§ 48. Celestial sphere. Basic points, lines and circles on the celestial sphere
A celestial sphere is a sphere of any radius with a center at an arbitrary point in space. Depending on the formulation of the problem, its center is taken to be the eye of the observer, the center of the instrument, the center of the Earth, etc.Let us consider the main points and circles of the celestial sphere, the center of which is taken to be the eye of the observer (Fig. 72). Let's draw a plumb line through the center of the celestial sphere. The points of intersection of the plumb line with the sphere are called zenith Z and nadir n.
Rice. 72.
The plane passing through the center of the celestial sphere perpendicular to the plumb line is called the plane of the true horizon. This plane, intersecting with the celestial sphere, forms a great circle called the true horizon. The latter divides the celestial sphere into two parts: above the horizon and below the horizon.
A straight line passing parallel to the center of the celestial sphere earth's axis, called the 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 celestial pole and is designated Pn, the other is the south celestial pole Ps.
The QQ plane passing through the center of the celestial sphere perpendicular to the axis of the world is called plane of the celestial equator. This plane, intersecting with the celestial sphere, forms a great circle - celestial equator, which divides the celestial sphere into northern and southern parts.
The great circle of the celestial sphere passing through the celestial poles, zenith and nadir, is called observer's meridian PN nPsZ. The mundi axis divides the observer's meridian into the midday PN ZPs and midnight PN nPs parts.
The observer's meridian intersects with the true horizon at two points: the north point N and the south point S. The straight line connecting the points of north and south is called midday line.
If you look from the center of the sphere to point N, then on the right there will be a point of east O st, and on the left - a point of west W. Small circles of the celestial sphere aa", parallel to the plane of the true horizon, are called almucantarates; small bb" parallel to the plane of the celestial equator, - heavenly parallels.
The circles of the celestial sphere Zon passing through the zenith and nadir points are called verticals. The vertical line passing through the points of east and west is called the first vertical.
The circles of the celestial sphere of PNoPs passing through the poles of the world are called declination circles.
The observer's meridian is both a vertical and a circle of declination. It divides the celestial sphere into two parts - eastern and western.
The celestial pole located above the horizon (below the horizon) is called the elevated (lowered) celestial pole. The name of the elevated celestial pole is always the same as the name of the latitude of the place.
The axis of the world makes an angle with the plane of the true horizon equal to geographical latitude of the place.
The position of luminaries on the celestial sphere is determined using spherical coordinate systems. In nautical astronomy, horizontal and equatorial coordinate systems are used.
The celestial sphere is an imaginary sphere of arbitrary radius, used in astronomy to describe the relative positions of luminaries in the sky. For simplicity of calculations, its radius is taken equal to one; The center of the celestial sphere, depending on the problem being solved, is combined with the observer’s pupil, with the center of the Earth, Moon, Sun, or even with an arbitrary point in space.
The idea of the celestial sphere arose in ancient times. It was based on the visual impression of the existence of a crystal dome of the sky, on which the stars seemed to be fixed. The celestial sphere in the minds of ancient peoples was the most important element of the Universe. With the development of astronomy, this view of the celestial sphere disappeared. However, the geometry of the celestial sphere, laid down in ancient times, as a result of development and improvement, received modern look, in which for the convenience of various calculations it is used in astrometry.
Let us consider the celestial sphere as it appears to the Observer at mid-latitudes from the surface of the Earth (Fig. 1).
Two straight lines, the position of which can be established experimentally using physical and astronomical instruments, play an important role in defining concepts related to the celestial sphere. The first of them is a plumb line; This is a straight line that coincides at a given point with the direction of gravity. This line, drawn through the center of the celestial sphere, intersects it at two diametrically opposite points: the upper one is called the zenith, the lower one is called the nadir. The plane passing through the center of the celestial sphere perpendicular to the plumb line is called the plane of the mathematical (or true) horizon. The line of intersection of this plane with the celestial sphere is called the horizon.
The second straight line is the axis of the world - a straight line passing through the center of the celestial sphere parallel to the axis of rotation of the Earth; There is a visible daily rotation of the entire sky around the axis of the world. The points of intersection of the axis of the world with the celestial sphere are called the North and South poles of the world. The most noticeable of the stars near the North Pole is the North Star. There are no bright stars near the South Pole of the world.
The plane passing through the center of the celestial sphere perpendicular to the axis of the world is called the plane of the celestial equator. The line of intersection of this plane with the celestial sphere is called the celestial equator.
Let us recall that the circle that is obtained when the celestial sphere is intersected by a plane passing through its center is called a great circle in mathematics, and if the plane does not pass through the center, then a small circle is obtained. The horizon and celestial equator represent great circles of the celestial sphere and divide it into two equal hemispheres. The horizon divides the celestial sphere into visible and invisible hemispheres. The celestial equator divides it into the Northern and Southern Hemispheres, respectively.
During the daily rotation of the sky, the luminaries rotate around the axis of the world, describing small circles on the celestial sphere, called daily parallels; luminaries, 90° distant from the poles of the world, move along the great circle of the celestial sphere - the celestial equator.
Having defined the plumb line and the axis of the world, it is not difficult to define all other planes and circles of the celestial sphere.
The plane passing through the center of the celestial sphere, in which both the plumb line and the axis of the world lie simultaneously, is called the plane of the celestial meridian. The great circle from the intersection of this plane with the celestial sphere is called the celestial meridian. That of the points of intersection of the celestial meridian with the horizon, which is closer to the North Pole of the world, is called the north point; diametrically opposite - the point of the south. The straight line passing through these points is the noon line.
Points on the horizon that are 90° from the north and south points are called east and west points. These four points are called the main points of the horizon.
Planes passing through a plumb line intersect the celestial sphere in great circles and are called verticals. The celestial meridian is one of the verticals. The vertical perpendicular to the meridian and passing through the points of east and west is called the first vertical.
By definition, the three main planes - the mathematical horizon, the celestial meridian and the first vertical - are mutually perpendicular. The plane of the celestial equator is perpendicular only to the plane of the celestial meridian, forming a dihedral angle with the plane of the horizon. At the geographic poles of the Earth, the plane of the celestial equator coincides with the plane of the horizon, and at the equator of the Earth it becomes perpendicular to it. In the first case, at the geographic poles of the Earth, the axis of the world coincides with a plumb line and any of the verticals can be taken as the celestial meridian, depending on the conditions task at hand. In the second case, at the equator, the axis of the world lies in the plane of the horizon and coincides with the noon line; The North Pole of the world coincides with the point of north, and the South Pole of the world coincides with the point of south (see figure).
When using the celestial sphere, the center of which coincides with the center of the Earth or some other point in space, a number of features also arise, but the principle of introducing basic concepts - horizon, celestial meridian, first vertical, celestial equator, etc. - remains the same.
The main planes and circles of the celestial sphere are used when introducing horizontal, equatorial and ecliptic celestial coordinates, as well as when describing the features of the apparent daily rotation of the luminaries.
The great circle formed when the celestial sphere is intersected by a plane passing through its center and parallel to the plane of the earth's orbit is called the ecliptic. The visible annual movement of the Sun occurs along the ecliptic. The point of intersection of the ecliptic with the celestial equator, at which the Sun passes from Southern Hemisphere celestial sphere in the North, is called the point of the vernal equinox. The opposite point of the celestial sphere is called the autumnal equinox. A straight line passing through the center of the celestial sphere perpendicular to the ecliptic plane intersects the sphere at two poles of the ecliptic: the North Pole in the Northern Hemisphere and the South Pole in the Southern Hemisphere.
2.1.1. Basic planes, lines and points of the celestial sphere
A celestial sphere is an imaginary sphere of arbitrary radius with a center at a selected observation point, on the surface of which the luminaries are located as they are visible in the sky at some point in time from a given point in space. To correctly imagine an astronomical phenomenon, it is necessary to consider the radius of the celestial sphere to be much greater than the radius of the Earth (R sf >> R Earth), i.e., to assume that the observer is in the center of the celestial sphere, and the same point of the celestial sphere (the same the same star) is visible from different places on the earth's surface in parallel directions.
The celestial vault or sky is usually understood as the inner surface of the celestial sphere onto which celestial bodies (luminaries) are projected. For an observer on Earth, the Sun, sometimes the Moon, and even less often Venus are visible in the sky during the day. On a cloudless night, stars, the Moon, planets, sometimes comets and other bodies are visible. There are about 6000 stars visible to the naked eye. The relative positions of the stars almost do not change due to the large distances to them. Celestial bodies belonging to the Solar system change their position relative to the stars and each other, which is determined by their noticeable angular and linear daily and annual displacement.
The vault of heaven rotates as a single whole with all the luminaries located on it about an imaginary axis. This rotation is daily. If you observe the daily rotation of stars in the northern hemisphere of the Earth and face the north pole, then the rotation of the sky will occur counterclockwise.
Center O of the celestial sphere is the observation point. The straight line ZOZ" coinciding with the direction of the plumb line at the observation location is called a plumb or vertical line. The plumb line intersects with the surface of the celestial sphere at two points: at the zenith Z, above the observer's head, and at the diametrically opposite point Z" - the nadir. The great circle of the celestial sphere (SWNE), the plane of which is perpendicular to the plumb line, is called the mathematical or true horizon. The mathematical horizon is a plane tangent to the surface of the Earth at the observation point. The small circle of the celestial sphere (aMa"), passing through the luminary M, and the plane of which is parallel to the plane of the mathematical horizon, is called the almucantarate of the luminary. The large semicircle of the celestial sphere ZMZ" is called the circle of height, vertical circle, or simply the vertical of the luminary.The diameter PP" around which the celestial sphere rotates is called the mundi axis. The mundi axis intersects with the surface of the celestial sphere at two points: at the north celestial pole P, from which the celestial sphere rotates clockwise when looking at the sphere from the outside, and at the south pole of the world R". The world axis is inclined to the plane of the mathematical horizon at an angle equal to the geographic latitude of the observation point φ. The great circle of the celestial sphere QWQ"E, the plane of which is perpendicular to the axis of the world, is called the celestial equator. The small circle of the celestial sphere (bМb"), the plane of which is parallel to the plane of the celestial equator, is called the celestial or daily parallel of the luminary M. The great semicircle of the celestial sphere RMR* is called hour circle or circle of declination of the luminary.
The celestial equator intersects with the mathematical horizon at two points: at the east point E and at the west point W. The circles of heights passing through the points of east and west are called the first verticals - east and west.
The great circle of the celestial sphere PZQSP"Z"Q"N, the plane of which passes through the plumb line and the axis of the world, is called the celestial meridian. The plane of the celestial meridian and the plane of the mathematical horizon intersect along a straight line NOS, which is called the noon line. The celestial meridian intersects with the mathematical horizon at the north point N and at the south point S. The celestial meridian also intersects with the celestial equator at two points: at the upper point of the equator Q, which is closer to the zenith, and at the lower point of the equator Q", which is closer to the nadir.
2.1.2. Luminaries, their classification, visible movements.
Stars, Sun and Moon, planets
In order to navigate the sky, bright stars united into constellations. There are 88 constellations in the sky, of which 56 are visible to an observer located in the middle latitudes of the Earth’s northern hemisphere. All constellations have proper names, associated with the names of animals (Ursa Major, Lion, Dragon), names of heroes Greek mythology(Cassiopeia, Andromeda, Perseus) or the names of objects whose outlines resemble (Northern Crown, Triangle, Libra). Individual stars in the constellations are designated by letters of the Greek alphabet, and the brightest of them (about 200) received “proper” names. For example, α Canis Major– “Sirius”, α Orion – “Betelgeuse”, β Perseus – “Algol”, α Ursa Minor – “Pole Star”, near which the point of the north pole of the world is located. The paths of the Sun and Moon against the background of the stars almost coincide and come through twelve constellations, which are called zodiac constellations, since most of them are named after animals (from the Greek “zoon” - animal). These include the constellations of Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces. The trajectory of Mars across the celestial sphere in 2003 |
Even in ancient times, 5 luminaries were noticed, similar to stars, but “wandering” through the constellations. They were called planets - “wandering luminaries”. Later, 2 more planets were discovered and a large number of smaller ones celestial bodies(dwarf planets, asteroids).
Planets most time move along the zodiacal constellations from west to east ( straight movement), but part of the time – from east to west (retrograde movement).
| Your browser does not support the video tag. The movement of stars in the celestial sphere |