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, the imaginary spherical surface began to be called the celestial sphere.
Celestial sphere 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, to study the 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 number of points and lines are built on it. For example, some of the stars of the Big Dipper "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 place of observation is called sheer or vertical line... She crosses the celestial sphere at points zenith(the upper point of intersection of the plumb line with the celestial sphere) and nadira(point of 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, - this is a large circle of the celestial sphere passing through the zenith, luminary and nadir.
Axis of the world- a straight line passing through the center of the celestial sphere parallel to the axis of rotation of the Earth, crossing 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 North Star is located, is called North Pole of the World, the opposite point is The south pole of the world... The North Star is located at an angular distance of about 1 ° (more precisely 44 ′) from the North Pole of the world.
The large circle passing through the center of the celestial sphere and perpendicular to the axis of the world is called celestial equator... He divides the celestial sphere into two parts: North hemisphere with a summit at the North Pole of the world and Yuzhnoe- with a summit at the South Pole of the world.
Declination circle luminaries - a large circle of the celestial sphere passing through the poles of the world and the luminary.
Diurnal 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 poles of the world is called heavenly meridian... The celestial meridian intersects with the true horizon at two diametrically opposite points. The intersection point of the true horizon and the celestial meridian, closest to the North Pole of the world, is called point north... The point of intersection of the true horizon and the celestial meridian, closest to the South Pole of the world, is called point south... The line connecting the points north and south is called midday line... It lies on the plane of the true horizon. Shadows from objects fall in the direction of the noon line at noon.
The true horizon also intersects with the celestial equator at two diametrically opposite points - point east and point west... For an observer standing in the center of the celestial sphere facing north, 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. The celestial sphere, its main points.
1. Horizontal and equatorial celestial coordinate systems.
2. Right ascension. The declination of the luminary.
3. Carrying out evening astronomical observations of the starry sky.
Celestial sphere. Major points, lines and circles on the celestial sphere
The celestial sphere is called a sphere of any radius centered at an arbitrary point in space. For its center, depending on the formulation of the problem, the eye of the observer, the center of the instrument, the center of the Earth, etc. are taken.
Consider the main points and circles of the celestial sphere, for the center of which is taken the eye of the observer (Fig. 72). Draw a plumb line through the center of the celestial sphere. The points of intersection of the plumb line with the sphere are called the zenith Z and nadir n.
Rice. 72.
The plane passing through the center of the celestial sphere perpendicular to the plumb line is calledplane of the true horizon.
This plane, intersecting with the celestial sphere, forms a large circle, called the true horizon. The latter divides the celestial sphere into two parts: suprahorizontal and subhorizontal.
The straight line passing through the center of the celestial sphere parallel to the earth's axis is called the y axis of the world. The points of intersection of the axis of the world with the celestial sphere are called poles of the world. One of the poles, corresponding to the poles of the Earth, is called the north pole of the world and denotes Pn, the other - the south pole of the world Ps.
The plane QQ "passing through the center of the celestial sphere perpendicular to the axis of the world is called the plane of the celestial equator. This plane, intersecting with the celestial sphere, forms the circumference of a great circle -celestial equator, which divides the celestial sphere into northern and southern parts.
The great circle of the celestial sphere passing through the poles of the world, zenith and nadir, is called observer meridian PN nPsZ. The axis of the world divides the observer's meridian into noon PN ZPs and midnight PN nPs.
The observer's meridian intersects with the true horizon at two points: the north point N and the south point S. The straight line connecting the points north and south is called the midday line.
If you look from the center of the sphere 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 calledalmucantaras; small bb "parallel to the plane of the celestial equator, -heavenly parallels.
The circles of the Zon celestial sphere passing through the zenith and nadir points are called verticals. The vertical passing through the points of east and west is called the first vertical.
The circles of the celestial sphere PNoPs passing through the poles of the world are called circles of declination.
The observer's meridian is both the vertical and the declination circle. He divides the celestial sphere into two parts - east and west.
The pole of the world located above the horizon (below the horizon) is called the elevated (lowered) pole of the world. The name of the elevated pole of the world is always the same name as the name of the latitude of a place.
The axis of the world with the plane of the true horizon makes an angle equal to the geographical latitude of the place.
The position of the luminaries on the celestial sphere is determined using spherical coordinate systems. In nautical astronomy, the horizontal and equatorial coordinate systems are used.
The concept of the celestial sphere originated in ancient times; it was based on the visual impression of the existence of a domed firmament. This impression is due to the fact that as a result of the enormous remoteness of the celestial bodies, the human eye is not able to assess the differences in the distances to them, and they appear to be equally distant. The ancient peoples associated this with the presence of a real sphere that bounds the whole world and carried 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 has disappeared. 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.
Elements of the celestial sphere
Plumb Line and Related Concepts
Chart showing ratio , and (in various definitions). Note that the zenith is the opposite of the nadir.
Plumb line - a straight line passing through the center of the celestial sphere and the observation point on the surface of the Earth. The plumb line intersects with the surface of the celestial sphere at two points - over the observer's head and under the feet of the observer.
True (mathematical) horizon - a large 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 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 bending of light rays in the atmosphere.
Circle height or vertical luminaries - a large semicircle of the celestial sphere passing through the luminary, zenith and nadir.Almucantarate (arab. " ») - a small circle of the celestial sphere, the plane of which is parallel to the plane of the mathematical horizon. The circles of height and almucantarates form a coordinate grid that sets the horizontal coordinates of the star.
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, if you look at the celestial sphere from the inside.
A large 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.
Diurnal parallel - a small circle of the celestial sphere, the plane of which is parallel to the plane of the celestial equator. Visible diurnal movements of the luminaries follow diurnal parallels. The declination circles and diurnal parallels form a coordinate grid on the celestial sphere, which sets the equatorial coordinates of the star.
Terms generated at the intersection of the concepts "Plumb line" and "Rotation of the celestial sphere"
The celestial equator intersects with the mathematical horizon atpoint east and point west ... The point to the east is the one at which the points of the rotating celestial sphere rise from the horizon. The semicircle of height passing through the east point is calledfirst vertical .
Heavenly meridian - a large circle of the celestial sphere, the plane of which passes through the plumb line and the axis of the world. The celestial meridian divides the surface of the celestial sphere into two hemispheres:eastern hemisphere and western hemisphere .
Midday line - the line of intersection of the plane of the celestial meridian and the plane of the mathematical horizon. The noon line and the celestial meridian cross the mathematical horizon at two points:point north and point south ... The north point is the one closer to the north pole of the world.
The annual movement of the Sun in the celestial sphere and related concepts
P, P "- poles of the world, T, T" - points of equinox, E, C - points of solstice, P, P "- poles of the ecliptic, PP" - axis of the world, PP "- axis of ecliptic, ATQT" - celestial equator, ETCT "- ecliptic
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 at which the ecliptic intersects the celestial equator are called points... V vernal equinox The sun in its annual movement passes from the southern hemisphere of the celestial sphere to the northern; vthe point of the autumnal equinox - from the northern hemisphere to the southern. Two points of the ecliptic that are 90 ° from the equinox and thus the most distant from the celestial equator are called points . Summer solstice point located in the northern hemisphere,winter solstice point - in the southern hemisphere. These four points are indicated by the symbols♈ ), the autumnal 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 ecliptic axis intersects with the surface of the celestial sphere at two points -north pole ecliptic lying in the northern hemisphere, andsouth pole ecliptic lying in the southern hemisphere. The north pole of the ecliptic has equatorial coordinates R.A. = 18h00m, Dec = + 66 ° 33 ", and is in the constellation and the south pole is R.A. = 6h00m, DECL = −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.
Topic 4. HEAVENLY SPHERE. ASTRONOMIC COORDINATE SYSTEMS
4.1. CELESTIAL SPHERE
Celestial sphere - an imaginary sphere of an arbitrary radius onto which the celestial bodies are projected. Serves for solving various astrometric tasks. 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 stars in the sky.
The concept of the Heavenly sphere originated in ancient times; it was based on the visual impression of the existence of a domed firmament. This impression is due to the fact that as a result of the enormous remoteness of the celestial bodies, the human eye is not able to assess the differences in the distances to them, and they appear to be equally distant. The ancient peoples associated this with the presence of a real sphere that bounds the whole world and carried numerous stars on its surface. Thus, in their view, the celestial sphere was the most important element of the universe. With the development of scientific knowledge, this view of the celestial sphere has disappeared. However, the geometry of the celestial sphere, laid down in antiquity, as a result of development and improvement, 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 the geometric relationships, it is assumed to be equal to unity. Depending on the problem to be solved, the center of the celestial sphere can be placed in the place:
where the observer is (topocentric celestial sphere),
to the center of the Earth (geocentric celestial sphere),
to the center of a planet (planetocentric 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 crossed by a straight line connecting the center of the celestial sphere with the luminary (with its center). When studying the relative position and apparent 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 large circle of the sphere has two poles, defined on it by the ends of a diameter perpendicular to the plane of this circle.
The 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 nadire - diametrically opposite point.
Mathematical horizon - a large 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 the top at nadir. The mathematical horizon may not coincide with the visible horizon due to the unevenness of the Earth's surface and different heights of observation points, as well as the curvature of light rays in the atmosphere.
Rice. 4.1. Celestial sphere
Axis of the world - the axis of the 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 there is a visible daily movement of stars due to the rotation of the Earth around its axis. The north pole of the world is in the constellation Ursa Minor, southern in the constellation Octant... As a result precession the poles of the world are shifted by about 20 "per year.
The height of the pole of the world is equal to the latitude of the observer's place. The pole of the world, located in the above-horizon part of the sphere, is called elevated, while the other pole of the world, located in the sub-horizon part of the sphere, is called lowered.
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 a summit at the north pole of the world, and Southern Hemisphere , with a summit at the south pole of the world.
The celestial equator intersects with 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.
Heavenly meridian - a large circle of the celestial sphere, the plane of which passes through the plumb line and the axis of the world. The celestial meridian divides the surface of the celestial sphere into two hemispheres - eastern hemisphere , with a top at a point east, and western hemisphere , with apex at the west point.
Midday line - the line of intersection of the plane of the celestial meridian and the plane of the mathematical horizon.
Heavenly meridian intersects the mathematical horizon at two points: point north and point south ... The north point is the one closer to the north pole of the world.
Ecliptic - the trajectory of the apparent annual motion 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 the celestial equator at two points - spring and autumn equinoxes ... At the vernal equinox, the Sun moves from the southern hemisphere of the celestial sphere to the northern, at the autumnal equinox, from the northern hemisphere of the celestial sphere to the southern.
The ecliptic points that are 90 ° from the equinox are called point summer solstice (in the northern hemisphere) and point winter solstice (in the southern hemisphere).
Axis ecliptic - diameter of the celestial sphere perpendicular to the plane of the ecliptic.
4.2. The main lines and planes of the celestial sphere
The ecliptic axis intersects with the surface of the celestial sphere at two points - north pole ecliptic lying in the northern hemisphere, and the south pole of the ecliptic, lying in the southern hemisphere.
Almucantarat (Arabic circle of equal heights) luminaries - a small circle of the celestial sphere passing through a luminary, the plane of which is parallel to the plane of the mathematical horizon.
Circle height or vertical a circle or vertical luminaries - a large semicircle of the celestial sphere passing through the zenith, luminary and nadir.
Diurnal parallel luminaries - a small circle of the celestial sphere passing through a luminary, the plane of which is parallel to the plane of the celestial equator. Visible diurnal movements of the luminaries follow diurnal parallels.
A circle declensions 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 stars in the sky or points on an imaginary celestial sphere. The coordinates of the luminaries or points are set 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 by the choice of the main plane. Depending on the task at hand, it may be more convenient to use one or another system. The most commonly used are the 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 the observation 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 the stars change continuously throughout 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 the letter 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 nadir is called a plumb line.
4.3. Horizontal coordinate system
The plane perpendicular to the plumb line at point O is called the plane of the mathematical horizon. On this plane, the direction to the south (geographic) and north is determined, for example, in the direction of the shortest shadow of the day from the gnomon. It will be the 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 line (ZNZ "S) is called the plane of the celestial meridian , and the plane passing through the celestial body - the vertical plane of the given celestial body ... The great circle in which she crosses the celestial sphere, called the vertical of a celestial body .
In a horizontal coordinate system, one coordinate is either luminary height h or its zenith distance z... Another coordinate is azimuth A.
Height h luminary is called the arc of the luminary's vertical from the plane of the mathematical horizon to the direction to the luminary. The heights are measured in the range from 0 ° to + 90 ° to the zenith and from 0 ° to -90 ° to the nadir.
The zenith distance z of the luminary called the arc of the vertical of the star from the zenith to the star. Zenith distances are measured in the range from 0 ° to 180 ° from zenith to nadir.
Azimuth A of the luminary is 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, west of the south point, in the range from 0 ° to 360 °. Sometimes azimuths are measured from 0 ° to + 180 ° west and from 0 ° to −180 ° east (in geodesy, azimuths are measured from the north point).
Features of changing the coordinates of celestial bodies
For a day, a 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 when φ is equal to 90 degrees, that is, at the North Pole. Therefore, all stars, those visible there will be non-setting (including the Sun for six months, see the longitude 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 ascending (h goes through 0 during the day)
non-calling (h is always greater than 0)
non-ascending (h is always less than 0)
The maximum height h of the star will be observed once a day during one of its two passages through the celestial meridian - the upper climax, and the minimum - during the second of them - the lower climax. The height h of the star increases from the lower to the upper culmination, and decreases from the upper to the lower one.
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 called the arc of the declination circle 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 in the range from 0 ° to + 90 ° to the north pole of the world and from 0 ° to -90 ° to the south pole of the world.
4.4. Equatorial coordinate system
The polar distance p of the star is the arc of the declination circle from the north pole of the world to the star, or the angle between the axis of the world and the direction to the star. Polar distances are measured in the range from 0 ° to 180 ° from the north pole of the world to the south.
The hour angle t of the star 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 star, or the dihedral angle between the planes of the celestial meridian and the circle of declination of the star. Hourly angles are counted towards the diurnal rotation of the celestial sphere, that is, to the west of the upper point of the celestial equator, in the range from 0 ° to 360 ° (in degrees) or from 0h to 24h (in hours). Sometimes hour angles are counted from 0 ° to + 180 ° (from 0h to + 12h) to the west and from 0 ° to −180 ° (from 0h to −12h) to the east.
Second equatorial coordinate system
In this system, as in the first equatorial one, 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. Right ascension (RA, α) of the star is the arc of the celestial equator from the vernal equinox to the declination circle of the star, or the angle between the direction to the vernal equinox and the plane of the declination circle of the star. Right ascensions are counted in the direction opposite to the daily rotation of the celestial sphere, in the range from 0 ° to 360 ° (in degrees) or from 0h to 24h (in hours).
RA is the astronomical equivalent of terrestrial longitude. Both RA and longitude measure the east-west angle along the equator; both measures are measured from point zero at the equator. For longitude, point zero is the prime meridian; for RA, the zero point is the place 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 in the celestial sphere from the plane of the celestial equator to the luminary and is usually expressed in degrees, minutes and seconds of arc. Declination is positive north of the celestial equator and negative south. The sign of the declension is always indicated, even if the declination is positive.
The declination of a celestial object passing through the zenith is equal to the observer's latitude (if we assume the north latitude with a + sign, and the south latitude 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 is δ
Ecliptic coordinate system
In this system, the main plane is the ecliptic plane. In this case, one coordinate is the ecliptic latitude β, and the other is the ecliptic longitude λ.
4.5. Relationship between ecliptic and second equatorial coordinate systems
The ecliptic latitude β of the luminary is called the arc of a 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 pole of the ecliptic and from 0 ° to -90 ° to the south pole of the ecliptic.
The ecliptic longitude λ of the star is the arc of the ecliptic from the vernal equinox to the circle of latitude of the star, or the angle between the direction to the point of the vernal equinox and the plane of the circle of latitude of the star. Ecliptic longitudes are measured in the direction of the apparent annual motion 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 galactic latitude b, and the other is galactic longitude l.
4.6. Galactic and second equatorial coordinate systems.
The galactic latitude b of the star is the arc of the circle of galactic latitude from the ecliptic to the star, or the angle between the plane of the galactic equator and the direction to the star.
Galactic latitudes are measured from 0 ° to + 90 ° to the galactic north pole and from 0 ° to −90 ° to the galactic south pole.
The galactic longitude l of the star is the arc of the galactic equator from the point of origin C to the circle of galactic latitude of the star, or the angle between the direction to the point of origin C and the plane of the circle of galactic latitude of the star. Galactic longitudes are counted counterclockwise as viewed from the Galactic North Pole, that is, east of the origin, C, from 0 ° to 360 °.
The 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 origin 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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Listed below are all the points of the five-letter celestial sphere. A short description is provided for each definition.
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North
One of the four conventionally accepted cardinal points, which is opposite to the south. On a geographic map, it is predominantly located at the top and is indicated by a capital letter C (international designation N - north).
The magnetized compass needle always points north. The etymology of this word comes from the Old Russian language, translated as "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. Britons James and John Ross were the first to talk about the existence of the North Pole. But the debate about who opened it first is still going on. Due to the harsh climate (in winter - about - 40C, in summer about 0C), the animal world is very scarce. It is mainly inhabited by polar bears, walruses, and seals. And because of the eternal ice, there is 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 to the east. On a geographic map, the west is indicated on the left by the letter Z (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 (“rolls down” beyond the horizon), due to the rotation of the Earth around an imaginary axis from west to east. Also called the West is 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 allowed in the word. So when borrowing the word zenith from the Arabic language, a rewriting error was made. In the Arabic word "zamt", which meant "the highest point of the firmament", they confused "m" with "in" and got the word "zanit", later it turned into "zenit". Zenith is a kind of imaginary heavenly point, which is located above the head of the observer.
Simply put, the zenith is a direction that points "up" from a given point on the earth, a direction that is strictly opposite to the direction of the force of gravity at a given location. The angle between the horizon and the zenith is 90. The term zenith also refers to the highest point that is reached by a certain 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 its highest point above the horizon at this location.
Nadir
This word is borrowed from the Arabic language. Nadir is a kind of imaginary celestial point where the celestial sphere and the vertical line downward from the observation point intersect. This point is located on the other half of the celestial sphere, invisible to humans because of the globe. The 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, nadir is the direction opposite to the direction of the zenith, which means the direction that coincides with the direction of the action of gravity.
Apex
This term has Latin roots. The exact meaning of the word apex "apex" is from the Latin "apex". Apex is a certain point located in the celestial sphere, in its direction space objects are moving at the moment. The opposite point is called antiapex. Since all objects in the Universe are under the influence of gravitational forces and do not move in a straight line, their apexes are constantly shifting.
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.
