Celestial sphere is an imaginary sphere of arbitrary radius with a center at an arbitrary point, on the surface of which the positions of the luminaries are plotted as they are visible in the sky at some point in time from a given point.

Celestial sphere rotates. It is not difficult to verify this simply by observing the change in the position of the celestial bodies relative to the observer or the horizon. If you point the camera at the Ursa Minor star and open the lens for several hours, the images of the stars on the photographic plate will describe arcs, the central angles of which are the same (Fig. 17). Material from the site

Due to the rotation of the celestial sphere, each luminary moves in a small circle, the plane of which is parallel to the plane of the equator - daily parallel. As can be seen from Figure 18, the daily parallel may intersect the mathematical horizon, but may not intersect it. The intersection of the horizon by a luminary is called sunrise, if it passes into the upper part of the celestial sphere, and by setting when the luminary passes into the lower part of the celestial sphere. In the event that the daily parallel along which the luminary moves does not cross the horizon, the luminary is called non-ascending or non-visitors depending on where it is located: always in the upper or always in the lower part of the celestial sphere.

§ 48. Celestial sphere. Basic points, lines and circles on the celestial sphere

A celestial sphere is a sphere of any radius with a center at an arbitrary point in space. Depending on the statement of the problem, its center is taken to be the eye of the observer, the center of the instrument, the center of the Earth, etc.

Let us consider the main points and circles of the celestial sphere, the center of which is taken to be the eye of the observer (Fig. 72). Let's draw a plumb line through the center of the celestial sphere. The points of intersection of the plumb line with the sphere are called zenith Z and nadir n.

Rice. 72.

The plane passing through the center of the celestial sphere perpendicular to the plumb line is called the plane of the true horizon. This plane, intersecting with the celestial sphere, forms a great circle called the true horizon. The latter divides the celestial sphere into two parts: above the horizon and below the horizon.

The straight line passing through the center of the celestial sphere parallel to the earth's axis is called the mundi axis. The points of intersection of the axis of the world with the celestial sphere are called poles of the world. One of the poles, corresponding to the poles of the Earth, is called the north celestial pole and is designated Pn, the other is the south celestial pole Ps.

The QQ plane passing through the center of the celestial sphere perpendicular to the axis of the world is called plane of the celestial equator. This plane, intersecting with the celestial sphere, forms a great circle - celestial equator, which divides the celestial sphere into northern and southern parts.

The great circle of the celestial sphere passing through the celestial poles, zenith and nadir, is called observer's meridian PN nPsZ. The mundi axis divides the observer's meridian into the midday PN ZPs and midnight PN nPs parts.

The observer's meridian intersects with the true horizon at two points: the north point N and the south point S. The straight line connecting the points of north and south is called midday line.

If you look from the center of the sphere to point N, then on the right there will be a point of east O st, and on the left - a point of west W. Small circles of the celestial sphere aa", parallel to the plane of the true horizon, are called almucantarates; small bb" parallel to the plane of the celestial equator, - heavenly parallels.

The circles of the celestial sphere Zon passing through the zenith and nadir points are called verticals. The vertical line passing through the points of east and west is called the first vertical.

The circles of the celestial sphere of PNoPs passing through the celestial poles are called declination circles.

The observer's meridian is both a vertical and a circle of declination. It divides the celestial sphere into two parts - eastern and western.

The celestial pole located above the horizon (below the horizon) is called the elevated (lowered) celestial pole. The name of the elevated celestial pole is always the same as the name of the latitude of the place.

The axis of the world makes an angle with the plane of the true horizon equal to geographical latitude of the place.

The position of luminaries on the celestial sphere is determined using spherical coordinate systems. In nautical astronomy, horizontal and equatorial coordinate systems are used.

The celestial sphere is an imaginary spherical surface of arbitrary radius, at the center of which the observer is located. Celestial bodies are projected onto celestial sphere.

Due to the small size of the Earth, in comparison with the distances to the stars, observers located in different places on the Earth's surface can be considered to be in center of the celestial sphere. In reality, no material sphere surrounding the Earth exists in nature. Celestial bodies move in the boundless cosmic space at very different distances from the Earth. These distances are unimaginably great, our vision is not able to evaluate them, therefore to a person all celestial bodies seem equally distant.

Over the course of a year, the Sun describes a large circle against the background of the starry sky. The annual path of the Sun across the celestial sphere is called the ecliptic. Moving around ecliptic. The sun crosses the celestial equator twice at the equinoctial points. This happens on March 21 and September 23.

The point on the celestial sphere that remains motionless during the daily movement of the stars is conventionally called the north celestial pole. The opposite point of the celestial sphere is called the south celestial pole. Residents of the northern hemisphere do not see it, because it is located below the horizon. A plumb line passing through the observer intersects the sky above at the zenith point and at the diametrically opposite point, called the nadir.

The axis of apparent rotation of the celestial sphere, connecting both poles of the world and passing through the observer, is called the axis of the world. On the horizon below the north celestial pole lies north point, the point diametrically opposite to it is south point. East and West points lie on the horizon and are 90° from the north and south points.

A plane passing through the center of the sphere perpendicular to the axis of the world forms celestial equator plane, parallel to the plane earth's equator. The plane of the celestial meridian passes through the poles of the world, the points of north and south, zenith and nadir.

Celestial coordinates

A coordinate system in which the reference is made from the equatorial plane is called equatorial. The angular distance of the star from the celestial equator is called, which varies from -90° to +90°. Declension considered positive north of the equator and negative south.

is measured by the angle between the planes of great circles, one of which passes through the poles of the world and a given luminary, the second - through the poles of the world and the vernal equinox point lying on the equator.

Horizontal coordinates Angular distance is the distance between objects in the sky, measured by the angle formed by the rays coming to the object from the observation point. The angular distance of the star from the horizon is called the height of the star above the horizon. The position of the luminary relative to the sides of the horizon is called azimuth. Counting is carried out from the south clockwise. and the height of the star above the horizon is measured with a theodolite. Angular units express not only the distances between celestial objects, but also the sizes of the objects themselves. The angular distance of the celestial pole from the horizon is equal to the geographic latitude of the area.

The height of the luminaries at the climax

The phenomena of the passage of luminaries through the celestial meridian are called culminations. The lower culmination is the passage of luminaries through the northern half of the celestial meridian. The phenomenon of a luminary passing through the southern half of the celestial meridian is called the upper culmination. The moment of the upper culmination of the center of the Sun is called true noon, and the moment of the lower culmination is called true midnight. The time interval between climaxes is half a day.

For non-setting luminaries both culminations are visible above the horizon, for rising and setting ones lower climax occurs below the horizon, below the north point. Every star culminates in a given area is always at the same height above the horizon, because its angular distance from the celestial pole and from the celestial equator does not change. The Sun and Moon change altitude by
which they culminate.

People in ancient times believed that all the stars were located on the celestial sphere, which as a whole revolved 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 body on the celestial sphere in relation to other space objects or ground landmarks. The concept of the celestial sphere is convenient to use even now, although we know that this sphere does not really exist.

Celestial sphere -an imaginary spherical surface of an arbitrary radius, in the center of which the observer’s eye is located, 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 time of sunrise and sunset.

Let's build a celestial sphere and draw a ray from its center towards the star A.

Where this ray intersects the surface of the sphere, we place a point A 1 representing this star. Star IN will be represented by a dot IN 1 . By repeating a similar operation for all observed stars, we obtain an image of the starry sky on the surface of the sphere - 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)
• How do the celestial spheres of two desk neighbors differ? (Center position).

To solve 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 the Celestial Sphere to study the visible arrangement of luminaries and phenomena that can be observed in the sky over the course of a 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 luminaries and considering only the angular distances between them. The distances between stars on the celestial sphere can only be expressed in angular measure. These angular distances are measured by the magnitude of the central angle between the rays directed at one and the other star, or their 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 (Pole Star) - 5 times greater - approximately 25°.

The simplest visual estimates of angular distances can also be carried out using the fingers of an outstretched hand.

We see only two luminaries - the Sun and the Moon - 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 it angular dimensions exceed 2–3". This means, in particular, that our eye distinguishes each individual luminous point (star) if the angular distance between them is greater than this value. In other words, we see an object as not a point only if if the distance to it exceeds its size 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, intersects the celestial sphere at points Z - zenith,Z’ - nadir.

Zenith- this is the highest point above the observer's head.

Nadir -point of the celestial sphere opposite to the zenith.

The plane perpendicular to the plumb line is calledhorizontal plane (or horizon plane).

Mathematical horizoncalled the line of intersection of the celestial sphere with a horizontal plane passing through the center of the celestial sphere.

With the naked eye, you can see about 6,000 stars in the entire sky, but we see only half of them, because the other half of the starry sky is blocked from us by the Earth. Do the stars move across the sky? It turns out that everyone is moving and at the same time. You can easily verify this 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 the horizon (rising) in the eastern part, others at this time are high above your head, 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 single whole. Now everyone knows well that The rotation of the sky 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 daily rotation of the Earth can be captured with a camera.

In the resulting image, each star left its mark in the form of a circular arc. But there is also a star whose movement throughout the night is almost imperceptible. This star was called Polaris. Over the course of a 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 located in the sky near the North Star. This point to which the Earth's rotation axis is directed is called north celestial pole. The arc described by the North Star has the smallest radius. But this arc and all the others - regardless of their radius and curvature - form the same part of the circle. If it were possible to photograph the paths of stars in the sky over a whole day, then the photograph would turn out to be complete circles - 360°. After all, a day is the period of a complete revolution of the Earth around its axis.

In an hour, the Earth will rotate 1/24 of a circle, i.e. 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 course of a day, the stars describe larger circles, the farther they are from the North Star.The axis of daily rotation of the celestial sphere is called (axis mundi).

RR"The points of intersection of the celestial sphere with the axis of the world are called poles of the world (dot - R north celestial pole, point - R"

south celestial pole).

Plane EAW.Q., perpendicular to the axis of the world PP" and passing through the center of the celestial sphere is calledplane of the celestial equator, and the line of its intersection with the celestial sphere iscelestial equator.

Celestial equator – a line of a circle 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: northern and southern.

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 listed names are associated with the apparent rotation of the celestial sphere, and it is a consequence of the actual rotation of the globe.

Plane passing through the zenith pointZ , center WITH celestial sphere and pole (dot the world is calledplane of the celestial meridian, and the line of its intersection with the celestial sphere formscelestial meridian line.

Celestial meridian – a great circle of the celestial sphere passing through the zenith Z, the celestial pole P, the south celestial pole P, nadir Z"

In any place on Earth, the plane of the celestial meridian coincides with the plane of the geographical meridian of this place.

Noon Line N.S. - this is the line of intersection of the meridian and horizon planes. N – north point, S – south point

It is so named because at midday shadows from vertical objects fall in this direction.

• What is the period of rotation of the celestial sphere? (Equal to the period of rotation of the Earth - 1 day).
• In what direction does the visible (apparent) rotation of the celestial sphere occur? (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 orbit around the Sun. The Earth's rotation axis 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 Earth's rotation axis shifts, while the inclination of the axis to the plane of the Earth's orbit remains constant. The Earth's axis seems to slide along the surface of the cone. (the same thing happens with the axis of an ordinary top at the end of rotation).

This phenomenon was discovered back in 125 BC. e. by the 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 the P - north pole of the world there is the North Star - α Ursa Minor. The polar star is the star that is currently located near the North Pole of the world. In our time, since about 1100, such a star is Alpha Ursa Minor - Kinosura. Previously, the title of Polaris was alternately assigned to π, η and τ Hercules, the stars Thuban 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 celestial pole was near α Draco - 2000 years ago. 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 (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 Ursa Major (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 identical in brightness to the stars of the “bucket” - this is the North Star.

In the constellation, which is often called the Little Dipper, the North Star is the brightest. But just like most of the stars in the Ursa Major bucket, Polaris is a star of second magnitude.

Summer (summer-autumn) triangle = star Vega (α Lyrae, 25.3 light years), star Deneb (α Cygnus, 3230 light years), star Altair (α Orlae, 16.8 light years)

Celestial coordinates

To find a star in the sky, you need to indicate which side of the horizon it is on and how high above it it is. For this purpose it is used horizontal coordinate system – azimuth And height. For an observer located anywhere on 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 ABOUT).

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 with the sphere - true, or mathematical, horizon.

Height luminary is measured along a circle passing through the zenith and luminary , and is expressed by the length of the arc of this circle from the horizon to the luminary. This arc and its corresponding angle are usually denoted by the letter h.

The height of the star, which is at the zenith, is 90°, at the horizon - 0°.

The position of the luminary relative to the sides of the horizon is indicated by its second coordinate - azimuth, lettered A. Azimuth is measured from the south point in a clockwise direction, so the azimuth of the south point is 0°, the west point is 90°, etc.

The horizontal coordinates of the luminaries continuously change 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 luminaries are measured to determine the time or geographic coordinates of various points on Earth. In practice, for example in geodesy, 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 luminaries in the sky, a coordinate system similar to that used in geography is used. - 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 indicated With using geographic coordinates - latitude and longitude.

Geographic latitude - 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 a given point and the plane of the prime meridian. Geographic longitude (λ) measured along the equator from the prime (Greenwich) meridian.

So, for example, Moscow has the following coordinates: 37°30" east longitude and 55°45" north latitude.

Let's introduce equatorial coordinate system, which indicates the position of the luminaries on the celestial sphere relative to each other.

Let's draw a line through the center of the celestial sphere parallel to the Earth's rotation axis - axis mundi. It will cross the celestial sphere at two diametrically opposite points, which are called The points of intersection of the celestial sphere with the axis of the world are called - (dot And R. The north pole of the world is called the one near which the North Star is located. A plane passing through the center of the sphere parallel to the plane of the Earth's equator, in cross-section with the sphere, forms a circle called celestial equator. The celestial equator (like the earth's) divides the celestial sphere into two hemispheres: the Northern and Southern. The angular distance of a star from the celestial equator is called declination. Declination is measured along a circle drawn through the celestial body and the poles of the world; it is similar to geographic latitude.

Declension- angular distance of the luminaries from the celestial equator. Declension is denoted by the letter δ. In the northern hemisphere, declinations are considered positive, in the southern hemisphere - negative.

The second coordinate, which indicates the position of the star in the sky, is similar to geographic longitude. This coordinate is called right ascension .

Right ascension is measured along the celestial equator from the vernal equinox γ, where the Sun occurs annually on March 21 (the day of the vernal equinox). It is measured from the vernal equinox γ counterclockwise, i.e., towards the daily rotation of the sky. Therefore, the luminaries rise (and set) in increasing order of their right ascension. - Right ascension the angle between the plane of a semicircle drawn from the celestial pole through the luminary (declension circle), and the plane of a semicircle drawn from the celestial pole through the point of the vernal equinox lying on the equator

(initial circle of declinations). Right ascension is symbolized by α(δ, α) Declination and right ascension

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 hours, 1° - 4 minutes;

15° - 1 hour, 15" -1 min, 15" - 1 s.

Therefore, a right ascension equal to, for example, 12 o'clock is 180°, and 7 hours 40 minutes corresponds to 115°.

If special accuracy is not needed, then the celestial coordinates for the stars can be considered unchanged. With the daily rotation of the starry sky, the point of the vernal equinox also rotates. Therefore, the positions of the stars relative to the equator and the vernal equinox do not depend either on the time of day or on the position of the observer on Earth.

The equatorial coordinate system is depicted on a moving star chart.
CELESTIAL SPHERE

Although the Moon, planets, Sun and stars are located at different distances from us, even the closest of them are so far away that we are not able to estimate their distance by eye. The direction towards a star does not change as we move across the Earth's surface. (True, it changes slightly as the Earth moves along its orbit, but this parallactic shift can only be noticed with the help of the most precise instruments.) It seems to us that the celestial sphere rotates, since the luminaries rise in the east and set in the west. The reason for this is the rotation of the Earth from west to east. The apparent rotation of the celestial sphere occurs around an imaginary axis that continues the earth's axis of rotation. This axis intersects the celestial sphere at two points called the north and south “celestial poles.” The celestial north pole lies about a degree from the North Star, and there are no bright stars near the south pole.

The Earth's rotation axis is tilted approximately 23.5° relative to the perpendicular to the plane of the Earth's orbit (to the ecliptic plane). The intersection of this plane with the celestial sphere gives a circle - the ecliptic, the apparent path of the Sun over a year. The orientation of the earth's axis in space remains almost unchanged. Therefore, every year in June, when the northern end of the axis is tilted towards the Sun, it rises high in the sky in the Northern Hemisphere, where the days become long and the nights short. Having moved to the opposite side of the orbit in December, the Earth turns out to be turned towards the Sun by the Southern Hemisphere, and in our north the days become short and the nights long.
see also SEASONS . However, under the influence of solar and lunar gravity, the orientation of the earth's axis gradually changes. The main movement of the axis caused by the influence of the Sun and Moon on the equatorial bulge of the Earth is called precession. As a result of precession, the earth's axis slowly rotates around a perpendicular to the orbital plane, describing a cone with a radius of 23.5° over 26 thousand years. For this reason, after a few centuries the pole will no longer be near the North Star. In addition, the Earth's axis undergoes small oscillations called nutation, which are associated with the ellipticity of the orbits of the Earth and the Moon, as well as with the fact that the plane of the Moon's orbit is slightly inclined to the plane of the Earth's orbit. As we already know, the appearance of the celestial sphere changes during the night due to the rotation of the Earth around its axis. But even if you observe the sky at the same time throughout the year, its appearance will change due to the Earth's revolution around the Sun. For a complete 360° orbit, the Earth requires approx. 3651/4 days - approximately one degree per day. By the way, a day, or more precisely a solar day, is the time during which the Earth rotates once around its axis in relation to the Sun. It consists of the time it takes for the Earth to rotate in relation to the stars (the “sidereal day”), plus a short time - about four minutes - required for the rotation, compensating for the Earth’s orbital movement per day by one degree. Thus, in a year approx. 3651/4 solar days and approx. 3661/4 stars.
When viewed from a specific point
Earth stars located near the poles are either always above the horizon or never rise above it. All other stars rise and set, and each day the rising and setting of each star occurs 4 minutes earlier than the previous day. Some stars and constellations rise in the sky at night winter time- we call them “winter”, while others call them “summer”. Thus, the appearance of the celestial sphere is determined by three times: the time of day associated with the rotation of the Earth; the time of year associated with revolution around the Sun; an epoch associated with precession (although the latter effect is hardly noticeable “by eye” even in 100 years).
Coordinate systems. Exist various ways to indicate the position of objects on the celestial sphere. Each of them is suitable for a specific type of task.
Alt-azimuth system. To indicate the position of an object in the sky in relation to the earthly objects surrounding the observer, an “alt-azimuth” or “horizontal” coordinate system is used. It indicates the angular distance of an object above the horizon, called “height,” as well as its “azimuth” - the angular distance along the horizon from a conventional point to a point lying directly below the object. In astronomy, azimuth is measured from the point south to the west, and in geodesy and navigation - from the point north to the east. Therefore, before using azimuth, you need to find out in which system it is indicated. The point in the sky directly above your head has a height of 90° and is called “zenith,” and the point diametrically opposite to it (under your feet) is called “nadir.” For many problems, a large circle of the celestial sphere, called the “celestial meridian”, is important; it passes through the zenith, nadir and poles of the world, and crosses the horizon at the points of north and south.
Equatorial system. Due to the rotation of the Earth, stars constantly move relative to the horizon and cardinal points, and their coordinates in the horizontal system change. But for some astronomy problems, the coordinate system must be independent of the observer’s position and time of day. Such a system is called "equatorial"; its coordinates resemble geographic latitudes and longitudes. In it, the plane of the earth's equator, extended to the intersection with the celestial sphere, defines the main circle - the “celestial equator”. The "declination" of a star resembles latitude and is measured by its angular distance north or south of the celestial equator. If the star is visible exactly at the zenith, then the latitude of the observation location is equal to the declination of the star. Geographic longitude corresponds to the “right ascension” of the star. It is measured east of the point of intersection of the ecliptic with the celestial equator, which the Sun passes in March, on the day of the beginning of spring in the Northern Hemisphere and autumn in the Southern. This point, important for astronomy, is called the “first point of Aries”, or the “vernal equinox point”, and is designated by the sign
Other systems. For some purposes, other coordinate systems on the celestial sphere are also used. For example, when studying the movement of bodies in solar system, use a coordinate system whose main plane is the plane of the earth's orbit. The structure of the Galaxy is studied in a coordinate system, the main plane of which is the equatorial plane of the Galaxy, represented in the sky by a circle passing along the Milky Way.
Comparison of coordinate systems. The most important details of the horizontal and equatorial systems are shown in the figures. In the table, these systems are compared with the geographic coordinate system.
Transition from one system to another. Often there is a need to calculate its equatorial coordinates from the alt-azimuthal coordinates of a star, and vice versa. To do this, it is necessary to know the moment of observation and the position of the observer on Earth. Mathematically, the problem is solved using a spherical triangle with vertices at the zenith, the north celestial pole and the star X; it is called the "astronomical triangle". The angle with the vertex at the north celestial pole between the meridian of the observer and the direction to some point on the celestial sphere is called the “hour angle” of this point; it is measured west of the meridian. The hour angle of the vernal equinox, expressed in hours, minutes and seconds, is called “sidereal time” (S. T. - sidereal time) at the observation point. And since the right ascension of a star is also the polar angle between the direction towards it and the point of the vernal equinox, sidereal time is equal to the right ascension of all points lying on the observer’s meridian. Thus, the hour angle of any point on the celestial sphere is equal to the difference between sidereal time and its right ascension:

Let the observer's latitude be j. If the equatorial coordinates of the star a and d are given, then its horizontal coordinates a and can be calculated using the following formulas: You can also solve the inverse problem: using the measured values ​​of a and h, knowing the time, calculate a and d. Declination d is calculated directly from the last formula, then H is calculated from the penultimate formula, and from the first, if sidereal time is known, a is calculated.
Representation of the celestial sphere. For many centuries, scientists have been searching the best ways representations of the celestial sphere for its study or demonstration. Two types of models were proposed: two-dimensional and three-dimensional. The celestial sphere can be depicted on a plane in the same way as the spherical Earth is depicted on maps. In both cases, it is necessary to select a geometric projection system. The first attempt to represent parts of the celestial sphere on a plane were rock paintings of star configurations in the caves of ancient people. Nowadays, there are various star maps, published in the form of hand-drawn or photographic star atlases covering the entire sky. Ancient Chinese and Greek astronomers conceptualized the celestial sphere in a model known as the "armillary sphere." It consists of metal circles or rings connected together so as to show the most important circles of the celestial sphere. Nowadays, star globes are often used, on which the positions of the stars and the main circles of the celestial sphere are marked. Armillary spheres and globes have a common drawback: the positions of the stars and the markings of the circles are marked on their outer, convex side, which we view from the outside, while we look at the sky “from the inside,” and the stars seem to us to be placed on the concave side of the celestial sphere. This sometimes leads to confusion in the directions of movement of stars and constellation figures. The most realistic representation of the celestial sphere is provided by a planetarium. The optical projection of stars onto a hemispherical screen from the inside allows you to very accurately reproduce the appearance of the sky and all kinds of movements of the luminaries on it.
see also
ASTRONOMY AND ASTROPHYSICS;
PLANETARIUM;
STARS .

Collier's Encyclopedia. - Open Society. 2000 .

- an imaginary auxiliary sphere of arbitrary radius onto which the celestial bodies are projected. It is used in astronomy to study the relative position and movement of space objects based on determining their coordinates on the celestial sphere... ... - an imaginary auxiliary sphere of arbitrary radius onto which celestial bodies are projected. It is used in astronomy to study the relative position and movement of space objects based on determining their coordinates on the celestial sphere.... ... encyclopedic Dictionary

An imaginary auxiliary sphere of arbitrary radius onto which the celestial bodies are projected; serves to solve various astrometric problems. The idea of ​​N. s. arose in ancient times; it is based on the visual... Great Soviet Encyclopedia

An imaginary sphere of arbitrary radius, in which the celestial bodies are depicted as they are visible from an observation point on the earth’s surface (topocentric n.s.) or as they would be visible from the center of the Earth (geocentric n.s.) or the center of the Sun … … Big Encyclopedic Polytechnic Dictionary

celestial sphere- dangaus sfera statusas T sritis fizika atitikmenys: engl. celestial sphere vok. Himmelskugel, f; Himmelssphare, f rus. celestial sphere, f; firmament, m pranc. sphère céleste, f … Fizikos terminų žodynas