), Candraw the ecliptic and the zodiac belt (width 18° ).

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

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

You can mark the position of the Sun every day for a year, then connecting the points with segments, approximating them with a smooth curve, and recording the coordinates of the Sun.

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

Shirotane ta!!! The sun is actually further south

The daily rotation of the Earth occurs with 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 (zodiacal circle, from the Greek ζῷον - living creature) - 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 through the zodiac move either up from the ecliptic or down.

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

The zodiac passes through 13 constellations, but the zodiac circle is divided into 12 equal parts, each of the 30° arcs is designated by a zodiac sign, a symbol of the corresponding zodiac constellation; Moreover, no zodiac sign 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 (Leo signs upright and inverted).

Zodiacal belt relative to the equator of the celestial sphere (width 46 55’ 23 degrees north and south from the equator) –23 27 – angle of inclination of the ecliptic plane to the equator

Modeling the ecliptic in the Vector system (see listing)

Modeling the movement of the Sun along the ecliptic in the Vector system

MOVEMENT OF THE PLANETS AROUND THE ZODIAC (see original ).
Observing the night sky from the Earth, the entire picture of the starry sky slowly turns during the night as a whole. This occurs due to the daily rotation of the Earth around its axis. Previously, people thought that, on the contrary, some huge sphere, to which the stars were fixedly attached, revolved around the Earth. This sphere was called the "sphere of 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. This, on the one hand, simplifies astronomical reasoning related to the apparent movement of the planets, and on the other hand, it leads to exactly the same picture of the starry sky visible from 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, which is the same thing, 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 a center in the Earth. Since the radius of the 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. 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 currently visible 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. It will be day in a given 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 local horizon of the observer.

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 in any way on this rotation. Nevertheless, we still have to take into account the daily rotation of the Earth when we need to check the visibility conditions of the planets in a particular horoscope. For now, we will assume that the observer sees everything. In other words, imagine an imaginary observer who sits in the center of a transparent Earth and sees the Sun, planets and stars at the same time.

Taking this point of view, it is easy to understand how the movement of planets across the starry sky, visible from the Earth, occurs. In fact, the position of any planet, as well as the Sun among the stars (as seen from the Earth), is determined by the direction of the ray directed from the Earth to the planet. If you mentally continue the ray 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 moment in time.
Since all the planets, including the Earth, revolve around the Sun, a ray directed from the Earth to any of the planets (including the Sun and 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, rotates. Accordingly, the Sun and all the planets slowly (but at different speeds) move relative to the fixed stars. The celestial path of each planet is obviously determined by the trajectory of the intersection point of the ray directed at the planet from the Earth and the imaginary sphere of fixed stars. Let us now note that all these rays are constantly in the same plane - the “plane of orbits” of the Solar system. In fact, 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 they are all the same plane - the “plane of orbits”. The intersection of this plane with the sphere of fixed stars will give the “star path” along which the annual movement of all planets (including the Sun and Moon) among the stars, visible from the Earth, will occur.

The simplest would be the star path of the Sun. The approximately uniform rotation of the Earth around the Sun turns, from the point of view of an observer on Earth, into the same uniform rotation of the Sun around the Earth. This comes 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 length of this period of time is called the “sidereal year” in astronomy.
The paths of movement 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 from time to time stop in the starry sky. Then they turn back, then turn again and continue moving in the main direction. This is the so-called retrograde motion of the planets. It was noticed a long time 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 with very high accuracy.

Here we have been talking all along about the annual movement of the Sun and 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 does not change anything in the starry sky at all. That is, it does not change the horoscope. Since the cause of daily motion 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 daily movement, neither the Sun nor the planets move along the sphere of fixed stars and rotate with it as a single 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. Stars located near the ecliptic form ZODIAC CONSTELLATIONS. The result is a closed belt of constellations, covering the vault of heaven and, as it were, strung on the ecliptic.

More precisely, the ecliptic is the circle of intersection of the Earth’s plane of rotation around the Sun with the imaginary sphere of fixed stars. The center of the Sun, lying in the ecliptic plane, can be taken as the center of the sphere. On 16.3 this is point O. However, in relation to distant stars, the movement 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 we know that the ecliptic rotates over the centuries, although very slowly. Therefore, the concept of instantaneous ecliptic for a given year or for a given epoch is introduced. The instantaneous position of the ecliptic for a particular era is called the ECLIPTIC OF A GIVEN EPOCH. For example, the position of the ecliptic on January 1, 2000 is called the "Year 2000 Ecliptic" or "J2000 Ecliptic" for short.

The "J" in the J2000 epoch is a reminder that in astronomy time is usually measured in Julian centuries. There is another way of astronomical calculation of time - in DAYS OF THE JULIAN PERIOD OF SCALIGERA. Scaliger proposed numbering consecutive days, 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 circle of the equator rotates quite quickly over 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 motion along the ecliptic, crosses the equator twice at these points. Point Q, through which the Sun passes into the northern hemisphere, is called the SPRING EQUINOX point. At this time, day is equal to night. The point opposite to it on the celestial sphere is the point of the AUTUMNAL EQUINOX. In Fig. 16.3 it is designated by R. Through the point of the autumnal equinox, the Sun moves into the southern hemisphere. At this point, day is also compared to night.

The points of the WINTER AND SUMMER SOLSTICES on the celestial sphere are also located on the ecliptic. The four points of the equinoxes and solstices divide the ecliptic into 4 equal parts.

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

In fact, 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 displacement of the vernal equinox point 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 vernal equinox according to the “old style” gradually moves to earlier and earlier days of March - at a speed 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.

Let us consider the 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 ecliptic plane at some point D, Fig. 16.3. Then the arc QD will represent the ECLIPTICAL LONGITUDE of point A, and the arc AD will represent its ECLIPTICAL LATITUDE. Recall that Q is the point of the vernal equinox.

Thus, ecliptic longitudes on the celestial sphere are measured from the vernal equinox point of that era, the ecliptic of which we have chosen in this case. In other words, the system of ecliptic coordinates on the celestial sphere is “tied” to a certain fixed epoch. However, once you have fixed the ecliptic and selected 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 MOMENT OF TIME.

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

Table

It must be said that the boundaries of the constellations in the starry sky are not entirely clearly defined. Therefore, any division of the ecliptic into zodiacal constellations is to some extent approximate and suffers from convention. Different authors give slightly different partitions.

slightly In this way, about A R

Rice. 15.2

Approximately the same breakdown is on the medieval star map of A. Durer, which was given above. The differences are again within 5 degrees of arc. This convention of boundaries between the zodiacal 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, “violating” any boundary between constellations on 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 by half the length of the constellations along the ecliptic.

This completely excluded the possibility of losing the correct solution due to minor inaccuracies in delimiting the zodiac constellations. In this case, naturally, a certain number of unnecessary solutions appeared. However, all of them were eliminated at the stage of verification based on private horoscopes and signs of planetary visibility.
In addition, at the last stage of our research, each of our final solutions was carefully checked using the Turbo-Sky computer program to ensure that the positions of all planets exactly corresponded to the indications of the original Egyptian zodiac.

However, not a single case of poor correspondence between the positions of the planets in the zodiac and in the final decision arose. In other words, all the final solutions we found - that is, the solutions that were tested for private horoscopes and for signs of the visibility of 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 thing: depicting the zodiac belt, constellations and the path of the Sun’s movement along them.

Listing

" Ecleptica - circle through three points

Ug_e=23.45

Ug_ep =9

Rr= 6.378

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

Set O = p(0,0,0)

Set E1 = p(0,0,Rr)

Set E2 = p(0, 0,-Rr)

Set E3 = PointSfera(-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 = PointSfera(-ug_e+9, 0, Rr , 0)

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

"First find the 3rd point.

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

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

Set Oc = CentrDuga3p (Zp11,Zp12,C1) "methodcalculatescentercirclethroughthreetchoki

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

SetN1 = NormPlosk (Zp11,Zp12,C1) " normal to the orbital plane

"Krug.ss Oc , Rp , N1" circle

"construct circles through three points

"First find the 3rd point.

"Zodical belt - circles through three points

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

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

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

Set Oc = CentrDuga3p (Zp21,Zp22,C2) "methodcalculatescentercirclethroughthreetchoki

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

SetN1 = NormPlosk (Zp21,Zp22,C2) " normal to the orbital plane

n11 = LastNmb

Krug.ssOc, Rp, N1" circle

Dubl

Obj.TranslateP(-0.37, 0.95, 0)

obj.scale=1.02

Dubl

Obj.TranslateP(-0.37, 0.95, 0)

obj.scale=0.98

n12 = LastNmb

MoveToGroupn11+1, n12+1, " grupa"

n13 = LastNmb

PolyPov.Reset

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

"let's setEarth

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

Dubl

SetFillColor 255,0,0

" Point on the circle from t

"First we activate the ecliptic line

CurrObjNmb= n61

Polyline.FromCurrObj360" we 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 along the ecliptic it begins from the point of the vernal equinox (Aries)?

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

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

So:

Arc.ssO,Rr, Rr, - 90 + Ug_ e, 270+ Ug_ e, Nn, 0 " change the start of movement

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 at the corresponding longitude. This can be done in the Vector system 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

You can place a picture or a sign at the “Libra” point.

You can also find other signs.

Below are different options for setting the zodiac belt

The figure shows that some constellations actually emerge from the ecliptic belt.

Here the zodiac belt is increased in width

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

The next stage: determine the position of the Sun on a particular day of a particular era.

Let's take the starting pointmethod of astronomical calculation of time - in DAYS OF THE JULIAN PERIOD according to Scaliger, who proposed numbering consecutive days starting from 4713 before AD For example, the Julian day of January 1, 1400 is 2232407. Question: What day will it be on January 1, 2012? Let's look on the Internet ., let's find the answer.

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

There is apparently no point in going back that far, so you need to be able to establish the periods of eras.

Eatcalculator how many days have passed between the 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 remaining). From here you can define how many eclipses of the Sun and Moon will there be if 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 per revolution of the Sun and, indeed, such a number of solar eclipses are observed - do the math.

.

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

From Masterweb

25.02.2018 08:00

Observing the starry sky has served people in all centuries to obtain the necessary information. We find astronomical tables among the Egyptians, Sumerians, and Mayans. Using them, ancient people determined the time of the beginning of agricultural work, river floods, solar and lunar eclipses, and created calendars. During the Great Geographical Discoveries, stars served as the only guide for ships on the ocean. Therefore, astronomical knowledge was vital. Anyone who has ever been interested in astronomy has heard the name “ecliptic.” This concept is found when describing the movement of celestial bodies and determining stellar coordinates. Let's look at what the ecliptic is.

Story

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

In Ptolemy's geocentric system of the world, the Sun revolved around the Earth along with other planets, and its path throughout 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. Using 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 "eclipse", which means "eclipse". Only on this line are solar and lunar eclipses 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 section of the sphere by the orbital plane of the geometric center of the Earth-Moon pair.

Plane

The plane of the ecliptic is formed by the orbit of the Earth-Moon system as it rotates around the Sun. The angle of inclination of the plane to the celestial equator is approximately 23 degrees. It changes over time. There is a special formula to calculate these changes. Fluctuations in the angle of inclination occur periodically - every 18.6 years. The range of change is approximately 18.42". The inclination oscillates every 40,000 years. All planets in the solar system have their own ecliptic angle.

Zodiac

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

The zodiac circle was first found in Babylon (Mesopotamia) in the 5th century BC. e. The sexagesimal system of calculation was adopted there, where a full circle is equal to 360 degrees. 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 were 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 1604, the last supernova in our Galaxy erupted in the constellation Ophiuchus. It was also observed by Johannes Kepler. In 1848, a nova outbreak 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. The coordinates are determined between the plane and the pole of the ecliptic. The main coordinates are ecliptic latitude and ecliptic longitude. Latitude is the angle between the ecliptic plane and an object. Longitude is the angle between the vernal equinox and the plane of latitude.

Types of coordinates

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

Zodiac coordinate system

This coordinate system is used in astrology. The main coordinate here is the zodiacal position, which is calculated based on the ecliptic longitude. Latitude is largely unused in this system. But in special cases it is determined in the same way as in astronomy. The annual movement 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 the heavenly bodies. Just as the development of chemistry was driven 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. According to astrologers, literally everything depends on the combination of the location of constellations and planets - 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 conclusions from the same premises do not always coincide. Modern science does not recognize astrology, considering it a pseudoscience. But each of us sometimes reads horoscopes. Almost everyone in astrology knows what the ecliptic is.

Flights in space

Many science fiction novels describe the adventures of spaceships and asteroids caught in 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 ecliptic plane. 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 is worth considering that returning back will also require large energy costs. In the future, spaceships with a solar sail that use the solar wind are being considered.

When you began to make your first observations of the sky, you probably more than once felt regret that you could not distinguish one star from another. But you really want to learn how to find the right constellation, planet or object in the sky.

We can help you navigate this variety of nocturnal fireflies. Don’t be afraid, you will succeed, especially when you realize that there is nothing difficult about it. Moreover, in the age of the Internet, there are on-line star maps and various virtual planetariums that easily display a realistic image of the sky in the desired area at the required time.

For example, for convenience, such a map is located via a link on the menu item of this site “Sky Map”. We click on it and get to the Astronet resource page, where we enter the data of the location and time of observation, and the parameters of the map itself into the proposed fields. Click "Go!" and the map will load, which you can print or view on your computer monitor.

We also recommend the free virtual planetarium Stellarium for better visualization. It is great for initial acquaintance with the starry sky. In it, too, in the program settings, it is necessary to indicate the coordinates of your observation location, so that it displays a real picture of the sky, and not the appearance of stars somewhere on the equator...

Firstly, before you start working with the map, you need to navigate the area according to the cardinal directions in order to understand where you have North (N), South (S), West (W), East (E). You can use a regular compass, or if you know at least one of the directions, then determining the other sides of the horizon will not be difficult.

Nothing complicated, this is done in the elementary grades of school. And if you know how to find the North Star, then determining the sides of the horizon at night will not be a problem for you. The North Star is always above the northern point of the horizon in the Northern Hemisphere.

Secondly, now let's go back to the map. The cardinal directions on it can be indicated in Latin letters: N - north, S - south, E - east, W - west. Turn the map so that the word representing the part of the horizon where you are facing is at the bottom. The star chart will then present a picture of the sky that can be seen from the horizon to the zenith (the point on the celestial sphere located directly overhead) or if you are using a full "circular" map of the entire sky, the zenith will be exactly in the middle of the circle.

Third In order to better navigate the variety of star points, people have long divided them into separate groups - CONSTELLATIONS, and mentally connecting bright stars with lines, giving them the names of animals or mythological heroes, depending on which figure resembled what. Today, astronomers use these ancient constellation names simply as references to 88 areas of the sky. With the help of constellations, they indicate in which of them a particular object is located. For example, if it is said that Mars is located in the constellation Cancer, then this will help to find the planet as easily as indicating that Bratsk is located in the Irkutsk region.

AND fourthly, more than 50 bright stars have their own names - Arabic, Greek or Latin. The names of bright or famous stars are indicated on the maps, for example Vega (in the constellation Lyra). Although many other stars also have names, astronomers usually designate them by letters of the Greek alphabet or by catalog numbers, such as θ Cygni.

But much fewer stars are visible in the city than indicated on the map. This is primarily due to citywide illumination from street lighting. And besides, the eye can only distinguish bright stars in the sky. Stellar magnitudes characterize the brightness of stars, i.e. how bright the star appears.

The magnitudes of the brightest stars are negative: the most “brilliant” star in the sky, Sirius, has a magnitude of -1.5m. The dimmer the stars appear, the greater their “positive” magnitude. For example, Polaris has +2m. Amateur telescopes are capable of distinguishing stars up to +14m in magnitude, and powerful ground-based observatories up to +30m. The human eye can only see stars up to +6m magnitude.

The magnitude scales of the stars will be indicated on your sky maps. Typically, the brighter the star, the bolder the dot that represents it will be.

If the stars were visible during the day, we would see the Sun moving eastward over the course of the year against a background of stars. The ECLIPTIC, the apparent path of the Sun against the background of distant stars, is also usually plotted on star globes and maps.

The ecliptic runs across the entire sky through 12 constellations, with a band width of approximately 16 degrees. Ancient astrologers called this belt of constellations the Zodiac. The Zodiac belt attracts special attention because the Moon and planets, when visible in the sky, also move near the ecliptic through these twelve constellations.

Well, all that remains are incomprehensible grid lines with hours and degrees on the map. These are celestial coordinates, just like the geographic coordinates of cities and objects on Earth. Knowing right ascension (vertical grid lines and expressed in hours and minutes) and declination (horizontal grid lines - in degrees), you can use them to find the location of a planet, star or asteroid on the celestial sphere.

And also, remember that the appearance of the starry sky changes due to the daily rotation of the Earth. Each subsequent night, compared to the previous night, the stars move a little to the west. From evening to evening the same star rises 4 minutes earlier. Over 30 days, these 4 minutes make a difference of 2 hours. In 12 months it will already be 24 hours. Therefore, in a year the appearance of the starry sky will be repeated. The appearance of the starry sky changes throughout the year due to the Earth's revolution around the Sun. Every year the Earth makes one revolution around the Sun.

So nothing complicated.

In the next part we will learn how to find the necessary objects in the starry sky.

Clear skies and successful observations!

- 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 close to the points of intersection of its orbit with the ecliptic. These points on the celestial sphere are called lunar nodes, the period of their revolution along the ecliptic, equal to approximately 18 years, is called saros, or the draconic period.

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

Angles of inclination of the orbits of the planets of the solar system to the ecliptic plane

Planet	Inclination to the ecliptic
Mercury	7.01°
Venus	3.39°
Earth	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 Story” (from the series “Stories about the Pilot Pirx”), the ecliptic plane is a prohibited zone for spaceships, but the pilot Pirx, 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 ecliptic plane by an out-of-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 Movement celestial bodies Astrodynamics Space flight Spacecraft orbits

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 wonderful, he serves decently, it’s so noble, and so is the deacon. Does this make it so sacred that people sing concerts in the choir? I don’t like it, it’s just self-indulgence!
Marya Dmitrievna loved Sundays and knew how to celebrate them. Her house was all washed and cleaned on Saturday; people and she were not working, everyone was dressed up for the holidays, and everyone was attending mass. Food was added to the master's dinner, and people were given vodka and roast goose or pig. But nowhere in the whole house was the holiday more noticeable than on Marya Dmitrievna’s broad, stern face, 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 she, with a stern look, dressed in the ceremonial shawl in which she made visits, stood up and announced that she was going to Prince Nikolai Andreevich Bolkonsky to explain to him about Natasha.
After Marya Dmitrievna left, a milliner 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 was putting on a sour cream bodice still without sleeves and bending her head, looking in the mirror at how the back was sitting, she heard in the living room the animated sounds of her father’s voice and another, female voice, which made her blush. It was Helen'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 charming one!] - she said to the blushing Natasha. - Charmante! [Charming!] No, this is not like anything, my dear Count,” she said to Ilya Andreich, who came in after her. – How to live in Moscow and not travel anywhere? No, I won't leave you alone! This evening M lle Georges is reciting 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. My husband is gone, he left for Tver, otherwise I would have sent him for you. Be sure to come, definitely, at nine o'clock. “She nodded her head to a milliner she knew, who sat down respectfully to her, and sat down on a chair next to the mirror, picturesquely spreading out 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 boasted about her new dress en gaz metallique, [made of metal-colored gas], which she received from Paris and advised Natasha to do the same.
“However, everything suits you, my lovely,” she said.
The smile of pleasure never left Natasha's face. She felt happy and blossoming under the praises of this dear Countess Bezukhova, who had previously seemed to her such an unapproachable and important lady, and who was now so kind to her. Natasha felt cheerful and felt almost in love with this so beautiful and such a 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 setting up her brother with Natasha amused her.
Despite the fact that she had previously been annoyed with Natasha for having taken Boris away from her in St. Petersburg, she now did not think about it, and with all her soul, 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 didn’t eat anything and sighed for you, my precious. Il est fou, mais fou amoureux de vous, ma chere. [He goes crazy, but he goes crazy with love for you, my dear.]
Natasha blushed crimson hearing these words.
- How she blushes, how she blushes, ma delicieuse! [my precious!] - said Helen. - 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 de deperir d'ennui. [Just because you love someone, my lovely, you should not live like a nun. Even if you are a bride, I am sure that your groom would prefer that you go out into society in his absence than die of boredom.]
“So she knows that I’m a bride, so she and her husband, with Pierre, with this fair Pierre,” thought Natasha, talked and laughed about it. So it’s 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 obviously loves me with all her heart,” Natasha thought. And why not have fun? thought Natasha, looking at Helen with surprised, wide-open eyes.

As a result of the Earth's movement in its orbit, it appears to an observer on Earth that the Sun is constantly moving across 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 stars are not visible during the daytime. Let us 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 altitude of the Sun changes throughout the year.

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

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 the section of the celestial sphere by the orbital plane of the barycenter of the Earth-Moon system.

The Earth, moving in its orbit, maintains a constant position of its axis of rotation in world space.

The angle of inclination of the Earth's rotation axis with the Earth's orbital plane is 66 °33", therefore, the angle between the Earth's orbital plane 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 due to the perturbations of the Earth's orbit from other planets, the true Sun is not always located exactly on the ecliptic, but may 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 inclination of the ecliptic to the equator fluctuates around 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 oscillations with a period of 18.6 years and an amplitude of 18.42″, as well as smaller ones.

In contrast to 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 close to the points of intersection of its orbit with the ecliptic. These points on the celestial sphere are called the lunar nodes; their cycle of rotation along the ecliptic, equal to approximately 18 years, is called the Saros, or Draconic period.

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

The ecliptic plane 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 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 luminaries in the vast 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 at which the ecliptic intersects the celestial equator are called the equinox points.

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; at the point of the autumn equinox - from the northern hemisphere to the southern. Two points of the ecliptic, spaced 90° from the equinoxes and thus furthest from the celestial equator, are called solstice points.

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

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

The ecliptic axis is the diameter of the celestial sphere perpendicular to the ecliptic plane. The ecliptic axis intersects with the surface of the celestial sphere at two points - the north pole of the ecliptic, which lies in the northern hemisphere, and the south pole of the ecliptic, which lies in the southern hemisphere. The north pole of the ecliptic has equatorial coordinates R.A. = 18h00m, Dec = +66°33", and is located 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 southern to northern. The Sun comes to this point every year on March 21st - the day of the vernal equinox.

The Aries point 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 luminary, towards the reverse western hour angles (or if viewed from the north pole, then counterclockwise). It is in this direction that the Sun and Moon move across the celestial sphere and, consequently, the right ascension of these luminaries increases.

The 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. Clarification of the size of the tropical year 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 direct ascension of the Sun varies almost uniformly throughout the year. The daily rate of change of the sun's right ascension is 360°/365.2422 1°/day.

The declination of the Sun 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 in the remaining 4 intermediate months.