Basic elements of the celestial sphere

The sky appears to the observer as a spherical dome surrounding him on all sides. In this regard, even in ancient times, the concept of the celestial sphere (vault of heaven) arose and its main elements were defined.

Celestial sphere called an imaginary sphere of arbitrary radius, on the inner surface of which, as it seems to the observer, the celestial bodies are located. It always seems to the observer that he is in the center of the celestial sphere (i.e. in Fig. 1.1).

Rice. 1.1. Basic elements of the celestial sphere

Let the observer hold a plumb line in his hands - a small massive weight on a thread. The direction of this thread is called plumb line. Let's draw a plumb line through the center of the celestial sphere. It will intersect this sphere at two diametrically opposite points called zenith And nadir. The zenith is located exactly above the observer's head, and the nadir is hidden by the earth's surface.

Let us draw a plane through the center of the celestial sphere perpendicular to the plumb line. It will cross the sphere in a great circle called mathematical or true horizon. (Recall that a circle formed by a section of a sphere by a plane passing through the center is called big; if the plane cuts the sphere without passing through its center, then the section forms small circle). The mathematical horizon is parallel to the observer's apparent horizon, but does not coincide with it.

Through the center of the celestial sphere we draw an axis parallel to the axis of rotation of the Earth and call it axis mundi(in Latin - Axis Mundi). The axis of the world intersects the celestial sphere at two diametrically opposite points called poles of the world. There are two poles of the world - northern And southern. The north celestial pole is taken to be the one in relation to which the daily rotation of the celestial sphere, arising as a result of the rotation of the Earth around its axis, occurs counterclockwise when looking at the sky from inside the celestial sphere (as we look at it). Near the north pole of the world is the North Star - Ursa Minor - the brightest star in this constellation.

Contrary to popular belief, Polaris is not the brightest star in the starry sky. It has a second magnitude and is not one of the brightest stars. An inexperienced observer is unlikely to quickly find it in the sky. It is not easy to search for the Polaris by the characteristic shape of the Ursa Minor bucket - the other stars of this constellation are even fainter than Polaris and cannot be reliable reference points. The easiest way for a novice observer to find the North Star in the sky is to navigate by the stars of the nearby bright constellation Ursa Major (Fig. 1.2). If you mentally connect the two outermost stars of the Ursa Major bucket, and , and continue the straight line until it intersects with the first more or less noticeable star, then this will be the North Star. The distance in the sky from the star Ursa Major to Polaris is approximately five times greater than the distance between the stars and Ursa Major.

Rice. 1.2. Circumpolar constellations Ursa Major
and Ursa Minor

The south celestial pole is marked in the sky by the barely visible star Sigma Octanta.

The point on the mathematical horizon closest to the north celestial pole is called north point. The farthest point of the true horizon from the north pole of the world is south point. It is also located closest to the south pole of the world. A line in the plane of the mathematical horizon passing through the center of the celestial sphere and the points of north and south is called noon line.

Let us draw a plane through the center of the celestial sphere perpendicular to the axis of the world. It will cross the sphere in a great circle called celestial equator. The celestial equator intersects with the true horizon at two diametrically opposite points east And west. The celestial equator divides the celestial sphere into two halves - Northern Hemisphere with its peak at the north celestial pole and Southern Hemisphere with its top at the south celestial pole. The plane of the celestial equator is parallel to the plane of the earth's equator.

The points north, south, west and east are called sides of the horizon.

The great circle of the celestial sphere passing through the celestial poles and, zenith and nadir Na, called celestial meridian. The plane of the celestial meridian coincides with the plane of the observer's earthly meridian and is perpendicular to the planes of the mathematical horizon and the celestial equator. The celestial meridian divides the celestial sphere into two hemispheres - eastern, with apex at the east point , And western, with apex at point west . The celestial meridian intersects the mathematical horizon at the points north and south. This is the basis for the method of orientation by stars on the earth's surface. If you mentally connect the zenith point, lying above the observer’s head, with the North Star and continue this line further, then the point of its intersection with the horizon will be the north point. The celestial meridian crosses the mathematical horizon along the noon line.

A small circle parallel to the true horizon is called almucantarate(in Arabic - a circle of equal heights). You can perform as many almucantarats as you like on the celestial sphere.

Small circles parallel to the celestial equator are called celestial parallels, they can also be carried out infinitely many. The daily movement of stars occurs along celestial parallels.

The great circles of the celestial sphere passing through the zenith and nadir are called height circles or vertical circles (verticals). Vertical circle passing through the points of east and west W, called first vertical. The vertical planes are perpendicular to the mathematical horizon and almucantarates.

Contents of the article

CELESTIAL SPHERE. When we observe the sky, all astronomical objects appear to be located on a dome-shaped surface, in the center of which the observer is located. 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, 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.

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. 365 1/4 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 relative to the stars (“sidereal day”), plus a short time—about four minutes—required for the rotation to compensate for the Earth’s orbital movement by one degree per day. Thus, in a year approx. 365 1/4 solar days and approx. 366 1/4 stars.

When observed from a certain point on the 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 in winter - we call them “winter”, while others are “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.

There are 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, the great 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. Right ascension values ​​are usually given in hours and minutes, considering 24 hours to be equal to 360°.

The equatorial system is used when observing with telescopes. The telescope is installed so that it can rotate from east to west around an axis directed towards the celestial pole, thereby compensating for the rotation of the Earth.

Other systems.

For some purposes, other coordinate systems on the celestial sphere are also used. For example, when studying the movement of bodies in the solar system, they 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 observer’s meridian 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” (Si. 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 are given a And d, then its horizontal coordinates A And can be calculated using the following formulas:

You can also solve the inverse problem: using the measured values A And h, knowing the time, calculate a And d. Declension d calculated directly from the last formula, then calculated from the penultimate one N, and from the first, if sidereal time is known, it is calculated a.

Representation of the celestial sphere.

For many centuries, scientists have searched for the best ways to represent the celestial sphere for 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.

Laboratory work

« MAIN ELEMENTS OF THE CELESTIAL SPHERE"

Purpose of the work: Study of the basic elements and daily rotation of the celestial sphere using its model.

Benefits: model of the celestial sphere (or a celestial planisphere replacing it); black globe; moving star map.

Brief theoretical information:

The visible positions of the celestial bodies are determined relative to the basic elements of the celestial sphere.

The main elements of the celestial sphere (Fig. 1) include:

Zenith points Z and nadir Z" , true or mathematical horizon NESWN, axis mundi RR", poles of the world ( R-northern and R"- southern), celestial equator QWQ" EQ celestial meridian РZSP "Z" NP and the points of intersection of the celestial meridian and the celestial equator with the true horizon, i.e. the point of the south S, north N, east E and west W.

The elements of the celestial sphere can be studied on its model (Fig. 2), which consists of several rings depicting the main circles of the celestial sphere. In ring 1, representing the celestial meridian, the axis is rigidly reinforced RR"- the axis of the world around which the celestial sphere rotates. End points R And R" of this axis lie on the celestial meridian and represent, respectively, the northern ( R) and southern ( R") poles of the world.

Metal circle 8 depicts the true or mathematical horizon, which should always be set in a horizontal position when working with a model of the celestial sphere. The world axis forms an angle with the plane of the true horizon equal to the geographic latitude at the observation point, and when installing the model at a given geographic latitude, this angle is fixed with a screw 11 , after which the true horizon 8 brought to a horizontal position by turning the ring 1 (celestial meridian), which is fixed in the stand 9 clamp 10 .

Around the axis RR"(the axes of the world) two rings fastened together rotate freely 2 And 3 , the planes of which are mutually perpendicular. These rings represent declination circles - large circles passing through the poles of the world. Although on the celestial sphere there are countless circles of declination passing through the poles of the world, on the model of the celestial sphere there are only four circles of declination (in the form of two complete rings), along which one can imagine the entire spherical surface. Attention should be paid to the fact that the circle of declination is not taken as a complete circle, but only its half, enclosed between the poles of the world. Thus, the two rings of the model depict four circles of declination of the celestial sphere, spaced from each other by 90°; they make it possible to demonstrate the equatorial coordinates of celestial bodies.

Ring 4 , the plane of which is perpendicular to the axis of the world, depicts the celestial equator. At an angle to it 23°.5 ring attached 5 , representing the ecliptic.

Rings representing the celestial meridian 1 , celestial equator 4 , ecliptic 5 , declination circles 2 And 3 and true horizon 8 , are great circles of the celestial sphere - their planes pass through the center O model in which the observer is conceived.

Perpendicular to the plane of the true horizon, restored from the center O model of the celestial sphere, intersects the celestial meridian at points called zenith Z(above the observer's head) and nadir Z" (the nadir is under the observer’s feet and hidden from him by the earth’s surface).

At the zenith, on the celestial meridian, the moving rater is strengthened 12 , with an arc freely rotating on it 13 , the plane of which also passes through the center of the model of the celestial sphere. Arc 13 depicts a circle of altitude (vertical) and allows you to demonstrate the horizontal coordinates of celestial bodies.

In addition to the large circles, the model of the celestial sphere shows two small circles 6 And 7 -two celestial parallels separated from the celestial equator by 23°.5. The remaining celestial parallels are not shown on the model. The planes of the celestial parallels do not pass through the center of the celestial sphere, they are parallel to the plane of the celestial equator and perpendicular to the axis of the world.

Two attachments are attached to the model of the celestial sphere, one in the form of a circle, the other in the form of an asterisk. These attachments serve to depict celestial bodies and can be mounted on any circle of the celestial sphere model.

In what follows, all elements of the celestial sphere model are referred to by the same terms that are accepted for the corresponding elements of the celestial sphere.

Due to the uniform rotation of the Earth around its axis in the direction from west to east (or counterclockwise), it appears to the observer that the celestial sphere rotates uniformly around the axis of the world RR" in the opposite direction, i.e. clockwise, if you look at it from the outside from the north celestial pole (or if the observer in the center of the sphere turns his back to the north celestial pole and his face to the south). During the day, the celestial sphere makes one revolution; this apparent rotation is called diurnal. The direction of daily rotation of the celestial sphere is shown in Fig. 1 arrow.

Using the model of the celestial sphere, one can clearly understand that although the celestial sphere rotates as a single whole, most of its main elements do not participate in the daily rotation of the sphere, remaining motionless relative to the observer. The celestial equator rotates in its plane along with the celestial sphere, sliding at the fixed points of east E and west W. In the process of daily rotation, all points of the celestial sphere (except for fixed points) cross the celestial meridian twice a day, once - its southern half (south of the north celestial pole, arc RZSR"), another time - its northern half (north of the north pole of the world, arc RNZ" P" ). These passages of points through the celestial meridian are called, respectively, the upper and lower culmination. Through the zenith Z and nadir Z" Not all, but only certain points of the celestial sphere pass through, the declination δ of which (as will be seen later) is equal to the geographic latitude φ of the observer’s place (δ = φ). Points of the celestial sphere located above the true horizon are visible to the observer; the hemisphere located under the true horizon is inaccessible to observations (in Fig. 1 it is indicated by vertical shading).

Arc NES the true horizon, above which the points of the celestial sphere rise, is called its eastern half and extends 180º from the point of north N, through the east point E, to the point south S. Opposite, western half SWN the true horizon, beyond which the points of the celestial sphere extend, also contains 180º and is also limited by the points of the south S and north N, but passes through the west point W. The eastern and western halves of the true horizon should not be confused with its sides, which are determined by its main points - the points of the east, south, west and north.

Particular attention should be paid to the fact that the celestial sphere is divided into the northern and southern hemispheres by the celestial equator, and not by the true horizon, above which the regions of both hemispheres, both northern and southern, are always located. The size of these areas depends on the geographic latitude of the observation site: the closer to the Earth’s north pole the observation site is (the larger its φ), the smaller the area of ​​the southern celestial hemisphere is accessible to observations, and the larger the area of ​​the northern celestial hemisphere is simultaneously visible above the true horizon (and in the southern hemisphere of the Earth - vice versa).

The duration of stay of points of the celestial sphere throughout the day above the true horizon (and below it) depends on the ratio of the declination δ of these points with the geographic latitude φ of the observation location, and for a certain φ - only on their declination δ. Since the celestial equator and the true horizon intersect at diametrically opposite points, any point on the celestial equator (δ = 0°) is always half a day above the true horizon and half a day below it, regardless of the geographic latitude at the observation site (except for the geographic poles of the Earth, φ = ± 90°).

To study the main elements of the celestial sphere, in the absence of a model, you can use the celestial planisphere (tablet 10), which, of course, is not as visual as a spatial model, but can still give a correct idea of ​​the main elements and the daily rotation of the celestial sphere. The planisphere is an orthogonal (rectangular) projection of the celestial sphere onto the plane of the celestial meridian and consists of a circle SZNZ" , depicting the celestial meridian, through the center ABOUT which a plumb line is drawn ZZ" and trace of the true horizon plane NS. Eastern points E and west W projected into the center of the planisphere. Degree divisions on the celestial meridian give altitude h almucantarats (small circles parallel to the true horizon), which above the true horizon is considered positive (h > 0°), and below it - negative (h< 0°).

axis mundi RR", celestial equator QQ" and the celestial parallels are depicted in the same projection on tracing paper, on which two positions of the ecliptic are also depicted in dotted lines, corresponding to its highest ξξ") and lowest (ξоξо") position above the true horizon. Degree digitization on tracing paper gives the angular distance of celestial parallels from the celestial equator, i.e. their declination δ, considered positive in the northern celestial hemisphere (δ > 0°), and negative in the southern celestial hemisphere (δ< 0°).

By placing tracing paper symmetrically on the circle of the celestial meridian and rotating it around a common center ABOUT at a certain angle of 90° - φ, we get the appearance of the celestial sphere (in projection onto the plane of the celestial meridian) at the geographic latitude φ. Then the location of the elements of the celestial sphere relative to the true horizon will immediately become clear. N.S. and relative to the observer located at the center ABOUT celestial sphere. The direction of the daily rotation of the celestial sphere around the axis of the world has to be depicted by arrows along the celestial equator and celestial parallels.

It is very useful to imagine the correspondence of the elements of the celestial sphere to the points and circles of the earth's surface. To make this correspondence clearer, it is best to imagine the radius of the celestial sphere as large as desired, but not infinite, since in the case of an infinitely large radius, sections of the sphere degenerate into a plane. For an arbitrarily large radius of the celestial sphere, the observer ABOUT, located at a certain point on the earth's surface, sees the celestial sphere in the same way as from the center of the Earth WITH(Fig. 3), but maintaining the same direction to the zenith Z. Then it becomes clear that the plumb line OZ is a continuation of the earth's radius CO at the observation point (the Earth is taken to be a sphere), axis of the world RR" identical to the earth's axis of rotation pp", poles of the world R And R" correspond to the geographic poles of the Earth r And p", celestial equator QQ" formed on the celestial sphere by the plane of the earth's equator qq" , and the celestial meridian RZR"Z"R formed on the celestial sphere by the plane of the earth's meridian pOqp"q" p on which the observer is located ABOUT. The plane of the true horizon is tangent to the surface of the Earth at the observation point ABOUT. This explains the immobility of the celestial meridian, zenith, nadir and true horizon relative to the observer, which rotate with him around the earth's axis. Poles of the world R And R" are also motionless relative to the observer, since they lie on the earth's axis, which does not participate in the daily rotation of the earth. Any earthly parallel kO with geographic latitude a corresponds to the celestial parallel TOZ. with declination and δ = φ. Therefore, the points of this celestial parallel pass through the zenith of the observation site ABOUT.

0 " style="border-collapse:collapse;border:none">

Name

Position relative to observer

Location relative to the true horizon

3. The globe can depict:

4. The moving map shows:

7. Matching dots and circles:

Drawing attached.

8. Three drawings are attached.

The celestial sphere is an imaginary sphere, arbitrarily
large radius, at the center of which the observer is located.
To the celestial sphere
stars are projected
Sun, Moon, planets.
Properties of the celestial sphere:
center of the celestial sphere
is chosen randomly.
For each observer -
your center, and observers
maybe a lot.
angular measurements on
sphere do not depend on it
radius.

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

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 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 passing through the points of east and west is called the first vertical.

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