Auxiliary celestial sphere
Coordinate systems used in geodetic astronomy
Geographic latitudes and longitudes of points on the earth's surface and azimuths of directions are determined from observations of celestial bodies - the Sun and stars. For this, it is necessary to know the position of the luminaries both relative to the Earth and relative to each other. The positions of the luminaries can be specified in expediently chosen coordinate systems. As is known from analytical geometry, to determine the position of the luminary s, you can use a rectangular Cartesian coordinate system XYZ or polar a, b, R (Fig. 1).
In a rectangular coordinate system, the position of the luminary s is determined by three linear coordinates X, Y, Z. In the polar coordinate system, the position of the luminary s is set by one linear coordinate, the radius vector R = Os and two angular ones: the angle a between the X axis and the projection of the radius vector onto the XOY coordinate plane, and the angle b between the XOY coordinate plane and the radius vector R. The relationship between rectangular and polar coordinates is described by the formulas
X = R cos b cos a,
Y = R cos b sin a,
Z = R sin b,
These systems are used in cases where the linear distances R = Os to celestial bodies are known (for example, for the Sun, Moon, planets, artificial satellites of the Earth). However, for many luminaries observed outside the solar system, these distances are either extremely large compared to the radius of the Earth, or are unknown. To simplify the solution of astronomical problems and to do without distances to the stars, it is assumed that all the stars are at an arbitrary, but the same distance from the observer. Usually this distance is taken equal to one, as a result of which the position of the luminaries in space can be determined not by three, but by two angular coordinates a and b of the polar system. It is known that the locus of points equidistant from a given point "O" is a sphere centered at this point.
Auxiliary celestial sphere - an imaginary sphere of arbitrary or unit radius, onto which images of celestial bodies are projected (Fig. 2). The position of any star s on the celestial sphere is determined using two spherical coordinates, a and b:
x = cos b cos a,
y = cos b sin a,
z = sin b.
Depending on where the center of the celestial sphere O is located, there are:
1)topocentric the celestial sphere - the center is on the surface of the Earth;
2)geocentric the celestial sphere - the center coincides with the center of mass of the Earth;
3)heliocentric the celestial sphere - the center is aligned with the center of the Sun;
4) barycentric celestial sphere - the center is at the center of gravity of the solar system.
The main circles, points and lines of the celestial sphere are shown in Fig. 3.
One of the main directions relative to the Earth's surface is the direction plumb line, or gravity at the observation point. This direction crosses the celestial sphere at two diametrically opposite points - Z and Z. "Point Z is located above the center and is called zenith, Z "- under the center and is called nadir.
Draw through the center a plane perpendicular to the plumb line ZZ. "The large NESW circle formed by this plane is called celestial (true) or astronomical horizon... This is the main plane of the topocentric coordinate system. It has four points S, W, N, E, where S - point south, N - North point, W - point west, E - point east... Direct NS is called midday line.
The straight line P N P S, drawn through the center of the celestial sphere parallel to the axis of rotation of the Earth, is called axis of the world... Points P N - north pole of the world; P S - south pole of the world... Around the axis of the World there is a visible daily movement of the celestial sphere.
Draw through the center a plane perpendicular to the axis of the world P N P S. The large circle QWQ "E, formed as a result of the intersection of this plane with the celestial sphere, is called celestial (astronomical) equator... Here Q - the highest point of the equator(above the horizon), Q "- the lowest point of the equator(under the horizon). The celestial equator and the celestial horizon intersect at points W and E.
The plane P N ZQSP S Z "Q" N, containing the plumb line and the axis of the World, is called true (celestial) or astronomical meridian. This plane is parallel to the plane of the earth's meridian and perpendicular to the plane of the horizon and equator. This is called the origin plane.
Draw through ZZ "a vertical plane perpendicular to the celestial meridian. The resulting circle ZWZ" E is called first vertical.
The great circle ZsZ "along which the vertical plane passing through the star s intersects the celestial sphere is called vertical or circle of heights of the sun.
The large circle P N sP S passing through the star perpendicular to the celestial equator is called around the declination of the luminary.
The small circle nsn "passing through the star parallel to the celestial equator is called diurnal parallel. The apparent diurnal movement of the luminaries occurs along diurnal parallels.
The small circle asa "passing through the star parallel to the celestial horizon is called circle of equal heights, or almucantara.
In a first approximation, the Earth's orbit can be taken as a flat curve - an ellipse, in one of the focuses of which is the Sun. The plane of the ellipse taken as the Earth's orbit , called a plane ecliptic.
In spherical astronomy, it is customary to talk about the apparent annual motion of the Sun. The large circle ЕgЕ "d, along which the apparent movement of the Sun occurs during the year, is called ecliptic... The plane of the ecliptic is inclined to the plane of the celestial equator at an angle approximately equal to 23.5 0. In fig. 4 shows:
g - vernal equinox point;
d - the point of the autumnal equinox;
E - the point of the summer solstice; E "- the point of the winter solstice; R N R S - axis of the ecliptic; R N - north pole of the ecliptic; R S - south pole of the ecliptic; e - inclination of the ecliptic to the equator.
Points and lines of the celestial sphere - how to find the almucantarat, where the celestial equator passes, which is the celestial meridian.
What is the Heavenly Sphere
Celestial sphere- an abstract concept, an imaginary sphere of an 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 simplicity 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's location.
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 sphere visible to him 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 hemisphere where the zenith is located, and subhorizontal hemisphere where the nadir is located.
Axis of the world (Earth axis)- a straight line around which there is a visible daily rotation of the celestial sphere. 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.
Midday 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 a given 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
Vertical luminary, 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 luminaries. 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 the other - 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.
3. Heavenly sphere. Basic planes, lines and points of the celestial sphere.
Under celestial sphere it is customary to understand a sphere of arbitrary radius, the center of which is at the point of observation, and all the celestial bodies or luminaries surrounding us are projected onto the surface of this sphere
The rotation of the celestial sphere for an observer on the surface of the Earth reproduces daily movement shone in the sky
ZOZ"- plumb (vertical) line,
SWNE- true (mathematical) horizon,
aMa"- almucantarat,
ZMZ"- a circle of height (vertical circle), or vertical
P 
OP"- the axis of rotation of the celestial sphere (axis of the world),
P- the north pole of the world,
P" - the south pole of the world,
Ð PON= j (latitude of the place of observation),
QWQ" E- celestial equator,
bMb"- diurnal parallel,
PMP"- declination circle,
PZQSP" Z" Q" N- celestial meridian,
NOS- midday line
4. Systems of celestial coordinates (horizontal, first and second equatorial, ecliptic).
Since the radius of the celestial sphere is arbitrary, the position of the star on the celestial sphere is uniquely determined by two angular coordinates, if the main plane and the origin are set.
In spherical astronomy, the following celestial coordinate systems are used:
Horizontal, 1st equatorial, 2nd equatorial, Ecliptic
Horizontal coordinate system
Main plane - the plane of the mathematical horizon
1
)Ð mOM
= h
(height)
0 £ h£ 90 0
–90 £ 0 h £ 0
or Ð ZOM = z (zenith distance)
0 £ z£ 180 0
z + h = 90 0
2) Р SOm = A(azimuth)
0 £ A£ 360 0
1st equatorial coordinate system
The main plane is the plane of the celestial equator
1) Р mOM= d (declination)
0 £ d £ 90 0
–90 0 £ d £ 0
or Ð POM = p (pole distance)
0 £ p£ 180 0
p+ d = 90 0
2) Р QOm = t (hour angle)
0 £ t£ 360 0
or 0 h £ t£ 24 h
All horizontal coordinates ( h, z, A) and hour angle t the first equatorial SC are continuously changing during the diurnal rotation of the celestial sphere.
The declination d does not change.
Must be entered instead of t such an equatorial coordinate, which would be measured from a point fixed on the celestial sphere.
2nd equatorial coordinate system
O 
main plane - the plane of the celestial equator
1) Р mOM= d (declination)
0 £ d £ 90 0
–90 0 £ d £ 0
or Ð POM = p (pole distance)
0
£
p£ 180 0
p+ d = 90 0
2) Ð ¡ Om= a (right ascension)
or 0 h £ a £ 24 h
The horizontal SC is used to determine the direction to the star relative to terrestrial objects.
The 1st equatorial SC is used mainly for determining the exact time.
2
-th equatorial SC is generally accepted in astrometry.
Ecliptic SC
The main plane is the plane of the ecliptic E¡E "d
The plane of the ecliptic is inclined to the plane of the celestial meridian at an angle ε = 23 0 26 "
PP "- axis of the ecliptic
E - the point of the summer solstice
E "- the point of the winter solstice
one) m = λ (ecliptic longitude)
2) mM= b (ecliptic latitude)
5. Daily rotation of the celestial sphere at different latitudes and phenomena associated with it. The daily movement of the sun. Change of seasons and thermal belts.
Measurements of the Sun's altitude at noon (i.e. at the moment of its upper culmination) at the same geographic latitude showed that the Sun's declination d Ÿ during the year varies from +23 0 36 "to -23 0 36", two times passing through zero.
Right ascension of the Sun a Ÿ throughout the year also constantly changes from 0 to 360 0 or from 0 to 24 h.
Considering the continuous change in both coordinates of the Sun, it can be established that it moves among the stars from west to east along a large circle of the celestial sphere, which is called ecliptic.
March 20-21, the Sun is at point ¡, its declination δ = 0 and right ascension a Ÿ = 0. On this day (vernal equinox) the Sun rises exactly at the point E and goes to the point W... The maximum height of the center of the Sun above the horizon at noon this day (upper climax): hŸ = 90 0 - φ + δ Ÿ = 90 0 - φ
Then the Sun will move along the ecliptic closer to point E, i.e. δ Ÿ> 0 and a Ÿ> 0.
On June 21-22, the Sun is at point E, its declination is maximum δ Ÿ = 23 0 26 ", and right ascension is a Ÿ = 6 h. At noon of this day (summer solstice), the Sun rises to its maximum height above the horizon: hŸ = 90 0 - φ + 23 0 26 "
Thus, in mid-latitudes, the Sun NEVER is at its zenith
Latitude of Minsk φ = 53 0 55 "
Then the Sun will move along the ecliptic closer to point d, i.e. δ Ÿ will start to decrease
Around September 23, the Sun will come to point d, its declination δ Ÿ = 0, right ascension a Ÿ = 12 h. This day (the beginning of the astronomical autumn) is called the day of the autumnal equinox.
On December 22-23 the Sun will be at point E ", its declination is minimal δ Ÿ = - 23 0 26", and right ascension a Ÿ = 18 h.
Maximum height above the horizon: hŸ = 90 0 - φ - 23 0 26 "
The change in the equatorial coordinates of the Sun is uneven throughout the year.
Declination changes fastest when the Sun moves near the equinox points, and slowest near the solstice points.
Right ascension, on the contrary, changes more slowly near the equinox points, and faster - near the solstice points.
The apparent motion of the Sun along the ecliptic is associated with the actual motion of the Earth in its orbit around the Sun, as well as with the fact that the Earth's axis of rotation is not perpendicular to the plane of its orbit, but makes an angle ε = 23 0 26 ".
If ε = 0, then at any latitude on any day of the year the day would be equal to the night (excluding refraction and the size of the Sun).
Polar days lasting from 24 h to six months and the corresponding nights are observed in the polar circles, the latitudes of which are determined by the conditions:
φ = ± (90 0 - ε) = ± 66 0 34 "
The position of the axis of the world and, consequently, the plane of the celestial equator, as well as points ¡and d, is not constant, but periodically changes.
Due to the precession of the earth's axis, the axis of the world describes a cone around the axis of the ecliptic with an opening angle of ~ 23.5 0 in 26,000 years.
Due to the disturbing action of the planets, the curves described by the poles of the world do not close, but contract into a spiral.
T 
.To. both the plane of the celestial equator and the plane of the ecliptic slowly change their position in space, then the points of their intersection (¡and d) slowly move to the west.
Travel speed (total annual precession in the ecliptic) per year: l = 360 0 /26 000 = 50,26"".
Total annual precession at the equator: m = l cos ε = 46.11 "".
At the beginning of our era, the vernal equinox was in the constellation Aries, from which it received its designation (¡), and the autumnal equinox was in the constellation Libra (d). Since then, point ¡has moved to the constellation Pisces, and point d to the constellation Virgo, but their designations have remained the same.
| " |
Astronomy answer book for grade 11 for lesson number 2 (workbook) - Heavenly sphere
1. Complete the sentence.
A constellation is a section of the starry sky with a characteristic observed group of stars.
2. Using the map of the starry sky, enter the constellation schemes with bright stars in the corresponding columns of the table. In each constellation, select the brightest star and indicate its name.
3. Complete the sentence.
The position of the planets is not indicated on star charts, since the charts are intended to describe the stars and constellations.
4. Place the following stars in decreasing order of magnitude:
1) Betelgeuse; 2) Spica; 3) Aldebaran; 4) Sirius; 5) Arcturus; 6) Capella; 7) Procyon; 8) Vega; 9) Altair; 10) Pollux.
| 4 | 5 | 8 | 6 | 7 | 1 | 3 | 9 | 2 | 10 |
5. Complete the sentence.
Stars of the 1st magnitude are 100 times brighter than stars of the 6th magnitude.
The ecliptic is the apparent annual path of the Sun among the stars.
6. What is called the celestial sphere?
An imaginary sphere of arbitrary radius.
7. Indicate the names of points and lines of the celestial sphere, indicated by numbers 1-14 in Figure 2.1.
- North pole of the world
- zenith; zenith point
- vertical line
- celestial equator
- west; west point
- center of the celestial sphere
- midday line
- south; point south
- skyline
- East; point east
- south pole of the world
- nadir; toka nadir
- north point
- line of the celestial meridian
8. Using Figure 2.1, answer the questions.
How is the axis of the world located relative to the earth's axis?
Parallel.
How is the axis of the world located relative to the plane of the celestial meridian?
Lies on a plane.
At what points does the celestial equator intersect with the horizon line?
At the points of the east and west.
At what points does the celestial meridian intersect with the horizon line?
At points north and south.
9. What observations convince us of the daily rotation of the celestial sphere?
If you watch the stars for a long time, the stars appear to be a single sphere.
10. Using a moving star chart, write in the table two or three constellations visible at latitude 55 ° in the Northern Hemisphere.
The solution to the 10th task corresponds to the reality of the events of 2015, however, not all teachers check the solution of the task of each student on the star map for compliance with reality
CELESTIAL SPHERE
When we observe the sky, all astronomical objects appear to be located on a domed surface with the observer in the center. This imaginary dome forms the upper half of an imaginary sphere, which is 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 of the star does not change as we move across the surface of the Earth. (True, it changes slightly as the Earth moves in 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 by about 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 the days are long and the 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 the 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, after a few centuries, the pole will no longer be near the North Star. In addition, the axis of the Earth performs 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 during which the Earth makes a revolution in relation to the stars ("sidereal days"), plus a short time - about four minutes - required for the rotation, which compensates for the Earth's orbital movement 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 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 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 in 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 the year associated with the revolution around the sun; 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 certain type of problem.
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 conventional 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, 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 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 geographic latitudes and longitudes. In it, the plane of the earth's equator, continued up 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 the "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. In the table, these systems are mapped 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 apex at the north pole of the world between the observer's meridian 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 point of observation. 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 a 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 to study or demonstrate. 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, a geometric projection system must be selected. 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 maps 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 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 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 seem 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 .
- 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 the determination of their coordinates on the celestial sphere. ... ... is 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 the determination of their coordinates on the celestial sphere. ... ... encyclopedic DictionaryAn imaginary auxiliary sphere of an arbitrary radius onto which the celestial bodies are projected; serves to solve various astrometric problems. Representation of N. with. originated in ancient times; it was based on the 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
