All celestial bodies are at unusually large and very different distances from us. But to us they seem equally distant and seem to be located on some sphere. When deciding practical problems in aviation astronomy, it is important to know not the distance to the stars, but their position on the celestial sphere at the moment of observation.
The celestial sphere is an imaginary sphere of infinite radius, the center of which is the observer. When examining the celestial sphere, its center is aligned with the observer's eye. The dimensions of the Earth are neglected, so the center of the celestial sphere is often combined with the center of the Earth. The luminaries are applied to the sphere in the position in which they are visible in the sky at some point in time from a given point of location of the observer.
The celestial sphere has a number of characteristic points, lines and circles. In Fig. 1.1, a circle of arbitrary radius depicts the celestial sphere, in the center of which, designated by point O, the observer is located. Let's consider the main elements of the celestial sphere.
The observer's vertical is a straight line passing through the center of the celestial sphere and coinciding with the direction of the plumb line at the observer's point. Zenith Z is the point of intersection of the observer's vertical with the celestial sphere, located above the observer's head. Nadir Z" is the point of intersection of the observer's vertical with the celestial sphere, opposite to the zenith.
The true horizon N E S W is a great circle on the celestial sphere, the plane of which is perpendicular to the observer’s vertical. The true horizon divides the celestial sphere into two parts: the above-horizon hemisphere, in which the zenith is located, and the subhorizon hemisphere, in which the nadir is located.
The world axis PP" is a straight line around which the visible daily rotation of the celestial sphere occurs.
Rice. 1.1. Basic points, lines and circles on the celestial sphere
The axis of the world is parallel to the axis of rotation of the Earth, and for an observer located at one of the poles of the Earth, it coincides with the axis of rotation of the Earth. The apparent daily rotation of the celestial sphere is a reflection of the actual daily rotation Earth around its axis.
The celestial poles are the points of intersection of the axis of the world with the celestial sphere. The celestial pole located in the constellation area Ursa Minor, is called the North Pole of the world P, and the opposite pole is called the South Pole.
The celestial equator is a large circle on the celestial sphere, the plane of which is perpendicular to the axis of the world. The plane of the celestial equator divides the celestial sphere into the northern hemisphere, in which the North Celestial Pole is located, and the southern hemisphere, in which the South Celestial Pole is located.
The celestial meridian, or observer's meridian, is a large circle on the celestial sphere, passing through the poles of the world, zenith and nadir. It coincides with the plane of the observer's earthly meridian and divides the celestial sphere into the eastern and western hemispheres.
The points of north and south are the points of intersection of the celestial meridian with the true horizon. The point closest to the North Pole of the world is called the north point of the true horizon C, and the point closest to South Pole of the world, - the point of the south South. The points of the east and west are the points of intersection of the celestial equator with the true horizon.
The noon line is a straight line in the plane of the true horizon connecting the points of north and south. This line is called midday because at noon according to local true solar time, the shadow of a vertical pole coincides with this line, i.e., with the true meridian of a given point.
The southern and northern points of the celestial equator are the points of intersection of the celestial meridian with the celestial equator. The point closest to the southern point of the horizon is called the south point of the celestial equator, and the point closest to the northern point of the horizon is called the north point
The vertical of a luminary, or the circle of altitude, is a large circle on the celestial sphere, passing through the zenith, nadir and luminary. The first vertical is the vertical passing through the points of east and west.
The circle of declination, or the hour circle of a luminary, RMR, is a large circle on the celestial sphere, passing through the poles of myoa and the luminary.
The daily parallel of a luminary is a small circle on the celestial sphere drawn through the luminary parallel to the plane of the celestial equator. The apparent daily movement of the luminaries occurs along daily parallels.
Almucantarat of the luminary AMAG is a small circle on the celestial sphere drawn through the luminary parallel to the plane of the true horizon.
The considered elements of the celestial sphere are widely used in aviation astronomy.
One of the most important astronomical problems, without which it is impossible to solve all other problems of astronomy, is determining the position of a celestial body on the celestial sphere.
Celestial sphere- this is an imaginary sphere of arbitrary radius, described from the eye of the observer, as from the center. We project the position of all celestial bodies onto this sphere. Distances on the celestial sphere can only be measured in angular units, in degrees, minutes, seconds or radians. For example, the angular diameters of the Moon and the Sun are approximately 0. o 5.
One of the main directions relative to which the position of the observed celestial body is determined is plumb line. A plumb line anywhere on the globe is directed toward the Earth's center of gravity. The angle between the plumb line and the plane of the earth's equator is called astronomical latitude.
The plane perpendicular to the plumb line is called horizontal plane.
At every point on the Earth, the observer sees half a sphere rotating smoothly from east to west along with the stars seemingly attached to it. This apparent rotation of the celestial sphere is explained by the uniform rotation of the Earth around its axis from west to east.
A plumb line intersects the celestial sphere at a point zenith, Z and at the point nadir, Z".
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| Rice. 2. Celestial sphere |
The great circle of the celestial sphere along which the horizontal plane passing through the eye of the observer (point C in Fig. 2) intersects with the celestial sphere is called true horizon. Recall that the great circle of the celestial sphere is a circle passing through the center of the celestial sphere. Circles formed by the intersection of the celestial sphere with planes that do not pass through its center are called small circles.
A line parallel to the earth's axis and passing through the center of the celestial sphere is called axis mundi. She crosses the celestial sphere in north pole of the world, P, and in south pole of the world P".
From Fig. 1 shows that the axis of the world is inclined to the plane of the true horizon at an angle. The apparent rotation of the celestial sphere occurs around the axis of the world from east to west, in the opposite direction to the true rotation of the Earth, which rotates from west to east.
The great circle of the celestial sphere, the plane of which is perpendicular to the axis of the world, is called celestial equator. The celestial equator divides the celestial sphere into two parts: northern and southern. The celestial equator is parallel to the Earth's equator.
A plane passing through a plumb line and the axis of the world intersects the celestial sphere along the line celestial meridian. The celestial meridian intersects the true horizon at points north, N, and south, S. And the planes of these circles intersect along noon line. The celestial meridian is a projection onto the celestial sphere of the terrestrial meridian on which the observer is located. Therefore, there is only one meridian on the celestial sphere, because an observer cannot be on two meridians at the same time!
The celestial equator intersects the true horizon at points east, E, and west, W. The EW line is perpendicular to the noon line. Point Q is the highest point of the equator, and Q" is the lowest point of the equator.
Great circles whose planes pass through a plumb line are called verticals. The vertical line passing through points W and E is called first vertical.
Great circles whose planes pass through the axis of the world are called declination circles or hour circles.
Small circles of the celestial sphere, the planes of which are parallel to the celestial equator, are called celestial or daily parallels. They are called diurnal because the daily movement of the heavenly bodies occurs along them. The equator is also a daily parallel.
A small circle of the celestial sphere, the plane of which is parallel to the plane of the horizon, is called almucantarate.
Questions
1 . Is there a place on Earth where the rotation of the celestial sphere occurs around a plumb line?
Tasks
1. Draw on the drawing the celestial sphere in projection onto the horizon plane.
Solution: As is known, the projection of any point A onto any plane is the point of intersection of the plane and the perpendicular drawn from point A to the plane. The projection of a segment perpendicular to a plane is a point. The projection of a circle parallel to a plane is the same circle on the plane, the projection of a circle perpendicular to the plane is a segment, and the projection of a circle inclined to the plane is an ellipse, the more flattened the closer the angle of inclination is to 90 o. Thus, in order to draw a projection of the celestial sphere onto any plane, it is necessary to lower perpendiculars from all points of the celestial sphere onto this plane. The sequence of actions is as follows. First of all, you need to draw a circle lying in the projection plane, in this case it will be the horizon. Then plot all the points and lines lying in the horizon plane. In this case, this will be the center of the celestial sphere C, and the points south S, north N, east E and west W, as well as the noon line NS. Next, we lower the perpendiculars onto the horizon plane from the remaining points of the celestial sphere and find that the projection of the zenith Z, nadir Z" and the plumb line ZZ" onto the horizon plane is the point coinciding with the center of the celestial sphere C (see Fig. 3). The projection of the first vertical is the segment EW, the projection of the celestial meridian coincides with the noon line NS. The points lying on the celestial meridian: the poles P and P", as well as the upper and lower points of the equator Q and Q", are therefore also projected onto the noon line. The equator is a great circle of the celestial sphere, inclined to the horizon plane, so its projection is an ellipse passing through the points east E, west W, and the projections of points Q and Q."
2. Draw on the drawing the celestial sphere in projection onto the plane of the celestial meridian.
Solution: Shown in Fig.4
3. Draw on the drawing the celestial sphere in projection onto the plane of the celestial equator.
4. Draw on the drawing the celestial sphere in projection onto the plane of the first vertical.
Points and lines of the celestial sphere - how to find the almucantarate, where the celestial equator passes, which is the celestial meridian.
What is the Celestial Sphere
Celestial sphere– an abstract concept, an imaginary sphere of infinite radius, the center of which is the observer. In this case, the center of the celestial sphere is, as it were, at the level of the observer’s eyes (in other words, everything that you see above your head from horizon to horizon is this very sphere). However, for ease of perception, we can consider the center of the celestial sphere and the center of the Earth; there is no mistake in this. The positions of stars, planets, the Sun and the Moon are plotted on the sphere in the position in which they are visible in the sky at a certain moment in time from a given point of location of the observer.
In other words, although observing the position of the stars on the celestial sphere, we, being in different places on the planet, will constantly see a slightly different picture, knowing the principles of the “working” of the celestial sphere, by looking at the night sky we can easily navigate the area using simple technology. Knowing the view overhead at point A, we will compare it with the view of the sky at point B, and by the deviations of familiar landmarks, we will be able to understand where exactly we are now.
People have already come up with this idea a long time ago a whole series tools that make our task easier. If you navigate the “terrestrial” globe simply using latitude and longitude, then a whole series of similar elements - points and lines, are also provided for the “celestial” globe - the celestial sphere.
The celestial sphere and the position of the observer. If the observer moves, then the entire sphere visible to him will move.
Elements of the celestial sphere
The celestial sphere has a number of characteristic points, lines and circles; let us consider the main elements of the celestial sphere.
Observer vertical
Observer vertical- a straight line passing through the center of the celestial sphere and coinciding with the direction of the plumb line at the observer’s point. Zenith- the point of intersection of the observer’s vertical with the celestial sphere, located above the observer’s head. Nadir- the point of intersection of the observer’s vertical with the celestial sphere, opposite to the zenith.
True horizon- a large circle on the celestial sphere, the plane of which is perpendicular to the observer’s vertical. The true horizon divides the celestial sphere into two parts: above-horizon hemisphere, at which the zenith is located, and subhorizontal hemisphere, in which the nadir is located.
Axis mundi ( Earth's axis) - a straight line around which the visible daily rotation of the celestial sphere occurs. The axis of the world is parallel to the axis of rotation of the Earth, and for an observer located at one of the poles of the Earth, it coincides with the axis of rotation of the Earth. The apparent daily rotation of the celestial sphere is a reflection of the actual daily rotation of the Earth around its axis. The celestial poles are the points of intersection of the axis of the world with the celestial sphere. The celestial pole, located in the region of the Ursa Minor constellation, is called North Pole world, and the opposite pole is called South Pole.
A great circle on the celestial sphere, the plane of which is perpendicular to the axis of the world. The plane of the celestial equator divides the celestial sphere into northern hemisphere, in which the North Pole is located, and southern hemisphere, where the South Pole is located.
Or the observer's meridian is a large circle on the celestial sphere, passing through the poles of the world, zenith and nadir. It coincides with the plane of the observer's earthly meridian and divides the celestial sphere into eastern And western hemisphere.
North and south points- the point of intersection of the celestial meridian with the true horizon. The point closest to the North Pole of the world is called the north point of the true horizon C, and the point closest to the South Pole of the world is called the south point S. The points of the east and west are the points of intersection of the celestial equator with the true horizon.
Noon Line- a straight line in the plane of the true horizon connecting the points of north and south. This line is called midday because at noon according to local true solar time, the shadow of a vertical pole coincides with this line, i.e., with the true meridian of a given point.
The intersection points of the celestial meridian with the celestial equator. The point closest to the southern point of the horizon is called south point of the celestial equator, and the point closest to the northern point of the horizon is north point of the celestial equator.
Vertical of the luminary
Vertical of the luminary, or height circle, - a large circle on the celestial sphere, passing through the zenith, nadir and luminary. The first vertical is the vertical passing through the points of east and west.
Declension circle, or , is a large circle on the celestial sphere, passing through the poles of the world and the luminary.
A small circle on the celestial sphere drawn through the luminary parallel to the plane of the celestial equator. The apparent daily movement of the luminaries occurs along daily parallels.
Almucantarat luminaries
Almucantarat luminaries- a small circle on the celestial sphere drawn through the luminary parallel to the plane of the true horizon.
All the elements of the celestial sphere noted above are actively used to solve practical problems of orientation in space and determining the position of luminaries. Depending on the purpose and measurement conditions, two different systems are used spherical celestial coordinates.
In one system, the luminary is oriented relative to the true horizon and is called this system, and in the other, relative to the celestial equator and is called.
In each of these systems, the position of the star on the celestial sphere is determined by two angular quantities, just as the position of points on the surface of the Earth is determined using latitude and longitude.
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. In order 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.
Under firmament or the 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. Mutual position stars almost does 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 geographical latitude observation points 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 the 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 their own names associated with the names of animals (Ursa Major, Leo, Dragon), the names of heroes Greek mythology(Cassiopeia, Andromeda, Perseus) or the names of objects whose outlines resemble (Northern Crown, Triangle, Libra). Individual stars in constellations are designated by letters 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 – “ North 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 large number smaller ones celestial bodies(dwarf planets, asteroids).
The planets move most of the time across the zodiacal constellations from west to east (direct motion), but part of the time from east to west (retrograde motion).
| Your browser does not support the video tag. The movement of stars in the celestial sphere |
