Introduction

1. History

2 Elements of the celestial sphere

• 2.1 Plumb line and related concepts

  2.2 Daily rotation of the celestial sphere and related concepts

  2.3 The terms generated at the intersections of the concepts "Plumb line" and "Rotation of the celestial sphere"

  2.4 Annual motion of the Sun in the celestial sphere and related concepts

3 Curious facts

Introduction

The celestial sphere is divided by the celestial equator.

Celestial sphere- an imaginary sphere of arbitrary radius, onto which celestial bodies are projected: serves to solve various astrometric problems. The eye of the observer is taken as the center of the celestial sphere; in this case, the observer can be both on the surface of the Earth and at other points in space (for example, he can be referred to the center of the Earth). For a terrestrial observer, the rotation of the celestial sphere reproduces the diurnal movement of the stars in the sky.

Each celestial body corresponds to a point in the celestial sphere, in which it is crossed by a straight line connecting the center of the sphere with the center of the star. When studying the positions and apparent motions of luminaries on the celestial sphere, one or another system of spherical coordinates is chosen. Calculations of the positions of the luminaries on the celestial sphere are made using celestial mechanics and spherical trigonometry.

1. History

The concept of the celestial 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 unable to assess the differences in the distances to them, and they appear to be equally distant. Among the ancient peoples, this was associated with the presence of a real sphere that bounds the whole world and carries 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, this 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, received a modern form, in which it is used in astrometry.

2. Elements of the celestial sphere

Precession of the equinoxes of planet Earth, due to which the change of seasons is possible

2.1. Plumb Line and Related Concepts

Plumb line- a straight line passing through the center of the celestial sphere and the observation point on the surface of the Earth. The plumb line intersects with the surface of the celestial sphere at two points - zenithover the observer's head and nadireunder the feet of the observer.

Mathematical horizon- a large circle of the celestial sphere, the plane of which is perpendicular to the plumb line. The mathematical horizon divides the surface of the celestial sphere into two hemispheres: visible hemispherewith the top at the zenith and invisible hemispherewith the top in nadir. The mathematical horizon does not coincide with the visible horizon due to the elevation of the observation point above the earth's surface, as well as due to the bending of light rays in the atmosphere.

Circle heightor verticalluminaries - a large semicircle of the celestial sphere passing through the luminary, zenith and nadir. Almucantarat(Arabic "circle of equal heights") - a small circle of the celestial sphere, the plane of which is parallel to the plane of the mathematical horizon. The circles of height and almucantarates form a coordinate grid that sets the horizontal coordinates of the star.

2.2. Daily rotation of the celestial sphere and related concepts

Axis of the world- an imaginary line passing through the center of the world around which the celestial sphere rotates. The axis of the world intersects with the surface of the celestial sphere at two points - north pole of the worldand south pole of the world... The rotation of the celestial sphere occurs counterclockwise around the north pole, if you look at the celestial sphere from the inside.

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 celestial sphere into two hemispheres: northernand southern.

Declination circle- a large circle of the celestial sphere passing through the poles of the world.

Diurnal parallel- a small circle of the celestial sphere, the plane of which is parallel to the plane of the celestial equator. Visible diurnal movements of the luminaries follow diurnal parallels. The declination circles and diurnal parallels form a coordinate grid on the celestial sphere, which sets the equatorial coordinates of the star.

2.3. Terms generated at the intersection of the concepts "Plumb line" and "Rotation of the celestial sphere"

The celestial equator intersects the mathematical horizon at point eastand point west... The point east is the one at which the points of the rotating celestial sphere rise from the horizon. The semicircle of height passing through the east point is called first vertical.

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 hemisphereand western hemisphere.

Noon line- the line of intersection of the plane of the celestial meridian and the plane of the mathematical horizon. The noon line and the celestial meridian cross the mathematical horizon at two points: point northand point south... The north point is the one closer to the north pole of the world.

2.4. The annual movement of the Sun in the celestial sphere and related concepts

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

Ecliptic- a large circle of the celestial sphere, along which the apparent annual movement of the Sun takes place. The plane of the ecliptic intersects with the plane of the celestial equator at an angle ε \u003d 23 ° 26 ".

The two points at which the ecliptic meets the celestial equator are called equinox points. IN vernal equinoxThe sun in its annual movement passes from the southern hemisphere of the celestial sphere to the northern; in the point of the autumnal equinox- from the northern hemisphere to the southern. The two points of the ecliptic that are 90 ° from the equinox and thus the most distant from the celestial equator are called solstice points. Summer solstice pointlocated in the northern hemisphere, winter solstice point- in the southern hemisphere.

Ecliptic axis- the diameter of the celestial sphere perpendicular to the plane of the ecliptic. The axis of the ecliptic intersects with the surface of the celestial sphere at two points - north pole eclipticlying in the northern hemisphere, and south pole eclipticlying in the southern hemisphere. The north pole of the ecliptic has equatorial coordinates R.A. \u003d 18h00m, Dec \u003d + 66 ° 33 ", and is in the constellation Draco.

Circle of ecliptic latitude, or simply circle of latitude- a large semicircle of the celestial sphere passing through the poles of the ecliptic.

3. Curious facts

Word zenithcame to us from the Arabic language, where it is pronounced as deputy... Rewritten in Latin letters as zamt, it was later distorted by scribes, becoming zanit, and then zenith.

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Dreams are the activity of our subconscious and psyche, which continues to work even in sleep. The psyche is called upon to solve our daily problems using the method of predicting the most likely outcome of events. Thus, what may be in a state unconscious by us, but is determined latently, is expressed through dreams. All we need to do is learn how to interpret dreams, which will become the key to knowing ourselves. For example, quite often dreams help in the early diagnosis of diseases, help us pay attention to the state of health in time. Also, dreams often reveal our desires through the realization of what actually causes difficulties. In this case, the mechanism of displacement of unpleasant information is triggered, followed by replacement with more pleasant information. Dreams can even become an assistant in search of answers to questions that are exciting in reality.

Celestial sphere - an abstract concept, an imaginary sphere of infinitely large radius, the center of which is the observer. In this case, the center of the celestial sphere is, as it were, at the eye level of the observer (in other words, everything that you see above your head from horizon to horizon is this very sphere). However, for ease of perception, it can be considered the center of the celestial sphere and the center of the Earth, there is no mistake in this. The positions of the stars, planets, the Sun and the Moon are applied to the sphere in such a position in which they are visible in the sky at a certain point in time from a given point of the observer.

In other words, although observing the position of the luminaries on the celestial sphere, we, being in different places of the planet, will constantly see a slightly different picture, knowing the principles of the “work” of the celestial sphere, looking at the night sky we can easily navigate the terrain using a simple technique. Knowing the view overhead at point A, we will compare it with the view of the sky at point B, and by the deviations of familiar landmarks, we will be able to understand exactly where we are now.

People have long come up with a number of tools to facilitate our task. If you are guided by the "earthly" globe simply with the help of latitude and longitude, then a number of similar elements - points and lines are provided for the "heavenly" globe - the celestial sphere.

The celestial sphere and the position of the observer. If the observer moves, then the entire visible sphere will also move.

Elements of the celestial sphere

The celestial sphere has a number of characteristic points, lines and circles, let us consider the main elements of the celestial sphere.

Observer vertical

Observer vertical - a straight line passing through the center of the celestial sphere and coinciding with the direction of the plumb line at the point of the observer. Zenith - the point of intersection of the observer's vertical with the celestial sphere, located above the observer's head. Nadir - the point of intersection of the vertical of the observer with the celestial sphere, opposite the zenith.

True horizon - a large circle on the celestial sphere, the plane of which is perpendicular to the vertical of the observer. The true horizon divides the celestial sphere into two parts: overhorizontal hemispherewhere the zenith is located, and subhorizontal hemispherewhere the nadir is located.

Axis of the world (Earth axis) - a straight line around which the visible daily rotation of the celestial sphere occurs. The axis of the world is parallel to the axis of rotation of the Earth, and for an observer located at one of the poles of the Earth, it coincides with the axis of rotation of the Earth. The apparent daily rotation of the celestial sphere is a reflection of the actual daily rotation of the Earth around its axis. The poles of the world are the points of intersection of the axis of the world with the celestial sphere. The pole of the world, located in the constellation Ursa Minor, is called North Pole the world, and the opposite pole is called South Pole.

A large circle on the celestial sphere, the plane of which is perpendicular to the axis of the world. The plane of the celestial equator divides the celestial sphere into northern hemisphere, in which the North Pole of the world is located, and southern hemisphere, in which the South Pole of the world is located.

Or the meridian of the observer - a large circle on the celestial sphere passing through the poles of the world, zenith and nadir. It coincides with the plane of the terrestrial meridian of the observer and divides the celestial sphere into eastern and western hemisphere.

North and South points - points of intersection of the celestial meridian with the true horizon. The point closest to the North Pole of the world is called the point of the north of the true horizon C, and the point closest to the South Pole of the world is the point in the south of the Y. Points of the east and west are the intersection of the celestial equator with the true horizon.

Noon line - a straight line in the plane of the true horizon, connecting the points of the north and south. This line is called midday because at noon local true solar time the shadow from the vertical pole coincides with this line, that is, with the true meridian of this point.

Points of intersection of the celestial meridian with the celestial equator. The point closest to the southern point of the horizon is called point south of the celestial equator, and the point closest to the northern point of the horizon is point north of the celestial equator.

Vertical luminary

Luminaries vertical, or circle of height, - a large circle on the celestial sphere passing through the zenith, nadir and luminary. The first vertical is the vertical passing through the points of east and west.

Declination circle, or, - a large circle on the celestial sphere, passing through the poles of the world and the luminary.

A small circle on the celestial sphere drawn through the star parallel to the plane of the celestial equator. The apparent diurnal movement of the luminaries occurs along diurnal parallels.

Almucantarat luminaries

Almucantarat luminaries - a small circle on the celestial sphere, drawn through the star parallel to the plane of the true horizon.

All the elements of the celestial sphere noted above are actively used to solve practical problems of orientation in space and to determine the position of the stars. Two different systems are used depending on the purpose and measurement conditions. spherical celestial coordinates.

In one system, the luminary is oriented relative to the true horizon and this system is called, and in another - relative to the celestial equator and is called.

In each of these systems, the position of the star on the celestial sphere is determined by two angular quantities, just as the position of points on the surface of the Earth is determined using latitude and longitude.

CELESTIAL SPHERE
When we observe the sky, all astronomical objects appear to be located on a domed surface with the observer at the center. This imaginary dome forms the upper half of an imaginary sphere called the "celestial sphere". It plays a fundamental role in indicating the position of astronomical objects.

Although the Moon, planets, the Sun and stars are located at different distances from us, even the closest ones are so far away that we are not able to estimate their distance by eye. The direction of the star does not change as we move across the surface of the Earth. (True, it changes slightly as the Earth moves in its orbit, but this parallax displacement can be noticed only with the help of the most accurate instruments.) It seems to us that the celestial sphere rotates, since the stars 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 crosses the celestial sphere at two points called the north and south "poles of the world." The North Pole of the world lies about a degree from the North Star, and there are no bright stars near the South Pole.

The axis of rotation of the Earth is tilted approximately 23.5 ° relative to the perpendicular drawn to the plane of the Earth's orbit (to the plane of the ecliptic). The intersection of this plane with the celestial sphere gives a circle - the ecliptic, the visible path of the Sun for a year. The orientation of the earth's axis in space remains almost unchanged. Therefore, every year in June, when the north end of the axis is tilted towards the Sun, it rises high in the sky in the Northern Hemisphere, where days become long and nights are 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 are becoming short and the nights long.
see also SEASONS . However, under the influence of solar and lunar attraction, the orientation of the earth's axis is still gradually changing. The main movement of the axis caused by the influence of the Sun and Moon on the Earth's equatorial swelling is called precession. As a result of the precession, the earth's axis slowly rotates around the perpendicular to the orbital plane, describing a cone with a radius of 23.5 ° in 26 thousand years. For this reason, in a few centuries the pole will no longer be near the North Star. In addition, the Earth's axis makes small oscillations, called nutation, and associated with the ellipticity of the orbits of the Earth and the Moon, as well as the fact that the plane of the lunar 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 revolution of the Earth around the Sun. For a complete orbit around 360 ° Earth, approx. 3651/4 days - about a degree per day. By the way, a day, or rather 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 ("sidereal days"), plus a short time - about four minutes - required for the rotation, which compensates for the orbital movement of the Earth by one degree per day. Thus, in a year approx. 3651/4 sunny days and approx. 3661/4 star.
When viewed from a specific point
The star lands near the poles are either always above the horizon or never rise above it. All other stars rise and set, and each day the rise and fall of each star occurs 4 minutes earlier than on the previous day. Some stars and constellations rise in the sky at night during the winter - we call them "winter" and others - "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 orbiting the sun; the epoch associated with precession (although the latter effect is hardly noticeable "by eye" even in 100 years).
Coordinate systems. There are various ways to indicate the position of objects on the celestial sphere. Each of them is suitable for certain types of tasks.
Alt-azimuth system. To indicate the position of an object in the sky in relation to the terrestrial objects surrounding the observer, an "alt-azimuth", or "horizontal" coordinate system is used. It indicates the angular distance of the object above the horizon, called "height", as well as its "azimuth" - the angular distance along the horizon from a conditional point to a point lying directly under the object. In astronomy, azimuth is measured from a point south to west, and in geodesy and navigation, from a point north to east. Therefore, before using the azimuth, you need to find out in which system it is indicated. The point of the sky, located directly above the head, has a height of 90 ° and is called "zenith", and the point diametrically opposite to it (under the feet) is "nadir". For many tasks, the 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 points north and south.
Equatorial system. Due to the rotation of the Earth, stars are constantly moving relative to the horizon and cardinal points, and their coordinates in the horizontal system change. But for some tasks of astronomy, the coordinate system must be independent of the position of the observer and the time of day. This system is called "equatorial"; its coordinates resemble geographical latitudes and longitudes. In it, the plane of the earth's equator, extended to the intersection with the celestial sphere, sets the basic 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 site is equal to the declination of the star. Geographic longitude corresponds to "right ascension" of the star. It is measured east of the 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", and is denoted by the sign
Other systems. For some purposes, other coordinate systems on the celestial sphere are also used. For example, when studying the motion of bodies in the solar system, a coordinate system is used, the main plane of which 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. The table maps these systems to a geographic coordinate system.
Transition from one system to another. It is often necessary to calculate its equatorial coordinates from the alt-azimuth coordinates of a star, and vice versa. For 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 pole of the world and the star X; it is called the "astronomical triangle". The angle with the apex at the north pole of the world between the meridian of the observer and the direction to any point in 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" (Si. T. - sidereal time) at the observation point. And since the right ascension of a star is also the polar angle between the direction to it and to 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 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 \u200b\u200ba and h, knowing the time, calculate a and d. The declination d is calculated directly from the last formula, then H is calculated from the penultimate one, and a is calculated from the first, if sidereal time is known.
Representation of the celestial sphere. For centuries, scientists have searched for the best ways to represent the celestial sphere for study or demonstration. Two types of models have been proposed: two-dimensional and three-dimensional. The celestial sphere can be depicted on a plane in the same way as a spherical earth is depicted on maps. In both cases, it is necessary to select a geometric projection system. The first attempt to represent areas of the celestial sphere on a plane was rock carvings of stellar configurations in the caves of ancient people. Today, there are various star charts published as hand-drawn or photographic star atlases covering the entire sky. Ancient Chinese and Greek astronomers envisioned the celestial sphere in a pattern known as the "armillary sphere." It consists of metal circles or rings connected together to represent 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 disadvantage: the position of the stars and the markings of the circles are plotted on their outer, convex side, which we consider from the outside, while we look at the sky "from the inside", and the stars appear to be placed on the concave side of the celestial sphere. This sometimes leads to confusion between the directions of movement of the stars and the figures of the constellations. The most realistic representation of the celestial sphere is given by the planetarium. The optical projection of the stars onto a hemispherical screen from the inside makes it possible to very accurately reproduce the view of the sky and all kinds of movements of the stars on it.
see also
ASTRONOMY AND ASTROPHYSICS;
PLANETARIUM;
STARS .

Collier's Encyclopedia. - Open Society. 2000 .

The Big Encyclopedic Dictionary is an imaginary auxiliary sphere of arbitrary radius onto which the heavenly bodies are projected. It is used in astronomy to study the relative position and movement of space objects based on the determination of 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 tasks. Representation of N. page. originated in ancient times; it was based on visual ... ... Great Soviet Encyclopedia

An imaginary sphere of an arbitrary radius, on which a swarm of 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: angl. celestial sphere vok. Himmelskugel, f; Himmelssphäre, f rus. celestial sphere, f; firmament, m pranc. sphère céleste, f ... Fizikos terminų žodynas

§ 48. Heavenly sphere. Major points, lines and circles on the celestial sphere

The celestial sphere is a sphere of any radius centered at an arbitrary point in space. For its center, depending on the formulation of the problem, the eye of the observer, the center of the instrument, the center of the Earth, etc. are taken.

Consider the main points and circles of the celestial sphere, for the center of which is taken the eye of the observer (Fig. 72). 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.

Figure: 72.

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

The straight line passing through the center of the celestial sphere parallel to the earth's axis is called the y axis of the world. 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 pole of the world and denoted by Pn, the other - the south pole of the world 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 the circumference of 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 poles of the world, zenith and nadir, is called observer meridian PN nPsZ. The axis of the world divides the observer's meridian into the noon PN ZPs and the midnight PN nPs.

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 north and south is called the midday line.

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

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

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

The observer's meridian is both the vertical and the declination circle. He divides the celestial sphere into two parts - east and west.

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

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

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