Basic concepts of astronomy. Counting time
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 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 movement is highly 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 geographical coordinates points on the surface of the Earth and azimuths of direction to terrestrial objects, when studying the irregularities of the daily rotation of the Earth, when establishing zero points on the scales of other time measurement systems. This system, although widely used in astronomy, in Everyday life uncomfortable. 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 - , zeropoint - 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, new system time measurements - 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.
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) determining the geographical coordinates (longitude) of the area according to the data of 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 in the presentation of 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 steps |
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 |
Work at the blackboard, independent solution of problems 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 a general concept of 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. In 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 geographical 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 moment 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 the 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 the watch. 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 noon line (the projection of the celestial meridian onto a horizontal surface) and the direction to the numbers 6, 8, 10... indicating 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, ripening of fruits, collection of medicinal herbs, changes in the behavior and life of animals, changes in the weather, 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-sani, jumada al-ulya, jumada al-akhira, rajab, shaban, 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 activity.
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.Lunar-solar 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 wide 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 according to 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
At the observatories there are instruments with the help of which they determine the time in the most accurate way - they check the clock. Time is set according to the position occupied by the luminaries above the horizon. In order for the observatory clock to run as accurately and evenly as possible in the interval between evenings, when they are checked by the position of the stars, the clock is placed in deep cellars. In such cellars, all year round, constant temperature. This is very important as temperature changes affect the running of the clock.
To transmit accurate time signals by radio, the observatory has special sophisticated clock, electrical and radio equipment. The exact time signals transmitted from Moscow are among the most accurate in the world. Determining the exact time from the stars, keeping time with accurate clocks and transmitting it by radio - all this constitutes the Time Service.
WHERE ASTRONOMERS WORK
Astronomers conduct scientific work at observatories and astronomical institutes.
The latter are mainly engaged in theoretical research.
After the Great October Socialist Revolution in our country, the Institute of Theoretical Astronomy was established in Leningrad, the Astronomical Institute. P.K. Sternberg in Moscow, astrophysical observatories in Armenia, Georgia and a number of other astronomical institutions.
The training and education of astronomers takes place at universities at the Mechanics and Mathematics or Physics and Mathematics faculties.
The main observatory in our country is Pulkovo. It was built in 1839 near St. Petersburg under the guidance of a prominent Russian scientist. In many countries, it is rightly called the astronomical capital of the world.
Simeiz observatory in the Crimea after the Great Patriotic War was completely restored, and not far from it a new observatory was built in the village of Partizanskoye near Bakhchisarai, where the largest reflecting telescope in the USSR with a mirror with a diameter of 1 ¼ m is now installed, and a reflector with a mirror with a diameter of 2.6 m will soon be installed - the third in size in the world. Both observatories now form one institution - the Crimean Astrophysical Observatory of the USSR Academy of Sciences. There are astronomical observatories in Kazan, Tashkent, Kiev, Kharkov and other places.
At all observatories we have scientific work according to an agreed plan. Achievements in astronomical science in our country are helping broad sections of the working people develop a correct, scientific idea of the world around us.
Many astronomical observatories exist in other countries as well. Of these, the oldest of the existing ones are the most famous - Paris and Greenwich, from the meridian of which geographic longitudes on the globe are counted (recently, this observatory was moved to a new location, further from London, where there are many interferences for night sky observations). The largest telescopes in the world are installed in California at the Mount Palomar, Mount Wilson and Lick observatories. The last one was built in late XIX century, and the first two - already in the XX century.
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Obtaining time points solves only the first task of the time service. The next task is to store the exact time in the intervals between its astronomical definitions. This problem is solved with the help of astronomical clocks.
In order to obtain a high accuracy of time reading in the manufacture of astronomical clocks, as far as possible, all sources of error are taken into account and eliminated, and the most favorable conditions are created for their operation.
The most important part of a clock is the pendulum. The springs and wheels serve as a transmission mechanism, the arrows serve as pointers, and the pendulum measures the time. Therefore, in astronomical clocks, they try to create the best possible conditions for its operation: to make the temperature of the room constant, to eliminate shocks, to weaken air resistance, and, finally, to make the mechanical load as small as possible.
To ensure high accuracy, the astronomical clock is placed in a deep basement, protected from shocks. The room is maintained at a constant temperature all year round. To reduce air resistance and eliminate the effect of changes in atmospheric pressure, the pendulum of the clock is placed in a casing in which the air pressure is slightly reduced (Fig. 20).
An astronomical clock with two pendulums (Short's clock) has a very high accuracy, of which one - not free, or "slave" - is associated with transmission and indicating mechanisms, and it is controlled by another - a free pendulum, not connected to any wheels and springs ( Fig. 21).
The free pendulum is placed in a deep basement in a metal case. This case creates a reduced pressure. The connection of a free pendulum with a non-free one is carried out through two small electromagnets, near which it swings. The free pendulum controls the "slave" pendulum, causing it to swing in time with itself.
It is possible to achieve a very small error in the readings of the clock, but it cannot be completely eliminated. However, if the clock is running incorrectly, but it is known in advance that they are in a hurry or behind by a certain number of seconds per day, then it is not difficult to calculate the exact time from such incorrect clocks. To do this, it is enough to know what the course of the clock is, that is, how many seconds per day they are in a hurry or behind. Correction tables are compiled for a given instance of an astronomical clock over the course of months and years. The hands of astronomical clocks almost never show the time accurately, but with the help of correction tables it is quite possible to obtain timestamps with an accuracy of thousandths of a second.
Unfortunately, the clock does not stay constant. When external conditions change - room temperature and air pressure - due to the always existing inaccuracies in the manufacture of parts and the operation of individual parts, the same clock can change its course over time. Change, or variation, of the course of a watch is the main indicator of the quality of its work. The smaller the variation of the clock rate, the better the clock.
Thus, a good astronomical clock may be too hasty and too slow, may run ahead or lag even tenths of a second a day, and yet they can reliably keep time and give sufficiently accurate readings, if only their behavior is constant, i.e., the diurnal variation is small.
In Short's pendulum astronomical clock, the daily variation of the rate is 0.001-0.003 sec. For a long time, such high accuracy remained unsurpassed. In the fifties of our century, engineer F. M. Fedchenko improved the suspension of the pendulum and improved its thermal compensation. This allowed him to design a watch whose daily rate variation was reduced to 0.0002-0.0003 seconds.
V last years The design of astronomical clocks was no longer taken up by mechanics, but by electricians and radio engineers. They made watches in which, instead of pendulum oscillations, elastic vibrations of a quartz crystal were used to count time.
A plate cut appropriately from a quartz crystal has interesting properties. If such a plate, called piezoquartz, is compressed or bent, then electric charges of different signs appear on its opposite surfaces. If an alternating electric current is applied to the opposite surfaces of the piezoelectric plate, then the piezoquartz oscillates. The lower the attenuation of the oscillatory device, the more constant the oscillation frequency. Piezoquartz has exceptionally good properties in this respect, since the damping of its oscillations is very small. This is widely used in radio engineering to maintain a constant frequency of radio transmitters. The same property of piezoquartz - the high constancy of the oscillation frequency - made it possible to build very accurate astronomical quartz clocks.
Quartz clocks (Fig. 22) consist of a radio-technical generator stabilized by piezoelectric quartz, frequency division cascades, a synchronous electric motor and a dial with pointer arrows.
The radio generator generates a high-frequency alternating current, and the piezoquartz maintains a constant frequency of its oscillations with great accuracy. In frequency division stages, the frequency of the alternating current is reduced from several hundred thousand to several hundred oscillations per second. A synchronous electric motor running on low-frequency alternating current rotates pointers, closes relays that give time signals, etc.
The speed of rotation of a synchronous electric motor depends on the frequency of the alternating current that it is powered by. Thus, in a quartz watch, the speed of rotation of the pointer hands is ultimately determined by the oscillation frequency of the piezoquartz. The high constancy of the oscillation frequency of the quartz plate ensures the uniformity of the course and the high accuracy of the indications of the quartz astronomical clock.
Currently, quartz watches of various types and purposes are being manufactured with a daily rate variation not exceeding hundredths and even thousandths of a second.
The first designs of quartz watches were quite bulky. After all, the natural frequency of oscillations of a quartz plate is relatively high, and in order to count seconds and minutes, it is necessary to reduce it using a number of frequency division cascades. Meanwhile, the tube radio devices used for this purpose take up a lot of space. In recent decades, semiconductor radio engineering has developed rapidly, and miniature and microminiature radio equipment has been developed on its basis. This made it possible to build small-sized portable quartz watches for sea and air navigation, as well as for various expeditionary work. These portable quartz chronometers are no larger and heavier than conventional mechanical chronometers.
However, if a mechanical marine chronometer of the second class has a daily rate error of no more than ±0.4 seconds, and of the first class - no more than ±0.2 seconds, then modern quartz portable chronometers have a daily rate instability of ±0.1; ±0.01 and even ±0.001 sec.
For example, the "Chronotom" manufactured in Switzerland has dimensions of 245X137X100 mm, and the instability of its course per day does not exceed ±0.02 seconds. Stationary quartz chronometer "Isotom" has a long-term relative instability of no more than 10 -8, ie, the error in the daily cycle is about ±0.001 sec.
However, quartz watches are not without serious shortcomings, the presence of which is essential for high-precision astronomical measurements. The main disadvantages of quartz astronomical clocks are the dependence of the frequency of quartz oscillations on temperature environment and "aging of quartz", i.e., a change in the frequency of its oscillations over time. The first drawback was overcome by careful temperature control of the part of the clock in which the quartz plate is located. The aging of quartz, which leads to a slow drift of the clock, has not yet been eliminated.
"Molecular clock"
Is it possible to create a device for measuring time intervals that has a higher accuracy than pendulum and quartz astronomical clocks?
In search of suitable methods for this, scientists turned to systems in which molecular vibrations occur. Such a choice, of course, was not accidental, and it was he who predetermined further success. "Molecular clocks" made it possible at first to increase the accuracy of time measurement by thousands, and by borrowing hundreds of thousands of times. However, the path from the molecule to the time indicator turned out to be complex and very difficult.
Why was it not possible to improve the accuracy of pendulum and quartz astronomical clocks? In what way did molecules turn out to be better than pendulums and quartz plates in terms of measuring time? What is the principle of operation and device of the molecular clock?
Recall that any watch consists of a block in which periodic oscillations occur, a counting mechanism for counting their number, and a device in which the energy necessary to maintain them is stored. However, the clock accuracy is mainly depends on the stability of the work of that element which measures time.
To increase the accuracy of pendulum astronomical clocks, their pendulum is made of a special alloy with a minimum coefficient of thermal expansion, placed in a thermostat, suspended in a special way, located in a vessel from which air is pumped out, etc. As is known, all these measures made it possible to reduce stroke variations astronomical pendulum clocks to thousandths of a second per day. However, the gradual wear of moving and rubbing parts, slow and irreversible changes in structural materials, in general - the "aging" of such watches did not allow for further improvement in their accuracy.
In astronomical quartz clocks, time is measured by an oscillator stabilized by quartz, and the accuracy of the readings of these clocks is determined by the constancy of the oscillation frequency of the quartz plate. Over time, irreversible changes occur in the quartz plate and the electrical contacts associated with it. Thus, this master element of a quartz watch "gets old". In this case, the oscillation frequency of the quartz plate changes somewhat. This is the reason for the instability of such clocks and puts a limit to further increase in their accuracy.
Molecular clocks are designed in such a way that their readings are ultimately determined by the frequency of electromagnetic vibrations absorbed and emitted by molecules. Meanwhile, atoms and molecules absorb and emit energy only intermittently, only in certain portions, called energy quanta. These processes are currently presented as follows: when an atom is in a normal (unexcited) state, then its electrons occupy the lower energy levels and, at the same time, are at the closest distance from the nucleus. If atoms absorb energy, such as light, then their electrons jump to new positions and are located somewhat further from their nuclei.
Let us denote the energy of the atom, corresponding to the lowest position of the electron, through Ei, and the energy corresponding to its more distant location from the nucleus, through E 2 . When atoms, radiating electromagnetic oscillations (for example, light), from an excited state with energy E 2 pass into an unexcited state with energy E 1, then the emitted portion electromagnetic energy is equal to ε \u003d E 2 -E 1. It is easy to see that the given relation is nothing but one of the expressions of the law of conservation of energy.
Meanwhile, it is known that the energy of a light quantum is proportional to its frequency: ε = hv, where ε is the energy of electromagnetic oscillations, v is their frequency, h = 6.62 * 10 -27 erg * sec - Planck's constant. From these two relations it is not difficult to find the frequency v of the light emitted by the atom. Obviously, v \u003d (E 2 - E 1) / h sec -1
Each atom of a given type (for example, an atom of hydrogen, oxygen, etc.) has its own energy levels. Therefore, each excited atom, during the transition to the lower states, emits electromagnetic oscillations with a well-defined set of frequencies, i.e., it gives a glow characteristic only for it. The situation is exactly the same with molecules, with the only difference that they have a number of additional energy levels associated with the different arrangement of their constituent particles and with their mutual motion,
Thus, atoms and molecules are capable of absorbing and emitting electromagnetic vibrations of only a limited frequency. The stability with which atomic systems do this is extremely high. It is billions of times higher than the stability of any macroscopic devices that perceive or emit certain types of vibrations, for example, strings, tuning forks, microphones, etc. This is explained by the fact that in any macroscopic devices, for example, machines, measuring instruments, etc. ., the forces that ensure their stability are in most cases only tens or hundreds of times greater than the external forces. Therefore, over time and as external conditions change, the properties of such devices change somewhat. This is why musicians have to tune their violins and pianos so often. On the contrary, in microsystems, such as atoms and molecules, there are such strong forces between the particles that make them up that ordinary external influences are much smaller in magnitude. Therefore, ordinary changes in external conditions - temperature, pressure, etc. - do not cause any noticeable changes within these microsystems.
This explains the high accuracy of spectral analysis and many other methods and instruments based on the use of atomic and molecular vibrations. This is what makes it so attractive to use these quantum systems as a master element in astronomical clocks. After all, such microsystems do not change their properties over time, that is, they do not "age".
When engineers started designing molecular clocks, the methods of excitation of atomic and molecular vibrations were already well known. One of them is that high-frequency electromagnetic oscillations are applied to a vessel filled with one or another gas. If the frequency of these oscillations corresponds to the excitation energy of these particles, then resonant absorption of electromagnetic energy occurs. After some time (less than a millionth of a second), the excited particles (atoms and molecules) spontaneously pass from the excited state to the normal state, and at the same time they themselves emit quanta of electromagnetic energy.
It would seem that the next step in designing such a clock should be to count the number of these oscillations, because the number of swings of the pendulum is calculated in the pendulum clock. However, such a direct, "frontal" path turned out to be too difficult. The fact is that the frequency of electromagnetic oscillations emitted by molecules is very high. For example, in the ammonia molecule for one of the main transitions, it is 23,870,129,000 periods per second. The frequency of electromagnetic oscillations emitted by various atoms is of the same order of magnitude or even higher. No mechanical device is suitable for counting the number of such high-frequency vibrations. Moreover, conventional electronic devices also turned out to be unsuitable for this.
A way out of this difficulty was found with the help of an original detour. Ammonia gas was placed in a long metal tube (waveguide). For ease of handling, this tube is coiled. High-frequency electromagnetic oscillations were supplied from the generator to one end of this tube, and a device was installed at its other end to measure their intensity. The generator made it possible, within certain limits, to change the frequency of the electromagnetic oscillations excited by it.
For the transition of ammonia molecules from an unexcited to an excited state, a well-defined energy and, accordingly, a well-defined frequency of electromagnetic oscillations are needed (ε \u003d hv, where ε is the quantum energy, v is the frequency of electromagnetic oscillations, h is Planck's constant). As long as the frequency of the electromagnetic oscillations produced by the generator is greater or less than this resonant frequency, the ammonia molecules do not absorb energy. When these frequencies coincide, a significant number of ammonia molecules absorb electromagnetic energy and pass into an excited state. Of course, in this case (due to the law of conservation of energy) at the end of the waveguide where the measuring device is installed, the intensity of electromagnetic oscillations is less. If you smoothly change the frequency of the generator and record the readings of the measuring device, then at the resonant frequency, a dip in the intensity of electromagnetic oscillations is detected.
The next step in designing a molecular clock is precisely to exploit this effect. For this, a special device was assembled (Fig. 23). In it, a high-frequency generator equipped with a power supply generates high-frequency electromagnetic oscillations. To increase the constancy of the frequency of these oscillations, the generator is stabilized with. using a piezoelectric crystal. In existing devices of this type, the oscillation frequency of the high-frequency generator is chosen to be several hundred thousand periods per second in accordance with the natural oscillation frequency of the quartz plates used in them.
Rice. 23. Scheme of "molecular clock"
Since this frequency is too high to directly control any mechanical device, it is reduced to several hundred oscillations per second with the help of a frequency division unit, and only after that it is fed to signal relays and a synchronous electric motor that rotates pointer arrows located on the watch face. Thus, this part of the molecular clock repeats the scheme of the quartz clocks described earlier.
In order to excite the ammonia molecules, part of the electromagnetic oscillations generated by the high frequency generator is applied to an alternating current frequency multiplier (see Fig. 23). The frequency multiplication factor in it is chosen so as to bring it to the resonant one. From the output of the frequency multiplier, electromagnetic oscillations enter the waveguide with ammonia gas. The device at the output of the waveguide - the discriminator - notes the intensity of the electromagnetic oscillations that have passed through the waveguide and acts on the high-frequency generator, changing the frequency of the oscillations excited by it. The discriminator is designed in such a way that when oscillations with a frequency below the resonant frequency arrive at the input of the waveguide, it adjusts the generator, increasing the frequency of its oscillations. If, however, oscillations with a frequency higher than the resonant frequency arrive at the input of the waveguide, then it reduces the frequency of the generator. In this case, the tuning to resonance is the more accurate, the steeper the absorption curve goes. Thus, it is desirable that the dip in the intensity of electromagnetic oscillations, due to the resonant absorption of their energy by molecules, be as narrow and deep as possible.
All these interconnected devices - generator, multiplier, ammonia gas waveguide and discriminator - are a circuit feedback, in which the ammonia molecules are excited by the generator and at the same time control it, forcing it to generate oscillations of the desired frequency. Thus, the molecular clock ultimately uses ammonia molecules as the frequency and time standard. In the first molecular ammonia clock, developed according to this principle by G. Lyons in 1953, the rate instability was about 10 -7, i.e., the frequency change did not exceed ten millionths. Subsequently, the instability was reduced to 10 -8 , which corresponds to an error in measuring time intervals by 1 sec for several years.
In general, this is, of course, excellent accuracy. However, it turned out that in the constructed device the electromagnetic energy absorption curve turned out to be far from being as sharp as expected, but rather "smeared". Accordingly, the accuracy of the entire device turned out to be significantly lower than expected. Careful studies of these molecular clocks carried out in subsequent years made it possible to find out that their readings depend to some extent on the design of the waveguide, as well as on the temperature and pressure of the gas contained in it. It was found that these effects are the sources of instability of such clocks and limit their accuracy.
In the future, these defects in the molecular clock have not been completely eliminated. However, it was possible to come up with other, more perfect types quantum time meters.
Atomic cesium clock
Further improvement in frequency and time standards has been achieved on the basis of a clear understanding of the reasons for the shortcomings of ammonia molecular clocks. Recall that the main disadvantages of ammonia molecular clocks are some "smearing" of the resonant absorption curve and the dependence of the renderings of these clocks on the temperature and pressure of the gas in the waveguide.
What are the reasons for these defects? Can they be eliminated? It turned out that the spreading of the resonance occurs as a result of the thermal motion of gas particles filling the waveguide. After all, some of the gas particles move towards the electromagnetic wave and therefore for them the oscillation frequency is somewhat higher than that given by the generator. Other gas particles, on the contrary, move from the incoming electromagnetic wave, as if running away from it; for them, the frequency of electromagnetic oscillations is somewhat lower than the nominal one. Only for a relatively small number of motionless gas particles, the frequency of electromagnetic oscillations perceived by them is equal to the nominal one, i.e. given by the generator.
The described phenomenon is the well-known longitudinal Doppler effect. It is he who leads to the fact that the resonance curve is flattened and smeared and the dependence of the current strength at the output of the waveguide on the velocity of gas particles is found, i.e. on the gas temperature.
A group of scientists from the American Bureau of Standards managed to cope with these difficulties. However, what they did was, in general, a new and much more accurate standard of frequency and time, although some already known things were used.
This device no longer uses molecules, but atoms. These atoms do not just fill the vessel, but move in a beam. And so that the direction of their movement is perpendicular to the direction of propagation of the electromagnetic wave. It is easy to understand that in this case there is no longitudinal Doppler effect. The device uses cesium atoms, the excitation of which occurs at a frequency of electromagnetic oscillations equal to 9,192,631,831 periods per second.
The corresponding device is mounted in a tube, at one end of which there is an electric furnace 1, which heats the metal cesium up to evaporation, and at the other end there is a detector 6, which counts the number of cesium atoms that have reached it (Fig. 24). Between them are: the first magnet 2, the waveguide 3, which supplies high-frequency electromagnetic oscillations, the collimator 4, and the second magnet 5. fields created by permanent magnets, and a high-frequency electromagnetic field supplied by a waveguide from the generator to the tube so that the direction of wave propagation is perpendicular to the direction of particle flight.
Such a device makes it possible to solve the first part of the problem: to excite atoms, that is, to transfer them from one state to another, and at the same time to avoid the longitudinal Doppler effect. If researchers had limited themselves to this improvement only, then the accuracy of the device would have increased, but not by much. Indeed, in a beam of atoms emitted from an incandescent source, there are always unexcited and excited atoms. Thus, when the atoms that have flown out of the source fly through the electromagnetic field and are excited, then a certain number of excited atoms are added to the already existing excited atoms. Therefore, the change in the number of excited atoms turns out to be relatively not very large and, consequently, the effect of the action of electromagnetic waves on the particle beam turns out to be not very sharp. It is clear that if at first there were no excited atoms at all, and then they appeared, then the overall effect would be much more contrasting.
So, an additional task arises: in the section from the source to the electromagnetic field, skip the atoms that are in the normal state and remove the excited ones. Nothing new had to be invented to solve it, since back in the forties of our century, Rabbi, and then Ramsey, developed the corresponding methods for spectroscopic studies. These methods are based on the fact that all atoms and molecules have certain electrical and magnetic properties, and these properties are different for excited and unexcited particles. Therefore, in electrical and magnetic fields excited and unexcited atoms and molecules deviate differently.
In the described atomic cesium clock, on the path of the particle beam between the source and the high-frequency electromagnetic field, permanent magnet 2 (see Fig. 24) was installed in such a way that the unexcited particles were focused on the collimator slit, and the excited ones were removed from the beam. The second magnet 5, standing between the high-frequency electromagnetic field and the detector, on the contrary, was installed in such a way that unexcited particles were removed from the beam, and only excited ones were focused on the detector. Such a double separation leads to the fact that only those particles reach the detector, which were unexcited before entering the electromagnetic field, and then in this field passed into an excited state. In this case, the dependence of the detector readings on the frequency of electromagnetic oscillations turns out to be very sharp and, accordingly, the resonance curve of the absorption of electromagnetic energy turns out to be very narrow and steep.
As a result of the measures described, the driving unit of the atomic cesium clock turned out to be able to respond even to a very small detuning of the high-frequency generator, and thus a very high stabilization accuracy was achieved.
The rest of the device, in general, repeats the principle diagram of a molecular clock: a high-frequency generator controls an electric clock and simultaneously excites particles through frequency multiplication circuits. A discriminator connected to a cesium tube and a high-frequency generator reacts to the operation of the tube and adjusts the generator so that the frequency of oscillations produced by it coincides with the frequency at which the particles are excited.
All this device as a whole is called the atomic cesium clock.
In the first models of cesium clocks (for example, the cesium clock of the National Physical Laboratory of England), the instability was only 1 -9 . In devices of this type, developed and built in recent years, the instability has been reduced to 10 -12 -10 -13 .
It has already been said before that even the best mechanical astronomical clocks, due to the wear of their parts, change their course somewhat over time. Even quartz astronomical clocks are not without this drawback, since due to the aging of quartz, there is a slow drift of their readings. No frequency drift was found in cesium atomic clocks.
When comparing different instances of these clocks, the frequency of their oscillations was observed to coincide within ± 3 * 10 -12, which corresponds to an error of only 1 second in 10,000 years.
However, this device is not without drawbacks: distortions of the shape of the electromagnetic field and the relative short duration of its impact on beam atoms limit further increase in the accuracy of measuring time intervals using such systems.
Astronomical clock with a quantum generator
Another step towards increasing the accuracy of measuring time intervals was made using molecular generators- appliances that use radiation of electromagnetic waves by molecules.
This discovery was unexpected and natural. Unexpected - because it seemed that the possibilities of the old methods were exhausted, while there were no others. Natural - because a number of well-known effects already constituted almost all parts of the new method and it only remained to properly combine these parts. However, a new combination of known things is the essence of many discoveries. It always takes a lot of courage to think in order to come up with it. Quite often, after this is done, everything seems very simple.
Devices in which radiation from molecules is used to obtain a frequency standard are called masers; this word is formed from the initial letters of the expression: microwave amplification by stimulated emission of radiation, i.e. amplification of centimeter-range radio waves using induced radiation. Currently, devices of this type are most often called quantum amplifiers or quantum generators.
What prepared the discovery of the quantum generator? What is its principle of operation and device?
Researchers knew that when excited molecules, such as ammonia, switch to more low levels energy and emit electromagnetic radiation the natural width of these emission lines is extremely small, at least many times smaller than the absorption linewidth used in molecular clocks. Meanwhile, when comparing the frequency of two oscillations, the sharpness of the resonance curve depends on the width of the spectral lines, and the achievable stabilization accuracy depends on the sharpness of the resonance curve.
It is clear that researchers were extremely interested in the possibility of achieving a higher accuracy in measuring time intervals using not only absorption, but also the emission of electromagnetic waves by molecules. It would seem that everything is already there for this. Indeed, in the waveguide of a molecular clock, excited ammonia molecules spontaneously emit light, i.e., they pass to lower energy levels and at the same time emit electromagnetic radiation with a frequency of 23,870,129,000 periods per second. The width of this spectral emission line is indeed very small. In addition, since the molecular clock waveguide is filled with electromagnetic oscillations supplied from the generator, and the frequency of these oscillations is equal to the frequency of energy quanta emitted by ammonia molecules, then in the waveguide induced radiation of excited ammonia molecules, the probability of which is much greater than spontaneous. Thus, this process increases the total number of radiation events.
Nevertheless, for the observation and use of molecular radiation, a system such as a molecular clock waveguide turned out to be completely unsuitable. Indeed, in such a waveguide there are much more unexcited ammonia particles than excited ones, and even taking into account induced radiation, the acts of absorption of electromagnetic energy occur much more often than the acts of emission. In addition, it is not clear how to isolate the energy quanta emitted by molecules in such a waveguide when the same volume is filled with electromagnetic radiation from the generator, and this radiation has the same frequency and much greater intensity.
Isn't it true that all processes turn out to be so mixed up that at first glance it seems impossible to single out the right one from them? However, it is not. After all, it is known that excited molecules differ in their electrical and magnetic properties from unexcited ones, and this makes it possible to separate them.
In 1954-1955. this problem was brilliantly solved by N. G. Basov and A. M. Prokhorov in the USSR and by Gordon, Zeiger, and Towns in the USA*. These authors took advantage of the fact that the electrical state of excited and unexcited ammonia molecules is somewhat different and, flying through an inhomogeneous electric field, they deviate differently.
* (J. Singer, Mathers, IL, M., 1961; Basov N. G., Letokhov V. S. Optical frequency standards, UFN, vol. 96, no. 4, 1968.)
Recall that between two electrically charged parallel plates, for example, the plates of a capacitor, a uniform electric field is created; between a charged plate and a point or two charged points - inhomogeneous. If electric fields are depicted using lines of force, then uniform fields are represented by lines of the same density, and inhomogeneous fields by lines of unequal density, for example, less near the plane and more near the point where the lines converge. Methods for obtaining inhomogeneous electric fields of one form or another have long been known.
A molecular generator is a combination of a source of molecules, an electrical separator, and a resonator assembled in a tube from which air is pumped out. For deep cooling, this tube is placed in liquid nitrogen. This achieves high stability of the entire device. The source of particles in the molecular generator is a bottle with a narrow opening filled with ammonia gas. Through this hole, a narrow beam of particles enters the tube at a certain speed (Fig. 25a).
The beam always contains unexcited and excited ammonia molecules. However, usually there are much more unexcited than excited. In the tube, in the path of these particles, there is a capacitor charged with electricity, consisting of four rods, the so-called quadrupole capacitor. In it, the electric field is inhomogeneous, and has such a shape (Fig. 25, b) that, passing through it, unexcited ammonia molecules scatter to the sides, and excited ones deviate towards the axis of the tube and are thus focused. Therefore, particles are separated in such a condenser and only excited ammonia molecules reach the other end of the tube.
At this other end of the tube there is a vessel of a certain size and shape - the so-called resonator. Once in it, the excited ammonia molecules, after a certain short period of time, spontaneously pass from the excited state to the unexcited state and, at the same time, emit electromagnetic waves a certain frequency. About this process they say that the molecules are highlighted. Thus, it is possible not only to obtain molecular radiation, but also to isolate it.
Consider further development these ideas. Electromagnetic radiation of resonant frequency, interacting with unexcited molecules, transfers them to an excited state. The same radiation, interacting with excited molecules, transfers them to an unexcited state, thus stimulating their radiation. Depending on which molecules are more, unexcited or excited, the process of absorption or induced emission of electromagnetic energy prevails.
By creating in a certain volume, for example, a resonator, a significant predominance of excited ammonia molecules and applying electromagnetic oscillations of the resonant frequency to it, it is possible to amplify the microwave frequency. It is clear that this amplification occurs due to the continuous pumping of excited ammonia molecules into the resonator.
The role of the resonator is not limited to the fact that it is a vessel in which the emission of excited molecules occurs. Since electromagnetic radiation of the resonant frequency stimulates the radiation of excited molecules, the greater the density of this radiation, the more actively this process of induced radiation proceeds.
By choosing the dimensions of the resonator in accordance with the wavelength of these electromagnetic oscillations, it is thus possible to create conditions for the occurrence of standing waves in it (similar to the choice of the dimensions of organ pipes for the occurrence of standing waves of the corresponding elastic sound oscillations in them). Having made the walls of the resonator from the appropriate material, it is possible to ensure that they reflect electromagnetic oscillations with the least losses. Both of these measures make it possible to create a high density of electromagnetic energy in the resonator and thus increase the efficiency of the entire device as a whole.
Ceteris paribus, the gain in this device is the greater, the higher the flux density of excited molecules. It is remarkable that at some sufficiently high flux density of excited molecules and suitable parameters of the resonator, the radiation intensity of the molecules becomes large enough to cover various energy losses, and the amplifier turns into a molecular generator of microwave oscillations - the so-called quantum generator. In this case, it is no longer necessary to supply high-frequency electromagnetic energy to the resonator. The process of stimulated emission of some excited particles is supported by the emission of others. Moreover, under suitable conditions, the process of generating electromagnetic energy does not stop even if some of it is diverted to the side.
Quantum oscillator with very high stability Gives high-frequency electromagnetic oscillations of a strictly defined frequency and can be used to measure time intervals. It does not need to run continuously. It is enough Periodically at certain intervals to compare the frequency of the electric generator of the astronomical clock with this molecular frequency standard and, if necessary, introduce a correction.
An astronomical clock corrected by a molecular ammonia generator was built in the late fifties. Their short-term instability did not exceed 10 -12 per 1 minute, and the long-term instability was about 10 -10, which corresponds to distortions in the counting of time intervals of only 1 sec in several hundred years.
Further improvement in frequency and time standards was achieved on the basis of the same ideas and the use of some other particles as a working medium, such as thallium and hydrogen. In this case, the quantum generator operating on a beam of hydrogen atoms, developed and built in the early sixties by Goldenberg, Klepner and Ramsay, turned out to be especially promising. This generator also consists of a particle source, a separator and a resonator mounted in a tube (Fig. 26) immersed in an appropriate coolant. The source emits a beam of hydrogen atoms. In this beam there are unexcited and excited hydrogen atoms, and there are much more unexcited than excited ones.
Since excited hydrogen atoms differ from unexcited ones in their magnetic state (magnetic moment), their separation is no longer an electric, but a magnetic field created by a pair of magnets. The resonator of the hydrogen generator also has significant features. It is made in the form of a flask made of fused quartz, the inner walls of which are coated with paraffin. Due to multiple (about 10,000) elastic reflections of hydrogen atoms from the paraffin layer, the length of flight of particles and, accordingly, their residence time in the resonator, in comparison with a molecular generator, increases thousands of times. In this way, it is possible to obtain very narrow spectral emission lines of hydrogen atoms and, in comparison with a molecular generator, reduce the instability of the entire device by a factor of thousands.
Modern designs of astronomical clocks with a hydrogen quantum generator have surpassed the cesium atomic beam standard in their performance. No systematic drift was found. Their short-term instability is only 6 * 10 -14 per minute, and long-term - 2 * 10 -14 per day, which is ten times less than that of the cesium standard. The reproducibility of clock readings with a hydrogen quantum generator is ±5*10 -13 , while the reproducibility of the cesium standard is ±3*10 -12 . Consequently, the hydrogen generator is about ten times better in this indicator as well. Thus, with the help of a hydrogen astronomical clock, it is possible to provide an accuracy of time measurement of the order of 1 sec for an interval of about a hundred thousand years.
Meanwhile, a number of studies in recent years have shown that this high accuracy of measuring time intervals, achieved on the basis of atomic beam generators, is not yet the limit and can be improved.
Transmission of the exact time
The task of the time service is not limited to obtaining and storing the exact time. An equally important part of it is such an organization of the transfer of exact time, in which this accuracy would not be lost.
In the old days, the transmission of time signals was carried out using mechanical, sound or light devices. In St. Petersburg, a cannon fired at exactly noon; one could also check one's watch against the tower clock of the Institute of Metrology, now named after D. I. Mendeleev. In seaports, a falling ball was used as a time signal. From the ships in the port, one could see how exactly at noon the ball broke off from the top of a special mast and fell to its foot.
For the normal course of modern intensive life, it is very important to provide accurate time railways, post, telegraph and big cities. It does not require such high accuracy as with astronomical and geographical works, but it is necessary that, to the nearest minute, in all parts of the city, in all parts of our vast country, all clocks show the same time. This task is usually solved with the help of an electric clock.
In the watch industry of railways and communications institutions, in the watch industry of a modern city, electric clocks play an important role. Their device is very simple, and yet, with an accuracy of one minute, they show the same time in all points of the city.
Electric clocks are primary and secondary. Primary electric clocks have a pendulum, wheels, escapement and are real time meters. Secondary electric clocks are only pointers: there is no clockwork in them, but there is only a relatively simple device that moves the hands once a minute (Fig. 27). With each opening of the current, the electromagnet releases the anchor and the "dog" attached to the anchor, resting against the ratchet wheel, turns it by one tooth. Signals electric current are fed to the secondary clock either from the central installation or from the primary electric clock. In recent years, talking clocks have appeared, designed on the principle of sound films, which not only show, but also tell the time.
For transmission exact time now serve mainly electrical signals sent by telephone, telegraph and radio. Over the past decades, the technique of their transmission has been improved, and the accuracy has increased accordingly. In 1904, Bigourdant transmitted rhythmic time signals from the Paris Observatory, which were received by the Montsouris Observatory with an accuracy of 0.02-0.03 sec. In 1905, the Washington Naval Observatory began regular transmission of time signals; from 1908, rhythmic time signals began to be transmitted from eiffel tower, and since 1912 from the Greenwich Observatory.
Currently, the transmission of accurate time signals is carried out in many countries. In the USSR, such transmissions are conducted by the State Astronomical Institute named after V.I. P.K. Sternberg, as well as a number of other organizations. At the same time, a number of different programs are used to transmit readings of mean solar time by radio. For example, the broadcast time signal program is transmitted at the end of every hour and consists of six short pulses. The beginning of the last of them corresponds to the time of this or that hour and 00 min 00 sec. In maritime and air navigation, a program of five series of 60 pulses and three series of six short signals, separated by longer signals, is used. In addition, there are a number of special time signal programs. Information about various special time signal programs is published in special publications.
The error in the transmission of time signals for broadcast programs is about ±0.01 - 0.001 sec, and for some special ones ±10 -4 and even ±10 -5 sec. Thus, at present, methods and devices have been developed that allow you to receive, store and transmit time with a very high degree accuracy.
Recently, significant new ideas have been implemented in the field of storing and transmitting accurate time. Suppose that it is necessary that at a number of points in any territory the accuracy of the readings of the clocks standing there be no worse than ± 30 seconds, provided that all these clocks work continuously throughout the year. Such requirements apply, for example, to city and railway clocks. The requirements are not very strict, however, in order to fulfill them using autonomous watches, it is necessary that the daily rate of each instance of the watch be better than ± 0.1 seconds, and this requires precision quartz chronometers.
Meanwhile, if this problem is solved using common time system, consisting of primary clocks and a large number of secondary clocks associated with them, then only primary clocks should have high accuracy. Therefore, even with an increased cost for the primary clock and a correspondingly low cost for the secondary clock, good accuracy can be achieved throughout the system at a relatively low total cost.
Of course, in this case, you need to make sure that the secondary clock itself does not introduce errors. The previously described secondary clock with a ratchet wheel and a pawl, in which the hand moves once a minute on a signal, sometimes malfunctions. Moreover, over time, the error of their testimony accumulates. In modern secondary clocks, various kinds of verification and correction of readings are used. Even greater accuracy is provided by the secondary clock, which uses alternating current of industrial frequency (50 Hz), the frequency of which is strictly stabilized. The main part of this watch is a synchronous electric motor driven by alternating current. Thus, in this clock, the alternating current itself is a continuous time signal with a repetition period of 0.02 seconds.
Currently, the World-wide Synchronization of Atomic Clocks (WOSAC; the name is composed of the first letters of the words: World-wide Synchronization of Atomic Clocks) has been created. The main primary clock of this system is located in Rome, New York, USA, and consists of three atomic cesium clocks, the readings of which are averaged. Thus, the accuracy of the time reading is equal to (1-3)*10 -11 . These primary clocks are connected to a worldwide network of secondary clocks.
The test showed that when transmitting accurate time signals via WHOAC from the state of New York (USA) to the island of Oahu (Hawaii), i.e. approximately 30,000 km, time indications were coordinated with an accuracy of 3 microseconds.
The high accuracy of storage and transmission of time stamps, achieved today, makes it possible to solve complex and new problems of deep space navigation, as well as, although old, but still important and interesting questions about motion. crust.
Where are the continents going?
Now we can return to the problem of the motion of continents, described in the previous chapter. This is all the more interesting because in the half century that has passed since the appearance of Wegener's works to our time, scientific disputes around these ideas have not yet subsided. For example, W. Munk and G. Macdonald wrote in 1960: "Some of Wegener's data are undeniable, but most of his arguments are entirely based on arbitrary assumptions." And further: "Great shifts of the continents took place before the invention of the telegraph, medium shifts - before the invention of radio, and after that practically no shifts were observed."
These caustic remarks are not without foundation, at least in their first part. Indeed, the longitudinal measurements that Wegeper and his collaborators once made during their expeditions to Greenland (in one of which Wegener tragically died) were performed with an accuracy insufficient for a rigorous solution of the problem. This was also noted by his contemporaries.
One of the most convinced supporters of the theory of the movement of continents in its modern version is P. N. Kropotkin. In 1962, he wrote: "Paleomagnetic and geological data indicate that during the Mesozoic and Cenozoic, the leitmotif of the movement of the earth's crust was the fragmentation of two ancient continents - Laurasia and Gondwana and the spread of their parts towards the Pacific Ocean and towards the Tethys geosynclinal belt." Recall that Laurasia covered North America, Greenland, Europe and the entire northern half of Asia, Gondwana - the southern continents and India. The Tethys Ocean stretched from the Mediterranean through the Alps, the Caucasus and the Himalayas to Indonesia.
The same author further wrote: “The unity of Gondwana has now been traced from the Precambrian to the middle of the Cretaceous, and its fragmentation now looks like a long process that began in the Paleozoic and reached a particularly large scale from the middle of the Cretaceous. Eighty million years have passed since that time. Consequently, the distance between Africa and South America increased at a rate of 6 cm per year. The same speed is obtained from paleomagnetic data for the movement of Hindustan from the southern hemisphere to the northern one. "Having reconstructed the location of the continents in the past using paleomagnetic data, P. N. Kropotkin came to the conclusion that" - at that time the continents were really knocked together into such a block , which resembled the outlines of the Wegenerian primary continental platform".
So, the sum of the data obtained by different methods shows that the current location of the continents and their outlines were formed in the distant past as a result of a series of faults and a significant movement of continental blocks.
The question of the current movement of the continents is decided on the basis of the results of longitudinal studies carried out with sufficient accuracy. What in this case means sufficient accuracy can be seen from the fact that, for example, at the latitude of Washington, a change in longitude of one ten-thousandth of a second corresponds to a shift of 0.3 cm. Since the estimated speed of movement is about 1 m per year, and modern time services already If it is possible to determine time points, store and transmit exact time with an accuracy of thousandths and ten thousandths of a second, then to obtain convincing results, it is enough to carry out the corresponding measurements at intervals of several years or several tens of years.
For this purpose, in 1926, a network of 32 observation points was created and astronomical longitudinal studies were carried out. In 1933, repeated astronomical longitudinal studies were carried out, and 71 observatories were already involved in the work. These measurements, carried out at a good modern level, although over a not very long time interval (7 years), showed, in particular, that America is not moving away from Europe by 1 m per year, as Wegener thought, but is approaching it at approximately the speed 60 cm per year.
Thus, with the help of very accurate longitudinal measurements, the presence of the modern movement of large continental blocks was confirmed. Moreover, it was possible to find out that separate parts of these continental blocks have a slightly different movement.
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 according to the PCZN 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 convert 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 different 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 "mean 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 - geographical 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 measured east of the "zero" (Greenwich) meridian and is numerically equal to the time interval between the culminations 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 point 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 cancels the transition to summer time, which has been in effect 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 04/23/1996, 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 midday 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 N- 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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