What lines and points of the celestial sphere are. Lessons
Arbitrary radius, onto which celestial bodies are projected: serves to solve various astrometric problems. As a rule, the eye of the observer is taken as the center of the celestial sphere. For an observer on the surface of the Earth, the rotation of the celestial sphere reproduces the daily movement of the stars in the sky.
The concept of the Heavenly sphere originated in ancient times; it was based on the visual impression of the existence of a domed firmament. This impression is due to the fact that as a result of the enormous remoteness of the celestial bodies, the human eye is not able to assess the differences in the distances to them, and they appear to be equally distant. The ancient peoples associated this with the presence of a real sphere that bounds the whole world and carried numerous stars on its surface. Thus, in their view, the celestial sphere was the most important element of the universe. With the development of scientific knowledge, such a view of the celestial sphere has disappeared. However, the geometry of the celestial sphere, laid down in antiquity, as a result of development and improvement, has received a modern form, in which it is used in astrometry.
The radius of the celestial sphere can be taken as anything: in order to simplify the geometric relationships, it is assumed to be equal to unity. Depending on the problem to be solved, the center of the celestial sphere can be placed in the place:
- where the observer is (topocentric celestial sphere),
- to the center of the Earth (geocentric celestial sphere),
- to the center of a planet (planetocentric celestial sphere),
- to the center of the Sun (heliocentric celestial sphere) or to any other point in space.
Each luminary on the celestial sphere corresponds to a point at which it is crossed by a straight line connecting the center of the celestial sphere with the luminary (with its center). When studying the relative position and apparent movements of the luminaries on the celestial sphere, one or another is chosen), determined by the main points and lines. The latter are usually large circles of the celestial sphere. Each large circle of the sphere has two poles, defined on it by the ends of a diameter perpendicular to the plane of this circle.
The names of the most important points and arcs on the celestial sphere
Plumb line
Lever line(or vertical line) - passing through the center of the celestial sphere and coinciding with the direction of the thread at the place of observation. For an observer on the surface, the plumb line passes through the center of the Earth and the observation point.
Zenith and Nadir
The plumb line intersects with the surface of the celestial sphere at two points - zenith, above the observer's head, and nadire- diametrically opposite point.
Mathematical horizon
Mathematical horizon- a large circle of the celestial sphere, which is perpendicular to the plumb line. The mathematical horizon divides the surface of the celestial sphere into two halves: visible for the observer, with the top at the zenith, and invisible, with the top at nadir. The mathematical horizon, generally speaking, does not coincide with visible horizon due to the unevenness of the Earth's surface and different heights of observation points, as well as the curvature of light rays in the atmosphere.
Axis of the world
P, P "- poles of the world, T, T" - points of equinox, E, C - points of solstice, P, P "- poles of the ecliptic, PP" - axis of the world, PP "- axis of ecliptic, ATQT" - celestial equator, ETCT "- ecliptic
Axis of the world- an imaginary line crossing the celestial sphere at the north and south poles (the celestial sphere rotates around it).
Poles of the world
The axis of the world intersects with the surface of the celestial sphere at two points - north pole of the world and the southern pole of the world... The North Pole is the one from which the rotation of the celestial sphere occurs clockwise, if you look at the sphere outside.
Looking at the celestial sphere from within, (which we usually do when observing the starry sky), then in the vicinity of the north pole of the world its rotation occurs counterclockwise, and in the vicinity of the south pole of the world - clockwise.
Celestial equator
Celestial equator- a large circle of the celestial sphere, the plane of which is perpendicular to the axis of the world. The celestial equator divides the surface of the celestial sphere into two hemispheres: North hemisphere, with a summit at the north pole of the world, and Southern Hemisphere, with a summit at the south pole of the world.
East and West points
The celestial equator intersects with the mathematical horizon at two points: point east and point of west... The east point is the one at which the points of the rotating celestial sphere cross the mathematical horizon, passing from the invisible hemisphere to the visible one.
Heavenly meridian
Heavenly meridian- a large circle of the celestial sphere, the plane of which passes through the plumb line and the axis of the world. The celestial meridian divides the surface of the celestial sphere into two hemispheres - eastern hemisphere, with a top at a point east, and western hemisphere, with apex at the west point.
Midday line
Half-day line- the line of intersection of the plane of the celestial meridian and the plane of the mathematical horizon.
North and South points
The celestial meridian intersects with the mathematical horizon at two points: point of the north and point of the south... The north point is the one closer to the north pole of the world.
[Ecliptic
Ecliptic- the great circle of the celestial sphere, the intersection of the celestial sphere and the plane of the orbit of the Earth-Moon system. The visible annual movement along the celestial sphere is carried out with great accuracy along the ecliptic. The plane of the ecliptic intersects with the plane of the celestial equator at an angle ε = 23 ° 26 ".
α = 192.85948 ° β = 27.12825 °
called northern galactic pole, and the point diametrically opposite to it is southern galactic pole.
The great circle of the celestial sphere, the plane of which is perpendicular to the line connecting the galactic poles, is called galactic equator.
The names of arcs on the celestial sphere associated with the position of the stars
Almucantarat
Almucantarate- Arab. circle of equal heights
Almucantarat luminaries - a small circle of the celestial sphere passing through a luminary, the plane of which is parallel to the plane of the mathematical horizon.
Vertical circle
Circle of heights or vertical circle or vertical luminaries - a large semicircle of the celestial sphere passing through the zenith, luminary and nadir.
Diurnal parallel
Diurnal parallel luminaries - a small circle of the celestial sphere passing through a luminary, the plane of which is parallel to the plane of the celestial equator. Visible diurnal movements of the luminaries follow diurnal parallels.
Declination circle
Declination circle luminaries - a large semicircle of the celestial sphere passing through the poles of the world and the luminary.
Circle of ecliptic latitude
Circle of ecliptic latitude, or simply circle of latitude luminaries - a large semicircle of the celestial sphere passing through the poles of the ecliptic and the luminary.
Circle of galactic latitude
Circle of galactic latitude luminaries - a large semicircle of the celestial sphere passing through the galactic poles and the luminary.
The sky is midnight stars in myriads
Glitters to sleepless gaze,
His wondrous crown shines with the Pleiades,
Aldebaran burns.
Those magnificent stars, radiant beauty
Quickly my gaze passed,
It flew around everything, but, falling on Polar,
Suddenly, as if chained, he became.
I see: the light round dance turns -
You are motionless alone.
The face of the blue sky changes wonderfully -
You are unfailingly faithful.
Isn't it from the heart of a dreamer
Mil your mysterious ray?
Say: aren't you in the right hand of the creator,
Asterisk, eternity is the key?
V. Benediktov
Lesson 3/3
Theme: Changing 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 conversion of the degree standard to the hour and vice versa.
Tasks
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1. Educational: to introduce the concepts: daily movement of luminaries; celestial sphere and horizontal coordinate system; precession; setting, non-rising, non-setting luminaries; culmination, to continue the formation of the ability to work with PKZN and astronomical methods of orientation in the terrain by the stars. On astronomical research methods of astronomical observations and measurements and goniometric astronomical instruments (altimeter, theodolite, etc.). About cosmic phenomena - the rotation of the Earth around its axis and about its consequences - celestial phenomena: sunrise, sunset, daily movement and culminations of luminaries (stars).
2. Upbringing: to promote the formation of the skill of identifying cause-and-effect relationships, on practical ways of applying astrometric knowledge.
3. Developing: using problematic 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 a degree measure into an hour 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 of visibility of celestial bodies and the course of celestial phenomena; find the North Star in the sky and navigate through it in the terrain.
Equipment:
During the classes:
- Repetition of the material (8-10 min)
1) Analysis of s / r from the last lesson (consider the task that caused the difficulty).
2) Dictation.
- How many constellations are there in the sky? ...
- How many stars can be counted with the naked eye in the sky? [about 6000].
- Write down the name of any constellation.
- What letter represents the brightest star? [α-alpha].
- Which constellation is the North Star? [M. Medveditsa].
- What types of telescopes do you know? [reflector, refractor, mirror-lens].
- Purpose of the telescope. [increases the angle of view, collects large lights].
- What are the types of celestial bodies known to you? [planets, satellites, comets, etc.].
- Name any star you know.
- Special research institution for observations. [observatory].
- What is a star in the sky characterized by, depending on the apparent brightness. [stellar magnitudes].
- A streak of light that crosses the sky and is visible on a bright starry night [Milky Way].
- How to determine the direction to the north? [along the Polar Star].
- Decipher the notation Regulus (α Leo). [constellation Leo, star α, Regulus].
- Which star is brighter in the sky α or β? [α].
Evaluated:“5” ≥ 14, “4” ≥ 11, “3” ≥8 PKZN, model of the celestial sphere. Astronomical calendar. Photo of the circumpolar region of the sky. Conversion table of the degree standard to the hour. CD- "Red Shift 5.1" (video fragment = Excursions - Star Islands - Orientation in the sky, Stories - Heavenly sphere).
II. New material (15 min)
| A) Orientation in the sky CD- "Red Shift 5.1" (video fragment = 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 mentally draw a straight line through the stars of the Big Dipper (the first 2 stars of the "bucket") and count 5 distances between these stars along it. In this place, next to the straight line, we will see a star that is almost the same in brightness with the stars of the "bucket" - this is the North Star (Fig on the left). |  |
Overview of the starry sky on September 15, 21 hours. Summer (summer-autumn) triangle = star Vega (a Lyrae, 25.3 light years), star Deneb (a Cygnus, 3230 light years), star Altair (a Eagle, 16.8 light years). | |
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B) Photo of the circumpolar region of the sky. |
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| 1) Star - light trail, circle per day 2) The center is close to the North Star |
diurnal rotation of the firmament - the position of the stars relative to each other does not change | |||||||||||||||||||||||||||||||
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The observed daily rotation of the celestial sphere (from east to west) is an apparent phenomenon that reflects the actual rotation of the globe around its axis (from west to east). // hint - daily rotation according to the movement of the Sun //. |
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| In reality, stars move in space and the distance to them is different. After all, if, for example, evaluate 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 the differences in distances to objects, and a maximum of 2 km. And at large distances, a person unconsciously uses other criteria - compares the apparent 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 cease to distinguish which tree is closer (farther), and even more so we will not be able to estimate the distance between them. From a certain moment it will seem to us that the trees equally distant from us... 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, α Centauri, is 275,400 times greater than to the Sun. Therefore, in the sky, it seems to us that all the stars are at the same distance. At best, human eyes can only distinguish distances within 2 km. The locus of points equidistant from the point that is the center is called a sphere. It seems to us that all the heavenly 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, due to their remoteness, is imperceptible and the diurnal movement of the stars occurs synchronously. Therefore, the apparent integrity of the apparent daily rotation of the celestial sphere arises. = What is the center of the celestial sphere? ( The observer's eye) = What is the radius of the celestial sphere? ( Arbitrary) = What is the difference between the celestial spheres of two neighbors on a desk? ( Center position). = Can it be argued that these areas are the same? Compare the distance to your neighbor with the radius of the celestial sphere. |
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 For the solution of many practical problems, the 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 Celestial sphere- an imaginary sphere of arbitrary radius (arbitrarily large), in the center of which is the observer's eye. The stars, the sun, the moon, planets, etc., are projected onto such a sphere, abstracting from the actual distances to the stars and considering only the angular distance between them.
So:
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| C) Celestial sphere and horizontal coordinate system | ||||||||||||||||||||||||||||||||
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 PP 1 - Axis of the world= axis of apparent rotation of the celestial sphere (parallel to the axis of rotation of the Earth). .gif) R and R 1 - Poles of the world(north and south). ZZ 1 plumb (vertical) line. Z - zenith, Z 1 - nadir= points of intersection of the plumb line with the celestial sphere. True horizon - a plane perpendicular to the plumb line ZZ1 and passing through the center O (the observer's eye). Heavenly meridian - a large circle of the celestial sphere passing through the zenith Z, the pole of the world P, the south pole of the world P ", nadir Z" NS - midday line. N - north point, S - point south. Vertical (height circle) - a semicircle of the celestial sphere ZOM. Celestial 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:
To get a better idea of 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.
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.jpg) The earth moves in an orbit around the sun. The axis of rotation of the Earth is inclined to the orbital plane at an angle  66.5 ° (shown with a sheet of cardboard pierced with a knitting needle). Due to the action of gravitational forces from 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 seems to slide along the surface of the cone. (the same happens with the axis of an ordinary top at the end of rotation). This phenomenon was discovered as early as 125 BC. NS. Greek astronomer Hipparchus and named precession... The earth's axis makes one revolution in 25,776 years - this period is called platonic year... Now near P - the north pole of the world is the North Star - α M. Medveditsa. Further, the title of Polar was alternately assigned to π, η and τ of Hercules, to the stars Tuban and Kokhab. The Romans did not have the North Star at all, and Kohab and Kinosura (α Ursa Minor) were called Guardians. At the beginning of our chronology - the pole of the world was near α Dragon - 2000 years ago, and α Ursa Minor became the polar star in 1100. In 2100, the pole of the world will be only 28 "from the North Star - now 44". In 3200, the constellation Cepheus will become polar. In 14000, Vega (α Lyrae) will be polar. |
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| Horizontal coordinate system | ||||||||||||||||||||||||||||||||
| h - height- the angular distance of the star from the horizon (< МОА), измеряется в градусах, минутах, секундах; от 0 о до 90 о) A - azimuth- the angular distance of the vertical of the star from the point of the south (< SOА) в направлении суточного движения светила, т.е. по часовой стрелке; измеряется в градусах минутах и секундах от 0 о до 360 о). | ||||||||||||||||||||||||||||||||
| The horizontal coordinates of the star changes during the day. A" Equivalent to altitude → zenith distance Z = 90 o - h[forms 1] |
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| Climax - the phenomenon of crossing the celestial meridian by the luminary. | ||||||||||||||||||||||||||||||||
 Luminary M during the day describes a diurnal parallel - a small circle of the celestial sphere, the plane of which is ^ the axis of the world and passes through the eye  observer. M 3- the sunrise point, M 4- entry point, M 1- upper culmination (h max; A = 0 o), M 2- lower culmination (h min; A = 180 o) According to the diurnal movement, the luminaries are divided into: 1 - non-ascending 2 - (ascending - descending ) ascending and descending 3 - non-occuring ... What does the Sun, the Moon refer to? (2) |
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| III Securing the material(15 minutes). | ||||||||||||||||||||||||||||||||
| A) Questions | ||||||||||||||||||||||||||||||||
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| B) practical work on PKZN. | ||||||||||||||||||||||||||||||||
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| V) 1.Convert 3 hours, 6 hours into a degree measure (3.15 = 45 0, 90 0) 2. Convert 45 o, 90 o in hourly measure (3 hours, 6 hours) 3. What is more than 3 h 25 m 15 s or 51 o 18 "15"? (When translating, it will turn out 51 about 18 "45", that is, the hourly value is more) |
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| G) Test. For a phrase from the left column, choose a continuation from the right that suits the meaning. | ||||||||||||||||||||||||||||||||
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People in ancient times believed that all the stars are located on the celestial sphere, which as a whole revolves around the Earth. Already more than 2,000 years ago, astronomers began to use methods that made it possible to indicate the location of any star in the celestial sphere in relation to other space objects or landmarks. It is convenient to use the concept of the celestial sphere even now, although we know that this sphere does not really exist.
Heavenly sphere -an imaginary spherical surface of arbitrary radius, in the center of which is the observer's eye, and onto which we project the position of the celestial bodies.The concept of the celestial sphere is used for angular measurements in the sky, for the convenience of reasoning about the simplest visible celestial phenomena, for various calculations, for example, calculating the times of sunrise and sunset.
Let's construct a celestial sphere and draw a ray from its center towards the star A.
Where this ray crosses the surface of the sphere, place a point A 1 depicting this star. Star V will be represented by a dot IN 1 . Repeating a similar operation for all observed stars, we get on the surface of the sphere an image of the starry sky - a star globe. It is clear that if the observer is in the center of this imaginary sphere, then for him the direction to the stars themselves and to their images on the sphere will coincide.
- What is the center of the celestial sphere? (Eye of the Observer)
- What is the radius of the celestial sphere? (Arbitrary)
- What is the difference between the celestial spheres of two neighbors on the desk? (Center position).
For the solution of many practical problems, the 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 the celestial sphere to study the apparent arrangement of the luminaries and phenomena that can be observed in the sky during the day or many months. The stars, the sun, the moon, planets, etc., are projected onto such a sphere, abstracting from the actual distances to the stars and considering only the angular distance between them. Distances between stars on the celestial sphere can be expressed only in angular measure. These angular distances are measured by the value of the central angle between the rays directed to one and the other star, or the corresponding arcs on the surface of the sphere.
For an approximate estimate of the angular distances in the sky, it is useful to remember the following data: the angular distance between the two extreme stars of the Ursa Major bucket (α and β) is about 5 °, and from α Ursa Major to α Ursa Minor (Polar Star) - 5 times more - about 25 °.
The simplest eye estimates of angular distances can also be carried out using the fingers of an outstretched hand.
Only two luminaries - the Sun and the Moon - we see as disks. The angular diameters of these disks are almost the same - about 30 "or 0.5 °. The angular sizes of planets and stars are much smaller, so we see them simply as luminous points. To the naked eye, an object does not look like a point if its angular dimensions exceed 2 –3 ". This means, in particular, that our eye distinguishes each separately luminous point (star) if the angular distance between them is greater than this value. In other words, we see an object as non-point only if the distance to it exceeds its dimensions by no more than 1700 times.
Plumb line Z, Z ' passing through the eye of the observer (point C), located in the center of the celestial sphere, crosses the celestial sphere at points Z - zenith,Z '- nadir.
Zenith- this highest point above the head of the observer.
Nadir -opposite the zenith point of the celestial sphere.
The plane perpendicular to the plumb line is calledhorizontal plane (or horizon plane).
Mathematical horizonthe line of intersection of the celestial sphere with a horizontal plane passing through the center of the celestial sphere is called.
With the naked eye, about 6,000 stars can be seen in the entire sky, but we see only half of them, because the other half of the starry sky is hidden from us by the Earth. Are the stars moving across the sky? It turns out that everyone is moving and, moreover, at the same time. This is easy to verify by observing the starry sky (focusing on certain objects).
Due to its rotation, the appearance of the starry sky changes. Some stars are just emerging from behind the horizon (rising) in its eastern part, others at this time are high overhead, and still others are already hiding behind the horizon in the western side (setting). At the same time, it seems to us that the starry sky rotates as a whole. Now everyone knows well that the rotation of the firmament is an apparent phenomenon caused by the rotation of the Earth.
A picture of what happens to the starry sky as a result of the Earth's daily rotation can be captured by a camera.
In the resulting image, each star has left its trail in the form of a circular arc. But there is also such a star, the movement of which is almost imperceptible throughout the night. This star was named Polar. During the day, it describes a circle of small radius and is always visible at almost the same height above the horizon in the northern side of the sky. The common center of all concentric star trails is in the sky near the North Star. This point, to which the axis of rotation of the Earth is directed, is called north pole of the world. The arc described by Polaris has the smallest radius. But this arc and all the others - regardless of their radius and curvature - make up the same part of the circle. If it was possible to photograph the paths of the stars in the sky for a whole day, then the photograph would turn out to be full circles - 360 °. After all, a day is a period of a complete revolution of the Earth around its axis. In an hour, the Earth will rotate by 1/24 of a circle, that is, by 15 °. Consequently, the length of the arc that the star will describe during this time will be 15 °, and in half an hour - 7.5 °.
During the day, the stars describe the larger circles, the farther from the Pole Star they are.
The axis of the diurnal rotation of the celestial sphere is calledaxis of the world (PP ").
The points of intersection of the celestial sphere with the axis of the world are calledpoles of the world(point R - north pole of the world, point R" - south pole of the world).
The North Star is located near the North Pole of the world. When we look at the North Star, more precisely, at a fixed point next to it - the north pole of the world, the direction of our gaze coincides with the axis of the world. The South Pole of the world is located in the southern hemisphere of the celestial sphere.
Plane EAWQ, perpendicular to the axis of the world PP "and passing through the center of the celestial sphere, is calledthe plane of the celestial equator, and the line of its intersection with the celestial sphere -celestial equator.
Celestial 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.
The celestial equator divides the celestial sphere into two hemispheres: north and south.
The axis of the world, the poles of the world and the celestial equator are similar to the axis, poles and equator of the Earth, since the names listed are associated with the apparent rotation of the celestial sphere, and it is a consequence of the actual rotation of the globe.
The plane passing through the zenith pointZ , Centre WITH celestial sphere and pole R the world is calledthe plane of the celestial meridian, and the line of its intersection with the celestial sphere formscelestial meridian line.
Heavenly meridian - a large circle of the celestial sphere passing through the zenith Z, the pole of the world P, the south pole of the world P ", nadir Z"
In any place on the Earth, the plane of the celestial meridian coincides with the plane of the geographic meridian of this place.
Midday line NS - this is the line of intersection of the planes of the meridian and the horizon. N - north point, S - south point
It is so named because at noon the shadows from vertical objects fall in this direction.
- 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 rotation of the Earth).
- 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).
- Do all points of the celestial sphere participate in the apparent rotation of the celestial sphere? (Points lying on the axis are at rest).
The earth moves in an orbit around the sun. The axis of rotation of the Earth is inclined to the orbital plane at an angle of 66.5 °. Due to the action of gravitational forces from the Moon and the Sun, the axis of rotation of the Earth is displaced, while the inclination of the axis to the plane of the Earth's orbit remains constant. The axis of the Earth seems to slide along the surface of the cone. (the same happens with the axis of an ordinary top at the end of rotation).
This phenomenon was discovered as early as 125 BC. NS. Greek astronomer Hipparchus and named precession.
The earth's axis completes one revolution in 25,776 years - this period is called the Platonic year. Now, near P - the north pole of the world, there is the Pole Star - α Ursa Minor. Polar is the name of the star that today is located near the North Pole of the world. In our time, since about 1100, such a star is the alpha of the Ursa Minor - Kinosura. Previously, the title of Polar was alternately assigned to π, η and τ of Hercules, to the stars Tuban and Kohab. The Romans did not have the North Star at all, and Kohab and Kinosura (α Ursa Minor) were called Guardians.
At the beginning of our chronology - the pole of the world was near the α Dragon - 2000 years ago. In 2100, the pole of the world will be only 28 "from the North Star - now 44". In 3200, the constellation Cepheus will become polar. In 14000, Vega (α Lyrae) will be polar.
How to find the North Star in the sky?
To find the North Star, you need to mentally draw a straight line through the stars of the Big Dipper (the first 2 stars of the "bucket") 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 brightness with the stars of the "bucket" - this is the North Star.
In the constellation, which is often called the Small Bucket, the North Star is the brightest. But just like most of the stars of the Big Dipper dipper, Polaris is a second-magnitude star.
Summer (summer-autumn) triangle = star Vega (α Lyrae, 25.3 light years), star Deneb (α Cygnus, 3230 light years), star Altair (α Eagle, 16.8 light years)
Celestial coordinates
To find a luminary in the sky, you need to indicate in which side of the horizon and how high above it it is. For this purpose, horizontal coordinate system – azimuth and height. For an observer located at any point on the Earth, it is not difficult to determine the vertical and horizontal directions.
The first of them is determined using a plumb line and is depicted in the drawing by a plumb line ZZ ", passing through the center of the sphere (point O).
The Z point located directly above the observer's head is called zenith.
A plane that passes through the center of the sphere perpendicular to the plumb line forms a circle when it intersects the sphere - true, or mathematical, horizon.
Height the luminary is counted along a circle passing through the zenith and the luminary , and is expressed by the length of the arc of this circle from the horizon to the luminary. This arc and the corresponding angle are usually denoted by the letter h.
The height of the star, which is at its zenith, is 90 °, on the horizon - 0 °.
The position of the star relative to the sides of the horizon is indicated by its second coordinate - azimuth, denoted by a letter A. Azimuth is measured from the south point clockwise, so the azimuth of the south point is 0 °, the west point is 90 °, and so on.
The horizontal coordinates of the luminaries change continuously over time and depend on the position of the observer on the Earth, because in relation to world space, the horizon plane at a given point on the Earth rotates with it.
The horizontal coordinates of the luminaries are measured to determine the time or geographic coordinates of various points on Earth. In practice, for example in geodesy, the height and azimuth are measured with special goniometric optical instruments - theodolites.
To create a star map depicting constellations on a plane, you need to know the coordinates of the stars. To do this, you need to choose a coordinate system that would rotate with the starry sky. To indicate the position of the luminaries in the sky, use a coordinate system similar to that used in geography, - equatorial coordinate system.
The equatorial coordinate system is similar to the geographic coordinate system on the globe. As you know, the position of any point on the globe can be specified with using geographic coordinates - latitude and longitude.
Geographic latitude - it is the angular distance of a point from the earth's equator. Geographic latitude (φ) is measured along the meridians from the equator to the poles of the Earth.
Longitude- the angle between the plane of the meridian of the given point and the plane of the prime meridian. Geographic longitude (λ) measured along the equator from the initial (Greenwich) meridian.
So, for example, Moscow has the following coordinates: 37 ° 30 "east longitude and 55 ° 45" north latitude.
Introduce equatorial coordinate system which indicates the position of the luminaries on the celestial sphere relative to each other.
Let us draw a line through the center of the celestial sphere, parallel to the axis of rotation of the Earth, - axis of the world. It will cross the celestial sphere at two diametrically opposite points, which are called poles of the world - R and R. The North Pole of the world is called the one near which the North Star is located. The plane passing through the center of the sphere parallel to the plane of the equator of the Earth, in section with the sphere forms a circle, called celestial equator. The celestial equator (like the earthly one) divides the celestial sphere into two hemispheres: the North and the South. The angular distance of the star from the celestial equator is called declination. Declination is measured in a circle drawn through the star and the poles of the world, it is similar to geographical latitude.
Declination- the angular distance of the stars from the celestial equator... Declination is designated by the letter δ. In the northern hemisphere, declination is considered positive, in the southern hemisphere - negative.
The second coordinate, which indicates the position of the star in the sky, is similar to the geographical longitude. This coordinate is called right ascension ... Right ascension is measured along the celestial equator from the vernal equinox γ, at which the Sun occurs annually on March 21 (on the vernal equinox). It is counted from the vernal equinox point γ counterclockwise, that is, towards the diurnal rotation of the sky. Therefore, the luminaries rise (and set) in the ascending order of their right ascension.
Right ascension - the angle between the plane of a semicircle drawn from the pole of the world through the star(declination circle), and the plane of a semicircle drawn from the pole of the world through the vernal equinox point lying on the equator(initial circle of declensions). Right ascension is designated by the letter α
Declination and right ascension(δ, α) called equatorial coordinates.
It is convenient to express declination and right ascension not in degrees, but in units of time. Considering that the Earth makes one revolution in 24 hours, we get:
360 ° - 24 h, 1 ° - 4 min;
15 ° - 1 h, 15 "-1 min, 15" - 1 s.
Therefore, right ascension, for example 12 hours, is 180 °, and 7 hours 40 minutes corresponds to 115 °.
If you do not need special accuracy, then the celestial coordinates for the stars can be considered unchanged. With the diurnal rotation of the starry sky, the vernal equinox also rotates. Therefore, the positions of the stars relative to the equator and the vernal equinox do not depend on the time of day or on the position of the observer on Earth.
The equatorial coordinate system is depicted on a moving map of the starry sky.
2.1.1. Basic planes, lines and points of the celestial sphere
The celestial sphere is called an imaginary sphere of an arbitrary radius centered at a selected point of observation, on the surface of which the luminaries are located as they are visible in the sky at some point in time from a given point in space. To correctly imagine an astronomical phenomenon, it is necessary to consider the radius of the celestial sphere to be much greater than the radius of the Earth (R sf >> R of the Earth), i.e., to assume that the observer is in the center of the celestial sphere, and the same point of the celestial sphere (one and the same star) is visible from different places on the earth's surface in parallel directions.
The vault or sky is usually understood as the inner surface of the celestial sphere onto which celestial bodies (luminaries) are projected. For an observer on Earth, the Sun is visible in the sky during the day, sometimes the Moon, and even less often Venus. On a cloudless night, the stars, the moon, planets, sometimes comets and other bodies are visible. There are about 6000 stars visible to the naked eye. The relative position of the stars remains almost unchanged due to the large distances to them. Celestial bodies related to the solar system change their position relative to the stars and each other, which is determined by their noticeable angular and linear daily and annual displacement.
The firmament rotates as a whole with all the luminaries on it about an imaginary axis. This rotation is daily. If we observe the diurnal rotation of stars in the northern hemisphere of the Earth and face the north pole, then the rotation of the sky will occur counterclockwise.
Center O of the celestial sphere - observation point. The straight line ZOZ "coinciding with the direction of the plumb line at the observation point is called a plumb or vertical line. The plumb line intersects with the surface of the celestial sphere at two points: at the zenith Z, above the observer's head, and at the diametrically opposite point Z" - nadir. The great circle of the celestial sphere (SWNE), the plane of which is perpendicular to the plumb line, is called the mathematical or true horizon. The mathematical horizon is a plane tangent to the Earth's surface at the observation point. The small circle of the celestial sphere (aMa "), passing through the luminary M, and the plane of which is parallel to the plane of the mathematical horizon, is called the almucantara of the luminary. The large semicircle of the celestial sphere ZMZ" is called the circle of height, the vertical circle, or simply the vertical of the luminary.The diameter PP ", around which the celestial sphere rotates, is called the axis of the world. The axis of the world intersects with the surface of the celestial sphere at two points: at the north pole of the world P, from which the celestial sphere rotates clockwise, if you look at the sphere from the outside, and at the south pole of the world P ". The axis of the world is tilted to the plane of the mathematical horizon at an angle equal to the latitude of the observation point φ. The large circle of the celestial sphere QWQ "E, the plane of which is perpendicular to the axis of the world, is called the celestial equator. The small circle of the celestial sphere (bМb"), the plane of which is parallel to the plane of the celestial equator, is called the celestial or diurnal parallel of the star M. The large semicircle of the celestial sphere PMP * is called hour circle or declination circle of the star.
The celestial equator intersects with the mathematical horizon at two points: at the east point E and at the west point W. The circles of heights passing through the points of east and west are called the first verticals - east and west.
The great circle of the celestial sphere PZQSP "Z" Q "N, the plane of which passes through the plumb line and the axis of the world, is called the celestial meridian. The plane of the celestial meridian and the plane of the mathematical horizon intersect in a straight line NOS, which is called the noon line. The celestial meridian intersects with the mathematical horizon. at the north point N and at the south point S. The celestial meridian intersects with the celestial equator also at two points: at the upper point of the equator Q, which is closer to the zenith, and at the lower point of the equator Q ", which is closer to the nadir.
2.1.2. Luminaries, their classification, visible movements.
Stars, Sun and Moon, planets
In order to navigate the sky, bright stars are combined into constellations. There are 88 constellations in the sky, of which 56 are visible to an observer in the middle latitudes of the northern hemisphere of the Earth. All constellations have their own names associated with the names of animals (Ursa Major, Leo, Dragon), the names of the heroes of Greek mythology (Cassiopeia, Andromeda, Perseus) or the names of objects whose outlines resemble (Northern Crown, Triangle, Libra). Individual stars in the constellations are designated by letters of the Greek alphabet, and the brightest of them (about 200) received their "proper" names. For example, α Canis Major - "Sirius", α Orion - "Betelgeuse", β Perseus - "Algol", α Ursa Minor - "Polar Star", near which is the point of the north pole of the world. The paths of the Sun and the Moon against the background of the stars almost coincide and come in twelve constellations, which were named zodiacal, since most of them are called animals (from the Greek "zoon" - animal). These include the constellations Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces. The trajectory of Mars in the celestial sphere in 2003 |
Even in antiquity, 5 luminaries were seen, similar to stars, but "wandering" in the constellations. They were called planets - "wandering luminaries". Later, 2 more planets and a large number of smaller celestial bodies (dwarf planets, asteroids) were discovered.
The planets most of the time move along the zodiacal constellations from west to east (forward movement), but part of the time - from east to west (backward movement).
| Your browser does not support the video tag. The movement of stars in the celestial sphere |
Under celestial sphere it is customary to understand a sphere of arbitrary radius, the center of which is at the point of observation, and all the celestial bodies or luminaries surrounding us are projected onto the surface of this sphere
The rotation of the celestial sphere for an observer on the surface of the Earth reproduces daily movement shone in the sky
ZOZ"- plumb (vertical) line,
SWNE- true (mathematical) horizon,
aMa"- almucantarat,
ZMZ"- a circle of height (vertical circle), or vertical
P 
OP"- the axis of rotation of the celestial sphere (axis of the world),
P- the north pole of the world,
P" - the south pole of the world,
Ð PON= j (latitude of the place of observation),
QWQ" E- celestial equator,
bMb"- diurnal parallel,
PMP"- declination circle,
PZQSP" Z" Q" N- celestial meridian,
NOS- midday line
4. Systems of celestial coordinates (horizontal, first and second equatorial, ecliptic).
Since the radius of the celestial sphere is arbitrary, the position of the star on the celestial sphere is uniquely determined by two angular coordinates, if the main plane and the origin are set.
In spherical astronomy, the following celestial coordinate systems are used:
Horizontal, 1st equatorial, 2nd equatorial, Ecliptic
Horizontal coordinate system
Main plane - the plane of the mathematical horizon
1
)Ð mOM
= h
(height)
0 £ h£ 90 0
–90 £ 0 h £ 0
or Ð ZOM = z (zenith distance)
0 £ z£ 180 0
z + h = 90 0
2) Р SOm = A(azimuth)
0 £ A£ 360 0
1st equatorial coordinate system
The main plane is the plane of the celestial equator
1) Р mOM= d (declination)
0 £ d £ 90 0
–90 0 £ d £ 0
or Ð POM = p (pole distance)
0 £ p£ 180 0
p+ d = 90 0
2) Р QOm = t (hour angle)
0 £ t£ 360 0
or 0 h £ t£ 24 h
All horizontal coordinates ( h, z, A) and hour angle t the first equatorial SC are continuously changing during the diurnal rotation of the celestial sphere.
The declination d does not change.
Must be entered instead of t such an equatorial coordinate, which would be measured from a point fixed on the celestial sphere.
2nd equatorial coordinate system
O 
main plane - the plane of the celestial equator
1) Р mOM= d (declination)
0 £ d £ 90 0
–90 0 £ d £ 0
or Ð POM = p (pole distance)
0
£
p£ 180 0
p+ d = 90 0
2) Ð ¡ Om= a (right ascension)
or 0 h £ a £ 24 h
The horizontal SC is used to determine the direction to the star relative to terrestrial objects.
The 1st equatorial SC is used mainly for determining the exact time.
2
-th equatorial SC is generally accepted in astrometry.
Ecliptic SC
The main plane is the plane of the ecliptic E¡E "d
The plane of the ecliptic is inclined to the plane of the celestial meridian at an angle ε = 23 0 26 "
PP "- axis of the ecliptic
E - the point of the summer solstice
E "- the point of the winter solstice
1) m = λ (ecliptic longitude)
2) mM= b (ecliptic latitude)
5. Daily rotation of the celestial sphere at different latitudes and phenomena associated with it. The daily movement of the sun. Change of seasons and thermal belts.
Measurements of the Sun's altitude at noon (i.e. at the moment of its upper culmination) at the same geographic latitude showed that the Sun's declination d Ÿ during the year varies from +23 0 36 "to -23 0 36", two times passing through zero.
Right ascension of the Sun a Ÿ throughout the year also constantly changes from 0 to 360 0 or from 0 to 24 h.
Considering the continuous change in both coordinates of the Sun, it can be established that it moves among the stars from west to east along a large circle of the celestial sphere, which is called ecliptic.
March 20-21, the Sun is at point ¡, its declination δ = 0 and right ascension a Ÿ = 0. On this day (vernal equinox) the Sun rises exactly at the point E and goes to the point W... The maximum height of the center of the Sun above the horizon at noon this day (upper climax): hŸ = 90 0 - φ + δ Ÿ = 90 0 - φ
Then the Sun will move along the ecliptic closer to point E, i.e. δ Ÿ> 0 and a Ÿ> 0.
On June 21-22, the Sun is at point E, its declination is maximum δ Ÿ = 23 0 26 ", and right ascension is a Ÿ = 6 h. At noon of this day (summer solstice), the Sun rises to its maximum height above the horizon: hŸ = 90 0 - φ + 23 0 26 "
Thus, in mid-latitudes, the Sun NEVER is at its zenith
Latitude of Minsk φ = 53 0 55 "
Then the Sun will move along the ecliptic closer to point d, i.e. δ Ÿ will start to decrease
Around September 23, the Sun will come to point d, its declination δ Ÿ = 0, right ascension a Ÿ = 12 h. This day (the beginning of the astronomical autumn) is called the day of the autumnal equinox.
On December 22-23 the Sun will be at point E ", its declination is minimal δ Ÿ = - 23 0 26", and right ascension a Ÿ = 18 h.
Maximum height above the horizon: hŸ = 90 0 - φ - 23 0 26 "
The change in the equatorial coordinates of the Sun is uneven throughout the year.
Declination changes fastest when the Sun moves near the equinox points, and slowest near the solstice points.
Right ascension, on the contrary, changes more slowly near the equinox points, and faster - near the solstice points.
The apparent motion of the Sun along the ecliptic is associated with the actual motion of the Earth in its orbit around the Sun, as well as with the fact that the Earth's axis of rotation is not perpendicular to the plane of its orbit, but makes an angle ε = 23 0 26 ".
If ε = 0, then at any latitude on any day of the year the day would be equal to the night (excluding refraction and the size of the Sun).
Polar days lasting from 24 h to six months and the corresponding nights are observed in the polar circles, the latitudes of which are determined by the conditions:
φ = ± (90 0 - ε) = ± 66 0 34 "
The position of the axis of the world and, consequently, the plane of the celestial equator, as well as points ¡and d, is not constant, but periodically changes.
Due to the precession of the earth's axis, the axis of the world describes a cone around the axis of the ecliptic with an opening angle of ~ 23.5 0 in 26,000 years.
Due to the disturbing action of the planets, the curves described by the poles of the world do not close, but contract into a spiral.
T 
.To. both the plane of the celestial equator and the plane of the ecliptic slowly change their position in space, then the points of their intersection (¡and d) slowly move to the west.
Travel speed (total annual precession in the ecliptic) per year: l = 360 0 /26 000 = 50,26"".
Total annual precession at the equator: m = l cos ε = 46.11 "".
At the beginning of our era, the vernal equinox was in the constellation Aries, from which it received its designation (¡), and the autumnal equinox was in the constellation Libra (d). Since then, point ¡has moved to the constellation Pisces, and point d to the constellation Virgo, but their designations have remained the same.