10-12 |
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Formation of concepts about tools for measuring, counting and storing time - hours and about the atomic standard of time |
Lecture |
7-10 |
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Formation of concepts about the main types of calendars and chronology systems |
Lecture, conversation |
7-10 |
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Problem solving |
board work, independent solution tasks in a notebook |
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Summarizing the material covered, summarizing the lesson, homework |
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Method of presenting the material
At the beginning of the lesson, you should test the knowledge acquired in the previous three lessons, updating the material intended for study with questions and tasks during a frontal survey and conversation with students. Some students perform programmed tasks, solving problems related to the use of a moving map of the starry sky (similar to the tasks of tasks 1-3).
A number of questions about the causes of celestial phenomena, the main lines and points of the celestial sphere, constellations, conditions for the visibility of luminaries, etc. matches the questions asked at the beginning of previous lessons. They are supplemented by questions:
1. Define the concepts of "brilliance of the star" and "magnitude". What do you know about the magnitude scale? What determines the brilliance 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? Sun's zenith distance? Azimuth of the sun? 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 the luminary? Polar distance? The hour angle of the sun? 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 right ascension of a star? What are the advantages and disadvantages of this celestial coordinate system?
1) How to navigate the terrain by the Sun? By the North Star?
2) How to determine geographical latitude terrain from astronomical observations?
Relevant programming tasks:
1) Collection of problems G.P. Subbotina, assignments NN 46-47; 54-56; 71-72.
2) Collection of problems E.P. Broken, tasks NN 4-1; 5-1; 5-6; 5-7.
3) Strout E.K. : test papers NN 1-2 of the topic "Practical foundations of astronomy" (converted to programmable 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 of time, units of measurement and counting of time, 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 hourly 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 frame of reference in which the Earth's motion is considered (whether it is related to fixed stars, Sun, etc.). The choice of reference system is reflected in the name of the unit of time.
2. The duration of time counting units is related to the conditions of visibility (culminations) of celestial bodies.
3. The introduction of the atomic time standard in science was due to the non-uniformity of the Earth's rotation, which was discovered with increasing clock accuracy.
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 the identification of local time with daylight savings time.
1. Time. Units of measurement and counting time
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 derived units of time are determined on the basis of astronomical observations of the course of celestial phenomena, due to: 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 calculate time in astrometry, they use different systems reference associated with certain celestial bodies or certain points of the celestial sphere. The most widespread are:
1. "stellar"the time associated with the movement of stars on the celestial sphere. Measured by the hour angle of the vernal equinox point: S \u003d t ^; t \u003d S - a
2. "solar"time associated: with the apparent 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 time interval as the true Sun (average solar time).
With the introduction in 1967 of the atomic time standard and the International SI system, the atomic second is used in physics.
Second - 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 by special calculations. V Everyday life mean solar time is used.
Determination of 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. Sidereal, mean solar and other seconds are obtained 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 complete revolution around its axis relative to any landmark.
Sidereal day - the period of rotation of the Earth around its axis relative to the fixed stars, is defined as the time interval between two successive upper climaxes of the vernal equinox.
True solar day - 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 of 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 revolves around the Sun in an elliptical (slightly elongated) orbit, the speed of the apparent movement of the Sun in the celestial sphere and, therefore, the duration of a true solar day will constantly change throughout the year: the fastest near the equinoxes (March, September), the slowest near the solstices (June, January).
To simplify the calculations of time in astronomy, the concept of a mean solar day has been introduced - the period of rotation of the Earth around its axis relative to the "mean Sun".
The mean solar day is defined as the time interval between two successive climaxes of the same name of the "mean Sun".
The mean solar day is 3 m 55.009 s shorter than the sidereal day.
24 h 00 m 00 s of sidereal time are equal to 23 h 56 m 4.09 s of mean solar time.
For definiteness of theoretical calculations, it is accepted ephemeris (table) second equal to the mean solar second on January 0, 1900 at 12 o'clock equal current time, not related to the rotation of the Earth. About 35,000 years ago, people noticed a periodic change in the appearance of the moon - a change in the lunar phases. Phase F celestial body (Moon, planets, etc.) is determined by the ratio of the largest 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.
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| Rice. 32. Changing the 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. The display of this movement is the apparent movement of the Moon against the background of the stars towards the rotation of the sky. Every day, the Moon moves eastward by 13° relative to the stars and completes a full circle in 27.3 days. So the second measure of time after the day was established - month(Fig. 32).
Sidereal (star) lunar month- the period of time during which the moon makes one complete revolution around the earth relative to the fixed stars. Equals 27 d 07 h 43 m 11.47 s .
Synodic (calendar) lunar month - the time interval between two successive phases of the same name (usually new moons) of the Moon. Equals 29 d 12 h 44 m 2.78 s .
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Rice. 33. Ways to focus on |
The totality of the phenomena of the visible movement of the Moon against the background of stars and the change in the phases of the Moon makes it possible to navigate the Moon on the ground (Fig. 33). The moon appears as a narrow crescent in the west and disappears in the rays of the morning dawn with the same narrow crescent in the east. Mentally attach a straight line to the left of the crescent moon. We can read in the sky either the letter "P" - "growing", the "horns" of the month are turned to the left - the month is visible in the west; or the letter "C" - "getting old", the "horns" of the month are turned to the right - the month is visible in the east. On a full moon, the moon is visible in the south at midnight.
As a result of observations of the change in the position of the Sun above the horizon for many months, a third measure of time arose - year.
A year is a period of time during which the Earth makes one complete revolution around the Sun relative to any reference point (point).
A sidereal year is a sidereal (stellar) period of the Earth's revolution around the Sun, equal to 365.256320 ... mean solar days.
Anomalistic year - the time interval between two successive passages of the average Sun through the point of its orbit (usually, perihelion), is equal to 365.259641 ... mean solar days.
A tropical year is the time interval between two successive passages of the average Sun through the vernal equinox, equal to 365.2422 ... mean solar days or 365 d 05 h 48 m 46.1 s.
Universal time is defined as local mean solar time at the zero (Greenwich) meridian.
The surface of the Earth is divided into 24 areas, bounded by meridians - Time Zones. The zero time zone is located symmetrically with respect to the zero (Greenwich) meridian. The belts are numbered from 0 to 23 from west to east. The real boundaries of the belts are aligned with the administrative boundaries of districts, regions or states. The central meridians of time zones are exactly 15º (1 hour) apart, so when moving from one time zone to another, time changes by an integer number of hours, and the number of minutes and seconds does not change. New calendar day (and New Year) start at date lines(demarcation line), passing mainly along the meridian of 180º east longitude near the northeastern border Russian Federation. To the west of the date line, the day of the month is always one more than to the 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 hemisphere 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 savings time is standard time, changed to an integer number of hours by government decree. For Russia, it is equal to the belt, plus 1 hour.
Moscow time - standard time of the second time zone (plus 1 hour):
Tm \u003d T 0 + 3
(hours).
Daylight Saving Time - standard time, changed by an additional plus 1 hour by government order for the period of summer time in order to save energy.
Due to the rotation of the Earth, the difference between the moments of the onset 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 climaxes of the same name of the same luminary 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 at the zero meridian. Expressed in degrees or hours, minutes and seconds.
To determine the geographic longitude of the area, it is necessary to determine the moment of climax of any luminary (usually the Sun) with known equatorial coordinates. By translating with the help of special tables or a calculator the time of observations from the mean solar to the stellar and knowing from the reference book the time of the culmination of this luminary on the Greenwich meridian, we can easily determine the longitude of the area. The only difficulty in the calculations is the exact conversion of units of time from one system to another. The moment of culmination can not be "guarded": it is enough to determine the height (zenith distance) of the luminary at any precisely fixed point in time, but the calculations will be quite complicated.
At the second stage of the lesson, students get acquainted with devices for measuring, storing and counting time - hours. The clock readings serve as a reference against which time intervals can be compared. Students should pay attention to the fact that the need to accurately determine moments and time intervals stimulated the development of astronomy and physics: until the middle of the twentieth century, astronomical methods of measuring, storing time and time standards underlay the world Time Service. The accuracy of the clock was controlled by astronomical observations. At present, the development of physics has led to the creation of more accurate methods for determining and standards of time, which began to be used by astronomers to study the phenomena that underlay the former methods of measuring time.
The material is presented in the form of a lecture, accompanied by demonstrations of the principle of operation and the internal structure of watches of various types.
2. Devices 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 of a 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. Sundial does not require winding, does not stop and always runs correctly. tilting the site so that the pole from the gnomon is aimed at the pole of the world, 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 a different value and are calculated by the formula: 
, where a is the angle between the midday line (the projection of the celestial meridian onto a 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 (15º, 30º, 45º)
Rice. 35. Equatorial sundial. Each hour on the dial corresponds to an angle of 15 degrees.
To measure time at night and in bad weather, hourglasses, fire and water clocks were invented.
Hourglasses are simple in design and accurate, but bulky and "wind up" only for a short time.
The fiery clock is a spiral or stick of a combustible substance with applied divisions. In ancient China, mixtures were created that burned for months without constant supervision. The disadvantages of these watches are: low accuracy (dependence of the burning rate on the composition of the substance and the weather) and the complexity of manufacturing (Fig. 36).
Water clocks (clepsydra) were used in all countries ancient world(Fig. 37 a, b).
Mechanical watches with weights and wheels were invented in the 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. The mechanical clock with a spring was 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 every 10,000,000 years!
With the help of these and many other modern physical instruments, it was possible to determine the values of the basic and derived units of time with very high accuracy. Many characteristics of the visible and true movement of cosmic bodies were refined, new cosmic phenomena were discovered, including changes in the speed of the Earth's rotation around its axis by 0.01-1 second during the year.
3. Calendars. chronology
A calendar is a continuous number system for large periods of time, based on the periodicity of natural phenomena, which is especially clearly manifested in celestial phenomena (the movement of heavenly bodies). The entire centuries-old history of human culture is inextricably linked with the calendar.
The need for calendars arose in such extreme antiquity, when people could not yet read and write. The calendars determined the onset of spring, summer, autumn and winter, the periods of flowering plants, fruit ripening, the collection of medicinal herbs, changes in the behavior and life of animals, weather changes, the 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 happen?" and allow you to regulate and plan life and economic activity people.
There are three main types of calendars:
1. Lunar the calendar, which is based on a synodic lunar month with a duration of 29.5 mean solar days. It originated over 30,000 years ago. The lunar year of the calendar contains 354 (355) days (11.25 days shorter than the solar year) 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-slani, 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 in 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 and 11 "leap years" of 355 days (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 is not fixed (it moves slowly from year to year): for example, 1421 AH began on April 6, 2000 and will end on March 25, 2001. Moon calendar adopted as a religious and state in the Muslim states of Afghanistan, Iraq, Iran, Pakistan, UAR and others. The solar and lunar-solar calendars are used in parallel for planning and regulating economic activities.
2.solar calendar based on the tropical year. It originated over 6000 years ago. It is currently accepted as the world calendar.
The "old style" Julian solar calendar contains 365.25 days. Designed by the Alexandrian astronomer Sosigenes, introduced by the emperor Julius Caesar in Ancient Rome in 46 BC and then spread throughout the world. In Russia, it was adopted in 988 AD. In the Julian calendar, the length of the year is defined as 365.25 days; three "simple" years have 365 days, one leap year - 366 days. There are 12 months of 30 and 31 days each in a year (except February). The Julian year is 11 minutes 13.9 seconds behind the tropical year. For 1500 years of its application, an error of 10 days has accumulated.
V Gregorian solar calendar "new style" the length of the year is 365, 242,500 days. In 1582, the Julian calendar was reformed by Pope Gregory XIII in accordance with the project of the Italian mathematician Luigi Lilio Garalli (1520-1576). The count 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 for every 400 years. An error of 1 day "overruns" for 2735 years. New centuries and millennia begin on January 1 of the "first" year of a given century and millennium: thus, the XXI century and III millennium of our era (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-famous Gregorian calendar of the "new style" was introduced in the country and all dates were shifted 13 days ahead.
The conversion of dates from the Julian calendar to the Gregorian calendar is carried out according to the formula: 
, where T G and T YU- dates according to the Gregorian and Julian calendars; n is an integer number of days, WITH is the number of complete centuries that have elapsed, WITH 1 is the nearest number of centuries, a multiple of four.
Other varieties of solar calendars are:
Persian calendar, which determined the duration of the tropical year at 365.24242 days; The 33-year cycle includes 25 "simple" and 8 "leap" years. Much more accurate than the Gregorian one: an error of 1 year "overruns" 4500 years. Designed by Omar Khayyam in 1079; was used on the territory of Persia and a number of other states until the middle of the 19th century.
The Coptic calendar is similar to the Julian one: there are 12 months of 30 days in a year; after 12 months in a "simple" year, 5 are added, in a "leap" year - 6 extra days. It is used in Ethiopia and some other states (Egypt, Sudan, Turkey, etc.) in the territory of the Copts.
3.lunisolar calendar, in which the motion of the Moon is consistent with the annual motion of the Sun. The year consists of 12 lunar months of 29 and 30 days each, to which "leap" years are periodically added to account for the movement of the Sun, containing an additional 13th month. As a result, "simple" years last 353, 354, 355 days, and "leap years" - 383, 384 or 385 days. It arose at the beginning of the 1st millennium BC, was used in Ancient China, India, Babylon, Judea, Greece, Rome. It is currently adopted 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 were created and are still used in some regions of the Earth, taking into account the apparent movement of the planets in the celestial sphere.
Eastern lunisolar-planetary 60 year old the calendar based on the periodicity of the motion of the Sun, Moon and the planets Jupiter and Saturn. It arose at the beginning of the II 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 (in the first 12 years there are 4371 days; in the second and fourth - 4400 and 4401 days; in the third and fifth - 4370 days). This period of time fits two 30-year cycles of Saturn (equal to the sidereal periods of its revolution T Saturn \u003d 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, 383, 384, 385 days in leap years. The beginning of the year in different states 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 is given in the Appendix.
The Central American calendar of the Mayan and Aztec cultures was used from about 300-1530 BC. AD It is based on the periodicity of the motion of the Sun, the Moon and the synodic periods of revolution of the planets Venus (584 d) and Mars (780 d). A "long" year lasting 360 (365) days consisted of 18 months of 20 days each and 5 public holidays. In parallel, for cultural and religious purposes, a "short year" of 260 days (1/3 of the synodic period of Mars circulation) was used, divided into 13 months of 20 days each; "numbered" weeks consisted of 13 days, which had their own number and name. The duration 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 20th 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 shortcomings in the form of: insufficient correspondence between the length of the tropical year and the dates of astronomical phenomena associated with the movement of the Sun in the celestial sphere, unequal and inconstant duration of the months, inconsistency in the numbers of the month and days of the week, inconsistencies in their names with the position in the calendar, etc. The inaccuracies of the modern calendar are manifested
Ideal eternal the calendar has an invariable structure that allows you to quickly and unambiguously determine the days of the week for any calendar date of the chronology. One of the best projects of perpetual calendars was recommended for consideration by the UN General Assembly in 1954: while 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, in the first month 31 days, in the second and third - 30 days. Each month has 26 business days. The first day of the year is always Sunday. The data for this project is given in the Appendix. It was not implemented for religious reasons. The introduction of a single world perpetual calendar remains one of the problems of our time.
The starting date and the subsequent system of reckoning are called era. The starting point of the era is called it 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 the chronology were associated with important legendary, religious or (less often) real events: the time of the reign of certain dynasties and individual emperors, wars, revolutions, Olympiads, the foundation of cities and states, the "birth" of a god (prophet) or the "creation of the world."
For the beginning of the Chinese 60-year cycle era, the date of the 1st year of the reign of Emperor Huangdi - 2697 BC is accepted.
In the Roman Empire, the account was kept from the "foundation of Rome" from April 21, 753 BC. and from the day of the accession of the emperor Diocletian on August 29, 284 AD.
V Byzantine Empire and later, according to tradition, in Russia - from the adoption of Christianity by Prince Vladimir Svyatoslavovich (988 AD) until the decree of Peter I (1700 AD), the years were counted "from the creation of the world": for the starting point was the date adopted is September 1, 5508 BC (the first year of the "Byzantine era"). In Ancient Israel (Palestine), the "creation of the world" took place 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 the systems of chronology, units of measurement and counting time.
Modern chronology - " our era", "new era"(AD)," the era from the birth of Christ "( R.H.), Anno Domeni ( A.D.- "year of the Lord") - is conducted from an arbitrarily chosen date of the birth of Jesus Christ. Because none historical document it is not indicated, and the Gospels contradict each other, the learned monk Dionysius the Small in 278 of the era of Diocletian 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 for which the numbers of months fall on exactly the same days of the week, and a 19-year "lunar circle" - a period of time for which the same phases of the moon fall on the same and the same days of the month. The product of the cycles of the "solar" and "lunar" circles, adjusted for the 30-year time of the life of Christ (28 ´ 19S + 30 = 572), gave the starting date of the modern chronology. The account of years according to the era "from the birth of Christ" "take root" very slowly: up to the XV 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 the Muslim world, July 16, 622 AD, is taken as the beginning of the chronology - the day of the Hijjra (the migration of the Prophet Mohammed from Mecca to Medina).
Translation of dates from the "Muslim" system of chronology 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.). A continuous count of days has been kept since January 1, 4713 BC.
As in previous lessons, students should be instructed to complete the table on their own. 6 information about the cosmic and celestial phenomena studied in the lesson. This is given no more than 3 minutes, then the teacher checks and corrects the work of students. Table 6 is supplemented with information:
The material is fixed when solving problems:
Exercise 4:
1. On January 1, the sundial shows 10 am. What time is your watch showing at this moment?
2. Determine the difference in the readings of an accurate clock and a chronometer running in sidereal time, 1 year after their simultaneous start.
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 an eclipse (occultation) of Jupiter's Moon can be observed in Vladivostok if it occurs at 1 h 50 m UTC, and the Moon sets in Vladivostok at 0 h 30 m local summer time.
5. How many days did 1918 contain in the RSFSR?
6. What is the maximum number of Sundays in February?
7. How many times a year does the sun rise?
8. Why is the Moon always turned to the Earth by the same side?
9. The captain of the ship measured the zenithal distance of the Sun at true noon on December 22 and found it equal to 66њ 33 ". The chronometer running on Greenwich time showed at the time of observation 11 h 54 m in the morning. Determine the coordinates of the ship and its position on the world map.
10. What are the geographical coordinates of the place where the height of the North Star is 64њ 12", and the climax of the star a Lyra occurs 4 h 18 m later than at the Greenwich Observatory?
11. Determine the geographical coordinates of the place where the upper climax of the star a - - didactics - tests - task
Time Service
The tasks of the exact time service are to determine the exact time, be able to save it and convey it to the consumer. If we imagine that the clock hand is the optical axis of a telescope directed vertically into the sky, then the dial is the stars, one after another falling into the field of view of this telescope. Registration of the moments of the passage of stars through the telescope sight - this is general principle classical definition of astronomical time. Judging by the megalithic monuments that have come down to us, the most famous of which is Stonehenge in England, this method of reticle serifs was successfully used even in the Bronze Age. The very name of the astronomical time service is now obsolete. Since 1988 this service has been called the International Earth Rotation Service http://hpiers.obspm.fr/eop-pc/.
The classical astronomical way of determining the exact time (Universal Time, UT) is associated with measuring the angle of rotation of any chosen meridian of the Earth relative to the "sphere of fixed stars". The chosen one, in the end, was the Greenwich meridian. However, in Russia, for example, the Pulkovo meridian was taken as zero for a long time. In fact, any meridian on which a telescope specialized for recording the moments of stellar passages (a transit instrument, a zenith tube, an astrolabe) is installed is suitable for solving the first task of the exact time service. But not any latitude is optimal for this, which is obvious, for example, due to the convergence of all meridians at the geographic poles.
From the method of determining astronomical time, its connection with the determination of longitudes on Earth and, in general, with coordinate measurements is obvious. In essence, this is a single task of coordinate-time support (CWO). The complexity of this problem is understandable, the solution of which lasted for many centuries and continues to be the most urgent problem of geodesy, astronomy and geodynamics.
When determining UT by astronomical methods, it is necessary to take into account:
- that the "sphere of fixed stars" does not exist, i.e., the coordinates of the stars (the "dial" of the star clock, which determines the accuracy of these clocks) must be constantly refined from observations,
- that the axis of rotation of the Earth under the influence of the gravitational forces of the Sun, the Moon and other planets performs complex periodic (precession and nutation) movements, described by rows of hundreds of harmonics,
- that observations are made from the surface of the Earth, which is complexly moving in space, and, therefore, it is necessary to take into account parallactic and aberrational effects,
- that telescopes on which UT observations are made have their own non-constant errors, which depend, in particular, on climatic conditions and are determined from the same observations,
- that observations take place "at the bottom" of the atmospheric ocean, which distorts the true coordinates of stars (refraction) in a way that is often difficult to take into account,
- that the axis of rotation itself "dangles" in the body of the Earth and this phenomenon, as well as a number of tidal effects and effects due to atmospheric influences on the rotation of the Earth, are determined from the observations themselves,
- that the rotation of the Earth around its axis, which until 1956 served as the standard of time, occurs unevenly, which is also determined from the observations themselves.
A standard is needed for accurate timing. The chosen standard - the period of the Earth's rotation - turned out to be not quite reliable. A solar day is one of the basic units of time, chosen long ago. But the speed of rotation of the Earth changes throughout the year, and therefore the average solar day is used, which differs from the true one up to 11 minutes. Due to the uneven motion of the Earth along the ecliptic, the accepted solar day is 24 hours more per year by 1 sidereal day, which is 23 hours 56 minutes 4.091 seconds, while the average solar day is 24 hours 3 minutes 56.5554 seconds.
In the 1930s, the uneven rotation of the Earth around its axis was established. The unevenness is connected, in particular: with the secular deceleration of the Earth's rotation due to tidal friction from the Moon and the Sun; non-stationary processes inside the Earth. The mean sidereal day due to the procession of the earth's axis is 0.0084 s shorter than the actual period of the earth's rotation. The tidal action of the Moon slows down the rotation of the Earth by 0.0023 s in 100 years. Therefore, it is clear that the definition of a second as a unit of time, constituting 1/86400 of a day, required clarification.
The year 1900 was taken as the unit of measurement of the tropical year (the duration between two successive passages of the center of the Sun through the vernal equinox) equal to 365.242196 days, or 365 days 5 hours 48 minutes 48.08 seconds. Through it, the duration of a second = 1/31556925.9747 of the tropical year 1900 is determined.
In October 1967 in Paris, the 13th General Conference of the International Committee for Weights and Measures determines the duration of the atomic second - the time interval during which 9,192,631,770 vibrations occur, corresponding to the frequency of cure (absorption) by a Cesium atom - 133 during a resonant transition between two hyperfine energy levels the ground state of the atom in the absence of disturbances from external magnetic fields and is recorded as radio emission with a wavelength of about 3.26 cm.
The accuracy of atomic clocks is an error of 1s in 10,000 years. Error 10-14s.
On January 1, 1972, the USSR and many countries of the world switched to the atomic time standard.
Radio-broadcast time signals are transmitted over atomic clocks to accurately determine local time (i.e. geographical longitude- the location of strong points, finding the moments of the climax of the stars), as well as for aviation and marine navigation.
The first accurate time signals on the radio began to be transmitted by the station in Boston (USA) in 1904, from 1907 in Germany, from 1910 in Paris (radio station eiffel tower). In our country, from December 1, 1920, the Pulkovo Observatory began transmitting a rhythmic signal through the New Holland radio station in Petrograd, and from May 25, 1921, through the Moscow Oktyabrskaya radio station on Khodynka. The organizers of the radio technical service of the time in the country were Nikolai Ivanovich DNEPROVSKY (1887-1944), Alexander Pavlovich Konstantinov (1895-1937) and Pavel Andreevich Azbukin (1882-1970).
By a decree of the Council of People's Commissars in 1924, the Interdepartmental Committee of the Time Service was organized at the Pulkovo Observatory, which from 1928 began to publish bulletins of summary moments. In 1931, two new time services were organized in the SAI and TSNIIGAiK, and the time service of the Tashkent Observatory began regular work.
In March 1932, the first astrometric conference was held at the Pulkovo Observatory, at which a decision was made: to create a time service in the USSR. In the pre-war period, there were 7 time services, and in Pulkovo, the SAI and Tashkent, rhythmic time signals were transmitted by radio.
The most accurate clock used by the service (stored in the basement at constant pressure, temperature, etc.) was Short's double-pendulum clock (accuracy ± 0.001 s / day), F.M. Fedchenko (± 0.0003 s / day), then they began to use quartz (with their help, the uneven rotation of the Earth was discovered) before the introduction of atomic clocks, which are now used by the time service. Lewis Essen (England), experimental physicist, creator of quartz and atomic clocks, in 1955 created the first atomic frequency (time) standard on a cesium atomic beam, which resulted in a time service based on the atomic frequency standard three years later.
According to the atomic standard of the USA, Canada and Germany, TAI is established from January 1, 1972 - the average value of atomic time, on the basis of which the UTC (universal coordinate time) scale was created, which differs from the mean solar time by no more than 1 second (with an accuracy of ± 0.90 sec). Every year UTC is corrected by 1 second on December 31 or June 30.
In the last quarter of the 20th century, extragalactic astronomical objects - quasars - were already used for the purposes of determining the Universal Time. At the same time, their broadband radio signal is recorded on two radio telescopes separated by thousands of kilometers (very long baseline radio interferometers - VLBI) in a synchronized scale of atomic time and frequency standards. In addition, systems based on observations of satellites (GPS - Global Positioning System, GLONASS - global navigation satellite system and LLS - Laser Location of Satellites) and corner reflectors installed on the Moon (Laser Location of the Moon - LLL) are used.
Astronomical concepts
Astronomical Time. Until 1925, in astronomical practice, the moment of the upper culmination (noon) of the mean sun was taken as the beginning of the mean solar day. Such time was called mean astronomical or simply astronomical. The mean solar second was used as the unit of measurement. Since January 1, 1925, it has been replaced by universal time (UT)
Atomic time (AT - Atomic Time) was introduced on January 1, 1964. An atomic second is taken as a unit of time, equal to the time interval during which 9,192,631,770 oscillations occur, corresponding to the frequency of radiation between two levels of the hyperfine structure of the ground state of the cesium-133 atom in the absence of external magnetic fields. AT carriers are more than 200 atomic time and frequency standards located in more than 30 countries of the world. These standards (clocks) are constantly compared with each other through the GPS / GLONASS satellite system, with the help of which the international atomic time scale (TAI) is derived. On the basis of comparison, it is believed that the TAI scale does not differ from imaginary absolutely accurate clocks by more than 0.1 microseconds per year. AT is not related to the astronomical way of determining time, based on measuring the speed of the Earth's rotation, therefore, over time, the AT and UT scales can diverge by a significant amount. To exclude this from January 1, 1972, Coordinated Universal Time (UTC) was introduced.
Universal Time (UT - Universal Time) has been used since January 1, 1925 instead of astronomical time. It is counted from the lower culmination of the mean sun on the Greenwich meridian. Since January 1, 1956, three universal time scales have been defined:
UT0 - universal time, determined on the basis of direct astronomical observations, i.e. the time of the instantaneous Greenwich meridian, the position of the plane of which is characterized by the instantaneous position of the Earth's poles;
UT1 is the time of the mean Greenwich meridian, determined by the average position of the Earth's poles. It differs from UT0 in corrections for the displacement of the geographic pole due to the displacement of the Earth's body relative to its axis of rotation;
UT2 is the "smoothed" UT1 seasonally adjusted time angular velocity rotation of the earth.
Coordinated Universal Time (UTC). UTC is based on the AT scale, which, if necessary, but only on January 1 or July 1, can be corrected by entering an additional negative or positive second so that the difference between UTC and UT1 does not exceed 0.8 seconds. The time scale of the Russian Federation UTC(SU) is reproduced by the State Standard of Time and Frequency and is consistent with the scale of the international time bureau UTC. Currently (early 2005) TAI - UTC = 32 seconds. There are many sites where you can take the exact time, for example, on the server of the International Bureau of Weights and Measures (BIPM) http://www.bipm.fr/en/scientific/tai/time_server.html.
A sidereal day is the time interval between two successive climaxes of the same name at the vernal equinox on the same meridian. The moment of its upper climax is taken as the beginning of a sidereal day. There is true and mean sidereal time depending on the chosen vernal equinox point. The average sidereal day is equal to 23 hours.56 minutes 04.0905 seconds of a mean solar day.
True solar time is an uneven time determined by the movement of the true sun and expressed in fractions of a true solar day. The unevenness of true solar time (the equation of time) is due to 1) the inclination of the ecliptic to the equator and 2) the uneven movement of the sun along the ecliptic due to the eccentricity of the Earth's orbit.
A true solar day is the time interval between two successive climaxes of the same name of the true sun on the same meridian. The moment of the lower culmination (midnight) of the true sun is taken as the beginning of a true solar day.
Mean solar time is the uniform time determined by the movement of the mean sun. It was used as a standard of uniform time with a scale of one mean solar second (1/86400 fraction of a mean solar day) until 1956.
The mean solar day is the time interval between two successive climaxes of the same name of the mean sun on the same meridian. The moment of the lower climax (midnight) of the mean sun is taken as the beginning of the mean solar day.
The mean (equatorial) sun is a fictitious point on the celestial sphere, moving uniformly along the equator with the average annual speed of the true Sun along the ecliptic.
The mean ecliptic sun is a fictitious point on the celestial sphere, moving uniformly along the ecliptic with the average annual speed of the true sun. The movement of the mean ecliptic sun along the equator is uneven.
The vernal equinox is the one of the two points of intersection of the equator and the ecliptic on the celestial sphere, which the center of the sun passes in the spring. There are true (moving due to precession and nutation) and average (moving only due to precession) points of the vernal equinox.
A tropical year is the time interval between two successive passages of the mean sun through the midpoint of the vernal equinox, equal to 365.24219879 mean solar days or 366.24219879 sidereal days.
The equation of time is the difference between true solar time and mean solar time. It reaches +16 minutes in early November and -14 minutes in mid-February. Published in Astronomical Yearbooks.
Ephemeris time (ET - Ephemeris time) - an independent variable (argument) in celestial mechanics (Newtonian theory of motion celestial bodies). Introduced since January 1, 1960 in astronomical yearbooks as more uniform than Universal Time, aggravated by long-term irregularities in the Earth's rotation. Determined from observation of bodies solar system(mostly the moon). The unit of measurement is the ephemeris second as 1/31556925.9747 fraction of the tropical year for the moment 1900 January 0.12 ET, or, otherwise, as 1/86400 fraction of the duration of the mean solar day for the same moment.
1.2. Measuring time in astronomy
1.2.1. General provisions
One of the tasks of geodetic astronomy, astrometry and space geodesy is to determine the coordinates of celestial bodies at a given point in time. The construction of astronomical time scales is carried out by national time services and the International Time Bureau.
All known methods for constructing continuous time scales are based on batch processes, For example:
- rotation of the Earth around its axis;
- the Earth's orbit around the Sun;
- the revolution of the Moon around the Earth in orbit;
- pendulum swing under the action of gravity;
- elastic vibrations of a quartz crystal under the action of alternating current;
- electromagnetic vibrations of molecules and atoms;
- radioactive decay of atomic nuclei and other processes.
The time system can be set with the following parameters:
1) mechanism - a phenomenon that provides a periodically repeating process (for example, the daily rotation of the Earth);
2) scale - a period of time for which the process is repeated;
3) starting point , zeropoint - the moment of the beginning of the repetition of the process;
4) a way of counting time.
In geodetic astronomy, astrometry, celestial mechanics, systems of sidereal and solar time are used, based on the rotation of the Earth around its axis. This periodic motion is the highest degree uniform, not limited in time and continuous throughout the existence of mankind.
In addition, in astrometry and celestial mechanics,
Ephemeris and dynamic time systems , as the ideal
the structure of a uniform time scale;
System atomic time– practical implementation of an ideally uniform time scale.
1.2.2. sidereal time
Sidereal time is denoted by s. The parameters of the sidereal time system are:
1) mechanism - the rotation of the Earth around its axis;
2) scale - sidereal day, equal to the time interval between two successive upper climaxes of the vernal equinox point
v observation point;
3) the starting point on the celestial sphere is the point of the vernal equinox, the null point (the beginning of the sidereal day) is the moment of the upper climax of the point;
4) counting method. The measure of sidereal time is the hour angle of a point
spring equinox, t. It is impossible to measure it, but the expression is true for any star
therefore, knowing the star's right ascension and calculating its hour angle t, one can determine sidereal time s.
Distinguish true, average and quasi-true gamma points (the separation is due to the astronomical factor nutation, see paragraph 1.3.9), relative to which it is measured true, mean and quasi-true sidereal time.
The sidereal time system is used in determining the geographical coordinates of points on the surface of the Earth and the azimuths of the direction to terrestrial objects, in studying the irregularities of the Earth's daily rotation, and in establishing the zero points of the scales of other time measurement systems. This system, although widely used in astronomy, is inconvenient in everyday life. The change of day and night, due to the visible daily movement of the Sun, creates a very definite cycle in human activity on Earth. Therefore, the calculation of time has long been based on the daily movement of the Sun.
1.2.3. True and mean solar time. Equation of time
True solar time system (or true solar time- m ) is used for astronomical or geodetic observations of the Sun. System parameters:
1) mechanism - the rotation of the Earth around its axis;
2) scale - true solar day- the time interval between two consecutive lower culminations of the center of the true Sun;
3) starting point - the center of the disk of the true Sun - , zero point - true midnight, or the moment of the lower culmination of the center of the disk of the true Sun;
4) counting method. The measure of true solar time is the geocentric hour angle of the true Sun t plus 12 hours:
m = t + 12h .
The unit of true solar time - a second, equal to 1/86400 of a true solar day, does not meet the basic requirement for a unit of time - it is not constant.
The reasons for the inconstancy of the true solar time scale are
1) uneven motion of the Sun along the ecliptic due to the ellipticity of the Earth's orbit;
2) an uneven increase in the direct ascension of the Sun during the year, since the Sun is on the ecliptic, inclined to the celestial equator at an angle of approximately 23.50.
Due to these reasons, the use of the system of true solar time in practice is inconvenient. The transition to a uniform solar time scale occurs in two stages.
Stage 1 transition to dummy the mean ecliptic sun. On dan-
At this stage, uneven motion of the Sun along the ecliptic is excluded. The uneven motion in an elliptical orbit is replaced by uniform movement in a circular orbit. The true Sun and the mean ecliptic Sun coincide when the Earth passes through the perihelion and aphelion of its orbit.
Stage 2 transition to the mean equatorial sun, moving equal to
numbered along the celestial equator. Here, the uneven increase in the right ascension of the Sun, due to the tilt of the ecliptic, is excluded. The true Sun and the mean equatorial Sun simultaneously pass the points of the spring and autumn equinoxes.
As a result of these actions, a new time measurement system is introduced - mean solar time.
Mean solar time is denoted by m. The parameters of the mean solar time system are:
1) mechanism - the rotation of the Earth around its axis;
2) scale - average day - the time interval between two successive lower climaxes of the average equatorial Sun eq ;
3) starting point - mean equatorial sun equiv , nullpoint - mean midnight , or the moment of the lower climax of the mean equatorial Sun;
4) counting method. The measure of mean time is the geocentric hourly angle of the mean equatorial Sun t equiv plus 12 hours.
m = t equiv + 12h.
It is impossible to determine the mean solar time directly from observations, since the mean equatorial Sun is a fictitious point on the celestial sphere. Mean solar time is calculated from true solar time, determined from observations of the true sun. The difference between true solar time m and mean solar time m is called equation of time and is denoted:
M - m = t - t sr.eq. .
The equation of time is expressed by two sinusoids with annual and semi-annual
new periods:
1 + 2 -7.7m sin (l + 790 )+ 9.5m sin 2l,
where l is the ecliptic longitude of the mean ecliptic Sun.
The graph is a curve with two maxima and two minima, which in the Cartesian rectangular coordinate system has the form shown in Fig. 1.18.
Fig.1.18. Graph of the Equation of Time
The values of the equation of time range from +14m to –16m .
In the Astronomical Yearbook, for each date, the value of E is given, equal to
E \u003d + 12 h.
WITH given value, the relationship between the mean solar time and the hourly angle of the true Sun is determined by the expression
m = t -E.
1.2.4. Julian days
When accurately determining the numerical value of the time interval between two distant dates, it is convenient to use the continuous count of the day, which in astronomy is called Julian days.
The beginning of the calculation of Julian days is Greenwich Mean Noon on January 1, 4713 BC, from the beginning of this period, the average solar day is counted and numbered so that each calendar date corresponds to a specific Julian day, abbreviated as JD. So, the epoch 1900, January 0.12h UT corresponds to the Julian date JD 2415020.0, and the epoch 2000, January 1, 12h UT - JD2451545.0.
I am happy to live exemplary and simple:
Like the sun - like a pendulum - like a calendar
M. Tsvetaeva
Lesson 6/6
Topic Fundamentals of measuring time.
Target Consider the time counting system and its relationship with geographic longitude. Give an idea of the chronology and calendar, determining the geographical coordinates (longitude) of the area according to astrometric observations.
Tasks
:
1. educational: practical astrometry about: 1) astronomical methods, instruments and units of measurement, counting and keeping time, calendars and chronology; 2) determining the geographical coordinates (longitude) of the area according to the data of astrometric observations. Services of the Sun and exact time. Application of astronomy in cartography. 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 their consequences - celestial phenomena: sunrise, sunset, daily and annual visible movement and culminations of the luminaries (Sun, Moon and stars), change of phases of the Moon .
2. nurturing: 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 the dates of the Julian and Gregorian calendars; polytechnic and labor education in the presentation of material on instruments for measuring and storing time (hours), calendars and chronology systems, and on practical methods for applying astrometric knowledge.
3. Educational: the formation of skills: solve problems for calculating the time and dates of the chronology and transferring time from one storage system and account to another; perform exercises on the application of the basic formulas of practical astrometry; use a mobile map of the starry sky, reference books and the Astronomical calendar to determine the position and conditions for the visibility of celestial bodies and the course of celestial phenomena; determine the geographical coordinates (longitude) of the area according to astronomical observations.
Know:
1st level (standard)- time counting systems and units of measurement; the concept of noon, midnight, day, the relationship of time with geographic longitude; zero meridian and universal time; zone, local, summer and winter time; translation methods; our reckoning, the origin of our calendar.
2nd level- time counting systems and units of measurement; concept of noon, midnight, day; connection of time with geographic longitude; zero meridian and universal time; zone, local, summer and winter time; translation methods; appointment of the exact time service; the concept of chronology and examples; the concept of a calendar and the main types of calendars: lunar, lunisolar, solar (Julian and Gregorian) and the basics of chronology; the problem of creating a permanent calendar. Basic concepts of practical astrometry: the principles of determining the time and geographical coordinates of the area according to astronomical observations. Causes of daily observed celestial phenomena generated by the revolution of the Moon around the Earth (change of phases of the Moon, apparent movement of the Moon in the celestial sphere).
Be able to:
1st level (standard)- Find the time of the world, average, zone, local, summer, winter;
2nd level- Find the time of the world, average, zone, local, summer, winter; convert dates from old to new style and vice versa. Solve problems to determine the geographical coordinates of the place and time of observation.
Equipment: poster "Calendar", PKZN, pendulum and sundial, metronome, stopwatch, quartz clock Earth Globe, tables: some practical applications astronomy. CD- "Red Shift 5.1" (Time-show, Stories about the Universe = Time and seasons). Model of the celestial sphere; wall map of the starry sky, map of time zones. Maps and photographs of the earth's surface. Table "Earth in outer space". Fragments of filmstrips"Visible movement of heavenly bodies"; "Development of ideas about the Universe"; "How Astronomy Refuted Religious Ideas about the Universe"
Interdisciplinary communication: Geographical coordinates, time counting and orientation methods, map projection(geography, 6-8 cells)
During the classes
1. Repetition of what has been learned(10 min).
a) 3 people on individual cards.
1.
1. At what height in Novosibirsk (φ= 55º) does the Sun culminate on September 21? [for the second week of October, according to the PKZN δ=-7º, then h=90 o -φ+δ=90 o -55º-7º=28º]
2. Where on earth are no stars of the southern hemisphere visible? [at the North Pole]
3. How to navigate the terrain by the sun? [March, September - sunrise in the east, sunset in the west, noon in the south]
2.
1. Sun's midday altitude is 30º and its declination is 19º. Determine the geographic latitude of the observation site.
2. How are the daily paths of stars relative to the celestial equator? [parallel]
3. How to navigate the terrain using the North Star? [direction north]
3.
1. What is the declination of a star if it culminates in Moscow (φ= 56 º
) at a height of 69º?
2. How is the axis of the world relative to the earth's axis, relative to the horizon plane? [parallel, at the angle of the geographical latitude of the observation site]
3. How to determine the geographical latitude of the area from astronomical observations? [measure the angular height of the North Star]
b) 3 people at the board.
1. Derive the formula for the height of the luminary.
2. Daily paths of the luminaries (stars) at different latitudes.
3. Prove that the height of the world pole is equal to the geographic latitude.
v) The rest on their own
.
1. What is the highest height Vega reaches (δ=38 o 47") in the Cradle (φ=54 o 04")? [maximum height at the top culmination, h=90 o -φ+δ=90 o -54 o 04 "+38 o 47"=74 o 43"]
2. Select any bright star and write down its coordinates.
3. In what constellation is the Sun today and what are its coordinates? [for the second week of October according to the PCDP in cons. Virgo, δ=-7º, α=13 h 06 m]
d) in "Red Shift 5.1"
Find the Sun:
What information can be obtained about the Sun?
- what are its coordinates today and in what constellation is it located?
How does the declination change? [decreases]
- which of the stars with its own name is closest in angular distance to the Sun and what are its coordinates?
- prove that the Earth is currently moving in orbit approaching the Sun (from the visibility table - the angular diameter of the Sun is growing)
2.
new material
(20 minutes)
Need to pay student attention:
1. The length of the day and year depends on the frame of reference in which the motion of the Earth is considered (whether it is associated with fixed stars, the Sun, etc.). The choice of reference system is reflected in the name of the unit of time.
2. The duration of time counting units is related to the conditions of visibility (culminations) of celestial bodies.
3. The introduction of the atomic time standard in science was due to the non-uniformity of the Earth's rotation, which was discovered with increasing clock accuracy.
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.
Time counting systems. Relationship with geographic longitude.
Thousands of years ago, people noticed that many things in nature repeat themselves: the Sun rises in the east and sets in the west, summer follows winter and vice versa. It was then that the first units of time arose - day month Year
. Using the simplest astronomical instruments, it was found that there are about 360 days in a year, and in about 30 days the silhouette of the moon goes through a cycle from one full moon to the next. Therefore, the Chaldean sages adopted the sexagesimal number system as the basis: the day was divided into 12 night and 12 day hours
, the circle is 360 degrees. Every hour and every degree was divided by 60 minutes
, and every minute - by 60 seconds
.
However, subsequent more accurate measurements hopelessly spoiled this perfection. It turned out that the Earth makes a complete revolution around the Sun in 365 days 5 hours 48 minutes and 46 seconds. The moon, on the other hand, takes from 29.25 to 29.85 days to bypass the Earth.
Periodic phenomena accompanied by daily rotation of the celestial sphere and the apparent annual movement of the Sun along the ecliptic
underlie various systems time accounts. Time- the main physical quantity characterizing the successive change of phenomena and states of matter, the duration of their existence.
Short- day, hour, minute, second
Long- year, quarter, month, week.
1.
"stellar"the time associated with the movement of stars on the celestial sphere. Measured by the hour angle of the vernal equinox point: S \u003d t ^; t \u003d S - a
2.
"solar"time associated: with the apparent 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 time interval as the true Sun (average solar time).
With the introduction in 1967 of the atomic time standard and the International SI system, the atomic second is used in physics.
Second- 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 by special calculations. Mean solar time is used in everyday life
. The basic unit of sidereal, true and mean solar time is the day. We get 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. Day- the period of time during which the Earth makes one complete rotation around its axis relative to any landmark.
sidereal day- the period of rotation of the Earth around its axis relative to the fixed stars, is defined as the time interval between two successive upper climaxes of the vernal equinox.
true solar day- 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 climaxes of the same name of the center of the solar disk.
Due to the fact that the ecliptic is inclined to the celestial equator at an angle of 23 about 26 ", and the Earth revolves around the Sun in an elliptical (slightly elongated) orbit, the speed of the apparent movement of the Sun in the celestial sphere and, therefore, the duration of a true solar day will constantly change throughout the year : the fastest near the equinoxes (March, September), the slowest near the solstices (June, January) To simplify the calculations of time in astronomy, the concept of a mean solar day is introduced - the period of rotation of the Earth around its axis relative to the "average Sun".
Mean solar day are defined as the time interval between two successive climaxes of the same name of the "middle Sun". They are 3 m 55.009 s shorter than a sidereal day.
24 h 00 m 00 s of sidereal time are equal to 23 h 56 m 4.09 s of mean solar time. For definiteness of theoretical calculations, it is accepted ephemeris (table) second equal to the mean solar second on January 0, 1900 at 12 o'clock equal current time, not related to the rotation of the Earth.
About 35,000 years ago, people noticed a periodic change in the appearance of the moon - a change in the lunar phases. Phase F celestial body (Moon, planets, etc.) is determined by the ratio of the largest width of the illuminated part of the disk d to its diameter D: F=d/D. Line terminator separates the dark and light parts of the luminary's disk. The moon moves around the earth in the same direction in which the earth rotates around its axis: from west to east. The display of this movement is the apparent movement of the Moon against the background of the stars towards the rotation of the sky. Every day, the Moon moves to the east by 13.5 o relative to the stars and completes a full circle in 27.3 days. So the second measure of time after the day was established - month.
Sidereal (star) lunar month- the period of time during which the moon makes one complete revolution around the earth relative to the fixed stars. Equals 27 d 07 h 43 m 11.47 s .
Synodic (calendar) lunar month- the time interval between two successive phases of the same name (usually new moons) of the moon. Equals 29 d 12 h 44 m 2.78 s . .jpg)
The totality of the phenomena of the visible movement of the Moon against the background of stars and the change in the phases of the Moon makes it possible to navigate the Moon on the ground (Fig.). The moon appears as a narrow crescent in the west and disappears in the rays of the morning dawn with the same narrow crescent in the east. Mentally attach a straight line to the left of the crescent moon. We can read in the sky either the letter "P" - "growing", the "horns" of the month are turned to the left - the month is visible in the west; or the letter "C" - "getting old", the "horns" of the month are turned to the right - the month is visible in the east. On a full moon, the moon is visible in the south at midnight.
As a result of observations of the change in the position of the Sun above the horizon for many months, a third measure of time arose - year.
Year- the period of time during which the Earth makes one complete revolution around the Sun relative to any reference point (point).
sidereal year- sidereal (stellar) period of the Earth's revolution around the Sun, equal to 365.256320 ... mean solar days.
anomalistic year- the time interval between two successive passages of the average Sun through the point of its orbit (usually perihelion) is equal to 365.259641 ... mean solar days.
tropical year- the time interval between two successive passages of the average Sun through the vernal equinox, equal to 365.2422... mean solar days or 365 d 05 h 48 m 46.1 s.
Universal Time defined as local mean solar time at the zero (Greenwich) meridian ( That, UT- Universal Time). Because in everyday life local time you can’t use it (since it’s one in the Cradle, and another in Novosibirsk (different λ
)), which is why it was approved by the Conference at the suggestion of a Canadian railway engineer Sanford Fleming(February 8 1879
when speaking at the Canadian Institute in Toronto) standard time, dividing the globe into 24 time zones (360:24 = 15 o, 7.5 o from the central meridian). The zero time zone is located symmetrically with respect to the zero (Greenwich) meridian. The belts are numbered from 0 to 23 from west to east. The real boundaries of the belts are aligned with the administrative boundaries of districts, regions or states. The central meridians of time zones are exactly 15 o (1 hour) apart, so when moving from one time zone to another, time changes by an integer number of hours, and the number of minutes and seconds does not change. The new calendar day (and the New Year) starts on date lines(demarcation line), passing mainly along the meridian of 180 o east longitude near the northeastern border of the Russian Federation. To the west of the date line, the day of the month is always one more than to the 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 hemisphere of the Earth.
Therefore, the International Meridian Conference (1884, Washington, USA) in connection with the development of the telegraph and railway transport introduces:
- the beginning of the day from midnight, and not from noon, as it was.
- the initial (zero) meridian from Greenwich (Greenwich Observatory near London, founded by J. Flamsteed in 1675, through the axis of the observatory's telescope).
- counting system standard time
Standard time is determined by the formula: T n = T 0 + n
, where T 0
- universal time; n- time zone number.
Daylight saving time- standard time, changed to an integer number of hours by government decree. For Russia, it is equal to the belt, plus 1 hour.
Moscow time- daylight saving time of the second time zone (plus 1 hour): Tm \u003d T 0 + 3
(hours).
Summer time- standard standard time, which is changed by an additional plus 1 hour by government order for the period of summer time in order to save energy resources. Following the example of England, which introduced summer time for the first time in 1908, now 120 countries of the world, including the Russian Federation, annually switch to summer time.
Time zones of the world and Russia
Next, students should be briefly introduced to astronomical methods for determining the geographical coordinates (longitude) of the area. Due to the Earth's rotation, the difference between noon or culmination times ( climax. What is this phenomenon?) 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.
For example: one of you is in Novosibirsk, the second in Omsk (Moscow). Which of you will observe the upper culmination of the center of the Sun earlier? And why? (note, it means that your clock is on the time of Novosibirsk). Conclusion- depending on the location on Earth (meridian - geographic longitude), the climax of any luminary is observed at different times, that is time is related to geographic longitude
or T=UT+λ, and the time difference for two points located on different meridians will be T 1 -T 2 \u003d λ 1 - λ 2.Geographic longitude (λ
) of the area is counted east of the "zero" (Greenwich) meridian and is numerically equal to the time interval between the climaxes of the same name of the same luminary on the Greenwich meridian ( UT) and at the observation point ( T). Expressed in degrees or hours, minutes and seconds. To determine
geographic longitude of the area, it is necessary to determine the moment of climax of any luminary (usually the Sun) with known equatorial coordinates. By translating with the help of special tables or a calculator the time of observations from the mean solar to the stellar and knowing from the reference book the time of the culmination of this luminary on the Greenwich meridian, we can easily determine the longitude of the area. The only difficulty in the calculations is the exact conversion of units of time from one system to another. The moment of culmination can not be "guarded": it is enough to determine the height (zenith distance) of the luminary at any precisely fixed moment in time, but then the calculations will be quite complicated.
Clocks are used to measure time. From the simplest, used in antiquity, is gnomon
- a vertical pole in the center of a horizontal platform with divisions, then sand, water (clepsydra) and fire, up to mechanical, electronic and atomic. An even more accurate atomic (optical) time standard was created in the USSR in 1978. An error of 1 second occurs every 10,000,000 years!
Timekeeping system in our country
1) From July 1, 1919, it is introduced standard time(Decree of the Council of People's Commissars of the RSFSR of February 8, 1919)
2) In 1930 it is established Moscow (maternity)
the time of the 2nd time zone in which Moscow is located, moving one hour ahead compared to the standard time (+3 to the Universal or +2 to the Central European) in order to provide a brighter part of the day in the daytime (decree of the Council of People's Commissars of the USSR of 06/16/1930 ). The time zone distribution of the edges and regions changes significantly. Canceled in February 1991 and restored again from January 1992.
3) The same Decree of 1930 abolishes the transition to summer time, which has been in force since 1917 (April 20 and return on September 20).
4) In 1981, the transition to summer time resumes in the country. Decree of the Council of Ministers of the USSR of October 24, 1980 "On the procedure for calculating time on the territory of the USSR" summer time is introduced
by transferring the hands of the clock to 0 hours on April 1 an hour forward, and on October 1 an hour ago since 1981. (In 1981, daylight saving time was introduced in the vast majority of developed countries - 70, except for Japan). In the future, in the USSR, the translation began to be done on the Sunday closest to these dates. The resolution made a number of significant changes and approved a newly compiled list of administrative territories assigned to the corresponding time zones.
5) In 1992, by the Decrees of the President, canceled in February 1991, maternity (Moscow) time was restored from January 19, 1992, while maintaining the transfer to summer time on the last Sunday of March at 2 am one hour ahead, and to winter time on the last Sunday of September at 3 one hour of the night one hour ago.
6) In 1996, by Decree of the Government of the Russian Federation No. 511 of April 23, 1996, summer time is extended by one month and now ends on the last Sunday of October. In Western Siberia, the regions that were previously in the MSK + 4 zone switched to MSK + 3 time, joining the Omsk time: Novosibirsk region May 23, 1993 at 00:00, Altai Territory and the Republic of Altai May 28, 1995 at 4:00, Tomsk Region May 1, 2002 at 3:00, Kemerovo Region March 28, 2010 at 02:00. ( the difference with universal time GMT remains 6 hours).
7) From March 28, 2010, during the transition to summer time, the territory of Russia began to be located in 9 time zones (from the 2nd to the 11th inclusive, with the exception of the 4th - Samara region and Udmurtia on March 28, 2010 at 2 a.m. they switched to Moscow time) with the same time within each time zone. The boundaries of time zones pass along the borders of the subjects of the Russian Federation, each subject is included in one zone, with the exception of Yakutia, which is included in 3 zones (MSK + 6, MSK + 7, MSK + 8), and the Sakhalin region, which is included in 2 zones ( MSK+7 on Sakhalin and MSK+8 on the Kuril Islands).
So for our country in winter time T= UT+n+1 h , a in summer time T= UT+n+2 h
You can offer to do laboratory (practical) work at home: Laboratory work"Determining the coordinates of the terrain from observations of the Sun"
Equipment: gnomon; chalk (pegs); "Astronomical calendar", notebook, pencil.
Work order:
1. Determination of the noon line (meridian direction).
With the daily movement of the Sun across the sky, the shadow from the gnomon gradually changes its direction and length. At true noon, it has the smallest length and shows the direction of the noon line - the projection of the celestial meridian onto the plane of the mathematical horizon. To determine the noon line, it is necessary in the morning hours to mark the point at which the shadow from the gnomon falls and draw a circle through it, taking the gnomon as its center. Then you should wait until the shadow from the gnomon touches the circle line for the second time. The resulting arc is divided into two parts. The line passing through the gnomon and the middle of the noon arc will be the noon line.
2. Determining the latitude and longitude of the area from the observations of the Sun.
Observations begin shortly before the moment of true noon, the onset of which is fixed at the moment of the exact coincidence of the shadow from the gnomon and the noon line according to well-calibrated clocks running according to standard time. At the same time, the length of the shadow from the gnomon is measured. By the length of the shadow l at true noon at the time of its occurrence T d according to standard time, using simple calculations, determine the coordinates of the area. Previously from the relation tg h ¤ \u003d N / l, where H- height of the gnomon, find the height of the gnomon at true noon h ¤ .
The latitude of the area is calculated by the formula φ=90-h ¤ +d ¤, where d ¤ is the solar declination. To determine the longitude of the area, use the formula λ=12h+n+Δ-D, where n- time zone number, h - equation of time for a given day (determined according to the data of the "Astronomical calendar"). For winter time D = n+1; for summer time D = n + 2.
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