§ 48. Celestial sphere. Basic points, lines and circles on the celestial sphere
A celestial sphere is a sphere of any radius centered at an arbitrary point in space. For its center, depending on the statement of the problem, take the eye of the observer, the center of the tool, the center of the Earth, etc.Consider the main points and circles of the celestial sphere, for the center of which the eye of the observer is taken (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 the zenith Z and the nadir n.
Rice. 72.
The plane passing through the center of the celestial sphere perpendicular to the plumb line is called true horizon plane. This plane, intersecting with the celestial sphere, forms a circle of a great circle, called the true horizon. The latter divides the celestial sphere into two parts: the above-horizon and sub-horizon.
A straight line passing through the center of the celestial sphere parallel earth's axis, is called the axis y of the world. The points of intersection of the axis of the world with the celestial sphere are called the 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 called the south celestial pole Ps.
The plane QQ" 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 circle of a large 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 meridian of the observer PN nPsZ. The axis of the world divides the meridian of the observer into noon PN ZPs and midnight PN nPs parts.
The meridian of the observer intersects with the true horizon at two points: the north point N and the south point S. The straight line connecting the north and south points is called noon line.
If you look from the center of the sphere to point N, then the east point O st will be on the right, and the west point W will be on the left. 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, - celestial parallels.
Circles of the celestial sphere Zon passing through the zenith and nadir points are called verticals. The vertical passing through the points east and west is called the first vertical.
Circles of the celestial sphere PNoPs passing through the celestial poles are called declination circles.
The meridian of the observer is both a vertical and a circle of declination. It divides the celestial sphere into two parts - eastern and western.
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 of the same name with 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 geographic latitude of the place.
The position of the luminaries on the celestial sphere is determined using spherical coordinate systems. In nautical astronomy, horizontal and equatorial coordinate systems are used.
TEST . Celestial sphere (Gomulina N.N.)
1. The celestial sphere is:
A) an imaginary sphere of infinitely large radius, circumscribed around the center of the Galaxy;
B) a crystal sphere, on which, according to the ancient Greeks, luminaries are attached;
C) an imaginary sphere of arbitrary radius, the center of which is the eye of the observer.
D) an imaginary sphere - the conditional boundary of our Galaxy.
2. Celestial sphere:
A) is motionless, the Sun, the Earth, other planets and their satellites move along its inner surface;
B) rotates around an axis passing through the center of the Sun, the period of rotation of the celestial sphere is equal to the period of revolution of the Earth around the Sun, that is, one year;
C) rotates around the earth's axis with a period equal to the period of the earth's rotation around its axis, i.e. one day;
D) rotates around the center of the Galaxy, the period of rotation of the celestial sphere is equal to the period of rotation of the Sun around the center of the Galaxy.
3. The reason for the daily rotation of the celestial sphere is:
BUT) Proper movement stars;
B) The rotation of the Earth around its axis;
C) the movement of the earth around the sun;
D) The movement of the Sun around the center of the Galaxy.
4. Center of the celestial sphere:
A) coincides with the eye of the observer;
B) coincides with the center of the solar system;
C) coincides with the center of the Earth;
D) coincides with the center of the Galaxy.
5. North Pole of the World at present:
A) coincides with the North Star;
B) is located 1 °.5 from a Ursa Minor;
C) is located near the brightest star in the entire sky - Sirius;
D) is located in the constellation Lyra near the star Vega.
6. Constellation Ursa Major makes a complete revolution around the North Star in a time equal to
A) one night
B) one day;
B) one month
D) one year.
7. The axis of the world is:
A) a line passing through the zenith Z and nadir Z "and passing through the observer's eye;
B) a line connecting the points of the south S and the north N and passing through the eye of the observer;
C) a line connecting the points of east E and west W and passing through the eye of the observer;
D) A line connecting the poles of the world P and P "and passing through the eye of the observer.
8. The poles of the world are called points:
A) points of north N and south S.
B) points of east E and west W.
C) the points of intersection of the axis of the world with the celestial sphere P and P ";
D) northern and South Pole and the Earth.
9. The zenith point is called:
10. The nadir point is called:
A) the point of intersection of the celestial sphere with a plumb line, located above the horizon;
B) the point of intersection of the celestial sphere with a plumb line, located under the horizon;
C) the point of intersection of the celestial sphere with the axis of the world, located in the northern hemisphere;
D) the point of intersection of the celestial sphere with the axis of the world, located in the southern hemisphere.
11. The celestial meridian is called:
A) a plane passing through the noon line NS;
B) a plane perpendicular to the axis of the world P and P ";
C) a plane perpendicular to a plumb line passing through the zenith Z and nadir Z";
D) a plane passing through the north point N, the celestial poles P and P, the zenith Z, the south point S.
12. The noon line is called:
A) a line connecting the points of east E and west W;
B) a line connecting the points of the south S and the north N;
C) a line connecting the points of the pole of the world P and the pole of the world P";
D) a line connecting the points of the zenith Z and the nadir Z".
13. The apparent paths of the stars, when moving across the sky, are parallel
A) the celestial equator
B) celestial meridian;
B) the ecliptic
D) horizon.
14. Upper climax is:
A) the position of the luminary in which the height above the horizon is minimal;
B) the passage of the luminary through the zenith point Z;
C) the passage of the luminary through the celestial meridian and the achievement greatest height above the horizon;
D) the passage of the luminary at a height equal to the geographical latitude of the place of observation.
15. In the equatorial coordinate system, the main plane and main point are:
A) the plane of the celestial equator and the point of the vernal equinox g;
B) the plane of the horizon and the south point S;
C) meridian plane and south point S;
D) the plane of the ecliptic and the point of intersection of the ecliptic and the celestial equator.
16. Equatorial coordinates are:
A) declination and right ascension
B) zenith distance and azimuth;
B) altitude and azimuth;
D) zenith distance and right ascension.
17. Angle between the axis of the world and earth's axis is equal to: A) 66°.5; B) 0°; B) 90°; D) 23°.5.
18. The angle between the plane of the celestial equator and the axis of the world is: A) 66°.5; B) 0°; B) 90°; D) 23°.5.
19. The angle of inclination of the earth's axis to the plane of the earth's orbit is: A) 66°.5; B) 0°; B) 90°; D) 23°.5.
20. In what place on Earth does the daily movement of stars occur parallel to the horizon plane?
A) at the equator
B) at mid-latitudes northern hemisphere Earth;
B) at the poles
D) at mid-latitudes of the southern hemisphere of the Earth.
21. Where would you look for the North Star if you were at the equator?
A) at the zenith
B) on the horizon
22. Where would you look for the North Star if you were at the north pole?
A) at the zenith
B) at a height of 45 ° above the horizon;
B) on the horizon
D) at a height equal to the geographical latitude of the place of observation.
23. A constellation is called:
A) a certain figure of stars, in which the stars are combined conditionally;
B) a section of the sky with established boundaries;
B) the volume of the cone (co complex surface), going to infinity, the top of which coincides with the eye of the observer;
D) lines connecting the stars.
24. If the stars in our Galaxy move in different directions, and relative speed the movement of stars reaches hundreds of kilometers per second, it should be expected that the outlines of the constellations change noticeably:
(a) within one year;
B) for a time equal to the average duration of human life;
B) for centuries
D) for thousands of years.
25. In total, there are constellations in the sky: A) 150; B) 88; B) 380; D) 118.
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 |
| AT | AT | B | BUT | B | B | G | AT | BUT | B | G | B | BUT | AT | BUT | BUT | B | AT | BUT | AT | AT | BUT | B | G | B |
It seems to us that all the stars are located on some spherical surface of the sky and are equally distant from the observer. In fact, they are at different distances from us, which are so huge that the eye cannot notice these differences. Therefore, an imaginary spherical surface began to be called the celestial sphere.
Celestial sphere- this is an imaginary sphere of arbitrary radius, the center of which, depending on the problem being solved, is combined with one or another point in space. The center of the celestial sphere can be chosen at the place of observation (the eye of the observer), at the center of the Earth or the Sun, etc. The concept of the celestial sphere is used for angular measurements, for studying relative position and movement of space objects in the sky.
The visible positions of all the stars are projected onto the surface of the celestial sphere, and for the convenience of measurements, a series of points and lines are built on it. For example, some of the stars of the Ursa Major "bucket" are far from one another, but for an earthly observer they are projected onto the same part of the celestial sphere.
A straight line passing through the center of the celestial sphere and coinciding with the direction of the plumb line at the point of observation is called sheer or vertical line. It crosses the celestial sphere at points zenith(upper point of intersection of the plumb line with the celestial sphere) and nadir(the point on the celestial sphere opposite the zenith). The plane passing through the center of the celestial sphere and perpendicular to the plumb line is called plane of true or mathematical horizon.
vertical circle, or vertical luminary, is a large circle of the celestial sphere, passing through the zenith, the luminary and the nadir.
world axis- a straight line passing through the center of the celestial sphere parallel to the axis of rotation of the Earth, intersecting the celestial sphere at two diametrically opposite points.
The point of intersection of the axis of the world with the celestial sphere, near which the Polar Star is located, is called North Pole of the World, opposite point - South Pole of the World. Polaris is at a distance from the north celestial pole angular distance about 1° (more precisely 44′).
A large circle passing through the center of the celestial sphere and perpendicular to the axis of the world is called celestial equator. It divides the celestial sphere into two parts: North hemisphere with a peak at the North Pole of the World and Southern- with a peak at the South Pole of the world.
Declension circle luminaries - a large circle of the celestial sphere, passing through the poles of the world and the luminary.
Daily parallel- a small circle of the celestial sphere, the plane of which is perpendicular to the axis of the world.
The great circle of the celestial sphere passing through the zenith, nadir and celestial poles is called celestial meridian. The celestial meridian intersects with the true horizon at two diametrically opposite points. The point of intersection of the true horizon and the celestial meridian, closest to the North Pole of the world, is called north point. The point of intersection of the true horizon and the celestial meridian, closest to the South Pole of the World, is called south point. The line connecting the north and south points is called noon line. It lies on the plane of the true horizon. In the direction of the midday line, shadows from objects fall at noon.
The true horizon also intersects with the celestial equator at two diametrically opposite points - east point and west point. For an observer standing in the center of the celestial sphere facing the north point, the east point will be on the right and the west point on the left. Keeping this rule in mind, it is easy to navigate the terrain.
Lecture number 2. Celestial sphere, its main points.
1. Horizontal and equatorial systems of celestial coordinates.
2. Right ascension. Declination of the luminary.
3. Carrying out evening astronomical observations of the starry sky.
Celestial sphere. Basic points, lines and circles on the celestial sphere
A celestial sphere is a sphere of any radius centered at an arbitrary point in space. For its center, depending on the statement of the problem, take the eye of the observer, the center of the tool, the center of the Earth, etc.
Consider the main points and circles of the celestial sphere, for the center of which the eye of the observer is taken (Fig. 72). Draw through the center of the celestial sphere plumb line. The points of intersection of the plumb line with the sphere are called the zenith Z and the nadir n.
Rice. 72.
The plane passing through the center of the celestial sphere perpendicular to the plumb line is calledtrue horizon plane.
This plane, intersecting with the celestial sphere, forms a circle of a great circle, called the true horizon. The latter divides the celestial sphere into two parts: the above-horizon and sub-horizon.
A straight line passing through the center of the celestial sphere parallel to the earth's axis is called the axis of the world. The points of intersection of the axis of the world with the celestial sphere are called the 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 called the south celestial pole Ps.
The plane QQ" 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 circle of a large 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 meridian of the observer PN nPsZ. The axis of the world divides the meridian of the observer into noon PN ZPs and midnight PN nPs parts.
The meridian of the observer intersects with the true horizon at two points: the north point N and the south point S. The straight line connecting the north and south points is called noon line.
If you look from the center of the sphere to point N, then the east point O will be on the right st , and on the left - the west point W. Small circles of the celestial sphere aa "parallel to the plane of the true horizon are calledalmucantarates; small bb" parallel to the plane of the celestial equator, -celestial parallels.
Circles of the celestial sphere Zon passing through the zenith and nadir points are called verticals. The vertical passing through the points east and west is called the first vertical.
Circles of the celestial sphere PNoPs passing through the celestial poles are called declination circles.
The meridian of the observer is both a vertical and a circle of declination. It divides the celestial sphere into two parts - eastern and western.
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 of the same name with 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 geographic latitude of the place.
The position of the luminaries on the celestial sphere is determined using spherical coordinate systems. In nautical astronomy, horizontal and equatorial coordinate systems are used.
The concept of the celestial sphere arose 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 great distance heavenly bodies the human eye is unable to appreciate the differences in their distances, 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 development scientific knowledge such a view of the celestial sphere fell away. However, the geometry of the celestial sphere laid down in antiquity, as a result of development and improvement, received modern look, which is used in astrometry.
Elements of the celestial sphere
Plumb line and related concepts
Chart showing ratio , and (in various definitions). Note that the zenith is opposite to the nadir.
plumb line - a straight line passing through the center of the celestial sphere and an observation point on the surface of the Earth. The plumb line intersects with the surface of the celestial sphere at two points - over the observer's head and under the feet of the observer.
True (mathematical) horizon - a great circle of the celestial sphere, the plane of which is perpendicular to the plumb line. The true horizon divides the surface of the celestial sphere into two hemispheres:visible hemisphere with the top at the zenith andinvisible hemisphere with the top in the nadir. The true 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 curvature of light rays in the atmosphere.
height circle or vertical luminaries - a large semicircle of the celestial sphere, passing through the luminary, zenith and nadir.Almuqantarat (arab. " "") - a small circle of the celestial sphere, the plane of which is parallel to the plane of the mathematical horizon. Altitude circles and almucantarata form a coordinate grid that sets the horizontal coordinates of the luminary.
Daily rotation of the celestial sphere and related concepts
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 world and south pole of the world . The rotation of the celestial sphere occurs counterclockwise around the north pole, when viewed from the inside of the celestial sphere.
A great circle of the celestial sphere, the plane of which is perpendicular to the axis of the world and passes through the center of the celestial sphere. The celestial equator divides the celestial sphere into two hemispheres:northern and southern .
Luminary declination circle - a large circle of the celestial sphere, passing through the poles of the world and this luminary.
Daily parallel - a small circle of the celestial sphere, the plane of which is parallel to the plane of the celestial equator. The visible daily movements of the luminaries occur along daily parallels. Circles of declination and daily parallels form a coordinate grid on the celestial sphere that sets the equatorial coordinates of the star.
Terms born at the intersection of the concepts "Plumb line" and "Rotation of the celestial sphere"
The celestial equator intersects the mathematical horizon ateast point and west point . The point of the east is the one in which the points of the rotating celestial sphere rise from the horizon. The height semicircle passing through the east point is calledfirst vertical .
sky meridian - a large circle of the celestial sphere, the plane of which passes through the plumb line and the axis of the world. The celestial meridian divides the surface of the celestial sphere into two hemispheres:eastern hemisphere and western hemisphere .
noon line - the line of intersection of the plane of the celestial meridian and the plane of the mathematical horizon. The midday line and the celestial meridian cross the mathematical horizon at two points:north point and south point . The north point is the one that is closer to the north pole of the world.
Annual motion of the Sun in the celestial sphere and related concepts
P, P" - celestial poles, T, T" - equinox points, E, C - solstice points, P, P" - ecliptic poles, PP" - world axis, PP" - ecliptic axis, ATQT" - celestial equator, ETCT "- ecliptic
The great circle of the celestial sphere, along which the apparent annual movement occurs . The plane of the ecliptic intersects with the plane of the celestial equator at an angle ε = 23°26".
The two points where the ecliptic intersects the celestial equator are called points. AT vernal equinox point The sun in its annual movement passes from the southern hemisphere of the celestial sphere to the northern; inpoint of the autumnal equinox from the northern hemisphere to the southern. The two points on the ecliptic that are 90° from the equinoxes and thus the furthest from the celestial equator are called the points . Summer solstice point located in the northern hemispherewinter solstice point - in the southern hemisphere. These four points are symbolized♈ ), the autumn equinox - the sign of Libra (♎ ), the winter solstice - the sign of Capricorn (♑ ), the summer solstice - the sign of Cancer (♋ )
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 ecliptic pole , lying in the northern hemisphere, andsouth ecliptic pole located in the southern hemisphere. The north ecliptic pole has equatorial coordinates R.A. = 18h00m, Dec = +66°33", and is in the constellation , and the south pole is R.A. = 6h00m, Dec = -66°33" in constellation .
Circle of ecliptic latitude , or simply circle of latitude - a large semicircle of the celestial sphere, passing through the poles of the ecliptic.
3. Heavenly sphere. The main 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 located on the surface of the Earth reproduces diurnal movement shone in the sky
ZOZ"- sheer (vertical) line,
SWNE is the true (mathematical) horizon,
aMa"- almucantarat,
ZMZ" – height circle (vertical circle), or vertical
P 
OP" - the axis of rotation of the celestial sphere (the axis of the world),
P – North Pole peace,
P" - the south pole of the world,
Ð pon= j (latitude of the observation site),
QWQ" E- celestial equator
bMb"- diurnal parallel,
PMP"- circle of declination,
PZQSP" Z" Q" N- celestial meridian
NOS- noon 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 luminary on the celestial sphere is uniquely determined by two angular coordinates, if the main plane and the origin are given.
In spherical astronomy, the following celestial coordinate systems are used:
Horizontal, 1st equatorial, 2nd equatorial, ecliptic
Horizontal coordinate system
The main plane is the plane of the mathematical horizon
1
)Ð mOM
= h
(height)
0 £ h£900
–90 0 £ h £ 0
or Р ZOM = z (zenith distance)
0 £ z£180 0
z + h = 90 0
2) R 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 (declension)
0 £d £900
–90 0 £d £ 0
or Р POM = p (pole distance)
0 £ p£180 0
p+d = 90 0
2) R QOm = t (hour angle)
0 £ t£360 0
or 0h £ t£24h
All horizontal coordinates ( h, z, A) and hour angle t of the first equatorial SC continuously change during the daily rotation of the celestial sphere.
The declination d does not change.
Must be entered instead t such an equatorial coordinate, which would be counted from a point fixed on the celestial sphere.
2nd equatorial coordinate system
O 
the main plane is the plane of the celestial equator
1) Р mOM=d (declension)
0 £d £900
–90 0 £d £ 0
or Р POM = p (pole distance)
0
£
p£180 0
p+d = 90 0
2) Р ¡ Om= a (right ascension)
or 0 h £ a £ 24 h
The horizontal SC is used to determine the direction to the luminary relative to terrestrial objects.
The 1st equatorial SC is used primarily in 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" - the axis of the ecliptic
E - point of summer solstice
E" - winter solstice point
one) m = λ (ecliptic longitude)
2) mm= b (ecliptic latitude)
5. Daily rotation of the celestial sphere at different latitudes, phenomena associated with it. daily movement of the sun. Change of seasons and thermal zones.
Measurements of the height of the Sun at noon (i.e. at the moment of its upper culmination) at the same geographical 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.
The right ascension of the Sun a Ÿ during 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.
On March 20-21, the Sun is at point ¡, its declination δ Ÿ = 0 and right ascension a Ÿ = 0. On this day (the vernal equinox), the Sun rises exactly at the point E and enters the point W. The maximum height of the center of the Sun above the horizon at noon of 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. δŸ > 0 and aŸ > 0.
On June 21-22, the Sun is at point E, its declination is maximum δ Ÿ \u003d 23 0 26 ", and right ascension a Ÿ \u003d 6 h. At noon on this day (summer solstice), the Sun rises to its maximum height above the horizon: hŸ = 90 0 - φ + 23 0 26"
Thus, in the middle latitudes, the Sun is NEVER 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 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 during the year occurs unevenly.
The declination changes fastest when the Sun moves near the equinoxes, and slowest when the sun moves near the solstices.
Right Ascension, on the other hand, changes more slowly near the equinoxes and faster near the solstices.
The apparent movement of the Sun along the ecliptic is associated with the actual movement of the Earth in its orbit around the Sun, as well as with the fact that the axis of rotation of the Earth is not perpendicular to the plane of its orbit, but makes up 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 (without taking into account refraction and the size of the Sun).
Polar days, lasting from 24 h to half a year and the corresponding nights, are observed in the polar circles, the latitudes of which are determined by the conditions:
φ \u003d ± (90 0 - ε) \u003d ± 66 0 34 "
The position of the axis of the world and, consequently, the plane of the celestial equator, as well as the points ¡ and d, is not constant, but changes periodically.
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 for 26,000 years.
Due to the perturbing 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 their intersection points (¡ and d) slowly move to the west.
Movement 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 autumn equinox was in the constellation Libra (d). Since then, point ¡ has moved to the constellation Pisces, and point d has moved to the constellation Virgo, but their designations have remained the same.
| " |
