The theme of the lesson is "Change in the appearance of the starry sky during the year." The purpose of the lesson: To study the apparent annual movement of the Sun. The starry sky is the great book of nature. Who will be able to read it, before that, countless treasures of the cosmos will be revealed. On a cloudless and moonless night, far from populated areas, I distinguish about 3,000 stars. The entire celestial sphere contains about 6,000 stars visible to the naked eye. You see one of the oldest Stonehenge observatories, and these are modern telescopes on Mauna Kea in Hawaii. Astronomers of antiquity divided the starry sky into constellations. A constellation is a section of the celestial sphere, the boundaries of which are determined by a special decision of the International Astronomical Union. In total, there are 88 constellations in the celestial sphere. Most of the constellations named in the time of Hipparchus and Ptolemy have the names of animals or heroes of myths. To understand the apparent annual movement of the Sun, we need a map of the "Starry Sky". During the year, the Sun moves in a large circle of the celestial sphere. This great circle is called the ecliptic. The entire ecliptic of the Sun takes exactly one year. The constellations through which the ecliptic passes are called zodiacal, their number corresponds to the number of months in a year. So, together with the Sun, we set off on a journey through the zodiac constellations, paying attention to the bright stars in them. Aries. We will begin our journey on the day of the vernal equinox, (March 21) from the point of intersection of the ecliptic and the celestial equator. The brightest star in the constellation Aries is Gamal. (find a bright star) Taurus. In the eastern part of the sky, the constellation TAURUS flaunts. In the form of a calf, the ancient Greeks honored Zeus, the legend says that Zeus turned into a bull to kidnap the Phoenician princess Europa, while she and her friends were playing on the seashore. The brightest star in this constellation is Aldebaran. (find a bright star)
GEMINI two true friend. These are the Dioscuri Brothers (youths of God) CASTOR and POLLUX. There is a belief that they tame storms at sea, appearing on the tops of the masts of ships in the form of flames. (find a bright star) We have climbed the ecliptic to the maximum and are at the point of the summer solstice, having entered the constellation of Cancer (06/22), this day is the longest day. In the center of the constellation Cancer there is a star cluster Nursery. The philosopher Plato suggested that this is a hole in the "firmament of heaven", through which the souls of newborn babies descend to earth. The lion, according to legend, lived near the ancient Greek city of Nemea and devastated the surroundings. No one was able to kill him, as his skin was as hard as steel. Performing his first of twelve labors, Hercules stunned the beast and freed the city from its atrocities. (find a bright star) VIRGO. For many centuries, the appearance of the Virgin in the evening sky coincided with the harvest. Spica is "ear". Virgo is Athena, the goddess of fertility and peaceful labor. She taught people how to work. Athena is the patroness of science and the goddess of wisdom. The feast of Athena (Minerva) was celebrated by artisans and teachers, who then received payment for the education of children. And today, Teacher's Day is celebrated in the fall. (find a bright star) We cross the ecliptic again, on September 23, the day of the autumn equinox, i.e. day equals night. SCALES. Scales belong to the goddess of justice Dika. From the sting of Scorpio, at the behest of the Goddess of the hunt, Orion died. Sagittarius is the only one of the centaurs who was fair, wise and friendly to people. (find a bright star) Capricorn. Aquarius. Fishes. The gods settled in the sky A flock of FISH and CAPRICORN, AND DOLPHIN, and WHALE, But they all need water! Then they called AQUARIUS, Pours and pours, he does not regret! Everything around was flooded with water, Therefore, on the side of that, there are very few conspicuous Stars Barely shining half-heartedly. December 22, the winter solstice, is the longest night of the year. The constellation Capricorn begins with it. We have walked a circle around the sky. Crossed the ecliptic twice.
The ecliptic and the celestial equator intersect at the vernal equinox (March 21, Aries) and the autumnal equinox (September 23, Libra). On the day of the summer solstice (June 22) the sun rises to its maximum and on the day of the winter solstice (December 22) it descends to the plane of the celestial equator as much as possible. (identify the sun in these cards in your cards. And now three magic stars are being played. They will go to those who carefully traveled through the zodiac constellations, so: 1. Which star illuminates the bright talent of A. Pugacheva and all those who were born under this sign? (Gamal ) contributing to the manifestation of talent, (Magic star, you get it too) 2. Who knows, maybe it was this star in the constellation of Taurus that contributed to the development of mystical plots in the novel “The Master and Margarita” by Mikhail Bulgagov (aldebaran) (The magic star of eternal youth goes to you) 3. This star illuminates the path of the elected President of Russia D. Medvedev and all those who were born under the sign of VIRGO (Spica) (And may this star bring you good luck in the next elections) Astronavigation (orientation by the stars) has retained its significance in our age of satellites and atomic energy.It is necessary for navigators and astronauts, captains and pilots.Since ancient times, the polar star has been a guiding star for travelers, h to find it, you need to start by searching for the constellation Ursa Major. Seven of her bright stars- just a part largest constellation. But some imagination is already required to see a giant bear in all the other, fainter stars. Putting aside 5 times equal segments, we connect an imaginary line with the polar star. Below the polar star on the horizon is the north point. Knowing this, it is easy to navigate the terrain, find the cardinal points (north, south, east, west). (Find) Let's summarize. 1. How many constellations is the sky divided into? (88) 2. What is the ecliptic? (During the year, the Sun moves in a great circle of the celestial sphere. This great circle is called the ecliptic.) 3. At what points does the ecliptic and the celestial equator intersect?
(spring equinox on March 21 (Aries) and autumn equinox on September 23 (Libra) 4. What constellations are called zodiac? (The constellations through which the ecliptic passes are called zodiac) Why does the starry sky change during the year? Yes, because our dear planet , every day, and every hour makes a revolution, and from the Earth, when observed, it seems that it is not she who is spinning, but all the stars and the moon.I hope you are carried away by astronomy because the starry sky is a whole world, its silent beauty and mystery fascinates everyone. There is a belief that if you look at the starry sky often and for a long time, then one day the Universe can reveal all the secrets of the universe to you.With the help of the star chart that you now have, you can quickly determine which constellations and bright stars are visible on a given evening For the lesson, you get excellent grades, with the wish to LIVE ON THIS EARTH, DO NOT EXIT YOURSELF, and SHINE EVERYONE IN THE DARKNESS!
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Practical work No. 1
Theme: Study starry sky using a movable star chart
Target: get acquainted with the moving map of the starry sky,
learn to determine the conditions for the visibility of constellations
learn to determine the coordinates of the stars on the map
Working process:
Theory.
The appearance of the starry sky changes due to the daily rotation of the Earth. The change in the appearance of the starry sky depending on the season occurs due to the revolution of the Earth around the Sun. The work is devoted to acquaintance with the starry sky, solving problems on the conditions of visibility of constellations and determining their coordinates.
A moving map of the starry sky is shown in the figure.
Before starting work print a movable star chart, cut the oval of the overlay circle along the line corresponding to the geographical latitude of the observation site. The cutout line of the overlaid circle will depict the horizon line. Stick the star map and the patch circle on cardboard. From south to north of the overlay circle, stretch a thread that will show the direction of the celestial meridian.
On the map:
- stars are shown as black dots, the sizes of which characterize the brightness of the stars;
- nebulae are indicated by dashed lines;
- the north pole of the world is depicted in the center of the map;
- lines emanating from the north celestial pole show the location of the circles of declination. On the star chart for the two closest circles of declination, the angular distance is 1 hour;
- celestial parallels are plotted at 30°. With their help, you can count the declination of the luminaries δ;
- the points of intersection of the ecliptic with the equator, for which the right ascension is 0 and 12 hours, are called the points of the vernal g and W equinoxes;
- months and numbers are marked along the edge of the star map, and hours are on the overlay circle;
- the zenith is located near the center of the notch (at the point of intersection of the thread representing the celestial meridian with the celestial parallel, the declination of which is equal to the geographical latitude of the place of observation).
To determine the location of the celestial body, a month is necessary, the number indicated on the star map must be combined with the hour of observation on the overlay circle.
Celestial equator - a great circle of the celestial sphere, the plane of which is perpendicular to the axis of the world and coincides with the plane of the earth's equator. The celestial equator divides the celestial sphere into two hemispheres: the northern hemisphere, with its apex at the north celestial pole, and the southern hemisphere, with its apex at the south celestial pole. The constellations through which the celestial equator passes are called equatorial. Distinguish between southern and northern constellations.
Constellations of the Northern Hemisphere: Ursa Major and Ursa Minor, Cassiopeia, Cepheus, Draco, Cygnus, Lyra, Bootes, etc.
The southern ones include the Southern Cross, Centaurus, Fly, Altar, Southern Triangle.
Celestial pole - point on the celestial sphere around which the apparent daily movement of stars occurs due to the rotation of the Earth around its axis. The direction to the North Pole of the World coincides with the direction to the geographic north, and to the South Pole of the World coincides with the direction to the geographic south. The north pole of the world is located in the constellation Ursa Minor with the polarissima (a visible bright star located on the axis of rotation of the Earth) - the North Star, the south - in the constellation Octant.
Nebula - part of the interstellar medium that stands out by its radiation or absorption of radiation against the general background of the sky. Previously, any extended object motionless in the sky was called nebulae. In the 1920s, it became clear that there were many galaxies among the nebulae (for example, the Andromeda Nebula). After that, the term "nebula" began to be understood more narrowly, in the sense indicated above. Nebulae are made up of dust, gas, and plasma.
Ecliptic - a large circle of the celestial sphere, along which the apparent annual movement of the Sun occurs. The plane of the ecliptic is the plane of the Earth's revolution around the Sun (the Earth's orbit).
Depending on the place of the observer on Earth, the appearance of the starry sky and the nature of the daily movement of stars change. The daily paths of the luminaries on the celestial sphere are circles whose planes are parallel to the celestial equator.
Consider how the appearance of the starry sky changes at the poles of the Earth. The pole is a place on the globe where the axis of the world coincides with a plumb line, and the celestial equator coincides with the horizon.
For an observer located at the North Pole of the Earth, the North Star will be located at the zenith, the stars will move in circles parallel to the mathematical horizon, which coincides with the celestial equator. In this case, all stars with a positive declination will be visible above the horizon (at the South Pole, on the contrary, all stars with a negative declination will be visible), and their height will not change during the day.
Let's move to the middle latitudes that are familiar to us. Here already the axis of the world and the celestial equator are inclined to the horizon. Therefore, the daily paths of the stars will also be inclined towards the horizon. Therefore, at middle latitudes, the observer will be able to observe rising and setting stars.
Under sunrise the phenomenon of the luminary crossing the eastern part of the true horizon is understood, andunder sunset- the western part of this horizon.
In addition, some of the stars located in the northern circumpolar constellations will never fall below the horizon. Such stars are called non-entering.
And the stars located near the South Pole of the World for an observer at mid-latitudes will be non-ascending.
The daily paths of all, without exception, the stars are perpendicular to the horizon. Therefore, being at the equator, the observer will be able to see all the stars that rise and set during the day.
In general, in order for the luminary to rise and set, its absolute declination must be less than 
.
If 
, then in the Northern Hemisphere it will be non-descending (for the Southern Hemisphere - non-ascending).
Then it is obvious that those luminaries whose declination 
, are non-ascending for the Northern Hemisphere (or non-setting for the Southern).
Equatorial coordinate system - is a system of celestial coordinates, the main plane in which is the plane of the celestial equator.
1. Declination (δ) - the angular distance of the luminary M from the celestial equator, measured along the circle of declination. Usually expressed in degrees, minutes, and seconds of arc. The declination is positive north of the celestial equator and negative south of it. An object on the celestial equator has a declination of 0°. The declination of the north pole of the celestial sphere is +90° The declination of the south pole is -90°.
2. Right ascension of the luminary (α) - angular distance, measured along the celestial equator, from the vernal equinox to the point of intersection of the celestial equator with the circle of declination of the luminary.
The sequence of practical work:
Tasks of practical work:
Task 1. Determine the equatorial coordinates of Altair (α Eagle), Sirius (α Big Dog) and Vega (α Lyrae).
Task 2. Using a star map, find a star by its coordinates: δ = +35о; α = 1h 6m.
Task 3. Determine what the star δ Sagittarius is for an observer located at a latitude of 55o 15ʹ. To determine whether a star is ascending or non-rising in two ways: using the overhead circle of a moving star chart and using star visibility condition formulas.
Practical way. We place the movable circle on the star map and, when it rotates, we determine whether the star is ascending or setting.
theoretical way.
We use the star visibility conditions formulas:
If , then the star is ascending and setting.
If , then the star in the Northern Hemisphere is not setting
If , then the star in the Northern Hemisphere is non-ascending.
Task 4. Set a mobile map of the starry sky for the day and hour of observation and name the constellations located in the southern part of the sky from the horizon to the pole of the world; in the east - from the horizon to the pole of the world.
Task 5. Find the constellations located between the points of the west and north, October 10 at 21 o'clock. Check the correctness of the determination of the starry sky by visual observation.
Task 6. Find the constellations on the star map with the nebulae indicated in them and check whether they can be observed with the naked eye on the day and hour of the laboratory work.
Task 7. Determine whether the constellations of Virgo, Cancer will be visible. Libra at midnight September 15th? Which constellation will be near the horizon in the north at the same time?
Task 8. Determine which of the following constellations: Ursa Minor, Bootes, Charioteer, Orion - will not set for your latitude?
Task 9. Find any five constellations listed on the starry sky map: Big Dipper, Ursa Minor, Cassiopeia, Andromeda, Pegasus, Cygnus, Lyra, Hercules, Northern Crown - and determine the approximate celestial coordinates (declination, and right ascension) of the a-stars of these constellations.
Task 10. Determine which constellations will be near the horizon in the North, South, West and East on May 5 at midnight.
Control questions for consolidation theoretical material for practice:
1. What is the starry sky? ( The starry sky is a set of celestial bodies visible from the Earth at night, in the firmament. On a clear night, a person with good eyesight will see no more than 2-3 thousand twinkling points in the sky. Thousands of years ago, ancient astronomers divided the starry sky into twelve sectors and came up with names and symbols for them, by which they are known to this day..)
2. What are constellations? ( Constellations are sections into which the celestial sphere is divided for the convenience of orienting in the starry sky. In ancient times, constellations were called characteristic figures formed by bright stars..)
3. How many constellations are there today? ( Today there are 88 constellations. Constellations are different in terms of the area they occupy on the celestial sphere and the number of stars in them..)
4. List the main constellations or those that you know. ( Exist big constellations and small ones. The first include Ursa Major, Hercules, Pegasus, Aquarius, Bootes, Andromeda. The second - the Southern Cross, Chameleon, Flying Fish, Small Dog, Bird of Paradise. Of course, we have named only a small fraction, the most famous.)
5. What is a sky map? ( This is an image of the starry sky or part of it on a plane. Astronomers divided the sky map into 2 parts: southern and northern (by analogy with the hemispheres of the Earth.)
6. What is the celestial equator? ( Great circle of the celestial sphere, the plane of which is perpendicular to the axis of the world and coincides with the plane of the earth's equator.)
At the end of the practical work, the student must submit a report.
The report should include answers to all specified points of the work order and answers to control questions.
Bibliography
1. Vorontsov-Velyaminov B. A., Strout E. K. “Astronomy. Grade 11". Textbook with an electronic application - M .: Bustard, 2017
2. R. A. Dondukova "Studying the starry sky using a moving map" Guide to laboratory work M .: "Higher School" 2000
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Topic: Change in the appearance of the starry sky during the day
Target: To acquaint students with the celestial environment and its rotation, orientation in the sky. Consider the horizontal coordinate system, the change in coordinates and the concept of the culmination of the luminaries, the translation of a degree measure into an hour and vice versa.
Tasks:
1. Tutorial: introduce concepts: the daily movement of the luminaries; celestial sphere and horizontal coordinate system; precessions; setting, non-ascending, non-setting luminaries; culmination, to continue the formation of the ability to work with the PKZN and astronomical ways of orienting the terrain by the stars. About astronomical research methods, astronomical observations and measurements and goniometric astronomical instruments (altimeter, theodolite, etc.). About a cosmic phenomenon - the rotation of the Earth around its axis and its consequences - celestial phenomena: sunrise, sunset, daily movement and culminations of luminaries (stars).
2. Nurturing: to promote the formation of the skill of identifying cause-and-effect relationships, about practical ways to apply astrometric knowledge.
3. Educational: using problem situations, bring students to an independent conclusion that the view of the starry sky does not remain the same throughout the day, the formation of computational skills in translating degrees into hours and vice versa. Formation of skills: use a moving map of the starry sky, star atlases, the Astronomical calendar to determine the position and conditions for the visibility of celestial bodies and the flow of celestial phenomena; find the North Star in the sky and navigate by it on the ground.
Know:1stlevel(standard)- the concept of the celestial sphere and the direction of rotation of the sky, the characteristic points and lines of the celestial sphere, the celestial meridian, the vertical, the horizontal coordinate system, the zenith distance, the concept of the culmination of the luminary and precession, the conversion of a degree measure into an hour and vice versa. Use goniometric astronomical instruments: theodolite, altimeter. Find in the sky the main constellations and the brightest stars visible at this time of the year at a given time in a given area.
2ndlevel- the concept of the celestial sphere and the direction of rotation of the sky, the characteristic points and lines of the celestial sphere, the celestial meridian, the vertical, the horizontal coordinate system, the zenith distance, the concept of the culmination of the luminary and their division, precession, conversion of degrees to hours and vice versa. Use goniometric astronomical instruments: theodolite, altimeter. Find in the sky the main constellations and the brightest stars visible at this time of the year at a given time in a given area.
Be able to:1stlevel(standard)- build a celestial sphere with a mark of characteristic points and lines, show horizontal coordinates on the sphere, daily parallels of stars, show culmination points, produce the simplest translation hour measure to degree and vice versa, show constellations and bright stars on the PKZN, apply knowledge of basic concepts to solve quality objectives. Find the North Star in the sky and navigate the terrain using the North Star.
2ndlevel- build a celestial sphere with a mark of characteristic points and lines, show horizontal coordinates on the sphere, daily parallels of stars according to their division, show culmination points and zenith distance, convert hourly measure to degrees and vice versa, find constellations and bright stars, culmination of stars using PKZN in a certain period of time, apply knowledge of basic concepts to solve qualitative problems. Find the North Star in the sky and navigate the terrain using the North Star and using a star map; find in the sky the main constellations and the brightest stars visible at this time of the year at a given time in a given area; use a mobile map of the starry sky, star atlases, reference books, the Astronomical calendar to determine the position and conditions for the visibility of celestial bodies and the course of celestial phenomena.
Equipment : PKZN, model of the celestial sphere. Astronomical calendar. Photo of the circumpolar region of the sky. Table for converting degrees to hours. CD- "Red Shift 5.1" (video clip = Excursions - Star Islands - Orientation in the sky).
movelesson:
I Repetition material (8-10min).
1) Analysis of s / r from the last lesson (consider the task that caused difficulty).
2) Dictation.
1. How many constellations are there in the sky? .
3. Write down the name of any constellation.
4. What letter represents the brightest star? [b-alpha].
5. Which constellation includes the North Star? [M. Medveditsa].
6. What types of telescopes do you know? [reflector, refractor, mirror-lens].
7. Purpose of the telescope. [increases the angle of view, gathers large lights].
8. Name the types of celestial bodies known to you. [planets, satellites, comets, etc.].
9. Name any star you know.
10. Special scientific - research institution for observations. [observatory].
11. What characterizes a star in the sky, depending on the apparent brightness. [magnitudes].
12. A light streak crossing the sky and visible on a bright starry night. [Milky Way].
13. How to determine the direction to the north? [along the Polar Star].
14. Decipher the entry Regulus (b Leo). [constellation Leo, star b, Regulus].
15. Which star is brighter in the sky b or c? [b].
Estimated: “5” ? 14, “4” ? 11, “3” ?8
II.New material(15 min).
BUT) Orientationon thesky CD- "Red Shift 5.1" (video clip = Excursions - Star Islands - Orientation in the sky), although this section could have been included in the 2nd lesson.
"Who knows how to find the North Star in the sky?". To find the North Star, you need to through the stars Ursa Major(the first 2 stars of the "bucket") mentally draw a straight line and count 5 distances between these stars along it. In this place, next to the straight line, we will see a star, almost the same in brightness as the "bucket" stars - this is the Polar Star (figure on the left).
Review of the starry sky on September 15, 21:00. Summer (summer-autumn) triangle = star Vega (a Lyra, 25.3 light years), star Deneb (a Cygnus, 3230 light years), star Altair (a Eagle, 16.8 light years).
B) 1) Star - light trail, per day
2) Center - close to the North Star
Daily rotation of the sky - the position of the stars relative to each other does not change
Observable daily allowance rotation heavenly spheres (from east on the west) - apparent phenomenon, reflective valid rotation earthly ball around his axes (from west on the East).
// hint - daily rotation according to the movement of the Sun//
In reality, the stars move in space and the distance to them is different. After all, if, for example, to estimate by eye the distance to the trees outside the window. Which one is closer to us? How much? And now we will mentally delete these two trees. Up to 500 m, a person confidently determines differences in distances to objects, and up to a maximum of 2 km. And at large distances, a person unconsciously uses other criteria - he compares the visible angular dimensions, relies on the perspective of the visible picture. Therefore, if the trees are in an open area where there is nothing else, then, starting from a certain distance, we will no longer distinguish which tree is closer (further) and, moreover, we will not be able to estimate the distance between them. We will seem to a certain moment that trees equallyremovedfromUS. And in the sky, when the distance from the Earth to the Moon is 384,400 km, to the Sun - about 150 million km, and to the closest star, b Centauri, - 275,400 times more than to the Sun. Therefore, in the sky, it seems to us that all the luminaries are at the same distance. human eyes in the best case may making a difference distances only in within 2km.
The locus of points equidistant from a point that is the center is called a sphere. It seems to us that all the celestial bodies are located on the inner surface of a huge sphere. This impression is reinforced by the fact that the proper motion of the stars is imperceptible due to their remoteness, and the daily motion of the stars occurs synchronously. Therefore, there is an apparent integrity of the visible daily rotation of the celestial sphere.
What is the center of the celestial sphere? ( Eye observer)
What is the radius of the celestial sphere? ( Arbitrary)
What is the difference between the celestial spheres of two neighbors on the desk? ( Regulation center).
Can it be argued that these spheres are the same? Compare the distance to the neighbor with the radius of the celestial sphere.
For solving many practical problems, distances to celestial bodies do not play a role, only their apparent location in the sky is important. Angular measurements are independent of the radius of the sphere. Therefore, although the celestial sphere does not exist in nature, astronomers use the concept of heavenlysphere- an imaginary sphere of arbitrary radius (arbitrarily large), in the center of which is the observer's eye. Stars, the Sun, the Moon, planets, etc. are projected onto such a sphere, abstracting from the actual distances to the luminaries and considering only the angular distances between them.
The first mention of the "crystal spheres" by Plato (427-348, Ancient Greece). The first production of the celestial sphere was met by Archimedes (287-212, Ancient Greece), described in the work “On the production of the celestial sphere”.
The most ancient celestial globe "Globe Farnese" 3rd c. BC e. from marble is kept in Naples.
So:
What is the center of the celestial sphere? (eye of the observer).
What is the radius of the celestial sphere? (Arbitrary, but large enough).
What is the difference between the celestial spheres of two neighbors on the desk? (Center position).
IN)heavenlysphereAndhorizontalsystemcoordinates
RR 1 - Axis peace = axis of apparent rotation of the celestial sphere (parallel to the axis of rotation of the Earth)
R And R 1 - poles peace(North and South).
ZZ 1 sheer (vertical) line.
Z - zenith, Z 1 - nadir= points of intersection of the plumb line with the celestial sphere.
Figure 1 - Celestial sphere and horizontal coordinate system
True horizon - a plane perpendicular to the plumb line ZZ1 and passing through the center O (observer's eye).
Heavenly meridian - a great circle of the celestial sphere passing through the zenith Z, the celestial pole P, the south celestial pole R", nadir Z.
NS - noon line. N - north point, S south point.
vertical (circle of height) - a semicircle of the celestial sphere ZOM.
Heavenly equator - a circle line obtained from the intersection of the celestial sphere with a plane passing through the center of the celestial sphere perpendicular to the axis of the world.
So:
What is the rotation period of the celestial sphere? (Equal to the period of rotation of the Earth - 1 day).
In what direction does the apparent (apparent) rotation of the celestial sphere take place? (Opposite to the direction of the Earth's rotation).
What can be said about the relative position of the axis of rotation of the celestial sphere and the earth's axis? (The axis of the celestial sphere and the earth's axis will coincide).
Are all points of the celestial sphere involved in the apparent rotation of the celestial sphere? (Points lying on the axis are at rest).
To better imagine the rotation of the celestial sphere, see the following trick. Take an inflated balloon and pierce it through with a knitting needle. Now you can rotate the ball around the spoke - the axis.
Where is the observer on this model?
Where is the south and north poles of the world located on the globe?
Where on the ball should the North Star be drawn?
Specify the locus of points that do not change their location during rotation.
In what direction does the apparent rotation of the celestial sphere occur when viewed from the north pole (from the south pole)?
The earth moves in an orbit around the sun. The axis of rotation of the Earth is inclined to the plane of the orbit at an angle of 66.5 0 (shown using cardboard pierced with a needle). Due to the action of gravitational forces from the side of the Moon and the Sun, the axis of rotation of the Earth is shifted, while the inclination of the axis to the plane of the Earth's orbit remains constant. The axis of the Earth, as it were, slides along the surface of the cone. (the same happens with the y-axis of an ordinary top at the end of rotation). This phenomenon was discovered as early as 125 BC. e. Greek astronomer Hipparchus and named precession. One rotation of the earth's axis takes 25,735 years - this period is called platonicyear. Now near P - the north pole of the world is the Polar Star - b M. Medveditsa. Further, the title of Polar was alternately assigned to p, s and f of Hercules, the stars of Tuban and Kokhab. The Romans did not have the North Star at all, and Kokhab and Kinosuru (Ursa Minor) were called Guardians.
At the beginning of our chronology - the pole of the world was near b Dragon - 2000 years ago, and b Ursa Minor became the polar star in 1100. In 2100, the celestial pole will be only 28" from the North Star - now it is 44". In 3200, the constellation Cepheus will become polar. In 14000, Vega (b Lyra) will be polar.
Horizontal system coordinates
h-height- the angular distance of the luminary from the horizon (? MOA, measured in degrees, minutes, seconds; from 0 o to 90 o) BUT- azimuth- the angular distance of the vertical of the luminary from the south point (? SOА) in the direction of the daily movement of the luminary, i.e. clockwise; It is measured in degrees minutes and seconds from 0° to 360°).
Horizontal coordinates luminaries in flow days is changing.
BUT" Equivalent Altitude>Zenith Distance Z=90o - h[form 1]
climax - the phenomenon of crossing the heavenly meridian by the luminary.
Luminary M during the day describes a daily parallel - a small circle of the celestial sphere, the plane of which is the axis of the world and passes through the eye of the observer.
M 3 - sunrise point M 4 - point of entry, M 1 - upper climax (h max; A= 0 o), M 2 - lower climax (h min; A =180 o)
According to the daily movement of the luminaries are divided into:
1 - non-ascending 2 - (ascending - incoming ) ascending and descending 3 - non-approaching . What is the Sun, Moon? (2)
IIIAnchoring material (15 min).
BUT) Questions
1. What is the celestial sphere?
2. What lines and points of the celestial sphere do you know?
3. What observations prove the daily rotation of the celestial sphere (does this serve as proof of the rotation of the Earth around its axis).
4. Is it possible, using a horizontal coordinate system, to create maps of the starry sky?
5. What is a climax?
6. Based on the culmination, give the concept of non-setting, not ascending, - ascending-setting luminaries.
B) practical work on PCZN.
1. Name a few constellations that do not set in our area
2. Find the celestial meridian line.
3. What bright stars will culminate today between 20:00 and 21:00?
4. Find on the PKZN, for example, the star Vega, Sirius. What constellations are they in?
IN) 1. Convert 3 hours, 6 hours to a degree measure (3. 15 \u003d 45 0, 90 0)
2. Convert 45 o, 90 o to hourly measure (3 h, 6 h)
3. What is greater than 3 h 25 m 15 s or 51 o 18 "15"? (When translating, you get 51 about 18 "45", that is, the hourly value is greater)
G) Test. For the phrase from the left column, choose the continuation from the right that is appropriate in meaning
Table 1 - Test
|
1. The celestial sphere is called ... 2. The axis of the world is called ... 3. The poles of the world are called ... 4. The North Pole of the World is currently... 5. The plane of the celestial equator is called ... 6. Equator is... 7. The period of rotation of the celestial sphere is ... |
A. ... the point of intersection of the axis of rotation of the Sun with the celestial sphere. V. ... a plane perpendicular to the axis of the world and passing through the center of the celestial sphere. D. ... the period of rotation of the Earth around its axis, i.e. 1 day. D. ... an imaginary sphere of arbitrary radius, described around the center of the Sun, on the inner surface of which luminaries are applied E. ... the axis around which the Earth rotates, moving in world space G. ... near the star Vega in the constellation Lyra Z. ... the line of intersection of the celestial sphere and the plane of the celestial equator I. ... intersection points of the celestial sphere with the axis of the world. K. ... an imaginary sphere of arbitrary radius, described around an observer on Earth, on the inner surface of which luminaries are applied. L. ... the imaginary axis of the visible rotation of the celestial sphere. M. ... the period of rotation of the Earth around the Sun. |
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8. The angle between the axis of the world and the earth's axis is ... 9. The angle between the plane of the celestial equator and the axis of the world is ... 10. The angle between the plane of the celestial equator and the plane of the earth's equator 11. The angle of inclination of the earth's axis to the plane of the earth's orbit is ... 12. The angle between the plane of the earth's equator and the plane of the earth's orbit is ... |
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14. How many celestial spheres can you imagine if each person has two eyes, and there are over 6 billion people on Earth? 15. What is called the precession of the earth's axis and what is the reason for the precession? |
Table 2 - Answers
IVOutcome lesson
1) Questions:
What coordinates are included in the horizontal coordinate system?
What is height and how is it measured?
What is azimuth and how is it measured?
How to determine the zenith distance of a star?
2) Ratings
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Lesson 4/4
Topic: Change in the appearance of the starry sky during the year.
Target: He will get acquainted with the equatorial coordinate system, the visible annual movements of the Sun and the types of the starry sky (changes during the year), learn how to work according to the PKZN.
Tasks
:
1. educational: to introduce the concepts of the annual (apparent) movement of the luminaries: the Sun, the Moon, stars, planets and types of the starry sky; ecliptic; zodiac constellations; points of equinox and solstice. The reason for the "delay" of climaxes. Continue the formation of the ability to work with PKZN - finding the ecliptic, zodiac constellations, stars on the map by their coordinates.
2. nurturing: to promote the formation of the skill of identifying cause-and-effect relationships; only a thorough analysis of the observed phenomena makes it possible to penetrate into the essence of seemingly obvious phenomena.
3. Educational: using problem situations, bring students to an independent conclusion that the view of the starry sky does not remain the same throughout the year; updating students' knowledge of working with geographical maps, to form the skills and abilities of working with the PKZN (finding coordinates).
Know:
1st level (standard)- geographical and equatorial coordinates, points in the annual motion of the Sun, the inclination of the ecliptic.
2nd level- geographic and equatorial coordinates, points in the annual motion of the Sun, the inclination of the ecliptic, directions and causes of the displacement of the Sun above the horizon, zodiacal constellations.
Be able to:
1st level (standard)- set according to the PKZN for various dates of the year, determine the equatorial coordinates of the Sun and stars, find the zodiac constellations.
2nd level- set according to the PKZN for various dates of the year, determine the equatorial coordinates of the Sun and stars, find the zodiac constellations, use the PKZN.
Equipment: PCZN, celestial sphere. Geographic and star map. Model of horizontal and equatorial coordinates, photos of starry sky views at different times of the year. CD- "Red Shift 5.1" (the path of the Sun, Change of seasons). Video film "Astronomy" (part 1, fr. 1 "Star landmarks").
Interdisciplinary communication: Daily and annual movement of the Earth. The moon is a satellite of the Earth (natural science, 3-5 cells). Natural and climatic patterns (geography, 6 cells). Circular motion: period and frequency (physics, grade 9)
During the classes:
I. Student survey (8 min). You can test on the Heavenly sphere N.N. Gomulina, or:
1. At the blackboard
:
1. Celestial sphere and horizontal coordinate system.
2. The movement of the luminary during the day and the climax.
3. Translation of hourly measure into degrees and vice versa.
2. 3 people on cards
:
K-1
1. In which side of the sky is the luminary with horizontal coordinates: h=28°, A=180°. What is its zenith distance? (north, z=90°-28°=62°)
2. Name three constellations visible today during the day.
K-2
1. In which side of the sky is the star, if its coordinates are horizontal: h=34 0 , A=90 0 . What is its zenith distance? (west, z=90°-34°=56°)
2. Name three bright stars that we see during the day.
K-3
1. In which side of the sky is the star, if its coordinates are horizontal: h=53 0, A=270 o. What is its zenith distance? (east, z=90°-53°=37°)
2. Today the star is in its upper climax at 21:34. When is its next lower, upper climax? (after 12 and 24 hours, more precisely after 11 h 58 m and 23 h 56 m)
3. Others(on their own in pairs while they answer at the blackboard)
but) Convert to degrees 21 h 34 m, 15 h 21 m 15 s. resp = (21. 15 0 +34. 15 "=315 0 +510" =323 0 30", 15 h 21 m 15 s =15. 15 0 +21. 15 "+15. 15" =225 0 + 315 "+ 225"= 230 0 18"45")
b) Convert to hourly measure 05 o 15 "13 o 12" 24 "resp = (05 o 15" = 5 . 4 m +15 . 4 c \u003d 21 m , 13 o 12 "24" = 13 . 4 m +12 .4 s +24.1/15 s =52 m +48 s +1.6 s =52 m 49 s.6)
II. new material(20 minutes) Video film "Astronomy" (part 1, fr. 1 "Star landmarks").
b) The position of the luminary in the sky (celestial medium) is also uniquely determined - in equatorial coordinate system, where the celestial equator is taken as a reference point
. (equatorial coordinates were first introduced by Jan Havelia (1611-1687, Poland), in a catalog of 1564 stars compiled in 1661-1687) - an atlas of 1690 with engravings and is now used (textbook title).
Since the coordinates of the stars do not change for centuries, therefore, this system is used to create maps, atlases, catalogs [lists of stars]. The celestial equator is a plane passing through the center of the celestial sphere perpendicular to the axis of the world.
 |
points E-east, W-west - the point of intersection of the celestial equator with the points of the horizon. (Points N and S come to mind). |
| Declension circle - a large circle of the celestial sphere passing through the poles of the world and the observed luminary (points P, M, P "). | |
|
Equatorial coordinates: |
c) The annual movement of the Sun. There are luminaries [Moon, Sun, Planets] whose equatorial coordinates change rapidly. The ecliptic is the apparent annual path of the center of the solar disk across the celestial sphere.
Tilt to the plane of the celestial equator is currently at an angle 23 about 26", more precisely at an angle: ε = 23°26'21", 448 - 46", 815 t - 0", 0059 t² + 0", 00181 t³, where t is the number of Julian centuries that have elapsed since the beginning of 2000. This formula is valid for the next centuries. In longer periods of time, the inclination of the ecliptic to the equator fluctuates about the average value with a period of approximately 40,000 years. In addition, the inclination of the ecliptic to the equator is subject to short-period fluctuations with a period of 18.6 years and an amplitude of 18.42, as well as smaller ones (see Nutation).
The apparent motion of the Sun along the ecliptic is a reflection of the actual motion of the Earth around the Sun (proved only in 1728 by J. Bradley by the discovery of annual aberration).
|
space phenomena |
Celestial phenomena arising from these cosmic phenomena |
| Rotation of the Earth around its axis | Physical phenomena: 1) deviation of falling bodies to the east; 2) the existence of Coriolis forces. Displays of the true rotation of the Earth around its axis: 1) daily rotation of the celestial sphere around the axis of the world from east to west; 2) sunrise and sunset of the luminaries; 3) the culmination of the luminaries; 4) change of day and night; 5) daily aberration of the luminaries; 6) daily parallax of the luminaries |
| Rotation of the Earth around the Sun | Displays of the true rotation of the Earth around the Sun: 1) annual change in the appearance of the starry sky (apparent movement of heavenly bodies from west to east); 2) the annual movement of the Sun along the ecliptic from west to east; 3) change in the midday height of the Sun above the horizon during the year; a) change in the length of daylight hours during the year; b) polar day and polar night at high latitudes of the planet; 5) change of seasons; 6) annual aberration of the luminaries; 7) annual parallax of the stars |
.jpg) |
The constellations through which the ecliptic passes are called.
The number of zodiac constellations (12) is equal to the number of months in a year, and each month is indicated by the sign of the constellation in which the Sun is in that month. 13th constellation Ophiuchus excluded, even though the sun passes through it. "Red Shift 5.1" (the path of the Sun). |
|
|
|
| - vernal equinox. March 21
(day equals night). Sun coordinates: α ¤ =0 h, δ ¤ =0 o The designation has been preserved since the time of Hipparchus, when this point was in the constellation ARIES → now it is in the constellation FISH, In 2602 it will move into the constellation AQUARIUS. |
|
| -summer solstice. 22nd of June
(the longest day and the shortest night). Sun coordinates: α ¤ =6 h, ¤ \u003d + 23 about 26 " The designation has been preserved since the time of Hipparchus, when this point was in the constellation of Gemini, then it was in the constellation of Cancer, and since 1988 it moved into the constellation of Taurus. |
|
 |
- autumnal equinox. 23 September
(day equals night). Sun coordinates: α ¤ =12 h, δ tsize="2" ¤ =0 o The designation of the constellation Libra was preserved as the designation of the symbol of justice under the emperor Augustus (63 BC - 14 AD), now in the constellation Virgo, and in 2442 it will move to the constellation Leo. |
| - winter solstice. December 22
(the shortest day and the longest night). Sun coordinates: α ¤ =18 h, δ ¤ =-23 about 26" During the period of Hipparchus, the point was in the constellation of Capricorn, now in the constellation of Sagittarius, and in 2272 it will move into the constellation of Ophiuchus. |
Although the position of the stars in the sky is uniquely determined by a pair of equatorial coordinates, the view of the starry sky at the place of observation at the same hour does not remain unchanged.
Observing the culmination of the luminaries at midnight (the Sun at this time is in the lower culmination with right ascension on a star different from the culmination), you can notice that on different dates at midnight, different constellations pass near the celestial meridian, replacing each other. [These observations at one time led to the conclusion about the change in the right ascension of the Sun.]
Let's choose any star and fix its position in the sky. At the same place, the star will appear in a day, more precisely, in 23 hours 56 minutes. A day measured relative to distant stars is called stellar
(to be quite precise, a sidereal day is the time interval between two successive upper climaxes of the vernal equinox point). Where do the other 4 minutes go? The fact is that due to the movement of the Earth around the Sun, it shifts for an earthly observer against the background of stars by 1 ° per day. To "catch up" with him, the Earth needs these 4 minutes. (picture on the left)
Each subsequent night, the stars shift slightly to the west, rising 4 minutes earlier. In a year it will shift by 24 hours, that is, the view of the starry sky will be repeated. The entire celestial sphere will make one revolution in a year - the result of a reflection of the revolution of the Earth around the Sun.
So, the Earth makes one rotation around its axis in 23 hours 56 minutes. 24 hours - the average solar day - the time of revolution of the Earth relative to the center of the Sun.
III. Fixing the material (10 min)
1. Work on the PKZN (in the course of presenting new material)
a) finding the celestial equator, ecliptic, equatorial coordinates, equinox and solstice points.
b) determining the coordinates of, for example, stars: Chapel (α Aurigae), Deneb (α Cygnus) (Capella - α=5 h 17 m, δ=46 o; Deneb - α=20 h 41 m, δ=45 o 17")
c) finding stars by coordinates: (α=14.2 h, δ=20 o) - Arcturus
d) find where the Sun is today, in which constellations in the fall. (now the fourth week of September is in Virgo, the beginning of September is in Leo, Libra and Scorpio will pass in November)
2. Optional:
a) The star culminates at 14:15. When is its next lower, upper climax? (after 11:58 and 23:56, that is, at 2:13 and 14:11).
b) AES flew across the sky from the starting point with coordinates (α=18 h 15 m, δ=36 o) to the point with coordinates (α=22 h 45 m, δ=36 o). Through which constellations did the satellite fly.
IV. Lesson summary
1. Questions:
a) What is the need to introduce equatorial coordinates?
b) What are the remarkable days of the equinox, solstice?
c) At what angle is the plane of the Earth's equator inclined to the plane of the ecliptic?
d) Is it possible to consider the annual movement of the Sun along the ecliptic as evidence of the revolution of the Earth around the Sun?
Homework:§ 4, questions assignment for self-control (p. 22), p. 30 (pp. 10-12).
(it is advisable to distribute this list of works with explanations to all students for a year).
Can be given an assignment 88 constellations
"(one constellation for each student). Answer the questions:
- What is the name of this constellation?
- At what time of the year is it best to observe it at our (given) latitude?
- What type of constellation does it belong to: non-ascending, non-setting, setting?
- Is it a northern, southern, equatorial, zodiac constellation?
- Name interesting objects of this constellation and indicate them on the map.
- What is the name of the brightest star in the constellation? What are its main characteristics?
- Using a mobile map of the starry sky, determine the equatorial coordinates of the brightest stars in the constellation.
Lesson designed members of the circle "Internet technologies" - Prytkov Denis(10 cells) and Pozdnyak Victor(10 cells), Changed 23.09.2007
of the year
2. Ratings
| "Planetarium" 410.05 mb | The resource allows you to install on the computer of a teacher or student full version innovative educational and methodical complex "Planetarium". "Planetarium" - a selection of thematic articles - are intended for use by teachers and students in the lessons of physics, astronomy or natural science in grades 10-11. When installing the complex, it is recommended to use only English letters in folder names. | ||
| Demo materials 13.08 mb | The resource is a demonstration materials of the innovative educational and methodological complex "Planetarium". | Equatorial coordinate system 460.7 kb
The period of rotation of the Earth around its axis, measured relative to the stars and therefore called the sidereal (or sidereal) day, is about 4 minutes shorter than the mean solar day - the period of rotation of the Earth around its axis, measured relative to the Sun. This difference is due to the movement of the Earth around the Sun. Since the time by which we live, i.e. usual civil time, is associated with the average solar day, the moments of rising and setting of stars, measured at this time, are shifted every day by 4 minutes ahead compared to the previous day: the stars, as it were, slowly move across the night sky in westbound. At times they come so close to the Sun that they become invisible - there comes a forced seasonal break in the observation of these objects.
Rice. 14. Scheme of a simple goniometric tool for measuring the height and azimuth of the star. Height is measured using a plumb line, azimuth is determined by the scale of the horizontal circle, which rotates with the vertical rack.
It is known that the stars really make their own movements in space, changing their position relative to each other. However, the stars are located so far from us that any changes in their position become visible to the naked eye after centuries. Thanks to this circumstance, we can talk about the movement of the Sun, Moon, planets and other celestial bodies relative to "fixed" stars. The great circle of the celestial sphere, along which the Sun makes its way among the stars during the year, is called the ecliptic. The plane of the ecliptic is inclined at an angle of 23.5° to the terrestrial and celestial equators; this is explained by the fact that the inclination of the Earth's axis of rotation to the ecliptic is 66.5°. It is for this reason that the height of the Sun above the horizon changes throughout the year and the seasons change. Paths of the Moon and major planets solar system pass within the region of the celestial sphere with a width of 8 °, lying on both sides of the ecliptic. Ancient observers singled out in a strip about 16 ° wide, stretching along the ecliptic, 12 zodiac constellations, to which astrologers attached special importance. After many centuries, due to precession, the position of the main points of the ecliptic among the surrounding stars has changed. The sun and planets may also appear in the constellation Ophiuchus (Ophiuchus); this constellation, which received its name in ancient times, is not included in the zodiac. Modern astronomers consider astrology and "star signs" nothing more than religious prejudices and superstitions. But the ancient signs of the Zodiac are still used to designate the zodiac constellations, for example, the sign of the constellation Aries (Aries) T denotes one of the two most important points in the celestial sphere at which the ecliptic crosses the celestial equator.
Translation of celestial coordinates into angular measure 
Rice. 15. The poles of the world and the celestial equator are directly connected with the poles and the equator of the Earth. As the Earth rotates around its axis, all celestial bodies during the day cross the celestial meridian associated with the observer. 
Rice. 16. The belt of the zodiac constellations, along which the planets and the Moon make their visible path, is stretched along the ecliptic - the apparent path of the Sun among the stars.
