What is the name of the annual path of the sun among the stars. The apparent annual movement of the sun on the celestial sphere

Geographic coordinates — latitude and longitude — are the angles that define the position of a point on the surface of the globe. Something similar can be introduced in the sky.

To describe the relative positions and apparent movements of the luminaries, it is very convenient to place all the luminaries on the inner surface of an imaginary sphere of a sufficiently large radius, and the observer himself - in the center of this sphere. It was called the celestial sphere and systems of angular coordinates were introduced on it, similar to geographic ones.

ZENIT, NADIR, HORIZON

To measure coordinates, you need to have some points and lines on celestial sphere... Let's introduce them.

Take a thread and attach a weight to it. Grasping the free end of the thread and lifting the weight into the air, we get a segment of the plumb line. Let's continue it mentally until the intersection with the celestial sphere. The top point of intersection - the zenith - will be right above our head. The lower point - nadir - is not available for observation.

If you cross the sphere with a plane, you get a circle in the section. It will have its maximum size when the plane passes1 through the center of the sphere. This line is called the big circle. All other circles on the celestial sphere are small. A plane perpendicular to the plumb line and passing through the observer will cross the celestial sphere in a large circle called the horizon. Visually, this is the place where "the earth meets the sky"; we see only that half of the celestial sphere, which is located above the horizon. All points of the horizon are 90 ° from the zenith. "..

POLE OF THE WORLD, HEAVENLY EQUATOR,
HEAVENLY MERIDIAN

Let's trace how the stars move across the sky during the day. It is best to do this photographically, that is, point the camera with the shutter open at the night sky and leave it there for several hours. The photograph will clearly show that all the stars describe circles in the sky with the same center. The point corresponding to this center is called the pole of the world. In our latitudes above the horizon is the North Pole of the world (next to the Pole Star), and in the Southern Hemisphere of the Earth, a similar movement takes place relative to the South Pole of the world. The axis connecting the poles of the world is called the axis of the world. The daily movement of the luminaries occurs as if the entire celestial sphere rotated as one whole around the axis of the world in the direction from east to west. This movement, of course, is imaginary: it is a reflection of the true movement - the rotation of the Earth around its axis from west to east. Let's draw a plane through the observer perpendicular to the axis of the world. It will cross the celestial sphere in a large circle - the celestial equator, which divides it into two hemispheres - north and south. The celestial equator intersects the horizon at two points. These are the points of the east and west. And the great circle passing through both poles of the world, the zenith and nadir, is called the celestial meridian. It crosses the horizon at points north and south.

COORDINATE SYSTEMS IN THE HEAVENLY SPHERE

Let's draw a large circle through the zenith and the luminary, the coordinates of which we want to get. This is a section of the celestial sphere by a plane passing through the luminary, zenith and observer. Such a circle is called the vertical of the star. It naturally intersects with the horizon.

The angle between the directions to this intersection point and to the luminary shows the height (h) of the luminary above the horizon. It is positive for luminaries located above the horizon, and negative for those below the horizon (the height of the zenith point is always 90 "). Now we count along the horizon the angle between the directions to the south point and to the point of intersection of the horizon with the vertical of the luminary. The direction of reference is from south to west This angle is called the astronomical azimuth (A) and together with the height makes up the coordinates of the star in the horizontal coordinate system.

Sometimes, instead of height, the zenith distance (z) of the star is used - the angular distance from the star to the zenith. Zenith distance and altitude add up to 90 °.

Knowing the horizontal coordinates of a star allows you to find it in the sky. But the big inconvenience lies in the fact that the daily rotation of the celestial sphere leads to a change in both coordinates over time - fast enough and, what is most unpleasant, uneven. Therefore, coordinate systems are often used that are not associated with the horizon, but with the equator.

Let's again draw a large circle through our star. This time, let him pass through the pole of the world. Such a circle is called a circle of declensions. Let's mark the point of its intersection with the celestial equator. Declination (6) - the angle between the directions to this point and to the star - positive for the northern hemisphere of the celestial sphere and negative for the southern one. All points on the equator have declination of 0 °. Now let's mark two points celestial equator: in the first it intersects with the celestial meridian, in the second - with the declination circle of the star. The angle between the directions to these points, measured from south to west, is called the hour angle (t) of the star. It can be measured as usual - in degrees, but more often it is expressed in hours: the whole circle is divided not by 360 °, but by 24 hours.Thus, 1 hour corresponds to 15 °, and 1 ° - 1/15 hour, or 4 minutes ...

The daily rotation of the celestial sphere no longer catastrophically affects the coordinates of the star. The luminary moves in a small circle parallel to the celestial equator and called the diurnal parallel. In this case, the angular distance to the equator does not change, which means that the declination remains constant. The hour angle increases, but evenly: knowing its value at any moment in time, it is not difficult to calculate it for any other moment.

Nevertheless, it is impossible to make lists of the positions of the stars in this coordinate system, because one coordinate still changes over time. To obtain unchanged coordinates, the reference system must move along with all objects. This is possible, since the celestial sphere in its diurnal rotation moves as a whole.

Let's choose a point on the celestial equator that participates in the general rotation. There is no luminary at this point; the Sun is in it once a year (about March 21), when in its annual (not daily!) movement among the stars it moves from the southern celestial hemisphere to the northern one (see the article "The path of the Sun among the stars"). The angular distance from this point, called the vernal equinox point CY1) D ° steep declination of the star, measured along the equator in the opposite direction daily rotation, that is, from west to east, is called right ascension (a) of the luminary. It does not change with diurnal rotation and together with declination forms a pair of equatorial coordinates, which are given in various catalogs describing the positions of the stars in the sky.

Thus, in order to construct a system of celestial coordinates, one should select a certain basic plane passing through the observer and crossing the celestial sphere in a large circle. Then, through the pole of this circle and the luminary, another large circle is drawn, crossing the first, and the angular distance from the point of intersection to the luminary and the angular distance from some point on the main circle to the same point of intersection are taken as coordinates. In the horizontal coordinate system, the main plane is the horizon plane, in the equatorial one - the plane of the celestial equator.

There are also other celestial coordinate systems. So, to study the motions of bodies in the solar system, an ecliptic coordinate system is used, in which the main plane is the ecliptic plane (coinciding with the plane of the earth's orbit), and the coordinates are ecliptic latitude and ecliptic longitude. There is also a galactic coordinate system, in which the median plane of the galactic disk is taken as the main plane.

Traveling through the heavenly expanses among countless stars and nebulae, it is no wonder to get lost if you do not have a reliable map at hand. To compose it, you need to know exactly the positions of thousands of stars in the sky. And now part of the astronomers (they are called astrometrists) are doing the same thing that the stargazers of antiquity were working on: they patiently measure the coordinates of the stars in the sky, mostly the same ones, as if not trusting their predecessors and themselves

And they are absolutely right! "Fixed" stars in fact continuously change their positions - both due to their own motions (after all, the stars participate in the rotation of the Galaxy and move relative to the Sun), and due to changes in the coordinate system itself. The precession of the earth's axis leads to a slow movement of the pole of the world and the vernal equinox point among the stars (see the article "Playing with a top, or a Long story with polar stars"). That is why in the star catalogs containing the equatorial coordinates of the stars, the equinox date on which they are oriented is necessarily reported.

STARRY SKY OF VARIOUS LATITUDES

Daily allowance parallels of the luminariesin the middle latitudes.

Under good conditions of observation with the naked eye, about 3 thousand stars are visible in the sky at the same time, regardless of where we are, in India or in Lapland. But the picture starry sky depends on both the latitude of the site and the time of observation.

Now suppose that we decided to find out how many stars can be seen, say, without leaving Moscow. Having counted those 3 thousand luminaries that are currently above the horizon, we will take a break and return to the observation platform in an hour. We will see that the picture of the sky has changed! Some of the stars that were at the western edge of the horizon have sunk under the horizon, and now they are not visible. But from the eastern side, new stars rose. They will add to our list. During the day, the stars describe circles in the sky with the center at the pole of the world (see the article "Addresses of the luminaries on the celestial sphere"). The closer the star is to the pole, the less steep. It may turn out that the whole circle lies above the horizon: the star never sets. Such non-setting stars in our latitudes include, for example, the Big Dipper Bucket. As soon as it gets dark, we will immediately find it in the sky - at any time of the year.

Other luminaries, more distant from the pole, as we have seen, rise in the eastern side of the horizon and set in the western one. Those located near the celestial equator rise near the east point and set near the west point. The rise of some luminaries of the southern hemisphere of the celestial sphere is observed in our southeast, and set - in the southwest. They describe low arcs above the southern horizon.

The farther south a star is on the celestial sphere, the shorter its path above our horizon. Consequently, even further to the south, there are non-ascending luminaries whose diurnal paths lie completely below the horizon. What do you need to do to see them? Move south!

In Moscow, for example, you can observe Antares - a bright star in the constellation Scorpio. The "tail" of the Scorpion, dipping steeply to the south, is never seen in Moscow. However, as soon as we move to the Crimea - a dozen degrees south of latitude - and in the summer, above the southern horizon, it will be possible to see the whole figure of the heavenly Scorpio. The North Star in Crimea is located much lower than in Moscow.

On the contrary, if you move north from Moscow, polar Star, around which the rest of the stars lead their round dance, will rise higher and higher. There is a theorem that accurately describes this pattern: the height of the pole of the world above the horizon is equal to the latitude of the place of observation. Let us dwell on some of the corollaries that follow from this theorem.

Let's imagine that we got to the North Pole and from there we observe the stars. Our latitude is 90 "; which means that the pole of the world has a height of 90 °, that is, it is located at the zenith, right above our head. The luminaries describe daily circles around this point and move parallel to the horizon, which coincided with the celestial equator. None of them does not rise or set.Only the stars of the northern hemisphere of the celestial sphere are accessible to observation, that is, approximately half of all the luminaries of the firmament.

Let's go back to Moscow. The latitude is now about 56 °. "About" - because Moscow is stretched from north to south for almost 50 km, which is almost half a degree. The height of the pole of the world is 5b °, it is located in the northern part of the sky. In Moscow, you can already see some stars of the southern hemisphere, namely those with declination (b) exceeding -34 °. There are many bright ones among them: Sirius (5 \u003d -17 °), Rigel (6 - -8 e), Spica (5 \u003d -1I e ), Antares (6 \u003d -26 °), Fomal-gout (6 \u003d -30 °). Stars with declination greater than + 34 ° never set in Moscow. The stars of the southern hemisphere with declination below -34 "are not ascending; they cannot be observed in Moscow.

VISIBLE MOTION OF CO L H C A, LUNES AND PLANETS
PATH OF CO LUNS AMONG THE STAR

DAILY WAY CO LNTS

The sun reaches its greatest height, or, as astronomers say, climaxes. Noon is the upper culmination, and there is also the lower one - at midnight. In our mid-latitudes, the sun's lower culmination is not visible, as it occurs below the horizon. But beyond the Polar Steep, where the Sun sometimes does not set in summer, you can observe both the upper and lower climax.

In mid-latitudes, the apparent diurnal path throughout the year

The sun is shrinking, then increasing. It turns out to be smallest on the day of the winter solstice, and the largest on the day of the summer solstice. On the days of the equinox, the sun is at the celestial equator. These days it rises at the point to the east and sets at the point to the west.

In the period from the vernal equinox to the summer solstice, the place of sunrise shifts from the point east to the left, to the north. And the place of entry moves away from the west point to the right, also to the north. On the day of the summer solstice, the Sun appears in the northeast. At noon, it culminates at its highest altitude in a year. The sun sets in the northwest.

It should be borne in mind that due to refraction (i.e., refraction of light rays in the earth's atmosphere), the apparent height of the star is always greater than the true one. Therefore, the sun rises earlier and sets later than it would have been in the absence of the atmosphere.

So, the diurnal path of the Sun is a small circle of the celestial sphere, parallel to the celestial equator. At the same time, during the year, the Sun moves relative to the celestial equator to the north, then to the south. The day and night parts of his journey are not the same. They are equal only on the days of the equinox, when the Sun is at the celestial equator.

The sun went over the horizon. It got dark. Stars appeared in the sky. However, the day does not turn into night immediately. With the setting of the Sun, the Earth receives a weak diffused illumination for a long time, which fades out gradually, giving way to night darkness. This period is called twilight

Civil twilight. Nautical twilight.
Astronomical twilight

Twilight helps the vision to change from very high light conditions to low light and vice versa (at morning twilight). Measurements have shown that at mid-latitudes during twilight, the illumination decreases by half in about 5 minutes. This is enough for smooth vision adaptation. The gradual change in natural light strikingly distinguishes it from artificial. Electric lamps turn on and off instantly, forcing us to squint from the bright light or for a while "go blind" in the seeming pitch darkness.

There is no sharp boundary between twilight and night darkness. However, in practice, such a boundary has to be drawn: you need to know when to turn on street lights or beacon lights at airports and on rivers. That is why twilight has long been divided into three periods, depending on the depth of the sun's immersion under the horizon.

The earliest period - from the moment the Sun sets and until it sinks 6 ° below the horizon - is called civil twilight. At this time, a person sees in the same way as during the day, and there is no need for artificial lighting.

With the sinking of the Sun below the horizon from 6 to 12 ° navigational twilight sets in. During this period, natural illumination drops so much that it is no longer possible to read, and the visibility of surrounding objects greatly deteriorates. But the ship's navigator can still navigate the silhouettes of unlit shores. After the sun plunges 12 °, it becomes completely dark, but the dim light of dawn still interferes with seeing faint stars. This is astronomical twilight. And only when the Sun goes down 1 7-18 ° below the horizon, the faintest stars visible to the naked eye light up in the sky.

COAHUA ANNUAL WAY

The expression "the path of the Sun among the stars" will seem strange to some. After all, the stars are not visible during the day. Therefore, it is not easy to notice that the Sun is slowly, about 1 "per day, moving among the stars from right to left. But it is possible to trace how the appearance of the starry sky changes during the year. All this is a consequence of the Earth's revolution around the Sun.

The path of the apparent annual movement of the Sun against the background of the stars is called the ecliptic (from the Greek "eclipse" - "eclipse"), and the period of revolution along the ecliptic is called a sidereal year. It is equal to 365 days 6 hours 9 minutes 10 s, or 365.2564 average solar days.

Ecliptic and the celestial equator intersect at an angle of 23 ° 26 "at the points of the vernal and autumnal equinoxes. At the first of these points the Sun usually occurs on March 21, when it passes from the southern hemisphere of the sky to the northern. In the second, on September 23, when passing from the northern hemisphere to At the point farthest to the north of the ecliptic, the Sun occurs on June 22 (summer solstice), and to the south on December 22 (winter solstice). leap year these dates are shifted by one day.

Of the four points of the ecliptic, the main point is the vernal equinox. It is from it that "one of the celestial coordinates is counted - right ascension. It also serves to count the sidereal time and the tropical year - the time interval between two successive passages of the Sun's center through the vernal equinox. The tropical year determines the change of seasons on our planet.

Since the vernal equinox is slowly moving among the stars due to the precession of the earth's axis (see the article "Playing with a spinning top, or a long story with polar stars"), the duration of a tropical year is shorter than the duration of a stellar year. It is 365.2422 solar average days.

About 2 thousand years ago, when Hipparchus compiled his star catalog (the first one that has come down to us entirely), the vernal equinox was in the constellation Aries. By our time, it has moved almost 30 °, to the constellation Pisces. and the point of the autumnal equinox is from the constellation Libra to the constellation Virgo. But according to tradition, the points of equinox are designated by the signs of the former "equinox" constellations - Aries and Demons. The same happened with the points of the solstices: summer in the constellation Taurus is marked with the sign of Cancer 23, and winter in the constellation Sagittarius is marked by the sign of Capricorn.

The uneven movement of the Sun along the ecliptic leads to different lengths of the seasons. For inhabitants of the Northern Hemisphere, spring and summer are six days longer than autumn and winter. The Earth on July 2-4 is located 5 million kilometers further from the Sun than on January 2-3, and moves in its orbit more slowly in accordance with Kepler's second law. In summer, the Earth receives less heat from the Sun, but summer in the Northern Hemisphere is longer than winter. Therefore, the northern hemisphere of the Earth is warmer than the southern one.

MOTION AND PHASES OF THE MOON

The moon is known to change its appearance. It itself does not emit light, therefore only its surface illuminated by the Sun is visible in the sky - the daytime side. Moving across the sky from west to east, the Moon overtakes and surpasses the Sun in a month. At the same time, the lunar phases change: new moon, first quarter, full moon and last quarter.

On a new moon, the moon cannot be seen even through a telescope. It is located in the same direction as the Sun (only above or below it), and is turned towards the Earth by an unlit hemisphere. In one or two days, when the Moon moves away from the Sun, a narrow crescent can be observed a few minutes before its setting in the western side of the sky against the background of the evening dawn. The Greeks called the first appearance of the crescent moon after the new moon "neomenia" ("new moon *). This moment among the ancient peoples was considered the beginning of the lunar month.

Sometimes, for several days before and after the new moon, it is possible to notice the ash light of the moon. This faint glow from the nighttime part of the lunar disk is nothing more than sunlight reflected by the Earth onto the Moon. As the crescent grows larger, the ash light is paler! 4 and becomes invisible.

Farther and farther to the left of the Sun the Moon goes away. Its sickle grows every day, remaining convex to the right, towards the Sun. 7 days 10 hours after the new moon, a phase begins, called the first quarter. During this time, the Moon moved away from the Sun by 90 °. The sun's rays now illuminate only the right half of the lunar disk. After sunset, the moon is on the southern side of the sky and sets around midnight. Continuing to move from the Sun further and further to the east. The moon appears in the evening on the eastern side of the sky. She comes in after midnight, and every day later and later.

When our satellite is on the side opposite to the Sun (at an angular distance of 180 ° from it), the full moon comes. The full moon shines all night. It rises in the evening and sets in the morning. After 14 days 18 hours after the new moon, the Moon begins to approach the Sun from the right. The illuminated portion of the lunar disk decreases. Later, the moon rises above the horizon and by morning

The stars show the way

Even Odysseus kept the direction of the ship in accordance with the position of the Big Dipper in the sky. He was a skillful navigator who knew the starry sky well. He checked the course of his ship with the constellation, which sets exactly in the north-west. Odysseus knew how the Pleiades cluster moves during the night and, being guided by it, led the ship in the right direction.

But, of course, the North Star has always served as the main stellar compass. If you stand facing it, then it is easy to determine the sides of the horizon: in front there will be north, behind - south, on the right - east, left - west. Even in ancient times, this simple method allowed those who set off on a long journey to choose the right direction on land and at sea.

Astronavigation - orienteering by the stars - has retained its significance to this day. In aviation, navigation, land expeditions and in space flights, one cannot do without it.

Although the planes and sea \u200b\u200bvessels equipped with the latest radio navigation and radar equipment, there are situations when it is impossible to use the devices: suppose they are out of order or a storm has broken out in the earth's magnetic field. In such cases, the navigator of an airplane or ship must be able to determine its position and direction of movement along the Moon, stars or the Sun. And the astronaut cannot do without astronavigation. Sometimes he needs to turn the station in a certain way: for example, so that the telescope looks at the object under study, or to dock with an arriving transport ship.

Pilot-cosmonaut Valentin Vitalievich Lebedev recalls astronavigation training: “We are faced with a practical problem - to study the starry sky as best as possible, learn and study the constellations and reference stars ... After all, our field of view is limited - we are looking through the window. We needed to confidently determine the routes of transitions from one constellation to another, in order to come to a given area of \u200b\u200bthe sky in the shortest way and find the stars along which it was necessary to orient and stabilize the ship, providing a certain direction of the telescopes in space ... A significant part of our astronomical training took place at the Moscow Planetarium. ... From star to star, from constellation to constellation, we unraveled the labyrinths of star patterns, learned to find in them semantic and necessary lines of direction. "

NAVIGATION STARS

Navigation stars - the stars with the help of which in aviation, navigation and astronautics determine the location and course of the ship. Of the 6 thousand stars visible to the naked eye, 26 are considered navigational stars. These are the brightest stars, up to about 2 nd magnitude. For all these stars, tables of heights and azimuths have been compiled to facilitate the solution of navigation problems.

For orientation in the northern hemisphere of the Earth, 18 navigation stars are used. In the northern heavenly hemisphere, these are Polar, Arcturus, Vega, Capella, Aliot, Pollux, Alta-ir, Regulus, Aldebaran, Deneb, Betel-geyse, Procyon and Alferatz (Andromeda's star has three names: Alferatz, Alpharet and Sirrah; navigators the name Alferatz was adopted). To these stars are added 5 stars of the southern hemisphere of the sky; Sirius, Rigel, Spica, Antares and Fomalhaut.

Imagine a map of the stars of the northern celestial hemisphere. In its center is the North Star, and below the Big Dipper with neighboring constellations. We will not need a coordinate grid or constellation boundaries - after all, they are also absent in the real sky. We will learn to navigate only by the characteristic outlines of the constellations and the positions of bright stars.

To make it easier to find the navigation stars visible in the Northern Hemisphere of the Earth, the starry sky is divided into three sections (sectors): lower, right and left.

In the lower sector are the constellations Ursa Major, Ursa Minor, Bootes, Virgo, Scorpio and Leo. The conditional boundaries of the sector go from Polar to the right down and to the left down. The brightest star here is Arcturus (bottom left). It is indicated by the continuation of the "handle" of the Big Dipper Bucket. The bright star at the bottom right is Regulus (a Leo).

In the right sector are the constellations of Orion, Taurus, Auriga, Gemini, Canis Major and Canis Minor. The brightest stars are Sirius (it does not fall on the map, since it is in the southern celestial hemisphere) and Capella, then Rigel (it also does not fall on the map) and Betelgeuse from Orion (on the right at the edge of the map), Chug above is Aldebaran from Taurus, and below at the edge is Procyon of the Lesser Dog.

In the left sector - the constellations of Lyra, Cygnus, Eagle, Pegasus, Andromeda, Aries and Southern Pisces. The brightest star here is Vega, which, together with Altair and Deyeb, forms a characteristic triangle.

For navigation in the Southern Hemisphere of the Earth, 24 navigation stars are used, of which 16 are the same as in the Northern Hemisphere (excluding Polar and Betelgeuse). 8 more stars are added to them. One of them - Hamal - is from the northern constellation of Aries. The remaining seven are from the southern constellations: Canopus (a Carina), Achernar (a Eridani), Peacock (a Peacock), Mimosa (fj Southern Cross), Toliman (a Centauri), Atria (a Southern Triangle) and Kaus Australis (e Sagittarius ).

The most famous navigation constellation is the Southern Cross. Its longer "crossbar" almost exactly points to the south pole of the world, which lies in the constellation Octantus, where there are no visible stars.

To accurately find a navigation star, it is not enough to know in which constellation it is located. In cloudy weather, for example, only a fraction of the stars are observed. There is another limitation in space travel; only a small part of the sky is visible through the window. Therefore, it is necessary to be able to quickly recognize the desired navigation star by color and brilliance.

On a clear evening, try to make out the navigation stars in the sky, which every navigator knows by heart.

Every day, rising from the horizon in the eastern side of the sky, the Sun passes across the sky and hides again in the west. For residents of the Northern Hemisphere, this movement occurs from left to right, for southerners from right to left. At noon, the Sun reaches its greatest height, or, as astronomers say, climaxes. Noon is the upper culmination, and there is also the lower one - at midnight. In our mid-latitudes, the sun's lower culmination is not visible, as it occurs below the horizon. But beyond the Arctic Circle, where the Sun sometimes does not set in summer, one can observe both the upper and lower culminations.

At the geographic pole, the diurnal path of the Sun is practically parallel to the horizon. Appearing on the day of the vernal equinox, the Sun rises higher and higher for a quarter of a year, making circles above the horizon. On the day of the summer solstice, it reaches its maximum height (23.5?). The next quarter of the year, before the autumnal equinox, the Sun descends. This is a polar day. Then the polar night sets in for six months. In mid-latitudes, throughout the year, the apparent diurnal path of the Sun either decreases or increases. It turns out to be the smallest on the day of the winter solstice, and the largest on the day of the summer solstice. On the days of the equinox

The sun is at the celestial equator. At the same time, it rises at the point of the east and sets at the point of the west.

In the period from the vernal equinox to the summer solstice, the place of sunrise shifts slightly from the point of sunrise to the left, to the north. And the place of entry moves away from the west point to the right, although also to the north. On the day of the summer solstice, the Sun appears in the northeast, and at noon it culminates at its highest altitude in a year. The sun sets in the northwest.

Then the places of sunrise and sunset are shifted back to the south. On the winter solstice, the Sun rises in the southeast, crosses the celestial meridian at its minimum height, and sets in the southwest. It should be borne in mind that due to refraction (that is, the refraction of light rays in the earth's atmosphere), the apparent height of the star is always greater than the true one.

Therefore, the sun rises earlier and sets later than it would have been in the absence of the atmosphere.

The expression "the path of the sun among the stars" will seem strange to some. After all, the stars are not visible during the day. Therefore, it is not easy to notice that the Sun is slow, by about 1? per day, moves among the stars from right to left. But you can see how the appearance of the starry sky changes throughout the year. All this is a consequence of the revolution of the Earth around the Sun.

The path of the apparent annual movement of the Sun against the background of stars is called the ecliptic (from the Greek "eclipse" - "eclipse"), and the period of revolution along the ecliptic is called a sidereal year. It is equal to 265 days 6 hours 9 minutes 10 seconds, or 365, 2564 average solar days.

The ecliptic and the celestial equator intersect at an angle of 23? 26 "at the vernal and autumnal equinox points. In the first of these points, the Sun usually occurs on March 21, when it passes from the southern hemisphere of the sky to the northern one. In the second, on September 23, during the transition of their northern hemisphere At the ecliptic farthest to the north, the Sun occurs on June 22 (summer solstice), and to the south on December 22 (winter solstice) .In a leap year, these dates are shifted by one day.

Of the four points of the ecliptic, the main point is the vernal equinox. It is from it that one of the celestial coordinates is counted - right ascension. It also serves to count sidereal time and the tropical year - the time interval between two successive passages of the center of the Sun through the vernal equinox. The tropical year determines the seasons on our planet.

Since the vernal equinox moves slowly among the stars due to the precession of the earth's axis, the duration of the tropical year is less than the duration of the stellar one. It is 365.2422 solar average days. About 2 thousand years ago, when Hipparchus compiled his stellar catalog (the first one that has come down to us entirely), the vernal equinox was in the constellation Aries. By our time, it has moved almost 30?, To the constellation Pisces, and the autumnal equinox point - from the constellation Libra to the constellation Virgo. But according to tradition, the points of equinox are designated by the same signs of the previous "equinox" constellations - Aries and Libra. The same happened with the solstice points: summer in the constellation Taurus is marked with the sign of Cancer, and winter in the constellation Sagittarius is marked with the sign of Capricorn.

And finally, the last thing that is associated with the apparent annual motion of the Sun. Half of the ecliptic from the vernal equinox to the autumn (from March 21 to September 23), the Sun passes in 186 days. The second half, from the autumnal and spring equinox, - in 179 days (180 in a leap year). But the halves of the ecliptic are equal: each 180? Consequently, the Sun moves unevenly along the ecliptic. This unevenness is explained by a change in the speed of the Earth in an elliptical orbit around the Sun. The uneven movement of the Sun along the ecliptic leads to different lengths of the seasons. For residents of the northern hemisphere, for example, spring and summer are six days longer than autumn and winter. The Earth on June 2-4 is located 5 million kilometers from the Sun longer than January 2-3, and moves in its orbit more slowly in accordance with Kepler's second law. In the summer, the Earth receives from

The sun is less warm, but summer in the Northern Hemisphere is longer than winter. Therefore, in the Northern Hemisphere, the Earth is warmer than in the Southern.

Modern scientific thought defines the Zodiac as twelve constellations located in a strip 18 degrees wide along the apparent annual path of the Sun among the stars, called the Ecliptic, within which all the planets of the solar system move.
Thus, she does not distinguish between the NATURAL Zodiac, which exists in the sky, and its ASTROLOGICAL concept, which astrologers operate in their calculations.
On the first pages scientific papers in Astrology, you will find the following graphic images of the Zodiac (Fig. 1-4).

Why it is possible to twist the Zodiac left and right and even "convert" it, no one explains. Unless, of course, you do not take into account such explanations: the right-sided Zodiac is a tribute to ancient traditions, which cannot be violated; left-handed is also a tribute, but already achievements modern science, which proved that the Sun does not revolve around the Earth, but the Earth revolves around the Sun.
Further, after endowing each zodiac sign and planet with certain quality characteristics, you actually get the right to start an independent game of Astrology, which is best started with predicting your own fate. And already in the course of the game, it is proposed to observe some non-rigid rules, the acceptance and observance of which depends mainly on the taste of the player, the freedom to interpret these rules freely enough, to make their own significant additions and amendments to them, since "the end justifies the means."

Therefore, if we collect the basic principles inherent in the concept of the Zodiac, bit by bit, from different sources, we get the following, rather motley picture.
1. The apparent annual path of the Sun among the stars, or the Ecliptic, is a circle. That is, the movement of the Sun around the Earth is a cyclical process, and at least for this reason the Astrological Zodiac should be round, not rectangular.
2. The zodiac circle is divided into 12 equal parts by the number of the Zodiac constellations, named in the same way, in the same sequence as the Natural ones: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces.
3. Each Zodiac sign has its own natural energy, the quality of which is determined by the group of stars or constellations that is in it.
4. The energy of each planet has its own specific natural color, reflecting its individuality.
5. All processes occurring on Earth are caused to life by planetary energy, which is necessarily associated with it, and their course of development depends on the movement and mutual position of the planets relative to each other.
6. The original quality of the energy of the planets and signs of the Zodiac does not change over time.
7. The planet, passing through the signs of the Zodiac, is additionally "painted in the color" of the energy of the Sign through which it passes. (We are not yet considering the question of harmony and disharmony of this color.) Therefore, the quality of the energy coming from the planet to the Earth constantly changes depending on which Zodiac sign it is in at the moment.
8. For the beginning and end of the annual process of the Sun's movement around the Earth, the natural rhythm is taken, namely: The Spring Equinox point is the equality of the duration of the day and night on March 21. It is believed that it is at this moment that the Sun enters the beginning of Aries, in its zero degree, from which all the coordinates of the planets on the Zodiacal circle are calculated further during a given year.

Equinox on Earth occurs at the moment when the Sun in its motion hits the point of intersection of the Ecliptic with the Celestial Equator. In turn, the position of the Celestial equator is necessarily related to the angle of inclination of the constantly precessing Earth axis to the plane of the Ecliptic. Consequently, the Spring Equinox Point is not stationary, but mobile. Indeed, it moves along the Ecliptic at a speed of 1 ° in 72 years. Currently, this point is not in the zero degree of Aries, but in the first degree of Pisces. Thus, it turns out that the Natural and Astrological Zodiac are completely different things, and the entire modern scientific astrological basis is spreading at the seams.
True, some astrologers who are engaged in karmic Astrology believe that there are no contradictions here, but simply when constructing horoscopes, it is necessary to amend the coordinates of the planets, taking into account the precession, and then everything will fall into place.
And even though Aries will become Pisces, Gemini Taurus and so on, but this will not be considered a mistake, on the contrary, it will be a correction of the mistakes of those astrologers who are still mistaken in their calculations.
In confirmation of their correctness, they cite the horoscopes of two famous figures of our time: Vladimir Lenin and Adolf Hitler, who, according to ordinary Astrology, were born Taurus, but, according to the inner conviction of the karmists, Taurus, allegedly, cannot do what they have done, and only transformation them in Aries makes their deeds understandable, like twice two - four.
In order to understand this scientific chaos and determine specific landmarks in it, we will use the keys already known to us and first answer the main question: why does modern scientific Astrology fail?
The thing is that modern astrologers, paying tribute to the achievements of modern science, and most importantly, in order not to be branded as profane, in their theoretical reasoning proceed mainly from the HELIOCENTRIC picture of the World, but in their practical work use the achievements of ancient astrologers, who were guided by the ideas of GEOCENTRISM. The result is porridge.
We will be guided by the Canons of the Universe, but we will project them onto our planetary body. Therefore, for us, the planet Earth will become the center of the Universe, that is, that specific focal point in which we will consider the manifestation of these laws and their individual coloring.

§ 52. Apparent annual motion of the Sun and its explanation

Observing the diurnal movement of the Sun throughout the year, one can easily notice in its movement a number of features that differ from the diurnal movement of stars. The most typical of them are as follows.

1. The place of sunrise and sunset, and hence its azimuth, change from day to day. Starting from March 21 (when the Sun rises at the point in the east and sets at the point in the west) to September 23, the sunrise is observed in the northeastern quarter, and the sunset is observed in the northeastern quarter. At the beginning of this time, the points of sunrise and sunset move to the north, and then to reverse direction... On September 23, just like March 21, the Sun rises at the point of the east and sets at the point of the west. Starting from September 23 to March 21, a similar phenomenon will be repeated in the south-skeleton and south-west quarters. The movement of the sunrise and sunset points has a one-year period.

Stars always rise and set at the same points on the horizon.

2. The meridional height of the Sun changes every day. For example, in Odessa (cf \u003d 46 °, 5 N) on June 22, it will be the largest and equal to 67 °, then it will begin to decrease and on December 22, it will reach the lowest value of 20 °. After December 22, the meridional height of the Sun will begin to increase. This phenomenon is also an annual period. The meridional heights of stars are always constant. 3. The length of time between the culminations of a star and the Sun is constantly changing, while the length of time between two culminations of the same stars remains constant. So, at midnight, we see the culminating constellations that are currently on the opposite side of the sphere from the Sun. Then some constellations give way to others, and during the year at midnight all the constellations are successively culminated.

4. The length of the day (or night) is not constant throughout the year. This is especially noticeable if we compare the duration of summer and winter days at high latitudes, for example, in Leningrad. This happens because the time the Sun spends over the horizon during the year is different. The stars above the horizon are always the same amount of time.

Thus, the Sun, in addition to the daily movement performed together with the stars, also has a visible movement along the sphere with an annual period. This movement is called visible. the annual movement of the Sun across the celestial sphere.

We will get the most vivid idea of \u200b\u200bthis movement of the Sun if we determine its equatorial coordinates every day - right ascension a and declination b Then, using the found coordinates, we will plot points on the auxiliary celestial sphere and connect them with a smooth curve. As a result, we get a large circle on the sphere, which will indicate the path of the apparent annual motion of the Sun. The circle on the celestial sphere along which the Sun moves is called the ecliptic. The ecliptic plane is tilted to the equatorial plane at a constant angle g \u003d 23 ° 27 ", which is called the tilt angle ecliptic to the equator (fig. 82).

Figure: 82.

The apparent annual movement of the Sun along the ecliptic occurs in the direction opposite to the rotation of the celestial sphere, that is, from west to east. The ecliptic intersects the celestial equator at two points, which are called the equinox points. The point at which the Sun moves from the southern hemisphere to the northern, and therefore changes the name of the declination from south to north (i.e., from bS to bN), is called a point vernal equinox and is denoted by the Y. This sign denotes the constellation Aries, in which this point was once located. Therefore, it is sometimes called the point of Aries. Point T is currently in the constellation Pisces.

The opposite point, at which the Sun moves from the northern hemisphere to the southern one and changes the name of its declination from b N to b S, is called the point of the autumnal equinox. It is designated by the sign of the Libra constellation O, in which it was once located. Currently, the point of the autumnal equinox is in the constellation Virgo.

Point L is called summer point, and point L "- point winter solstices.

Let's trace the apparent movement of the Sun along the ecliptic throughout the year.

The Sun comes to the vernal equinox on March 21. Right ascension a and declination of the Sun b are equal to zero. Throughout the globe, the Sun rises at point O st and sets at point W, and day is equal to night. Since March 21, the Sun has been moving along the ecliptic towards the point of the summer solstice. Right ascension and declination of the Sun are continuously increasing. Astronomical spring is coming in the northern hemisphere, and autumn in the southern hemisphere.

On June 22, about 3 months later, the Sun comes to the point of the summer solstice L. Right ascension of the Sun a \u003d 90 °, and declination b \u003d 23 ° 27 "N. Astronomical summer begins in the northern hemisphere (the longest days and shortest nights), and in the south it is winter (the longest nights and the shortest days). As the Sun continues to move, its north declination begins to decrease, while right ascension continues to increase.

Approximately three months later, on September 23, the Sun comes to the autumnal equinox point Q. Right ascension of the Sun a \u003d 180 °, declination b \u003d 0 °. Since b \u003d 0 ° (as well as on March 21), then for all points on the earth's surface the Sun rises at point O st and sets at point W. Day will be equal to night. The name of the declination of the Sun changes from north 8n to south - bS. Astronomical autumn is coming in the northern hemisphere, and spring in the southern hemisphere. With further movement of the Sun along the ecliptic to the winter solstice point U, declination 6 and right ascension aO increase.

On December 22, the Sun comes to the point of the winter solstice L ". Right ascension a \u003d 270 ° and declination b \u003d 23 ° 27" S. Astronomical winter sets in in the northern hemisphere, and summer in the southern.

After December 22, the Sun moves to point T. The name of its declination remains south, but decreases, and right ascension increases. About 3 months later, on March 21, the Sun, having completed a full revolution along the ecliptic, returns to the point of Aries.

Changes in right ascension and declination of the Sun do not remain constant throughout the year. For approximate calculations, the daily change in right ascension of the Sun is taken equal to 1 °. The change in declination per day is taken equal to 0 °, 4 within one month before the equinox and one month after, and the change to 0 °, 1 within one month before the solstices and one month after the solstices; the rest of the time, the change in the declination of the Sun is taken equal to 0 °, 3.

The peculiarity of the change in the right ascension of the Sun plays an important role in the choice of the basic units for measuring time.

The vernal equinox moves along the ecliptic towards the annual motion of the Sun. Its annual displacement is 50 ", 27 or rounded 50", 3 (for 1950). Consequently, the Sun does not reach the original location relative to the fixed stars by a magnitude of 50 ", 3. For the Sun to travel the specified path, it will take 20 m m 24 s. For this reason, the spring

It comes before the Sun ends and its apparent annual motion is a full circle of 360 ° relative to fixed stars. The shift in the moment of the onset of spring was discovered by Hipparchus in the II century. BC e. from the observations of stars that he made on the island of Rhodes. He called this phenomenon the anticipation of the equinoxes, or precession.

The phenomenon of displacement of the vernal equinox point made it necessary to introduce the concepts of tropical and stellar years. The tropical year is called the period of time during which the Sun makes a full revolution in the celestial sphere relative to the vernal equinox T. "The duration of the tropical year is 365.2422 days. The tropical year is consistent with natural phenomena and precisely contains the full cycle of the seasons of the year: spring, summer, autumn and winter.

A sidereal year is called the period of time during which the Sun makes a complete revolution in the celestial sphere relative to the stars. The duration of a sidereal year is 365.2561 days. A sidereal year is longer than a tropical one.

In its apparent annual motion across the celestial sphere, the Sun passes among various stars located along the ecliptic. Even in ancient times, these stars were divided into 12 constellations, most of which were given the names of animals. The strip of sky along the ecliptic formed by these constellations was called the Zodiac (circle of animals), and the constellations - the zodiacal.

According to the seasons of the year, the Sun passes the following constellations:

From the joint motion of the Sun-annual along the ecliptic and diurnal due to the rotation of the celestial sphere, a general motion of the Sun along a spiral line is created. The extreme parallels of this line are located on both sides of the equator at distances of \u003d 23 °, 5.

On June 22, when the Sun describes the extreme diurnal parallel in the northern celestial hemisphere, it is in the constellation Gemini. In the distant past, the Sun was in the constellation Cancer. On December 22nd, the Sun is in the constellation Sagittarius, and in the past it was in the constellation Capricorn. Therefore, the extreme northern celestial parallel was called the Tropic of Cancer, and the southern - the Tropic of Capricorn. The corresponding earthly parallels with latitudes cp \u003d betax \u003d 23 ° 27 "in the northern hemisphere were called the Tropic of Cancer, or the northern tropic, and in the southern, the tropic of Capricorn, or the southern tropic.

In the joint movement of the Sun, which occurs along the ecliptic with the simultaneous rotation of the celestial sphere, there are a number of features: the length of the diurnal parallel above the horizon and below the horizon (and, consequently, the length of the day and night) changes, the meridional heights of the Sun, the points of sunrise and sunset, etc. All these phenomena depend on the relationship between the geographical latitude of a place and the declination of the Sun. Therefore, for an observer at different latitudes, they will be different.

Consider these phenomena in some latitudes:

1. The observer is at the equator, cp \u003d 0 °. The axis of the world lies in the plane of the true horizon. The celestial equator coincides with the first vertical. The diurnal parallels of the Sun are parallel to the first vertical, therefore the Sun in its diurnal movement never crosses the first vertical. The sun rises and sets daily. Day is always equal to night. The Sun is at its zenith twice a year - on March 21 and September 23.

Figure: 83.

2. The observer is at latitude φ
3. The observer is at latitude 23 ° 27 "
4. The observer is in latitude φ\u003e 66 ° 33 "N or S (Fig. 83). The belt is polar. The parallels φ \u003d 66 ° 33" N or S are called polar circles. In the polar belt, polar days and nights can be observed, that is, when the Sun is above the horizon for more than a day or more than a day below the horizon. The longer the latitude, the longer the polar days and nights. The sun rises and sets only on days when its declination is less than 90 ° -φ.

5. The observer is at the pole φ \u003d 90 ° N or S. The axis of the world coincides with the plumb line and, therefore, the equator is with the plane of the true horizon. The position of the observer's meridian will be uncertain, so parts of the world are missing. During the day, the sun moves parallel to the horizon.

On the days of the equinox, there are polar sunrises or sunsets. On solstice days, the height of the Sun reaches highest values... The height of the Sun is always equal to its declination. The polar day and the polar night last for 6 months.

Thus, due to various astronomical phenomena caused by the joint daily and annual movement of the Sun at different latitudes (passage through the zenith, the phenomena of the polar day and night) and the climatic features caused by these phenomena, the earth's surface is divided into tropical, temperate and polar belts.

Tropical belt is the part of the earth's surface (between latitudes φ \u003d 23 ° 27 "N and 23 ° 27" S), in which the Sun rises and sets every day, and during the year it is twice at the zenith. The tropical belt occupies 40% of the entire earth's surface.

Moderate belt is called the part of the earth's surface in which the sun rises and sets daily, but is never at its zenith. There are two temperate zones. In the northern hemisphere, between latitudes φ \u003d 23 ° 27 "N and φ \u003d 66 ° 33" N, and in the southern hemisphere between latitudes φ \u003d 23 ° 27 "S and φ \u003d 66 ° 33" S. Temperate belts occupy 50% of the earth's surface.

Polar belt is called the part of the earth's surface in which polar days and nights are observed. There are two polar belts. The North Polar Belt extends from latitude φ \u003d 66 ° 33 "N to the North Pole, and the southern one extends from φ \u003d 66 ° 33" S to the South Pole. They occupy 10% of the earth's surface.

For the first time, Nicolaus Copernicus (1473-1543) gave a correct explanation of the apparent annual motion of the Sun in the celestial sphere. He showed that the annual movement of the Sun in the celestial sphere is not its actual movement, but only the visible, reflecting the annual movement of the Earth around the Sun. Copernicus's system of the world has been called heliocentric. According to this system in the center solar system there is the Sun, around which the planets move, including our Earth.

The Earth simultaneously participates in two movements: it rotates around its axis and moves in an ellipse around the Sun. The rotation of the Earth around its axis causes the change of day and night. Its movement around the Sun causes the change of seasons. From the joint rotation of the Earth around its axis and movement around the Sun there is a visible movement of the Sun along the celestial sphere.

To explain the apparent annual motion of the Sun in the celestial sphere, let us use Fig. 84. In the center is the Sun S, around which the Earth moves counterclockwise. Earth axis maintains a constant position in space and makes an angle with the ecliptic plane equal to 66 ° 33 ". Therefore, the equatorial plane is inclined to the ecliptic plane at an angle e \u003d 23 ° 27". Next comes the celestial sphere with the ecliptic and the signs of the constellations of the Zodiac in their modern arrangement applied on it.

The Earth comes to position I on March 21. When viewed from Earth, the Sun is projected onto the celestial sphere at point T, which is currently in the constellation Pisces. The declination of the Sun is e \u003d 0 °. An observer at the Earth's equator sees the Sun at noon at its zenith. All terrestrial parallels are half illuminated, therefore, at all points of the earth's surface, day is equal to night. Astronomical spring begins in the northern hemisphere, and autumn begins in the southern.

Figure: 84.

The Earth comes to position II on June 22. Declination of the Sun b \u003d 23 °, 5N. When viewed from Earth, the Sun is projected into the constellation Gemini. For an observer at latitude φ \u003d 23 °, 5N, (The sun passes through the zenith at noon. Most of the diurnal parallels are illuminated in the northern hemisphere and less in the southern. The northern polar belt is illuminated and the southern one is not illuminated. The polar day lasts on the northern one, and on the south - polar night.In the northern hemisphere of the Earth, the sun's rays fall almost vertically, and in the southern - at an angle, so in the northern hemisphere there is an astronomical summer, and in the southern - winter.

In position III Earth comes September 23rd. The declination of the Sun is bo \u003d 0 ° and it is projected to the point of Libra, which is now in the constellation Virgo. An observer at the equator sees the Sun at noon at its zenith. All terrestrial parallels are half illuminated by the Sun, therefore, at all points on the Earth, day is equal to night. Astronomical autumn begins in the northern hemisphere, and spring begins in the southern.

On December 22nd, the Earth comes to position IV. The sun is projected into the constellation Sagittarius. Declination of the Sun 6 \u003d 23 °, 5S. In the southern hemisphere, most of the diurnal parallels are illuminated than in the northern, therefore, in the southern hemisphere, the day is longer than night, and in the northern - the opposite. The sun's rays fall almost vertically in the southern hemisphere, and at an angle to the northern. Therefore, astronomical summer begins in the southern hemisphere, and winter in the northern. The sun illuminates the southern polar belt and does not illuminate the northern one. A polar day is observed in the southern polar belt, and night in the northern one.

Corresponding explanations can be given for the rest of the intermediate positions of the Earth.

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True motion of the Earth - Apparent annual motion of the Sun on the celestial sphere - Celestial equator and ecliptic plane - Equatorial coordinates of the Sun throughout the year

The true movement of the earth

To understand the principle of the apparent movement of the Sun and other luminaries on the celestial sphere, let us first consider true motion of the earth... The earth is one of the planets. It rotates continuously around its axis.

Its rotation period is equal to one day, so it seems to an observer on Earth that all celestial bodies revolve around the Earth from east to west with the same period.

But the Earth not only revolves around its axis, but also revolves around the Sun in an elliptical orbit. It makes a complete revolution around the Sun in one year. The axis of rotation of the Earth is inclined to the orbital plane at an angle of 66 ° 33 ′. The position of the axis in space during the movement of the Earth around the Sun remains almost unchanged all the time. Therefore, the North and Southern hemisphere alternately are facing the sun, resulting in a change of seasons on the earth.

When observing the sky, you can see that the stars invariably maintain their relative position for many years.

The stars are "stationary" only because they are very far from us. The distance to them is so great that from any point of the earth's orbit they are visible equally.

But the bodies of the solar system - the Sun, the Moon and the planets, which are relatively close to the Earth, and we can easily notice the change in their positions. Thus, the Sun, along with all the luminaries, participates in the daily movement and at the same time has its own apparent movement (it is called annual movement) due to the movement of the Earth around the Sun.

Apparent annual motion of the Sun on the celestial sphere

The simplest annual movement of the Sun can be explained by the figure below. It can be seen from this figure that, depending on the position of the Earth in orbit, an observer from the Earth will see the Sun against the background of different ones. It will seem to him that it is constantly moving in the celestial sphere. This movement is a reflection of the Earth's revolution around the Sun. In a year, the Sun will make a complete revolution.

The large circle on the celestial sphere, along which the apparent annual movement of the Sun occurs, is called ecliptic... Ecliptic is a Greek word and in translation means eclipse... This circle was named so because the eclipses of the Sun and Moon occur only when both bodies are on this circle.

It should be noted that the plane of the ecliptic coincides with the plane of the Earth's orbit.

The apparent annual movement of the Sun along the ecliptic occurs in the same direction in which the Earth moves in its orbit around the Sun, i.e., it moves to the east. During the year, the Sun sequentially passes along the ecliptic of 12 constellations, which form a belt and are called zodiacal.

The zodiac belt is formed by the following constellations: Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn and Aquarius. Due to the fact that the plane of the Earth's equator is inclined to the plane of the Earth's orbit by 23 ° 27 ', plane of the celestial equator also inclined to the ecliptic plane at an angle of e \u003d 23 ° 27 ′.

The inclination of the ecliptic to the equator does not remain constant (due to the influence on the Earth of the forces of attraction of the Sun and the Moon), therefore in 1896, when approving the astronomical constants, it was decided to consider the inclination of the ecliptic to the equator averaged 23 ° 27'8 ″, 26.

Celestial equator and ecliptic plane

The ecliptic intersects the celestial equator at two points, which are called points of the spring and autumn equinoxes... The point of the vernal equinox is usually denoted by the sign of the constellation Aries T, and the point of the autumnal equinox by the sign of the constellation Libra -. The sun at these points is on March 21 and September 23, respectively. On these days on Earth, day is equal to night, the Sun exactly rises at the point of the east and sets at the point of the west.

The vernal and autumnal equinox points are the intersection of the equator and the ecliptic plane

The ecliptic points that are 90 ° from the equinox are called points of solstices... The point E on the ecliptic at which the Sun is highest relative to the celestial equator is called the summer solstice point, and the point E ', in which it occupies the lowest position, is called the point of the winter solstice.

At the point of the summer solstice, the Sun is on June 22, and at the winter solstice, on December 22. For several days close to the dates of the solstices, the noon height of the Sun remains almost unchanged, which is why these points received such a name. When the Sun is at the summer solstice, the day is the longest in the Northern Hemisphere and the night is the shortest, and when it is at the winter solstice, the opposite is true.

On the day of the summer solstice, the points of rising and setting of the Sun are as far north as possible from the points of east and west on the horizon, and on the day of the winter solstice they have the greatest distance to the south.

The movement of the Sun along the ecliptic leads to a continuous change in its equatorial coordinates, a daily change in noon altitude and movement along the horizon of the points of rising and setting.

It is known that the declination of the Sun is measured from the plane of the celestial equator, and right ascension - from the vernal equinox. Therefore, when the Sun is at the vernal equinox, its declination and right ascension are zero. During the year, the declination of the Sun in the present period varies from + 23 ° 26 ′ to -23 ° 26 ′, passing twice a year through zero, and right ascension from 0 to 360 °.

Equatorial coordinates of the Sun throughout the year

The equatorial coordinates of the Sun vary unevenly throughout the year. This is due to the uneven motion of the Sun along the ecliptic and the motion of the Sun along the ecliptic and the inclination of the ecliptic to the equator. The Sun passes half of its apparent annual path in 186 days from March 21 to September 23, and the second half in 179 days from September 23 to March 21.

The uneven motion of the Sun along the ecliptic is due to the fact that the Earth throughout the entire period of its revolution around the Sun moves in its orbit at a different speed. The sun is at one of the focuses of the Earth's elliptical orbit.

Of kepler's second law it is known that the line connecting the Sun and the planet describes equal areas at equal intervals. According to this law, the Earth, being closest to the Sun, that is, in perihelion, moves faster, and being farthest from the Sun, that is, in aphelion - slower.

Closer to the Sun, the Earth happens in winter, and further in summer. Therefore, on winter days, it moves in orbit faster than on summer. As a result, the daily change in right ascension of the Sun on the day of the winter solstice is 1 ° 07 ′, while on the day of the summer solstice it is only 1 ° 02 ′.

The difference in the speeds of the Earth's movement at each point of the orbit causes uneven changes in not only right ascension, but also the declination of the Sun. However, due to the inclination of the ecliptic to the equator, its change has a different character. The declination of the Sun changes most rapidly near the equinox points, and at the solstice points it hardly changes.

Knowing the nature of the change in the equatorial coordinates of the Sun makes it possible to make an approximate calculation of the right ascension and declination of the Sun.

To perform such a calculation, take the nearest date with the known equatorial coordinates of the Sun. Then it is taken into account that the right ascension of the Sun per day changes by an average of 1 °, and the declination of the Sun during the month before and after passing the equinox points changes by 0.4 ° per day; during the month before the solstices and after them - by 0.1 ° per day, and during the intermediate months between the indicated - by 0.3 °.