Angular distance
Municipal educational institution
"Secondary school number 9".
Methodical development
in astronomy
"Visible movement
Sun and Moon "
Miass - 2008
Introduction
The proposed methodological development "Visible Movement of the Sun and Moon" is intended for teachers of physics and astronomy, working according to the following Program and textbook:
Program for educational institutions: Physics. Astronomy. 7 - 11 cells / Comp. Yu.I. Dick, V.A. Korovin - M .: Bustard, 2006.
Textbook: Vorontsov-Velyaminov B.A. Astronomy. 11th grade: Textbook. for general education. institutions / B.A. Vorontsov-Velyaminov, E.K. Stout, - M .: Bustard, 2005.
The topic "Visible movement of the sun and moon" was chosen because it is relevant for the education of worldview concepts: cause-and-effect relationships in nature, in understanding the structure and movement of the bodies of the solar system, the cognizability of the surrounding world, the formation of scientific views of students.
The novelty of ideas lies in the possibility of using information and communication technologies in astronomy lessons, which allows you to spectacularly present some of the topics studied, makes it possible to use many illustrations, photographs and diagrams during the lesson. The use of new computer technologies makes it possible to diversify the methods and techniques used by the teacher in the lesson: explaining new material, preparing students for messages and reports using a presentation made using Microsoft PowerPoint. Test assignments during the study and consolidation of new material can be performed using a computer or printed on separate sheets. This form of work not only increases the interest of students in the subject, but also leads to an increase in the quality of knowledge.
The national regional component is presented in the form of calculations of the height of the Sun above the horizon, determination of climatic conditions, length of day and night for the city of Miass.
The purpose of my work- Creation of multimedia accompaniment to lessons on the topic "Visible Movement of the Sun and Moon". For each lesson, the goal, equipment, keywords, a plan for presenting new material, a lesson outline, homework, a method of monitoring students' knowledge are determined.
Tasks:
Development of students' interest in studying the subject through the use of distance technologies in the educational process.
Creation of presentation for lessons in the form of visual aids of a new generation.
Development of test tasks and laboratory work on the topic under study.
Lesson summaries and presentations to them are drawn up in accordance with the concept of personal-oriented learning:
Motivational stage
Determining or ensuring the motivational readiness of students for the lesson (setting students up for active work).
Actualization of subjective experience (determination of the attitude towards what the students came to the lesson with)
Updating basic knowledge.
Goal setting and planning.
Learning new material.
Reflection.
Methodical development includes:
Lesson planning.
Visible Movement of the Sun and Moon Web site.
Lesson notes.
The website and lesson notes have been compiled taking into account the age-specific psychological and pedagogical characteristics of the students.
The website "Visible Movement of the Sun, Moon and Planets" has passed the examination within the framework of the action "Examination of Digital Educational Resources" and is recognized as a digital educational resource ready for replication and widespread use. The organizers of the action are the almanac "Issues of informatization of education" and the magazine "School Director". The manual has been finalized taking into account the recommendations of the expert council.
The certificate of examination is in the Appendix.
Lesson planning
Visible movement of the Sun and Moon - 3 hours |
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Lesson topic | Equipment | The control | Homework |
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The Sun's annual path along the ecliptic | Computer Projector Movable star map Celestial sphere model Solar System Model Globe of earth Globe of the Moon | Frontal poll | Section 6, task 9 Presentations "Refraction of sun rays in the atmosphere" "White Nights" |
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Daily path of the Sun | Evaluation of presentations | ||||
Moon movement and phases | Frontal poll | ||||
Lesson notes
Lesson number 1.The Sun's annual path along the ecliptic
During the classes | ||||||||||||||||||||||
2. Studying new material with elements of repetition of the past. | ||||||||||||||||||||||
3. Work with a moving map of the starry sky (PKZN) and the celestial sphere (NS). | ||||||||||||||||||||||
4. Show of the presentation "Myths and legends about the zodiacal constellations" | ||||||||||||||||||||||
5. Consolidation of the studied material. Frontal poll. | ||||||||||||||||||||||
6. Homework. | ||||||||||||||||||||||
7. Grading for work in the lesson | ||||||||||||||||||||||
Two Astronomers Happened Together at a Feast And they argued very among themselves in the heat. One kept repeating: the Earth revolves around the Sun; Another, that the Sun leads all the planets with it; One was Copernicus, the other was known as Ptolemy. Then the cook decided the dispute with his smile. The owner asked: "Do you know the flow of stars? Tell me, how do you talk about this doubt? " He gave the following answer: "That Copernicus is right about that, I will prove the truth, to the Sun without being. Whoever saw a simple cook is such Who would spit the hearth around Zharkov? " M. Lomonosov Even in ancient times, observing the Sun, people discovered that its midday height changes throughout the year, as does the appearance of the starry sky. The movement of the Sun among the stars is an apparent phenomenon. The expression "the path of the sun among the stars" will seem strange to some. After all, the stars are not visible during the day. It is difficult to notice the movement of the Sun among the stars - after all, it shines during the day, "when it is already light," as the unforgettable Kozma Prutkov used to say. Therefore, it is not easy to notice that the Sun is moving slowly among the stars. This happens due to the annual revolution of the Earth around the Sun. Based on observations of the seasonal changes in the starry sky, it was concluded that the Sun moves across the sky, moving from one constellation to another, and completes a full revolution within a year. The circle of the celestial sphere, along which the apparent annual movement of the Sun occurs, was calledecliptic . Stellar year Is the period of the Sun's revolution along the ecliptic. |
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Observe on PKZN how the Sun moves through the zodiacal constellations throughout the year. To do this, draw the line "Earth - Sun - constellation". Since the vernal equinox is slowly moving among the stars due to the precession of the earth's axis, the sun passes its annual path not through 12, but through 13 constellations. Pay attention when the Sun is in any constellation, this constellation is not visible in this month. It is above us during the day. According to PKZN, determinein which constellation is the sun Today On your birthday. |
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Work with a model of the celestial sphere (NS) and with a moving map of the starry sky (PKZN). Reiteration: Consider the main points and lines of the NS: zenith, nadir, plumb line, pole of the world, axis of the world, celestial meridian, celestial equator, midday line, mathematical horizon, points: west, east, north, south, points of the spring and autumn equinox, summer and winter solstice. Show these points and lines on the celestial sphere and a moving map of the starry sky. |
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Tropical year - the time interval between two successive passages of the Sun through the vernal equinox. Due to the precession of the Earth's axis, the duration of the tropical year is shorter than the duration of the sidereal year. Give marks to students for work with the celestial sphere and PKZN. Show on NS: Inclination of the plane of the ecliptic and the plane of the celestial equator, The inclination of the earth's axis to the plane of the ecliptic. Find the points of the spring and autumn equinox at the PKZN, at which the planes of the ecliptic and the celestial equator intersect. Ecliptic at PKZN. |
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Using the PKZN, determine how the equatorial coordinates of the Sun change during the year. Determine the equatorial coordinates of the Sun by PKZN and fill in the table:
When explaining, use the "Changing seasons" diagram and the Earth's globe |
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The climate is determined by the inclination of the earth's axis to the plane of the ecliptic. Show key points and lines of the earth's orbit. Question: At what point is the speed of the Earth's movement around the Sun higher, and at which is lower? When does the Earth receive more energy from the Sun? |
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Question: Which is longer: summer or winter. Consider for the inhabitants of the Northern Hemisphere of the Earth. Consider for the inhabitants of the Earth's southern hemisphere. Output: Spring and summer in the northern hemisphere of the Earth are 6 days longer than autumn and winter. We live longer in the summer. Formulate a conclusion for the southern hemisphere of the Earth: 1. Winter and autumn in the Southern Hemisphere are 6 days longer than spring and summer |
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For the Northern Hemisphere of the Earth: When it is winter in the Northern Hemisphere of the Earth, the Earth is closer to the Sun - therefore, the Earth receives more energy from the Sun. This means that the winter will be less severe. When it is summer in the Northern Hemisphere of the Earth, the Earth is farther from the Sun - therefore the Earth receives less energy from the Sun. This means that in the Northern Hemisphere, the summer is cooler and the winter is warmer than in the Southern. Formulate your own conclusion for the southern hemisphere of the Earth. When it is winter in the Northern Hemisphere and summer in the Southern Hemisphere, the Earth is closer to the Sun at this time, there is more energy from the Sun. Summers in the Southern Hemisphere are warmer while winters are colder. The lowest temperature in Antarctica. But winter in the Southern Hemisphere is 6 days longer than summer. Due to the tilt of the earth's axis to the plane of the ecliptic, the Southern Hemisphere receives less solar energy than the Northern. The polar cap of the Southern Hemisphere is larger than the Northern one. General conclusion: in the Northern Hemisphere of the Earth is warmer than in the Southern. |
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Frontal survey by lesson: Why are there 13 zodiacal constellations at the present time? What are these constellations? |
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During the year, the Sun passes through the zodiacal constellations. Show the presentation "Myths and legends about the zodiacal constellations." |
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Homework: § 6, task 9. Creative task: prepare presentation messages "Refraction of sun rays in the Earth's atmosphere", "White nights". |
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Lesson number 2.Daily path of the Sun.
During the classes | 1. Setting the goals and objectives of the lesson | |
2. Checking homework Frontal poll. | ||
3. Studying new material with elements of repetition of the past. | ||
4. Messages - presentations of students "What is the refraction of sunlight", "White nights" | ||
5. Consolidation of the studied material. Lesson conclusions. | ||
6. Test "Movement of the Sun" | ||
7. Homework. | ||
8. Grading for work in the lesson |
Frontal poll: Why does the Sun's midday height change throughout the year? In what direction is the apparent annual movement of the Sun relative to the stars? What is a tropical year, a sidereal year? What is the difference between the zodiac constellations and the signs of the zodiac? What determines the climate on Earth? Which hemisphere of the earth is warmer: North or South? Review the main elements of the NN: ecliptic, points of the spring and autumn equinox,ecliptic, celestial equator, celestial meridian, noon line. During its diurnal movement, the Sun, like all the stars, twice crosses the celestial meridian - above the points of the south and north. The moment of crossing the celestial meridian is calledthe culmination of the luminary. In the momentupper climax above the point to the south, the Sun reaches its greatest height above the horizon, it happens at noon local time. Lower climax takes place over point north at midnight. The height of the Sun above the horizon changes due to the tilt of the earth's axis to the plane of the orbit. The height of the Sun above the horizon is related to the declination of the Sun at a given time and the latitude of the observation site. For an observer in the northern hemisphere of the Earth, the maximum height of the Sun above the horizon is June 22, the minimum is December 22. March 21 and September 23 The sun is at the celestial equator and has a declination of 0º. Both hemispheres of the Earth are illuminated by the Sun in the same way: the border of day and night passes exactly through the poles, and day is equal to night at all points of the Earth. Consider the diurnal paths of the Sun at different latitudes throughout the year using the model of the celestial sphere and the Earth's globe. Determine independently how the daily movement of the Sun occurs at different latitudes of the Earth's southern hemisphere. Messages - student presentations: What is sun refraction? White Nights. |
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Question: What are the phenomena associated with the refraction of sunlight in the atmosphere? The apparent height of the Sun is always greater than the actual height. At sunset, the Sun is flattened. conclusions about the diurnal movement of the Sun Regional component: Explain the length of day and night at different times of the year for our area. Why don't we see white nights in Miass? Homework: § 6, exercise 5. Sun movement test Give students grades for their work in the lesson. |
Lesson number 3. Movement and phases of the moon
During the classes | 1. Setting the goals and objectives of the lesson | |
2. Checking homework | ||
3. Learning new material | ||
4. Consolidation of the studied material | ||
5. Test "Movement and phases of the moon" | ||
6. Grade students for their work in the lesson | ||
7. Homework |
The moon is known to change its appearance. It itself does not emit light, therefore only the surface illuminated by the Sun is visible in the sky - the daytime side.
The moon is the celestial body closest to the Earth, its only satellite.
The moon revolves around the earth in the same direction in which the earth revolves around its axis.
Moving across the sky from west to east, the moon overtakes and overtakes the sun.
As the moon moves around the earth, its appearance changes - there is a change in lunar phases.
Limbo Is the visible edge of the lunar disk.
Terminator - a line dividing the illuminated and unlit surfaces of the Moon.
Phase angle - the angle between the directions from the Sun to the Moon and from the Moon to the Earth is called.
Moon phase Is the ratio of the area of \u200b\u200bthe illuminated part of the visible disk of the Moon to its entire area.
There are four main phases of the moon: new moon, first quarter, full moon, last quarter.
Draw a diagram of the change of lunar phases and a table "Phases of the Moon" in a notebook
At what time of day the Moon is above the horizon, as we see the hemisphere of the Moon facing the Earth - fully illuminated or partially illuminated - it all depends on the position of the Moon in orbit.
New moon - the beginning of the lunar month.
The Moon is in the same direction as the Sun, only above or below it, and is turned towards the Earth by an unlit hemisphere. The moon is not visible.
Two or three days later, the Moon appears in the west against the background of the evening dawn in the form of a narrow crescent with a bulge facing to the right - a growing month.
Sometimes the ashen light of the moon can be observed.
First quarter - the sun's rays illuminate only the right half of the lunar disk. After sunset, the moon is on the southern side of the sky and sets around midnight.
The beauty of the moon in full moon, when its surface reflects the sun's rays to the nighttime Earth as much as possible. It is not surprising that in folk tales and legends magical properties were attributed to the influence of the moon on everything earthly during this period.
After a week, only half of the lunar disk becomes visible again, but this is already its left side. Coming last quarter. The moon rises around midnight and shines until morning. By the time the Sun rises, the Moon is on the southern side of the sky. In this form, we can observe the moon even during the day in the southwestern part of the sky.
The width of the lunar crescent continues to decrease, and the Moon itself is gradually approaching the Sun from the right side. After a while, she is again invisible.
The phases of the new moon and full moon are called syzygies from the Greek word "syzygy" - connection.
From new moon to full moon, the moon is called young, since it seems to "grow" every day, and from full moon to new moon - old, as it "decreases".
How to distinguish a waning moon from a waxing one?
Rule for the northern hemisphere: if the view of the crescent moon is a letter FROMthen the moon old, and if, having mentally added a stick to the left of the disk, you see the letter Rthen this is the moon growing.
Sidereal (sidereal) month - one complete revolution of the Moon around the Earth.
Synodic month - the time interval between consecutive phases of the same name.
The synodic month is larger than the sidereal month, since the Earth revolves around the Sun together with the Moon. Having completed one revolution around the Earth in 27.3 days, the Moon returns to its place among the stars. But the Sun has already moved along the ecliptic to the east during this time. It takes another 2.2 days for the Moon to catch up with the Sun.
Consider the conditions for the visibility of the moon in different phases.
The moon's path across the sky passes close to the ecliptic, so the full moon rises from the horizon at sunset and approximately repeats the path it traveled six months earlier.
In summer, the sun rises high in the sky, while the full moon does not move far from the horizon.
In winter, the Sun is low, and the Moon, on the contrary, rises high and illuminates winter landscapes for a long time, giving the snow a blue tint.
Only one side of the Moon is visible from the Earth, but this does not mean that it does not rotate on its axis.
Experiment with the globe of the moon, moving it around the globe of the earth so that one side of the lunar globe is always facing it. The period of the Moon's revolution around the axis is equal to the period of the Moon's revolution around the Earth.
Question: Does the moon change day and night?
Two weeks - day and two weeks - night
Only the visible part of the Moon is observed from the Earth. But this is not 50% of the surface, but somewhat more.
The Moon revolves around the Earth in an ellipse, near perigee the Moon moves faster, and near apogee - slower. But the moon rotates around the axis evenly. As a result, there is libration in longitude. Its maximum possible value is 7 ° 54 '.
Libration in latitudearises from the inclination of the axis of rotation of the Moon to the plane of its orbit and the preservation of the direction of the axis in space when the Moon moves. The amount of libration is 6 ° 50 '.
Thanks to libration, we have the opportunity to observe from the Earth, in addition to the visible side of the Moon, also the adjacent narrow strips of the territory of its reverse side. In total, from Earth you can see 59 % lunar surface.
In its movement around the Earth, the Moon periodically obscures various more distant luminaries with its disk. This phenomenon is called covering the luminaries of the moon.
Such moments are calculated and used to refine the parameters of the Moon's orbit.
Most often, star coverings occur, less often planetary coverings.
Determine the phase of the moon from the photographs and explain the conditions for its visibility
Consolidation of the studied material:
Within what limits does the angular distance of the Moon from the Sun change?
How to determine the approximate angular distance from the Sun by the phase of the Moon?
How much does the right ascension of the moon change in a week?
What observations are needed to notice the movement of the moon around the earth?
What observations show that there is a change of day and night on the moon?
Why is the moon's ash light weaker than the glow of the rest of the moon visible shortly after the new moon?
Homework: § 7, exercise 6.
Web-site "Visible movement of the Sun and Moon"
Structureweb-site:
Explanatory note
History feed
This web page presents, in chronological order, historical information on the study of the apparent motion of the Sun, Moon and planets. This page can be referred to as reference material.
Presentation "Daily Path of the Sun"
Presentation "The annual path of the Sun along the ecliptic"
Presentation "Myths and Legends about the Zodiacal Constellations"
Sun movement test
Presentation "Movement and Phases of the Moon"
Moon Movement and Phase Test
The apparent movement of the sun
Moon movement and phases
This web page contains all the tests that are used in this methodological development to control the knowledge of students.
7.1. Sun movement test
7.2. Moon Movement and Phase Test
8. Sources
All electronic resources and printed publications that were used in the preparation of the methodological development are presented here.
The site navigation is very convenient and understandable.
Conclusion
I believe that the methodological development in astronomy "The Visible Movement of the Sun, Moon and Planets" is relevant, effective, convenient and quite interesting for both teachers and students.
Expected Result:
Improving the quality of teacher teaching through the use of visual aids of a new generation, the formation of new ways of organizing the educational process.
The growth of the quality of knowledge of students, their inclusion in educational activities of a creative nature, the development of creative, theoretical thinking in students, as well as the formation of so-called operational thinking aimed at choosing optimal solutions.
Increasing motivation for learning, interest in the subject being studied.
The use of new technologies allows:
organize various forms of students' activities for the independent extraction and presentation of knowledge;
apply the full range of capabilities of modern information and telecommunication technologies in the process of performing various types of educational activities, including such as registration, collection, storage, processing of information, interactive dialogue, modeling of objects, phenomena, processes.
manage the educational activities of students adequately to the intellectual level of a particular student, the level of his knowledge, abilities, skills, the peculiarities of his motivation, taking into account the implemented methods and the teaching aids used.
This methodological development can be used:
teachers when explaining new material, checking and consolidating knowledge,
with a distance learning method,
students in independent study of the topic.
Literature and electronic manuals
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Study... movementSuns and Moon and on its basis - methods for predicting eclipses. Hipparchus discovered that visibletrafficSuns and Moon ... us treatises byastronomy. Development new calendar ... like microorganisms. AT methodical In relation to exobiology is ...
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BYASTRONOMY O.S. Ugolnikov METHODOLOGICAL RECOMMENDATIONS bydeveloping assignments for school and ... Visiblemovement by disk Suns ...
All-Russian Olympiad for schoolchildren in astronomy methodological recommendations for the development of tasks for the school and municipal stages of the All-Russian Olympiad for schoolchildren in the 2011/2012 academic year
Guidelines... Visiblemovement and planetary configurations. Orbital inclination, knot line. Passage of planets by disk Suns ... and diffraction. ALL-RUSSIAN SCHOOL OLYMPIAD BYASTRONOMYMETHODOLOGICAL RECOMMENDATIONS bydeveloping requirements for conducting school and ...
All-Russian Olympiad for schoolchildren in astronomy methodological recommendations for the development of tasks for the school and municipal stages of the All-Russian Olympiad for schoolchildren in the 2010/2011 academic year
GuidelinesALL-RUSSIAN SCHOOL OLYMPIAD BYASTRONOMY O.S. Ugolnikov METHODOLOGICAL RECOMMENDATIONS bydeveloping assignments for school and ... Visiblemovement and planetary configurations. Orbital inclination, knot line. Passage of planets by disk Suns ...
Vorontsov - Velyaminov B.A. Astronomy, 11th grade: Textbook for general education. institutions / B.A. Vorontsov - Velyaminov, E.K. Stout, - M .: Bustard, 2005.
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ANGULAR DISTANCE
ANGULAR DISTANCE, in astronomy - the distance in the celestial sphere between two celestial bodies, measured along the arc of a great circle passing through them, with the observer in the center. For example, the angular distance between two stars of the Ursa Major, which are in line with the North Star, is 5 °.
Scientific and technical encyclopedic dictionary.
See what "ANGULAR DISTANCE" is in other dictionaries:
The arc length, expressed in angular units (that is, radians, degrees, arc minutes, or seconds), that corresponds to a given viewing angle. For example, the angular distance between two points on the celestial sphere is the angle between ... ... Astronomical Dictionary
angular distance - kampinis atstumas statusas T sritis Standartizacija ir metrologija apibrėžtis Atstumas, išreikštas kampo matavimo vienetais. atitikmenys: angl. angular distance vok. Winkelentfernung, f rus. angular distance, n pranc. distance angulaire, f ... Penkiakalbis aiškinamasis metrologijos terminų žodynas
angular distance - kampinis atstumas statusas T sritis fizika atitikmenys: angl. angular distance; angular separation vok. Winkelentfernung, f rus. angular distance, n pranc. distance angulaire, f… Fizikos terminų žodynas
Resolution is the ability of an optical device to measure the linear or angular distance between close objects, to show separately closely spaced objects. Contents 1 Angular resolution 2 Linear resolution 3 General information ... Wikipedia
This term has other meanings, see Angular. Village Uglovoe ukr. The corner of the Crimean cat. Acı Bolat Country ... Wikipedia
angular magnification - 3.1 angular magnification M: Angular magnification M of an optical device is the ratio of the viewing angle of an object resting on the entrance pupil of the device (aprib) to the viewing angle of the object with an eye without a device (agl) Note B ... ... Dictionary-reference book of terms of normative and technical documentation
The angular distance of a celestial body or an earthly object from the zenith. It is denoted by r, measured along the height circle from 0 to 180 °. It is related to the height h by the relation z \u003d 90 ° h ... Natural science. encyclopedic Dictionary
The angular distance of the celestial body from the zenith. It is designated as Z and is counted along the height circle from 0 to 180˚. It is related to the height h by the relation Z \u003d 90˚ h ... Astronomical Dictionary
The angular distance of a celestial body or an earthly object from the zenith. Denoted by z, it is counted along the height circle from 0 to 180º. It is connected with the height h by the relation z \u003d 90º - h. * * * ZENITH DISTANCE ZENITH DISTANCE, angular distance ... ... encyclopedic Dictionary
The distance between a pole and a given point on the earth's surface. An explanation of the 25,000 foreign words that have come into use in the Russian language, with the meaning of their roots. Mikhelson AD, 1865. POLAR DISTANCE Angular distance of the star from the visible ... ... Dictionary of foreign words of the Russian language
Image of Jupiter
Color image of the western hemisphere of the moon, including the East Sea, obtained by the American spacecraft "Galileo". The Vostochnoye Sea, 1000 km in diameter, is located to the left of the image center (20 S, 265 E). The right side of the image is the visible side of the Moon, the left side is the reverse side. The dark area above, to the right is the Ocean of Storms, the circular sea below it is the Sea of \u200b\u200bMoisture. Dark area on the left, below - South Pole - Aitken basin. The image was acquired through blue, red and near infrared filters from a distance of 560,000 km. (Galileo, P-37329)
The moon is a natural satellite of the Earth and the brightest object in the night sky. On the moon there is no atmosphere familiar to us, there are no rivers and lakes, vegetation and living organisms. The force of gravity on the Moon is six times less than on Earth. Day and night with temperature changes up to 300 degrees last two weeks. And, nevertheless, the Moon is increasingly attracting earthlings with the opportunity to use its unique conditions and resources.
Extraction of natural resources on Earth becomes more difficult every year. Scientists predict that humanity will enter a difficult period in the near future. The terrestrial habitat will exhaust its resources, so now it is necessary to begin to develop the resources of other planets and satellites. The moon, as the celestial body closest to us, will become the first object for extraterrestrial industrial production. The creation of a lunar base, and then a network of bases, is planned in the coming decades. Oxygen, hydrogen, iron, aluminum, titanium, silicon and other useful elements can be extracted from lunar rocks. Lunar soil is an excellent raw material for obtaining various building materials, as well as for the extraction of the isotope helium-3, which is capable of providing the Earth's power plants with safe and environmentally friendly nuclear fuel. The moon will be used for unique scientific research and observations. By studying the lunar surface, scientists can "look" into a very ancient period of our own planet, since the peculiarities of the development of the moon ensured the preservation of the surface relief for billions of years. In addition, the Moon will serve as an experimental base for developing space technologies, and in the future will be used as a key transport hub for interplanetary communications.
Quite a lot was known about the features of the surface of the visible hemisphere of the Moon thanks to telescopic observations. However, there was a problem with the names on the cards. Quite often, the same objects were named differently on different maps. Therefore, the International Astronomical Union proposed to draw up a map with names that would be considered officially recognized. This map of the visible hemisphere was compiled by Blag and Müller in 1935. In the ground photographs, details up to 700 meters in the center of the disc and 1200-2000 meters at the edge could be discerned. The best photographs of the lunar surface taken at various observatories in the world were selected by Kuiper for the Photographic Atlas of the Moon, published in 1960.
Various hypotheses were built regarding the reverse side, in particular, it was assumed that a giant depression, similar to the Ocean of Storms, was also there. It is possible to see the relief of the Moon's reverse hemisphere only with the help of spacecraft. Starting from the Earth on January 2, 1959, the Luna 1 station with a mass of 361 kg, for the first time reached the second cosmic velocity, and passed at a distance of six thousand kilometers from the Moon. The station housed scientific instruments for studying the radiation belts of the Earth, cosmic rays, meteoric particles, and solar radiation. The American Pioneer 4 AMS, weighing only 6 kg, launched on March 3, 1959, passed much further from the Moon - at a distance of 60,500 km. September 14, 1959 AMS Luna 2 has reached the lunar surface. Scientific instruments have shown that the Moon has practically no magnetic field of its own.
Probably the first of the astronomical phenomena that primitive man drew attention to was the change in the phases of the moon. It was she who allowed him to learn how to keep track of the day. And it is no coincidence, apparently, in many languages \u200b\u200bthe word "month" has a common root, consonant with the roots of the words "measure" and "Moon", for example, Latin mensis - month and mensuga - measure, Greek "mene" - Moon and " maine "- month, English moon - moon and month - month. And the Russian national name for the Moon is a month! In the Ukrainian language, these names are identical: "mkyats".
Sidereal month. Observing the position of the moon in the sky over several evenings, it is easy to see that it moves among the stars from west to east at an average speed of 13 °, 2 per day. The angular diameter of the Moon (as well as the Sun) is approximately 0 °, 5. Therefore, we can say that for every day the Moon shifts to the east by 26 of its diameters, and in one hour - by more than the value of its diameter. Having made a full circle in the celestial sphere, the Moon returns to the same star after 27.321661 days. This period of time is called a sidereal (i.e., stellar: sidus - a star in Latin) month.
Moon configurations and phases. As you know, the Moon, whose diameter is almost 4, and the mass is 81 times less than that of the Earth, revolves around our planet at an average distance of 384,000 km. The moon's surface is cold and glows with reflected sunlight. When the Moon revolves around the Earth or, as they say, when changing the configuration of the Moon (from the Latin configuro - I give the correct shape) - its positions relative to the Earth and the Sun, that part of its surface that is visible from our planet is illuminated by the Sun differently. The consequence of this is a periodic change in the phases of the moon (Fig.).
Figure: Configuration (1 - conjunction, 3 and 7 - quadrature, 5 - opposition) and phases of the moon (1 - new moon, 3 - first quarter, 5 - full moon, 7 - last, or third quarter; 2, 4, 6, 8 - intermediate phase)
When the Moon, in its motion, is between the Sun and the Earth (this position is called conjunction - conjunction), it faces the Earth with its unlit side, and then it is not visible at all. This is the new moon.
Appearing then in the evening sky, first in the form of a narrow crescent, the Moon after about 7 days is already visible in the form of a semicircle. This phase is called the first quarter. After another 8 days, the Moon takes a position directly opposite to the Sun and its side facing the Earth is completely illuminated by it. The full moon comes, at which time the moon rises at sunset and is visible in the sky all night. 7 days after the full moon, the last quarter begins, when the moon is again visible in the form of a semicircle, with its convexity turned in the other direction, and rises after midnight. Recall that if at the time of the new moon the moon's shadow falls on the Earth (more often it slips "above" or "below" our planet), a solar eclipse occurs. If the moon in the full moon plunges into the shadow of the Earth, a lunar eclipse is observed.
Synodic month. The period of time after which the phases of the moon repeat again in the same order is called a synodic month. It is equal to 29.53058812 days. The twelve synodic months are 354.36706 days. Thus, the synodic month is incommensurable neither with the days, nor with the tropical year: it does not consist of a whole number of days and does not fit without a remainder in a tropical year.
The indicated duration of the synodic month is its average value, which is obtained as follows: they calculate how much time has elapsed between two eclipses far apart from each other, how many times during this time the Moon changed its phases, and divide the first value by the second (moreover, several pairs are chosen and mean). Since the Moon moves around the Earth in an elliptical orbit, the linear and observed angular velocities of its motion at different points of the orbit are different. In particular, this latter varies from about 11 ° to 15 ° per day. The movement of the Moon and the force of gravity acting on it from the Sun is very complicated, because the magnitude of this force is constantly changing both in its numerical value and in the direction it has the greatest value in the new moon and the least in the full moon.
Figure: Deviation in the duration of synodic months in 1967-1986 from average
Neomenia. On average, the period from the disappearance of the moon in the rays of the rising sun and its appearance in the evening after sunset is 2-3 days. During these days, the Moon passes (in relation to the Sun) from the western side of the sky to the eastern, thereby transforming from a morning light into an evening one. The first appearance of the moon in the evening sky ("the birth of a new moon") was called by ancient Greek astronomers neomenia ("new moon"). It was from neoness that it was convenient to start counting the time in a month.
But, as just said, the length of a synodic month can be more than six hours shorter or longer than its average. Therefore, neomania can occur both a day earlier and a day later relative to the average expected date of the appearance of a new moon (Fig.). The deviation of the dates of the new moons from those calculated by the average duration of the synodic month is shown in Fig.
Figure: Deviation of the moments of new moons in 1967-1986 from calculated by the average duration of the synodic month
The moon is "high" and "low".The visibility conditions of the narrow crescent of the "new" Moon in the evening sky are to a large extent determined by the peculiarities of its movement around the Earth. The plane of the Moon's orbit is inclined to the ecliptic plane at an angle i \u003d 5 ° 9. Consequently, the Moon either “rises” above the ecliptic (“approaches” the north pole of the world) by ten of its apparent angular diameters, then “descends” under the ecliptic by the same amount. Twice during a period of 27.2122 days (this period of time is called a draconian month), the path of the Moon in the sky intersects with the ecliptic at points called the nodes of the lunar orbit.
The node, through which the Moon approaches the north pole of the world, is called an ascending node, the opposite is called a descending node. The line passing through the center of the Earth and connecting the nodes of the lunar orbit is called the line of nodes. As it is easy to be convinced by observing the Moon and comparing its positions among the stars on the map of the starry sky, the lunar nodes continuously move towards the Moon, i.e. to the west, making a complete revolution in 18.61 years. Annually the distance of the ascending node from. the vernal equinox decreases by about 20 °, and in one draconian month - by 1 °, 5.
Now let's see how the effect of the inclination of the lunar orbit plane affects the height of the moon at the upper climax. If the ascending node coincides (“almost coincides”) with the vernal equinox (and this is repeated every 18.61 years), then the inclination angle of the lunar orbit plane to the celestial equator is ε + i (28 °, 5). During this time period, the declination of the Moon changes from + 28 °, 5 to -28 °, 5 during 27.2 days (Fig.).
Figure: The limits of the change in the declination of the moon over 18.61 years
After 14 days, the declination of the Moon is already equal to its smallest value -28 °, 5, and its height at the upper culmination for the same latitude of 50 ° is only 11 °, 5. This will be the position of the "low" Moon: it is barely visible above the horizon even at the upper climax ...
It is easy to understand that in the spring the Moon reaches this highest position in the sky at the time of the first quarter in the evening, and its lowest in the last quarter in the morning. Conversely, in the fall, when the sun is near the autumnal equinox, the ecliptic arc in the evening sky is below the celestial equator, and the moon's orbit is even lower. Therefore, the Moon reaches the indicated lowest position in the first quarter, while in the last quarter in the morning it stands at its highest.
Due to the continuous movement of the nodes of the lunar orbit in 9.3 years, a descending node will already be located near the vernal equinox. The angle of inclination of the lunar orbit plane to the celestial equator will already be ε - i (18 °, 5). At latitude 50 °, the height of the Moon in the upper culmination at the highest 18 °, 5 is already 58 °, 5 (in the spring - in the first quarter, in the fall - in the last), the lowest, 14 days later - 21 °, 5 (in the spring - in the last quarter , in the fall - in the first). In intermediate years, the nodes of the lunar orbit pass the arcs of the ecliptic, on which the points of the solstices are located. In this case, the declination of the Moon during the month fluctuates from approximately + 23 °, 5 to -23 °, 5, as shown in Fig. The heights of the Moon in the upper culmination change accordingly.
In general, the conditions for the visibility of the Moon in the evening sky are primarily determined by the position of the ecliptic relative to the horizon: in the spring the Moon is always much higher than in the fall (Fig.).
Figure: Position of the young Moon in the evening sky: a) in spring, b) in autumn at the same angular distance from the Sun, 1 - position of the "upper" Moon, 2- position of the "lower" Moon
This effect, however, is significantly enhanced by the favorable orientation of the plane of the lunar orbit: the height of the Moon at the moment of its upper culmination in the spring evening sky at φ \u003d 50 ° is from 58 °, 5 to 68 °, 5, while in autumn it is from 11 °, 5 to 21 °, 5.
The angular distance of the ascending node of the lunar orbit from the vernal equinox on January 1, 1900 was equal to 259 °, 18. Using the formula W \u003d 259 °, 18-19 °, 34t, where t is the time in years, it is easy to calculate the moments of coincidence of these points; 1913.4, 1932.0, 1950.6, 1969.2 and 1987.8. Thus, the last "high moon" was observed at the beginning of 1969. Usually, as can be seen from Fig. near these moments, the declination of the moon changes very slowly from month to month. Therefore, the Moon is "high" for about three years, in this case - in 1968-1970. This event will be repeated again in 1986-1988. The "low" Moon was observed near the mean moments of 1904.1, 1922.7, 1941.3, 1959.9, 1978.5, 1997.1, etc.
From all that has been said, it follows that in the spring the observer can notice the narrow crescent moon after the new moon a day earlier than in the fall. This effect also depends on the geographic coordinates of the observer. In particular, at latitude 32 °, 5 (this is the latitude of Ancient Babylon), the time interval between conjunction and neo-amenia varies from 16 h 30 min in March to 42 h in September. At a latitude of 38 ° (latitude of Athens), from 23 to 69 hours.Experienced Polish astronomer, compiler of the first map of the visible side of the Moon, Jan Hevelius (1611-1687), observing the Moon in Gdansk, never saw it later than 27 hours before conjunction , not earlier than 40 hours after it.
Thus, to use such a seemingly easily noticeable phenomenon as a change in the phases of the moon to build a calendar is still a rather difficult matter ...
Surely many go into a stupor when they hear phrases like "the diameter of the moon is half a degree" or " angular distance between the components of a double star is 5 arc seconds. " What seconds, minutes and degrees can there be in the sky? Let's try to figure it out, as well as learn how to measure the distance between celestial objects with our own hands.
Everyone knows that the sky can be conventionally represented as a sphere onto which images of space objects are projected. And the observer is always in its center. In this regard, it is quite reasonable to express measurements in the sky in degrees. Thus, if we have two points in the sky, then the distance between them will be the angle formed by straight lines drawn from these points into the eye of the observer. Hard? Then check out the picture.
Everything became clear immediately, didn't it? there is an angle α between two objects in the image.
A total of 360 degrees in a circle, and 180 degrees in its half. Thus, between two opposite points on the horizon 180 °. between the horizon and the zenith point - 90 °.
The figure at the beginning of the article shows the distances between some stars in the constellations Large and Ursa Minor... They can be used to "calibrate" your fingers for celestial measurements. Average results are approximately as follows:
How it works? Just extend your arm fully and position your fingers as shown to measure angular distance between the objects of interest.
Degrees are quite large for celestial bodies. When talking about their size and the distance between them, minutes (′) and seconds (″) of the arc are often used. Everything is extremely simple here: in one degree there are 60 minutes, and in one minute ... guess how many seconds? The second of an arc is a very small value. Something like this angular diameter has a five-ruble coin from a distance of 4 kilometers. The naked eye, no matter how eagle he is, will never see her.