The ecliptic and its main points. What is the ecliptic
In popular science articles on the topics of space and astronomy, one can often come across the not entirely clear term "ecliptic". This word is often used by astrologers besides scientists. It is used to indicate the location of space objects distant from the solar system, to describe the orbits of celestial bodies in the system itself. So what is the "ecliptic"?
What's with the zodiac
The ancient priests, who were still observing the heavenly bodies, noticed one feature of the behavior of the Sun. It appears to move relative to the stars. Tracking its movement across the sky, observers noticed that exactly one year later, the Sun always returns to its starting point. Moreover, the "route" of movement from year to year is always the same. It is called the "ecliptic". This is the line along which our main luminary moves across the sky during the calendar year.
The stellar regions through which the path of the shining Helios ran in his golden chariot drawn by golden horses (this is how the ancient Greeks imagined our native star) were not left without attention.
The circle of 12 constellations along which the Sun moves was called the zodiac, and these constellations themselves are commonly called zodiac.
If according to the horoscope you are, say, Leo, then do not look in the sky at night in July, the month in which you were born. The Sun is in your constellation during this period, which means that you can see it only if you are lucky to catch a total solar eclipse.
ecliptic line
If you look at the starry sky during the day (and this can be done not only during a total solar eclipse, but also with the help of a conventional telescope), we will see that the sun is located at a certain point in one of the zodiac constellations. For example, in November this constellation will most likely be Scorpio, and in August - Leo. The next day, the position of the Sun will shift slightly to the left, and this will happen every day. And a month later (November 22), the luminary will finally reach the border of the constellation Scorpio and move to the territory of Sagittarius.
In August, it is clearly seen in the figure, the Sun will be in the boundaries of Leo. And so on. If every day we mark the position of the Sun on a star map, then in a year we will have a map with a closed ellipse drawn on it. So this very line is called the ecliptic.
When to watch
But to observe your constellations under which a person is born) will turn out in the month opposite to the date of birth. After all, the ecliptic is the route of the Sun, therefore, if a person is born in August under the sign of Leo, then this constellation is high above the horizon at noon, that is, when sunlight does not allow him to be seen.
But in February, Leo will decorate the midnight sky. On a moonless, cloudless night, it is perfectly “read” against the background of other stars. Those born under the sign of, say, Scorpio are not so lucky. The constellation is best seen in May. But to consider it, you need to stock up on patience and luck. It is better to go out of town, to an area without high mountains, trees and buildings. Only then will the observer be able to see the outline of Scorpio with its ruby Antares (alpha Scorpii, a bright blood-red star belonging to the class of red giants, having a diameter comparable to the size of the orbit of our Mars).
Why is the expression "plane of the ecliptic" used?
In addition to describing the stellar path of the annual motion of the Sun, the ecliptic is often considered as a plane. The expression "plane of the ecliptic" can often be heard when describing the position in space of various space objects and their orbits. Let's figure out what it is.
If we return in the scheme of motion of our planet around the mother star and the lines that can be drawn from the Earth to the Sun at different points in time, put together, it turns out that they all lie in the same plane - the ecliptic. This is a kind of imaginary disk, on the sides of which all 12 described constellations are located. If a perpendicular is drawn from the center of the disk, then in the northern hemisphere it will rest against a point on the celestial sphere with coordinates:
- declination +66.64°;
- right ascension - 18 h. 00 min.
And this point is located not far from both "bears" in the constellation Draco.
The axis of rotation of the Earth, as we know, is inclined to the axis of the ecliptic (at 23.44 °), due to which the planet has a change of seasons.
And our "neighbors"
Here is a summary of what the ecliptic is. In astronomy, researchers are also interested in how other bodies in the solar system move. As calculations and observations show, all the main planets revolve around the star in almost the same plane.
Most of all, the closest planet to the star is Mercury, which stands out from the overall slender picture, the angle between its plane of rotation and the ecliptic is as much as 7 °.
Of the planets of the outer ring, the orbit of Saturn has the largest angle of inclination (about 2.5 °), but given its enormous distance from the Sun - ten times farther than the Earth, this is excusable for the solar giant.
But the orbits of smaller cosmic bodies: asteroids, dwarf planets and comets deviate from the plane of the ecliptic much more strongly. So, for example, Pluto's twin, Eris, has an extremely elongated orbit.
Approaching the Sun at a minimum distance, it flies closer to the star than Pluto, at 39 AU. e. (a. e. - an astronomical unit equal to the distance from the Earth to the Sun - 150 million kilometers), in order to then again retire into the Kuiper belt. Its maximum removal is almost 100 AU. e. So its plane of rotation is inclined to the ecliptic by almost 45 °.
Ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic, ecliptic Zaliznyak's grammar dictionary
The plane of the ecliptic is clearly visible in this image taken in 1994 by the Clementine Lunar Reconnaissance Spacecraft. Clementine's camera shows (from right to left) the Moon illuminated by the Earth, the glare of the Sun rising over the dark part of the Moon's surface, and the planets Saturn, Mars and Mercury (three dots in the lower left corner)
Ecliptic (from (linea) ecliptica, from other Greek. ἔκλειψις - eclipse) - a large circle of the celestial sphere, along which the visible annual movement occurs. Respectively plane of the ecliptic- the plane of revolution of the Earth around the Sun (terrestrial). The 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 system -.
Description
Due to the fact that the orbit of the Moon is inclined relative to the ecliptic and due to the rotation of the Earth around the barycenter of the Moon-Earth system, as well as due to perturbations of the Earth's orbit from other planets, true sun is not always exactly on the ecliptic, but may deviate by several seconds of arc. We can say that the path passes along the ecliptic "middle sun".
The plane of the ecliptic is inclined to the plane of the celestial equator at an angle ε = 23°26′21.448″ - 46.8150″ t - 0.00059″ t² + 0.001813″ t³, where t is the number of Julian centuries since January 1, 2000. This formula is valid for the coming centuries. Over longer periods of time, the inclination of the ecliptic to the equator fluctuates about the average value 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; the above formula does not take them into account.
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 disturbances 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 period of revolution along the ecliptic, equal to about 18 years, is called the saros, or draconic period.
The plane of the ecliptic serves as the main 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 |
|---|---|
| 7.01° | |
| 3.39° | |
| 0° | |
| 1.85° | |
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 averaged 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 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 denoted 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 points of the WINTER AND SUMMER SOLSTICES 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 zodiacal 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 ) "methodcalculatescentercirclesthroughthreepoints
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" 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 ) "methodcalculatescentercirclesthroughthreepoints
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" 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.
INGoogle 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.
Eatcalculator 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.
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