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 bucket stars Ursa Major 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 away from North Pole peace on 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 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 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 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 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 enormous remoteness of the celestial bodies, the human eye is not able to appreciate the differences in the distances to them, and they appear to be equally distant. Among the ancient peoples, this was associated with the presence of a real sphere that bounds the whole world and carries numerous stars on its surface. Thus, in their view, the celestial sphere was the most important element of the universe. With 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 peace . 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 northern hemisphere to the south. 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.
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. To do 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 set in expediently chosen coordinate systems. As known from analytical geometry, to determine the position of the star 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 star s is determined by three linear coordinates X, Y, Z. In the polar coordinate system, the position of the star s is given by one linear coordinate, the radius vector R = Оs 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 coordinate plane XOY 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 Earth). However, for many luminaries observed outside solar system, these distances are either extremely large compared to the radius of the Earth, or unknown. To simplify the solution of astronomical problems and to do without distances to the luminaries, it is believed that all the luminaries are at an arbitrary, but the same distance from the observer. This distance is usually 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 body 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 celestial sphere - the center is on the surface of the Earth;
2)geocentric 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 located in 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 point of observation. This direction intersects the celestial sphere at two diametrically opposite points - Z and Z. The Z point is 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 great circle NESW 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 is south point,N- north point, W - point of the West, E- point of the East. The straight line NS is called noon 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. Visible happens around the axis of the World diurnal movement celestial sphere.
Let us draw a plane through the center, perpendicular to the axis of the world P N P S . The great circle QWQ "E, formed as a result of the intersection of this plane of the celestial sphere, is called celestial (astronomical) equator. Here Q is the highest point of the equator(above the horizon), Q "- the lowest point of the equator(under the horizon). The celestial equator and celestial horizon intersect at points W and E.
The plane P N ZQSP S Z "Q" N, containing a 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 the equator. It is called the initial coordinate 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 luminary s intersects the celestial sphere is called vertically or around the heights of the luminary.
The great 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 daily parallel. The visible daily movement of the luminaries occurs along the daily parallels.
A small circle asa "passing through the luminary in parallel heavenly horizon, is called circle of equal heights, or almucantarat.
In the first approximation, the Earth's orbit can be taken as a flat curve - an ellipse, in one of the foci of which is the Sun. The plane of the ellipse taken as the orbit of the Earth , called a plane ecliptic.
In spherical astronomy, it is customary to talk about apparent annual motion of the sun. The great 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 . On fig. 4 shown:
g is the vernal equinox point;
d is the point of the autumnal equinox;
E is the point of the summer solstice; E" - the point of the winter solstice; R N R S - the axis of the ecliptic; R N - the north pole of the ecliptic; R S - the south pole of the ecliptic; e - the inclination of the ecliptic to the equator.
Topic 4. HEAVENLY SPHERE. ASTRONOMIC COORDINATE SYSTEMS
4.1. CELESTIAL SPHERE
Celestial sphere - an imaginary sphere of arbitrary radius, onto which celestial bodies are projected. Serves for solving various astrometric problems. As a rule, the eye of the observer is taken as the center of the celestial sphere. For an observer on the surface of the Earth, the rotation of the celestial sphere reproduces the daily movement of the luminaries in the sky.
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 enormous remoteness of the celestial bodies, the human eye is not able to appreciate the differences in the distances to them, and they appear to be equally distant. Among the ancient peoples, this was associated with the presence of a real sphere that bounds the whole world and carries numerous stars on its surface. Thus, in their view, the celestial sphere was the most important element of the universe. With the development of scientific knowledge, 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, has received a modern form, in which it is used in astrometry.
The radius of the celestial sphere can be taken as anything: in order to simplify geometric relationships, it is assumed to be equal to one. Depending on the problem being solved, the center of the celestial sphere can be placed in the place:
where the observer is located (topocentric celestial sphere),
to the center of the Earth (geocentric celestial sphere),
to the center of a particular planet (planet-centric celestial sphere),
to the center of the Sun (heliocentric celestial sphere) or to any other point in space.
Each luminary on the celestial sphere corresponds to a point at which it is intersected by a straight line connecting the center of the celestial sphere with the luminary (with its center). When studying the relative position and visible movements of the luminaries on the celestial sphere, one or another coordinate system is chosen), determined by the main points and lines. The latter are usually large circles of the celestial sphere. Each great circle of a sphere has two poles, defined on it by the ends of a diameter perpendicular to the plane of the given circle.
Names of the most important points and arcs on the celestial sphere
plumb line (or vertical line) - a straight line passing through the centers of the Earth and the celestial sphere. The plumb line intersects with the surface of the celestial sphere at two points - zenith , above the observer's head, and nadir - diametrically opposite point.
math horizon - a great circle of the celestial sphere, the plane of which is perpendicular to the plumb line. The plane of the mathematical horizon passes through the center of the celestial sphere and divides its surface into two halves: visible for the observer, with the top at the zenith, and invisible, with a nadir apex. The mathematical horizon may not coincide with the visible horizon due to the unevenness of the Earth's surface and the different heights of observation points, as well as the curvature of light rays in the atmosphere.
Rice. 4.1. Celestial sphere
world axis - the axis of apparent rotation of the celestial sphere, parallel to the axis of the Earth.
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 .
Celestial pole - a point on the celestial sphere around which the apparent daily movement of stars occurs due to the rotation of the Earth around its axis. The north celestial pole is in the constellation Ursa Minor, southern in the constellation Octant. As a result precession The poles of the world are moving about 20" per year.
The height of the world pole is equal to the latitude of the observer's place. The celestial pole, located in the above-horizon part of the sphere, is called elevated, while the other celestial pole, located in the sub-horizon part of the sphere, is called reduced.
Celestial equator - a large circle of the celestial sphere, the plane of which is perpendicular to the axis of the world. The celestial equator divides the surface of the celestial sphere into two hemispheres: northern hemisphere , with its apex at the north celestial pole, and Southern Hemisphere , with a peak at the south celestial pole.
The celestial equator intersects the mathematical horizon at two points: point east and point west . The east point is the one at which the points of the rotating celestial sphere cross the mathematical horizon, passing from the invisible hemisphere to the visible one.
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 , with apex at the east point, and western hemisphere , with apex at the west point.
Midday line - line of intersection of the plane of the celestial meridian and the plane of the mathematical horizon.
sky meridian intersects 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.
Ecliptic - the trajectory of the apparent annual movement of the Sun in the celestial sphere. The plane of the ecliptic intersects with the plane of the celestial equator at an angle ε = 23°26".
The ecliptic intersects with the celestial equator at two points - spring and autumn equinoxes . At the point of the vernal equinox, the Sun moves from the southern hemisphere of the celestial sphere to the northern one, at the point of the autumn equinox, from the northern hemisphere of the celestial sphere to the southern one.
The points on the ecliptic that are 90° from the equinoxes are called dot summer solstice (in the northern hemisphere) and dot winter solstice (in the southern hemisphere).
Axis ecliptic - the diameter of the celestial sphere perpendicular to the plane of the ecliptic.
4.2. Main lines and planes of the celestial sphere
The axis of the ecliptic intersects with the surface of the celestial sphere at two points - north ecliptic pole , lying in the northern hemisphere, and south ecliptic pole, lying in the southern hemisphere.
Almukantarat (Arabic circle of equal heights) luminaries - a small circle of the celestial sphere, passing through the luminary, the plane of which is parallel to the plane of the mathematical horizon.
height circle or vertical a circle or vertical luminaries - a large semicircle of the celestial sphere, passing through the zenith, the luminary and the nadir.
Daily parallel luminaries - a small circle of the celestial sphere, passing through the luminary, the plane of which is parallel to the plane of the celestial equator. The visible daily movements of the luminaries occur along daily parallels.
A circle declination luminaries - a large semicircle of the celestial sphere, passing through the poles of the world and the luminary.
A circle ecliptic latitude , or simply the circle of latitude of the luminary - a large semicircle of the celestial sphere, passing through the poles of the ecliptic and the luminary.
A circle galactic latitude luminaries - a large semicircle of the celestial sphere, passing through the galactic poles and the luminary.
2. ASTRONOMIC COORDINATE SYSTEMS
The celestial coordinate system is used in astronomy to describe the position of luminaries in the sky or points on an imaginary celestial sphere. The coordinates of luminaries or points are given by two angular values (or arcs) that uniquely determine the position of objects on the celestial sphere. Thus, the celestial coordinate system is a spherical coordinate system, in which the third coordinate - distance - is often unknown and does not play a role.
Celestial coordinate systems differ from each other in the choice of the main plane. Depending on the task at hand, it may be more convenient to use one system or the other. The most commonly used are horizontal and equatorial coordinate systems. Less often - ecliptic, galactic and others.
Horizontal coordinate system
The horizontal coordinate system (horizontal) is a celestial coordinate system in which the main plane is the plane of the mathematical horizon, and the poles are the zenith and nadir. It is used in observations of stars and the movement of the celestial bodies of the solar system on the ground with the naked eye, through binoculars or a telescope. The horizontal coordinates of the planets, the Sun and stars change continuously during the day due to the daily rotation of the celestial sphere.
Lines and planes
The horizontal coordinate system is always topocentric. The observer is always at a fixed point on the earth's surface (marked with O in the figure). We will assume that the observer is in the Northern Hemisphere of the Earth at latitude φ. With the help of a plumb line, the direction to the zenith (Z) is determined as the upper point to which the plumb line is directed, and the nadir (Z ") as the lower one (under the Earth). Therefore, the line (ZZ") connecting the zenith and the nadir is called a plumb line.
4.3. Horizontal coordinate system
The plane perpendicular to the plumb line at the point O is called the plane of the mathematical horizon. On this plane, the direction to the south (geographical) and north is determined, for example, in the direction of the shortest shadow from the gnomon during the day. It will be shortest at true noon, and the line (NS) connecting south to north is called the noon line. The east (E) and west (W) points are taken 90 degrees from the south point, respectively, counterclockwise and clockwise, as viewed from the zenith. Thus, NESW is the plane of the mathematical horizon
The plane passing through the midday and plumb lines (ZNZ "S) is called plane of the celestial meridian , and the plane passing through the celestial body - the vertical plane of a given celestial body . The great circle in which she crosses the celestial sphere, called the vertical of a celestial body .
In the horizontal coordinate system, one coordinate is either star height h, or his zenith distance z. Another coordinate is the azimuth A.
Height h luminaries called the arc of the vertical of the luminary from the plane of the mathematical horizon to the direction of the luminary. Heights are measured within the range from 0° to +90° to the zenith and from 0° to −90° to the nadir.
The zenith distance z of the luminaries called the vertical arc of the luminary from the zenith to the luminary. Zenith distances are counted from 0° to 180° from zenith to nadir.
Azimuth A of the luminary called the arc of the mathematical horizon from the point of the south to the vertical of the star. Azimuths are measured in the direction of the daily rotation of the celestial sphere, that is, to the west of the south point, in the range from 0 ° to 360 °. Sometimes azimuths are measured from 0° to +180° to the west and from 0° to −180° to the east (in geodesy, azimuths are measured from the north point).
Features of changing the coordinates of celestial bodies
During the day, the star describes a circle perpendicular to the axis of the world (PP"), which at latitude φ is inclined to the mathematical horizon at an angle φ. Therefore, it will move parallel to the mathematical horizon only at φ equal to 90 degrees, that is, at the North Pole. Therefore, all stars, visible there, will not set (including the Sun for half a year, see the length of the day) and their height h will be constant.At other latitudes, the stars available for observation at a given time of the year are divided into:
incoming and outgoing (h passes through 0 during the day)
non-incoming (h is always greater than 0)
non-ascending (h is always less than 0)
The maximum height h of a star will be observed once a day during one of its two passages through the celestial meridian - the upper culmination, and the minimum - during the second of them - the lower culmination. From the lower to the upper culmination, the height h of the star increases, from the upper to the lower it decreases.
First equatorial coordinate system
In this system, the main plane is the plane of the celestial equator. In this case, one coordinate is the declination δ (less often, the polar distance p). Another coordinate is the hour angle t.
The declination δ of the luminary is the arc of the circle of declination from the celestial equator to the luminary, or the angle between the plane of the celestial equator and the direction to the luminary. Declinations are counted from 0° to +90° to the north celestial pole and from 0° to −90° to the south celestial pole.
4.4. Equatorial coordinate system
The polar distance p of the luminary is the arc of the circle of declination from the north pole of the world to the luminary, or the angle between the axis of the world and the direction to the luminary. Polar distances are measured from 0° to 180° from the north celestial pole to the south.
The hourly angle t of the luminary is the arc of the celestial equator from the upper point of the celestial equator (that is, the point of intersection of the celestial equator with the celestial meridian) to the circle of declination of the luminary, or the dihedral angle between the planes of the celestial meridian and the circle of declination of the luminary. Hourly angles are measured in the direction of the daily rotation of the celestial sphere, that is, to the west of the upper point of the celestial equator, ranging from 0 ° to 360 ° (in degrees) or from 0h to 24h (in hours). Sometimes hour angles are measured from 0° to +180° (0h to +12h) to the west and from 0° to −180° (0h to −12h) to the east.
Second equatorial coordinate system
In this system, as in the first equatorial system, the main plane is the plane of the celestial equator, and one coordinate is the declination δ (less often, the polar distance p). Another coordinate is right ascension α. The right ascension (RA, α) of the luminary is the arc of the celestial equator from the vernal equinox to the circle of declination of the luminary, or the angle between the direction to the vernal equinox and the plane of the circle of declination of the luminary. Right ascensions are counted in the direction opposite to the daily rotation of the celestial sphere, ranging from 0° to 360° (in degrees) or from 0h to 24h (in hours).
RA is the astronomical equivalent of Earth's longitude. Both RA and longitude measure the east-west angle along the equator; both measures are measured from the zero point at the equator. For longitude, zero point is the prime meridian; for RA, zero is the location in the sky where the Sun crosses the celestial equator at the vernal equinox.
Declination (δ) in astronomy is one of the two coordinates of the equatorial coordinate system. It is equal to the angular distance on the celestial sphere from the plane of the celestial equator to the luminary and is usually expressed in degrees, minutes and seconds of arc. The declination is positive north of the celestial equator and negative south. The declension always has a sign, even if the declension is positive.
The declination of a celestial object passing through the zenith is equal to the latitude of the observer (assuming north latitude is + and south latitude is negative). In the northern hemisphere of the Earth, for a given latitude φ, celestial objects with declination
δ > +90° − φ do not go beyond the horizon, therefore they are called non-setting. If the declination of the object δ
Ecliptic coordinate system
In this system, the main plane is the plane of the ecliptic. In this case, one coordinate is the ecliptic latitude β, and the other is the ecliptic longitude λ.
4.5. Relationship between the ecliptic and the second equatorial coordinate system
The ecliptic latitude β of the luminary is the arc of the circle of latitude from the ecliptic to the luminary, or the angle between the plane of the ecliptic and the direction to the luminary. Ecliptic latitudes are measured from 0° to +90° to the north ecliptic pole and from 0° to −90° to the south ecliptic pole.
The ecliptic longitude λ of the luminary is the arc of the ecliptic from the point of the vernal equinox to the circle of latitude of the luminary, or the angle between the direction to the point of the vernal equinox and the plane of the circle of latitude of the luminary. Ecliptic longitudes are measured in the direction of the apparent annual movement of the Sun along the ecliptic, that is, east of the vernal equinox in the range from 0 ° to 360 °.
Galactic coordinate system
In this system, the main plane is the plane of our Galaxy. In this case, one coordinate is the galactic latitude b, and the other is the galactic longitude l.
4.6. Galactic and second equatorial coordinate systems.
The galactic latitude b of the luminary is the arc of the circle of galactic latitude from the ecliptic to the luminary, or the angle between the plane of the galactic equator and the direction to the luminary.
Galactic latitudes are measured from 0° to +90° to the north galactic pole and from 0° to −90° to the south galactic pole.
The galactic longitude l of the luminary is the arc of the galactic equator from the reference point C to the circle of the luminary's galactic latitude, or the angle between the direction to the reference point C and the plane of the circle of the galactic latitude of the luminary. Galactic longitudes are counted counterclockwise when viewed from the north galactic pole, that is, east of the reference point C, ranging from 0° to 360°.
Reference point C is located near the direction to the galactic center, but does not coincide with it, since the latter, due to the slight elevation of the solar system above the plane of the galactic disk, lies approximately 1 ° south of the galactic equator. The reference point C is chosen so that the point of intersection of the galactic and celestial equators with right ascension 280° has a galactic longitude of 32.93192° (for epoch 2000).
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All points of the celestial sphere of five letters are listed below. A brief description is given for each of the definitions.
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North
One of the four conventionally accepted cardinal directions, which is opposite to the south. On the geographical map predominantly located at the top and is indicated capital letter C (international designation N - north).
A magnetized compass needle always points north. The etymology of this word comes from Old Russian language, in translation "cold", "cold wind". Also, the North (Far North) is called the area that lies in this direction. The Far North and the North Pole are part of the territory of Russia.
It should be noted that, as a geographical feature, the North Pole does not exist. This is a certain point that marks the axis of the Earth. The British James and John Ross were the first to tell about the existence of the North Pole. But the debate about who nevertheless discovered it first is still going on. Due to the harsh climate (in winter - about - 40C, in summer about 0C) animal world very scarce. Polar bears, walruses, seals mainly live here. And because of eternal ice no vegetation at all.
West
One of the four sides of the world conventionally accepted by man. The west point lies at the intersection of the celestial equator and the horizon, midway between north and south and opposite east. On the geographical map, the west is indicated on the left by the letter З (international designation - W "west"). The word came to us from ancient times. Originally, the word west meant "sunset" because the Sun sets in the west ("sets" below the horizon), due to the rotation of the Earth around an imaginary axis from west to east. The West is also called the area lying in this direction.
Zenith
The etymology of this word is very complex. The word zenith is considered an error word, i.e. when borrowing words from other languages, a mistake is made in the word. So when borrowing the word zenith from Arabic, a typing error was made. In the Arabic word "zamt", which meant "the highest point of the sky", "m" was confused with "in" and the word "zanit" was obtained, later it turned into "zenit". Zenith is a kind of imaginary celestial point, which is above the observer's head.
Simply put, the zenith is the direction that points "up" from a given point on the earth, a direction that is strictly opposite to the direction of gravity at that location. The angle between the horizon and the zenith is 90. The term zenith also refers to the highest point reached by some celestial body, as it moves in orbit. So the word zenith is often used to determine the position of the Sun. There is an expression "The sun is at its zenith", i.e. The sun has reached highest point above the horizon at that location.
Nadir
This word is borrowed from Arabic. A nadir is an imaginary celestial point at which the celestial sphere and a vertical line pointing down from the observation point intersect. This point is located on the other half of the celestial sphere, invisible to humans because of the globe. Nadir is opposite to the zenith point, i.e. under the feet of the observer, on the other side of the Earth. The angle between the nadir and the horizon is 90°. Simply put, the nadir is the direction opposite to the zenith, and therefore the direction that coincides with the direction of gravity.
Apex
This term has Latin roots. The exact meaning of the word apex is "apex" from the Latin "apex". Apex is a certain point that is located in the celestial sphere, space objects are moving towards it at the moment. The opposite point is called the antiapex. Since all objects in the universe are under the influence of gravitational forces and do not move in a straight line, then their apexes are constantly shifting.
