As a result of the movement of the Earth in its orbit, it seems to an observer on Earth that the Sun is constantly moving around the celestial sphere relative to the fixed stars.

True, it is not possible to observe the movement of the Sun relative to the stars, because. The stars are not visible during the daytime. We list some convincing facts about the movement of the Sun relative to the stars

1. At different times of the year, different stars are visible at midnight.

2. The meridional height of the Sun changes throughout the year.

3. The azimuths of sunrise and sunset also change, as well as the length of day and night.

Ecliptic(from Latin ecliptica - eclipse), a large circle of the celestial sphere, along which the visible annual movement of the Sun occurs.

A modern, more accurate definition of the ecliptic is a section of the celestial sphere by the plane of the orbit of the barycenter of the Earth-Moon system.

The Earth, moving along its orbit, maintains the same position of its axis of rotation in world space.

The angle of inclination of the Earth's axis of rotation with the plane of the Earth's orbit is 66°33", therefore, the angle between the plane of the Earth's orbit and the plane of the Earth's equator is 23°26".

The ecliptic is the projection of the plane of the earth's orbit onto the celestial sphere.

Because the plane of the celestial equator is a continuation of the earth's equator, and the plane of the ecliptic is the plane of the Earth's orbit, then the plane of the ecliptic makes an angle with the plane of the celestial equator = 23 ° 27 ".

Due to the fact that the Moon's orbit is inclined relative to the ecliptic and due to the rotation of the Earth around the barycenter of the Moon-Earth system, plus also due to the perturbations of the Earth's orbit from other planets, the true Sun is not always exactly on the ecliptic, but can deviate by several seconds of arc. We can say that the path of the "average Sun" passes along the ecliptic.

The plane of the ecliptic is inclined to the plane of the celestial equator at an angle: ε = 23°26′21.448″ - 46.815″ t - 0.0059″ t² + 0.00181″ t³, where t is the number of Julian centuries that have elapsed since the beginning of 2000. This formula is valid for the coming centuries. Over longer periods of time, the obliquity of the ecliptic to the equator fluctuates about the mean with a period of approximately 40,000 years.

In addition, the inclination of the ecliptic to the equator is subject to short-period fluctuations with a period of 18.6 years and an amplitude of 18.42″, as well as smaller ones.

Unlike the plane of the celestial equator, which changes its inclination relatively quickly, the plane of the ecliptic is more stable relative to distant stars and quasars, although it is also subject to slight changes due to perturbations from the planets of the solar system.

The name "ecliptic" is associated with the fact known since ancient times that solar and lunar eclipses occur only when the Moon is near the points of intersection of its orbit with the ecliptic. These points on the celestial sphere are called the lunar nodes, their cycle of revolution along the ecliptic, equal to about 18 years, is called the Saros, or Draconic period.

The ecliptic passes through the zodiac constellations and the constellation Ophiuchus.

The plane of the ecliptic serves as the main plane in the ecliptic celestial coordinate system.

Also, the ecliptic is of fundamental importance in astrology, most schools of this occult discipline include the interpretation of the positions of the heavenly bodies in the signs of the zodiac, that is, they consider their positions precisely on the ecliptic.

Also important for most schools of astrology, the angular distances between the luminaries in the overwhelming majority of cases are determined in astrology, taking into account only their ecliptic longitude, and in this sense, the aspects are “resonances” not so much between the real positions of the luminaries on the celestial sphere, but actually between their ecliptic projections, that is, between the points of the ecliptic - their ecliptic longitudes.

The two points where the ecliptic intersects the celestial equator are called the equinoxes.

At the point of the vernal equinox, the Sun in its annual movement passes from the southern hemisphere of the celestial sphere to the northern one; at the point of the autumnal equinox - from the northern hemisphere to the southern. The two points on the ecliptic that are 90° apart from the equinoxes and thus the furthest from the celestial equator are called the solstice points.

The summer solstice is in the northern hemisphere, the winter solstice is in the southern hemisphere.

These four points are denoted by zodiac symbols corresponding to the constellations in which they were at the time of Hipparchus (as a result of the prelude of the equinoxes, these points have shifted and are now in other constellations): the spring equinox - the sign of Aries (♈), the autumn equinox - the sign of Libra (♎) , the winter solstice - the sign of Capricorn (♑), the summer solstice - the sign of Cancer (♋).

The axis of the ecliptic is the diameter of the celestial sphere, perpendicular to the plane of the ecliptic. The axis of the ecliptic intersects with the surface of the celestial sphere at two points - the north ecliptic pole, which lies in the northern hemisphere, and the south ecliptic pole, which lies in the southern hemisphere. The north ecliptic pole has equatorial coordinates R.A. = 18h00m, Dec = +66°33", and is in the constellation Draco.

The circle of ecliptic latitude, or simply the circle of latitude, is a large semicircle of the celestial sphere passing through the poles of the ecliptic.

The Aries point is the point on the celestial sphere at which the Sun, in its apparent annual movement, changes its declination from south to north. The Sun comes to this point every year on March 21st - on the day of the spring equinox.

The point of Aries sets the reference point for one more coordinate - for right ascension.

Right ascension is the arc of the celestial equator from the point of Aries to the meridian of the star, in the direction of reverse western hourly angles (or if viewed from the north pole, then counterclockwise). It is in this direction that the Sun and Moon move in the celestial sphere and, consequently, the right ascension of these luminaries increases.

Tropical year is the period of time between two successive passages of the center of the Sun through the point of Aries. Its duration is 365.2422 days. This period is the basis of the calendar year. Refinement of the value of the tropical year has left its mark on the history of astronomy in the form of the Egyptian year, Julian and Gregorian styles.

For approximate calculations, it is necessary to know the daily changes in the coordinates of the Sun. The right ascension of the Sun varies almost uniformly throughout the year. The daily rate of change of the right ascension of the Sun is 360°/365.2422 1°/day.

The Sun's declination varies unevenly throughout the year.

0.4 ° / day for 1 month before and 1 month after the equinoxes;

0.1 ° / day for 1 month before and 1 month after the solstices;

0.3 °/day for the remaining 4 intermediate months.

- Moon .

Description

The name "ecliptic" is associated with the fact known since ancient times that solar and lunar eclipses occur only when the Moon is near the points of intersection of its orbit with the ecliptic. These points on the celestial sphere are called lunar nodes, their period of revolution along the ecliptic, equal to about 18 years, is called saros, or draconic period.

The plane of the ecliptic serves as the base plane in the ecliptic celestial coordinate system.

The angles of inclination of the orbits of the planets of the solar system to the plane of the ecliptic

Planet	Tilt to the ecliptic
Mercury	7.01°
Venus	3.39°
Land	0°
Mars	1.85°
Jupiter	1.31°
Saturn	2.49°
Uranus	0.77°
Neptune	1.77°

Ecliptic in literature

In Stanislav Lem's "Pirx's Tale" (from the series "Stories about the pilot Pirx") the ecliptic plane is a zone forbidden for spaceships, but the pilot Pirks, due to a number of circumstances, has to fly in it. That is why he manages to see a long-dead alien ship brought into the plane of the ecliptic by an off-system meteorite swarm.

see also

• Invariant plane ( English)

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Notes

Literature

• Panchenko D. Who found the Zodiac? // Antike Naturwissenschaft und ihre Rezeption. - 1998. - Vol. 9. - P. 33-44.
• Brack-Bernsen L.// Centaurus. - 2003. - Vol. 45.-P. 16–31.

Links

• // Encyclopedic Dictionary of Brockhaus and Efron: in 86 volumes (82 volumes and 4 additional). - St. Petersburg. , 1890-1907.
• Ecliptic- article from the Great Soviet Encyclopedia.

Laws and tasks Celestial sphere Orbit parameters Motion celestial bodies Astrodynamics Space flight SC orbits

An excerpt characterizing the Ecliptic

On Sunday morning, Marya Dmitrievna invited her guests to Mass at her parish of the Assumption on Mogiltsy.
“I don’t like these fashionable churches,” she said, apparently proud of her free-thinking. “There is only one God everywhere. Our priest is fine, he serves decently, it's so noble, and so is the deacon. Is it any holiness from this that they sing concerts on the kliros? I do not like, one pampering!
Marya Dmitrievna loved Sundays and knew how to celebrate them. Her house was all washed and cleaned on Saturday; people and she did not work, everyone was festively discharged, and everyone was at mass. Meals were added to the master's dinner, and people were given vodka and a roasted goose or pig. But on nothing in the whole house was the holiday so noticeable as on the broad, stern face of Marya Dmitrievna, which on that day assumed an unchanging expression of solemnity.
When they had drunk coffee after mass, in the living room with the covers removed, Marya Dmitrievna was informed that the carriage was ready, and with a stern look, dressed in a ceremonial shawl in which she made visits, she got up and announced that she was going to Prince Nikolai Andreevich Bolkonsky to explain to him about Natasha.
After Marya Dmitrievna's departure, a fashionista from Madame Chalmet came to the Rostovs, and Natasha, having closed the door in the room next to the living room, very pleased with the entertainment, began trying on new dresses. While she, putting on a bodice that was still sleeveless, and bending her head back, looked in the mirror at how her back was sitting, she heard in the living room the lively sounds of her father’s voice and another, female voice, which made her blush. It was Ellen's voice. Before Natasha had time to take off the bodice she was trying on, the door opened and Countess Bezukhaya entered the room, beaming with a good-natured and affectionate smile, in a dark purple, high-necked velvet dress.
Ah, ma delicieuse! [Oh, my lovely!] - she said to the blushing Natasha. - Charmante! [Charming!] No, it's not like anything, my dear count, - she said to Ilya Andreevich, who came in after her. - How to live in Moscow and not go anywhere? No, I won't leave you! This evening m lle Georges is declaiming at my place and some people will gather; and if you don't bring your beauties, who are better than m lle Georges, then I don't want to know you. There is no husband, he went to Tver, otherwise I would have sent him for you. By all means come, by all means, at the ninth hour. She nodded her head at the familiar fashionista, who respectfully crouched down to her, and sat down on an armchair near the mirror, picturesquely spreading the folds of her velvet dress. She did not stop chatting good-naturedly and cheerfully, constantly admiring Natasha's beauty. She examined her dresses and praised them, and also boasted of her new dress en gaz metallique [made of metal-colored gauze] which she had received from Paris and advised Natasha to do the same.
“However, everything suits you, my lovely,” she said.
A smile of pleasure never left Natasha's face. She felt happy and flourishing under the praises of this dear Countess Bezukhova, who had previously seemed to her such an impregnable and important lady, and who was now so kind to her. Natasha became cheerful and felt almost in love with this beautiful and such good-natured woman. Helen, for her part, sincerely admired Natasha and wanted to amuse her. Anatole asked her to set him up with Natasha, and for this she came to the Rostovs. The thought of bringing her brother together with Natasha amused her.
In spite of the fact that she had previously been annoyed with Natasha for having wrested Boris from her in Petersburg, now she did not even think about it, and with all her heart, in her own way, wished Natasha well. Leaving the Rostovs, she withdrew her protegee aside.
- Yesterday my brother dined with me - we were dying of laughter - he does not eat anything and sighs for you, my charm. Il est fou, mais fou amoureux de vous, ma chere. [He's crazy, but he's crazy in love with you, my dear.]
Natasha blushed purple upon hearing these words.
- How blushing, how blushing, ma delicieuse! [my charm!] - Helen said. - You should definitely come. Si vous aimez quelqu "un, ma delicieuse, ce n" est pas une raison pour se cloitrer. Si meme vous etes promise, je suis sure que votre promis aurait desire que vous alliez dans le monde en son absence plutot que deperir d "ennui. [From the fact that you love someone, my lovely, you should not live as a nun. Even if you're a bride, I'm sure your fiancé would rather have you go out into the world in his absence than die of boredom.]
“So she knows that I am a bride, so she and her husband, with Pierre, with this fair Pierre, Natasha thought, talked and laughed about it. So it was nothing." And again, under the influence of Helen, what had previously seemed terrible seemed simple and natural. “And she is such a grande dame, [important lady,] so sweet and so evidently loves me with all her heart,” thought Natasha. And why not have fun? thought Natasha, looking at Helen with surprised, wide-open eyes.

To understand the principle of the apparent motion of the Sun and other luminaries in the celestial sphere, we first consider the true motion of the earth. Earth is one of the planets. It continuously rotates around its axis.

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

But the Earth not only rotates around its axis, but also revolves around the Sun in an elliptical orbit. It completes one revolution around the Sun in one year. The axis of rotation of the Earth is inclined to the plane of the orbit 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 Northern and Southern hemispheres are alternately turned towards the Sun, as a result of which the seasons change on Earth.

When observing the sky, one can notice that the stars for many years invariably retain their relative position.

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

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 visible movement (it is called annual movement) due to the motion of the earth around the sun.

Apparent annual motion of the Sun on the celestial sphere

The most simple annual motion of the Sun can be explained by the figure below. From this figure it can be seen that, depending on the position of the Earth in orbit, an observer from the Earth will see the Sun against the background of different . It will seem to him that it is constantly moving around the celestial sphere. This movement is a reflection of the revolution of the Earth 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 means eclipse. This circle was named so because eclipses of the Sun and Moon occur only when both luminaries 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 orbit around the Sun, i.e., it moves to the east. During the year, the Sun successively passes through the ecliptic 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 plane of the ecliptic at an angle e=23°27′.

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

Celestial equator and ecliptic plane

The ecliptic intersects the celestial equator at two points called points of 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, respectively, is on March 21 and September 23. These days on Earth, day is equal to night, the Sun exactly rises in the east point and sets in the west point.

The points of the spring and autumn equinoxes are the intersections of the equator and the plane of the ecliptic

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

At the point of the summer solstice, the Sun occurs on June 22, and at the point of the winter solstice - on December 22. For several days close to the dates of the solstices, the midday height of the Sun remains almost unchanged, in connection with which these points got their name. When the Sun is at the summer solstice, the day in the Northern Hemisphere is longest and the night is shortest, and when it is at the winter solstice, the opposite is true.

On the day of the summer solstice, the points of sunrise and sunset are as far as possible north of the points of east and west on the horizon, and on the day of the winter solstice they are at 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 the noon height and a movement of the points of sunrise and sunset along the horizon.

It is known that the declination of the Sun is measured from the plane of the celestial equator, and right ascension - from the point of 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 through zero twice a year, and right ascension from 0 to 360°.

Equatorial coordinates of the Sun during the year

The equatorial coordinates of the Sun during the year change unevenly. This happens 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 covers half of its apparent annual path in 186 days from March 21 to September 23, and the other half in 179 days from September 23 to March 21.

The uneven movement of the Sun along the ecliptic is due to the fact that the Earth during the entire period of revolution around the Sun does not move in orbit at the same speed. The Sun is at one of the foci of the Earth's elliptical orbit.

From Kepler's second law It is known that the line connecting the Sun and the planet covers equal areas in equal periods of time. According to this law, the Earth, being closest to the Sun, i.e. in perihelion, moves faster, and being farthest from the Sun, i.e. in aphelion- slower.

Earth is closer to the Sun in winter, and further away in summer. Therefore, on winter days, it moves in orbit faster than on summer days. As a result, the daily change in the 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 velocities of the Earth's motion at each point of the orbit causes an uneven change in not only the 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 equinoxes, and at the solstices it almost does not change.

Knowing the nature of the change in the equatorial coordinates of the Sun allows us to make an approximate calculation of the right ascension and declination of the Sun.

To perform such a calculation, take the nearest date with 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 the passage of the equinoxes changes by 0.4 ° per day; during the month before and after the solstices - by 0.1 ° per day, and during the intermediate months between the indicated ones - by 0.3 °.

), candraw with narrow rectangles the ecliptic and the zodiacal belt (width 18° ).

Projections of the ecliptic on the Earth and on the celestial sphere

Projections of the zodiacal belt (transparency 33%) 18 degrees wide

It is possible to mark the position of the Sun every day during the year, then connecting the points with segments, approximating a smooth curve, fixing the coordinates of the Sun.

Old maps and the ecliptic on old maps inGoogle Earth.
Here the zodiac belt is full width between the tropics

Shirotane that!!! The sun is actually south

The daily rotation of the Earth is west on the East . And the sky and all objects on it will move from East to West. The sun rises in the East and sets in the West.

Zodiac (zodiac circle, from the Greek. ζῷον - a living being) - a belt on the celestial sphere, extending 9 ° on both sides of the ecliptic. The visible paths of the sun, moon and planets pass through the zodiac. At the same time, the Sun moves along the ecliptic, and the rest of the luminaries in their movement along the zodiac go up from the ecliptic, then down.

The starting point of the zodiac circle is considered to be the vernal equinox - the ascending node of the solar orbit, at which the ecliptic crosses the celestial equator.

The zodiac passes through 13 constellations, however, the zodiac circle is divided into 12 equal parts, each of the 30 ° arcs is indicated by the sign of the zodiac, the symbol of the corresponding zodiacal constellation; at the same time, no sign of the zodiac corresponds to the constellation Ophiuchus.

In modern astronomy, the symbols of the zodiac signs are used to designate the spring (Aries sign) and autumn (Libra sign) equinoxes and the ascending and descending nodes of the orbits of celestial bodies (the signs of Leo in direct and inverted form).

Zodiac belt relative to the equator of the celestial sphere (width 46 55 '23 degrees north and south of the equator) -23 27 - the angle of inclination of the ecliptic plane to the equator

Modeling the ecliptic in the "Vector" system (see listing)

Simulation of the motion of the Sun along the ecliptic in the Vector system

THE MOVEMENT OF THE PLANETS IN THE ZODIAC (original see ).
Watching the night sky from Earth, the whole picture of the starry sky slowly turns during the night as a whole. This is due to the daily rotation of the Earth around its axis. Previously, people thought that, on the contrary, a certain huge sphere, to which the stars are fixedly attached, revolves around the Earth. This sphere was called "the sphere of the fixed stars". A similar concept is used in astronomy today, although in reality such a sphere, of course, does not exist. However, it is often very convenient to assume that there is still a sphere of fixed stars. On the one hand, this simplifies astronomical reasoning related to the apparent motion of the planets, and on the other hand, it leads to exactly the same picture of the starry sky visible from the Earth as in reality.

The stars are located so far from the Earth compared to the bodies of the solar system that the distance to them can be considered infinite. Or, what is the same, very large and the same for all stars. Therefore, one can imagine that all the stars are really located on some sphere of a very large ("infinite") radius with the center in the Earth. Since the radius of an imaginary sphere is incomparably greater than the distance from the Earth to the Sun, we can just as well assume that the center of the sphere is located not in the Earth, but in the Sun. The planets, including the Earth, revolve around the Sun in orbits of finite radius. Moreover, the entire solar system is placed in the center of the stellar sphere, Fig. 16.2.

Rice. 16.2

rotationThe earth around its axis determines only the part of the starry sky that is visible at a given moment from a given point on the earth's surface. You can be on the earth's surface from the side of the Sun and see the Sun in the sky. There will be day in this place on the Earth. On the contrary, if the observer is on the other side of the Earth, then he will not see the Sun - it will be blocked for him by the Earth, along with half of the entire stellar sphere. But he will see stars and planets on the other half of the stellar sphere. The boundary of the visible and invisible halves of the stellar sphere is the observer's local horizon.

So, the daily rotation of the Earth around its axis determines only the visibility or invisibility of the Sun and planets at one time or another in one place or another on the earth's surface. The horoscope itself - that is, the location of the planets in the constellations of the Zodiac at the moment - does not depend on this rotation in any way. Nevertheless, we still have to take into account the daily rotation of the Earth when we need to check the conditions for the visibility of the planets in a particular horoscope. In the meantime, we will assume that the observer sees everything. In other words, let's imagine an imaginary observer who sits in the center of a transparent Earth and sees the Sun, planets and stars at the same time.

Having taken this point of view, it is easy to understand how the movement of the planets visible from the Earth in the starry sky takes place. In fact, the position of any planet, as well as the Sun among the stars (when viewed from the Earth), is determined by the direction of the beam directed from the Earth to the planet. If we mentally continue the beam until it intersects with the sphere of fixed stars, then it will "pierce" it at some point. This point will give the position of our planet among the stars at a given time.
Since all the planets, including the Earth, revolve around the Sun, the beam directed from the Earth to any of the planets (including the Sun and the Moon) rotates all the time, Fig. 16.2. Since both the beginning and the end of the segment, the continuation of which is the ray, are rotated. Accordingly, the Sun and all the planets slowly (but at different speeds) move relative to the fixed stars. The celestial path of each of the planets is obviously determined by the trajectory of the point of intersection of the beam directed at the planet from the Earth and the imaginary sphere of fixed stars. Note now that all these rays are constantly in the same plane - the "plane of orbits" of the solar system. Indeed, it is known in astronomy that the planes of rotation of the planets around the Sun are very close to each other, although they do not coincide exactly. Approximately, we can assume that all of them are the same plane - the "plane of orbits". The intersection of this plane with the sphere of fixed stars will give that "star path" along which the annual movement of all planets (including the Sun and Moon) among the stars, visible from the Earth, will take place.

The simplest will be the stellar path of the Sun. Approximately uniform rotation of the Earth around the Sun turns, from the point of view of an earthly observer, into the same uniform rotation of the Sun around the Earth. It boils down to the fact that the Sun moves among the stars in the same direction and at a constant speed. Coming full circle throughout the year. The exact value of this period of time is called in astronomy the "stellar year".
The paths of other planets are more complicated. They are obtained as a result of the interaction of two rotations: the rotation of the Earth - the beginning of the segment - and the rotation of the planet - the end of the segment that determines the direction to the planet. As a result, from the point of view of an earthly observer, the planets stop in the starry sky from time to time. Then they turn back, then turn again and continue moving in the main direction. This is the so-called backward movement of the planets. It was noticed long ago and the efforts of many ancient astronomers were devoted to its explanation. It must be said that the "ancient" theory of Ptolemy describes this phenomenon already with a very high accuracy.

Here we have been talking all the time about the annual movement of the Sun and the planets among the stars. As for the daily movement of the Sun across the sky - from sunrise to sunset and back - it does not shift the Sun relative to the stars and generally does not change anything in the starry sky. That is, the horoscope does not change. Since the reason for the daily movement is the rotation of the Earth around its axis, which does not affect the mutual configuration of the planets in the solar system. Therefore, during the daily movement, neither the Sun nor the planets move along the sphere of fixed stars and rotate with it as a whole.

Rice. 16.3

4. DIVISION OF THE ZODIAC BELT INTO CONSTELLATIONS.
Let us reproduce once again the geometry of the stellar sphere in Fig. 16.3 The annual path of the Sun, Moon and planets among the stars passes along the same circle on the celestial sphere, which in astronomy is called the ECLIPTIC. The stars located near the ecliptic form the ZODIAC CONSTELLATIONS. It turns out a closed belt of constellations, covering the firmament and, as it were, strung on the ecliptic.

More precisely, the ecliptic is the circumference of the intersection of the plane of rotation of the Earth around the Sun with an imaginary sphere of fixed stars. The center of the Sun, which lies in the plane of the ecliptic, can be taken as the center of the sphere. At 16.3 this is point O. However, in relation to distant stars, the motion of the Earth, as well as the distance from the Earth to the Sun, can be neglected and the Earth can be considered the fixed center of the celestial sphere.

Today it is known that the ecliptic rotates over the centuries, albeit very slowly. Therefore, the concept of an instantaneous ecliptic for a given year or for a given epoch is introduced. The instantaneous position of the ecliptic for a given epoch is called the ECLIPTIC OF THE GIVEN AGE. For example, the position of the ecliptic on January 1, 2000 is called the "ecliptic of the 2000 epoch" or, for short, the "ecliptic of J2000".

The "J" in the epoch J2000 reminds us that in astronomy time is usually measured in Julian ages. There is another way of astronomical calculation of time - in the DAYS OF THE JULIAN PERIOD SCALIGER. Scaliger proposed to number the days in a row, starting from 4713 BC. For example, the Julian day of January 1, 1400 is 2232407.

In addition to the ecliptic on the celestial sphere in Fig. 16.3 shows another large circle - the so-called EQUATOR. The equator on the celestial sphere is the circle along which the plane of the earth's equator intersects with an imaginary sphere. The circumference of the equator rotates quite quickly with time, constantly changing its position on the celestial sphere.

The ecliptic and equator intersect on the celestial sphere at an angle of approximately 23 degrees 27 minutes. The points of their intersection are designated by Q and R. The Sun in its annual movement along the ecliptic crosses the equator twice at these points. Point Q, through which the Sun passes into the northern hemisphere, is called the point of the SPINAL EQUINOX. At this time, day equals night. The opposite point on the celestial sphere is the point of the AUTUMN EQUINOX. On fig. 16.3 it is designated by R. Through the point of the autumnal equinox, the Sun passes into the southern hemisphere. At this point, the day is also compared to the night.

The WINTER AND SUMMER SOLSTICE points on the celestial sphere are also located on the ecliptic. The four equinoxes and solstices divide the ecliptic into four equal parts.

Over time, all four points of the equinoxes and solstices slowly move along the ecliptic in the direction of decreasing ecliptical longitudes. Such a movement is called in astronomy the precession of longitudes or simply precession. The precession rate is approximately 1 degree in 72 years. This shift in the points of the equinoxes and solstices leads to the so-called pre-equinoxes in the Julian calendar.

Indeed, since the Julian year is very close to the sidereal year - that is, to the period of revolution of the Earth around the Sun - the shift of the vernal equinox along the ecliptic entails a shift in the day of the vernal equinox in the Julian calendar (that is, according to the "old style") . Namely, the day of the spring equinox according to the "old style" gradually moves to ever earlier dates in March - at a rate of approximately 1 day in 128 years.

To determine the positions of celestial bodies, coordinates on the celestial sphere are needed. There are several such coordinate systems in astronomy. ECLIPTICAL COORDINATES.

Consider a celestial meridian passing through the ecliptic pole P and through a given point A on the celestial sphere, the coordinates of which must be determined. It will intersect the plane of the ecliptic at some point D, fig. 16.3. Then the QD arc will represent the ECLIPTICAL LONGITUDE of point A, and the AD arc will represent its ECLIPTICAL LATITUDE. Recall that Q is the vernal equinox.

Thus, the ecliptical longitudes on the celestial sphere are measured from the vernal equinox of the epoch whose ecliptic we have chosen in this case. In other words, the system of ecliptical coordinates on the celestial sphere is "tied" to some fixed epoch. However, once fixing the ecliptic and choosing a coordinate system on the celestial sphere, you can use it to set the positions of the Sun, Moon, planets and in general - any celestial bodies - AT ANY TIME.

In our calculations, to set the coordinates on the celestial sphere, we used the J2000 ecliptic of the epoch of January 1, 2000. As an approximate basis for distinguishing the zodiacal constellations by the ecliptical longitude J2000, we took the division of the ecliptic J1900 (January 1, 1900), proposed by T.N.Fomenko. This partition is made according to the outlines of the constellations on the map of the starry sky. In terms of the coordinates of the J2000 epoch (January 1, 2000), this partition looks like this:

table

I must say that the boundaries of the constellations in the starry sky are not clearly defined. Therefore, any division of the ecliptic into zodiac constellations is to some extent approximate and sins with conventionality. Various authors give somewhat different partitions.

slightly how about a R

Rice. 15.2

Approximately the same division is on the medieval star map of A. Dürer, which was given above. The differences are again within 5 degrees of the arc. This conventionality of the boundaries between the zodiac constellations had to be taken into account. We took it into account in our calculations in two ways. First, the astronomical horoscope date calculation program we wrote automatically added a 5-degree tolerance to all constellation boundaries. In other words, "violation" of any boundary between constellations from any side by no more than 5 degrees of arc was not considered a violation. Secondly, when deciphering the zodiacs and searching for preliminary astronomical solutions, we always somewhat expanded the boundaries of the intervals indicated on the zodiac for the planets. Namely, the planets were allowed to "climb" into neighboring constellations for half the length of the constellations along the ecliptic.

This completely ruled out the possibility of losing the correct solution due to minor inaccuracies in delimiting the zodiac constellations. In this case, of course, a certain number of redundant solutions appeared. However, all of them were eliminated at the stage of verification according to private horoscopes and signs of the visibility of the planets.
In addition, at the last stage of our study, each of the final solutions we received was carefully checked using the Turbo-Sky computer program to ensure that the positions of all the planets correspond exactly to the indications of the original Egyptian zodiac.

However, there was not a single case of poor correspondence between the positions of the planets on the zodiac and in the final solution. In other words, all the final solutions we found - that is, the solutions that passed the test for partial horoscopes and for signs of the visibility of the planets - turned out to be in very good agreement with their zodiacs and the location of the planets. Although, we repeat, during the initial search, this correspondence was checked only in a weakened version.

We will try to model all of the above in the Vector system, starting with the simplest: depict the zodiac belt, constellations and the path of the Sun along them.

Listing

" Ecliptic - a circle through three points

Ug_e=23.45

Ug_ep =9

Rr= 6.378

Krug.ssp(0,0,0), Rr , p(0,0,1)

SetO= p(0,0,0)

Set E1 = p(0,0,Rr)

SetE2= p(0,0,-Rr)

SetE3= PointSphere(-ug_e , 0, Rr , 0)

set Nn = NormPlosk (E1,E2 , E3)

Krug.ssp(0,0,0), Rr , Nn

Width=77

setcolor 0,0,255

Set Zp11 = PointSphere(-ug_e+9, 0, Rr , 0)

Set Zp12 = PointSphere(180-ug_e-9, 0, Rr , 0)

"First find the 3rd point.

" SetC= PointSphere (((-ug_e+9)+(180-ug_e-9))/2, 90, Rr , 0)

Set C1 = PointSphere(8.38, 86.08, Rr , 0)

set Oc = CentrDuga3p (Zp11,Zp12,C1 ) "methodcalculatesCentrecirclesacrossthreepoints

Rp= RadiusDuga3p (Zp11,Zp12,C1) " calculates the radius of a circle circumscribed around three points

setN1 = NormPlosk (Zp11,Zp12,C1) " normal to the plane of the orbit

"Krug.ss Oc , Rp , N1" a circle

"construct circles through three points

"First find the 3rd point.

"Zodical belt - circles through three points

Set Zp21 = PointSphere(-ug_e-9, 0, Rr , 0)

Set Zp22 = PointSphere(180-ug_e+9, 0, Rr , 0)

Set C2 = PointSphere(-8.38, 94, Rr , 0)

set Oc = CentrDuga3p (Zp21,Zp22,C2 ) "methodcalculatesCentrecirclesacrossthreepoints

Rp= RadiusDuga3p (Zp21,Zp22,C2) " calculates the radius of a circle circumscribed around three points

setN1 = NormPlosk (Zp21,Zp22,C2) " normal to the plane of the orbit

n11 = LastNmb

Krug.ssOc, Rp, N1" a circle

Double

Obj.TranslateP(-0.37, 0.95, 0)

obj.scale=1.02

Double

Obj.TranslateP(-0.37, 0.95, 0)

obj.scale=0.98

n12= LastNmb

MoveToGroupn11+1, n12+1, " group"

n13= LastNmb

PolyPov.Reset

PolyPov.SSp(0,0,0), n13, 20, 51, 0, 1

"let's askearth

Set N = p(0, 0, 1)

Arc.ssO, 0.5, 0.5, 90, -90, N, 0

n71= Vector.LastNmb()

RoundPov.ssP(0, 0, 0), n71, 51.51, -180.180

Double

SetFillColor 255,0,0

" Point on circle from t

"First activate the ecliptic line

CurrObjNmb= n61

Polyline.FromCurrObj360" redefine the ecliptic line with a polyline

hag = 1/360

Set A = Polyline.P (225.5*hag)

ngpoint.ssA

Width = 555

setcolor 255,0,0

Text.ssA, " scales"

How to model the movement so that on the ecliptic it starts from the vernal equinox (Aries)?

To do this, in the listing, we will replace the line for setting the ecliptic circle

" Krug.ssp(0,0,0), Rr, Nn

So:

Arc.ssORr, Rr, - 90 + Ug_ e, 270+ Ug_ e, Nn, 0 " change start of motion

The next task immediately arises: Set the Sun in one or another sign of the Zodiac.

VGoogle Earth set the longitude (see table) and latitude on the ecliptic according to the corresponding longitude. In the Vector system, this can be done parametrically(1/360 times the corresponding angle)

Example. Determine the position of the Sun in the constellation Libra. It will be (215+236)/2=225.5

To the point of "Libra" you can put a picture, a sign.

You can also find other signs.

Below are different options for setting the zodiac belt

The figure shows that some constellations actually come out of the ecliptic belt..

Here the zodiac belt is enlarged in width

According to the table, the location inconverted to J2000 epoch coordinates (January 1, 2000) signs:

The next step is to determine the position of the Sun on a particular day of a particular era.

Let's take the starting pointa way of astronomical calculation of time - in the DAYS OF THE JULIAN PERIOD according to Scaliger, who proposed to number the days in a row, starting from 4713 before AD For example, the Julian day of January 1, 1400 is 2232407. Question: what day will be on January 1, 2012? Let's search on the Internet ., let's find the answer.

Yes there is onecounter ; according to him, January 1, 2012 will be 2,456,262 days in the days of the Julian period.

Apparently, there is no point in climbing so far back, therefore one must be able to establish periods of epochs.

There iscalculator how many days have passed between two dates?

Rotation of the Sun and Moon around the Earth in the geocentric system Ptalomea So in a year the moon rotates around its axis 365/28 (thirteen times and one day in the remainder). From here you can define how many eclipses of the sun and moon will be from the condition that the earth, moon and sun lie in the same plane. Usually there are 5-6 of them. It is not difficult to simulate 13 revolutions of the Moon for one revolution of the Sun, and, indeed, there are so many solar eclipses - count.

.

The starry sky has always attracted people. Mysterious and endless space attracted and frightened. One of the important concepts in the modern astronomer...

By Masterweb

25.02.2018 08:00

Observation of the starry sky in all ages has served people to obtain the necessary information. We find astronomical tables among the Egyptians, the Sumerians, the Maya. According to them, ancient people determined the start time of agricultural work, river floods, solar and lunar eclipses, and created calendars. At the time of the great geographical discoveries, the stars served as the only guide for ships in the ocean. Therefore, astronomical knowledge was vital. Everyone who has ever been interested in astronomy has heard the name "ecliptic". This concept is found in describing the movement of celestial bodies, determining stellar coordinates. Consider what the ecliptic is.

Story

In ancient times, when people considered the Earth to be flat and covered with a heavenly bowl, the movement of the sun was explained in different ways. It was the god Ra among the Egyptians who sailed on his boat, or Helios among the Greeks ruled the chariot. But the path of these gods across the sky was repeated year after year.

In the geocentric system of the world of Ptolemy, the Sun revolved around the Earth along with other planets, and its path during the year was called the ecliptic of the sun. This imaginary line served as an important reference point for determining coordinates and was one of the main elements of the armillary sphere. With the help of the armillary sphere, stellar coordinates were determined, and the ecliptic on it usually represented a wide ring depicting the signs of the zodiac. What is the ecliptic in modern science?

Definition

After the discovery of Copernicus, it became clear that the movement of the Sun along the ecliptic, visible from the Earth, is explained by the movement of the Earth around the central luminary. But this concept has not ceased to exist. The word "ecliptic" comes from the ancient Greek "eclipsis", which means "eclipse". Only on this line solar and lunar eclipses are observed. Modern astronomy defines the ecliptic as the circle along which the sun moves throughout the year. To be more precise, this is the line of the section of the sphere by the plane of the orbit of the geometric center of the Earth-Moon pair.

Plane

The plane of the ecliptic forms the orbit of the Earth-Moon system during rotation around the Sun. The angle of inclination of the plane to the celestial equator is approximately 23 o. It changes over time. To calculate these changes, there is a special formula. Tilt angle fluctuations occur periodically - every 18.6 years. The range of variation is approximately 18.42". The tilt fluctuates every 40,000 years. All planets in the solar system have their own angle of the ecliptic.

Zodiac

In astronomy, the belt of the sky about 9 o on either side of the ecliptic is called the zodiacal belt. In it, the Sun passes through thirteen constellations. These are twelve well-known constellations of the ecliptic, accepted in astrology, and Ophiuchus.

For the first time, the zodiac circle is found in Babylon (Mesopotamia) in the 5th century BC. e. There, a sexagesimal calculus system was adopted, where a full circle is equal to 360 o. Initially, the Babylonians divided the sky into 36 sectors, then into 18 and 12. In each sector, a group of stars formed constellations. Each constellation was assigned special properties. Special points have been identified in the zodiac.

These are the spring equinox on March 21 (Pisces), the summer solstice on June 22 (Cancer), the autumn equinox on September 22 (Libra), and the winter solstice on December 22 (Capricorn).

Ophiuchus

The constellation Ophiuchus established itself on the ecliptic in the first half of the 20th century, when the boundaries and coordinates of the constellations were clarified. It is located between Scorpio and Sagittarius. Moreover, the Sun spends even more time in Ophiuchus than in Sagittarius. In the constellation of Ophiuchus, the last supernova in our Galaxy flared up in 1604. It was observed by Johannes Kepler. In 1848, a nova outburst was recorded. There are many interesting astronomical objects in the constellation Ophiuchus. This is a red dwarf - Barnard's star, many globular clusters and about 2500 variable stars. Scientists have discovered about 9 stars in this constellation.

Ecliptic coordinate system

Based on the ecliptic, there is a system of ecliptic stellar coordinates. The plane of the ecliptic was taken as the basis. Coordinates are defined between the plane and the pole of the ecliptic. The main coordinates are ecliptic latitude and ecliptic longitude. Latitude is the angle between the plane of the ecliptic and the object. Longitude is the angle between the vernal equinox and the plane of latitude.

Coordinate types

There are two types of ecliptic coordinates. In the first type, the center of the Earth is taken as the central point. Such a geocentric system is used mainly for calculations of lunar orbits. In the second type of coordinates, the center of the Sun is considered to be the center, and this system is used when calculating the orbits of the planets of the Solar System. Given the periodic fluctuations in the angle of the ecliptic, one must keep in mind the era when certain coordinates were determined. For this, the current coordinates of the ecliptic and Sun poles are constantly determined.

Zodiacal coordinate system

This coordinate system is used in astrology. The main coordinate here is the zodiacal position, which is calculated from the ecliptic longitude. Latitude is largely not used in this system. But in special cases it is defined in the same way as in astronomy. The annual motion of the Sun and the ecliptic serve as important indicators for astrology.

Astrology

At all times, people believed that human life is influenced by the location of heavenly bodies. Just as the development of chemistry was caused by the needs of alchemy, so the rapid development of astronomy in the Middle Ages was partly facilitated by astrology. Each constellation in astrology is credited with its own special influence on humanity as a whole and on each individual person. From the combination of the location of the constellations and planets, according to astrologers, literally everything depends - from a happy marriage to the state of financial markets. There are two major astrological systems - Western and Vedic. Each of them operates with its own postulates, and the conclusions from the same messages do not always coincide. Modern science does not recognize astrology, considering it pseudoscience. But each of us sometimes reads horoscopes. What is the ecliptic, in astrology, almost everyone knows

Flying in space

Many fantasy novels describe the adventures of spaceships, asteroids that fall into the belt, which is located between the orbits of Mars and Jupiter. Efremov, Strugatsky, Lem have such episodes. The asteroid belt, like all the planets of the solar system, rotates in the plane of the ecliptic. Maybe it's worth going beyond this plane and avoiding all possible collisions? Unfortunately, according to the laws of celestial mechanics, this requires a very large amount of energy and, accordingly, a large amount of additional fuel. In addition, it should be borne in mind that the return return will also require large energy costs. In the future, spacecraft with a solar sail that use the solar wind are considered.