Precession. Zodiac constellations Determination of geographic latitude

Astronomy solution book for grade 11 for lesson No. 7 (workbook) - Apparent motion of the Sun and Moon

1. Using a star chart, indicate through which constellations the annual path of the Sun passes.

Option 1.

Start your list of constellations at the vernal equinox.

Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius.

Option 2.

Start your list of constellations with the autumnal equinox.

Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces, Taurus, Gemini, Cancer.

2. Write down and explain the formula that calculates the height of the Sun at noon (or at its highest culmination).

h ☉ = (90° - φ) + δ ☉ , where h ☉ is the height of the Sun; φ - latitude of the area where observations are made; δ ☉ - declination of the Sun at the time of observation.

3. Fill in the empty cells and unfinished dates in the table.

4. Complete the sentences.

A synodic month is a period of changing lunar phases; it lasts 29 days.

A sidereal month is a complete revolution around the Sun and lasts 27.3 days.

The Moon always faces the Earth with the same hemisphere, since it makes one revolution around its axis in the same time.

5. Using Figure 7.1, draw a view of the Moon (in positions 1-8) and indicate the names of its phases (in positions 1, 3, 5, 7).

6. Consider Figures 7.2 and 7.3 and indicate for each case on which side of the horizon and at what time of day the Moon is observed. (The observer is in the Northern Hemisphere of the Earth.)

7. Complete the diagram of the occurrence of solar and lunar eclipses (Fig. 7.4) with the necessary constructions and mark shadows and penumbras on it. Using the diagram explaining the occurrence of eclipses, complete the sentences.

When the Moon enters the Earth's shadow, a total lunar eclipse occurs.

When the Moon enters the Earth's penumbra, a partial lunar eclipse occurs.

A total solar eclipse occurs when the disk of the Sun is completely covered by the Earth.

A partial solar eclipse occurs when the Sun is exposed to the penumbra of the Moon.

An annular eclipse of the Sun occurs if, at the time of the eclipse, the Moon's disk is too small to completely cover the Sun.

Eclipses are not observed every month, since the orbital planes of the Earth and the Moon must intersect at an angle of 5°09′.

8. In Figures 7.5 and 7.6, use arrows to indicate from which edge of the full Moon the lunar eclipse begins. From which edge of the solar disk does a solar eclipse begin? (The observer in both cases is in the Northern Hemisphere of the Earth.) What is the maximum duration of the total eclipse phase of the Moon and the maximum duration of the total eclipse of the Sun?

On the diagram of the Moon (Fig. 7.5), draw an arrow that points to the right; on the diagram of the Sun (Fig. 7.6), draw an arrow pointing to the left.

Maximum duration of a total lunar eclipse: 11 h 40 m

Maximum duration of total solar eclipse: 7 min 40 sec

If you try hard enough, everyone will remember the twelve signs of the Zodiac. But not everyone knows why these particular constellations were singled out.

Surprisingly, the sky above our heads does not stand still.

It is in continuous motion - only the location of the North Star is relatively constant. However, the ancient Greeks, and after them the entire Western civilization, identified twelve miracle constellations into a separate zodiac zone.

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The distribution of stars among various constellations was first given, it is believed, in Ptolemy's Almagest. The Ptolemaic constellations, with the exception of minor details, coincide with modern constellations.The names of these constellations in Ptolemy also, in the vast majority of cases, coincide with the names that we use today.

Zodiac comes from the Greek word zodion (Greek diminutive of zun - animal, diakos - wheel), one of the most common symbols in the cultures of Mesopotamia, Egypt, Judea, Greece, Rome, Northern Europe, Persia, India, Tibet, China, America.

The first evidence of a systematic understanding of zodiacal symbolism dates back to the time of Sargon of Akkad (2750 BC), during which astrologers predicted an eclipse of the sun.

Zodiac- the zone that is apparently crossed by the Sun once a year. It lies on both sides of the ecliptic at 18 degrees latitude and includes the movement of the Sun, planets, and Moon. Divided into 12 constellations.

In 700 BC. The Zodiac as a strip of constellations is mentioned in the scientific work “Mul-Apin”.

The author of this treatise lists 18 titles:

Stars, Heavenly Bull, Righteous Shepherd Anu, Old Man, Staff, Great Twins, Crab, Lion, Furrow, Libra, Scorpio, Pabilsag, Goat-Fish, Giant, Tails, Swallow, Anunitu and Mercenary.

The final list of fateful miracle constellations was formed under the influence of rational mathematics.

The zodiac belt was divided strictly into 12 parts of 30 degrees of the celestial sphere each:

Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius, Pisces.

By the way the Sun and Moon move along this strip, people have learned to predict the future. Some people believe, others not so much: if you divide the 8 billion living earthlings by 12, you get a lot of identical destinies. Nevertheless, the constellations are not forgotten and remain a wonderful discovery of the cosmic world order.

About 2 thousand years ago, the zodiac signs coincided with the zodiac constellations of the same name. The reason for the displacement of the zodiac signs relative to the zodiac constellations of the same name is the precession, or anticipation of the equinoxes, established by Hipparchus of Rhodes in the 2nd century BC.

In that distant era, during the time of Hipparchus, the point of the vernal equinox was in the constellation Aries, and therefore was designated by the sign of this constellation, the sign of Aries. Similarly, the summer solstice point was in the constellation Cancer, the autumn equinox point was in the constellation Libra, and the winter solstice point was in the constellation Capricorn.

But then they gradually shifted to the west and have been there for a long time: the point of the spring equinox in the constellation Pisces, and the point of the autumn equinox in the constellation Virgo. The summer solstice point has been located in the constellation Taurus since 1988.The shift of the vernal equinox point (it is indicated on maps by the sign of Aries) occurs towards the annual movement of the Sun by approximately 51" per year.

Constellations are areas of the starry sky, highlighted for ease of orientation on the celestial sphere and designation of stars.

On star maps, the brightest stars in a constellation are indicated in Greek letters with the addition of the name of the constellation, less bright ones - in Latin letters and numbers. The boundaries of the constellations usually run along celestial parallels and declination circles.

12 constellations are traditionally called zodiacal - those through which the center of the Sun passes during its annual rotation along the ecliptic. In the period from November 30 to December 17 (2014 era), the Sun is in the constellation Ophiuchus. Formally, this constellation is also a zodiacal one, but in astrology it is not considered a zodiac constellation.

Tags: Zodiac Constellations, origin of the zodiac, legends, Ptolemaic constellations, modern constellations

Why do the equinoxes fall on different dates from year to year?

The interval between two equinoxes of the same name is called the tropical year, which is used to measure time. Our normal everyday calendar contains an equal number of days - 365 days. A tropical year has approximately 365.2422 solar days, so the equinox occurs at different times of the day, moving forward by almost 6 hours each year. Over the course of four years, the date of the equinox shifts by almost a day and, if not for the intercalary day of a leap year (February 29), the moment of the equinox would continue to float further along the calendar. To compensate for this shift, the concept of a leap year was introduced, which returns the equinox to the previous date of the year. We also do not forget that the date of the equinox may differ due to differences in time zones.

Dates and times of the autumn equinoxes in 2012-2018 (Universal Time UTC-0)

2012 22 14:49
2013 22 20:44
2014 23 02:29
2015 23 08:20
2016 22 14:21
2017 22 20:02
2018 23 01:54

According to the folk calendar, golden autumn begins on this day, which will last until October 14. On the day of the autumnal equinox, the second half of Indian summer begins and, according to popular belief, what the weather will be like on this day, so will autumn be. Other folk signs say: the drier and warmer September is, the better the autumn will be, the later the real winter will come.

Painting by V.D. Polenov "Golden Autumn"

In Rus' The day of the autumn equinox was considered a holiday and was always celebrated with pies with cabbage, lingonberries and meat, as well as folk festivities. On this day, rowan tassels along with leaves were inserted in the evening between the window frames, believing that from that day on, when the sun began to weaken, the rowan tree would protect the house from the forces of darkness.

In Japan The autumn equinox is considered an official holiday and has been celebrated since 1878. On the day of the autumn equinox, the Japanese perform the rituals of the Buddhist holiday Higan, which go back to the depths of history, families go to bow to the graves of their ancestors, order prayers and provide the necessary ritual honors

In Mexico On the day of the autumn equinox, many try to visit the famous pyramid of Kukulcan (in the Mayan language - “feathered serpent”) in the ancient city of Chichen Itza. The pyramid is oriented in relation to the Sun in such a way that it is on the days of the spring and autumn equinox that the rays project the shadows of the platforms onto the edge of the main staircase in the form of alternating triangles of light and shadow, reminiscent of the contours of a snake.

Aries is undoubtedly one of the most famous zodiac constellations, despite the fact that there are no stars brighter than the second magnitude in its composition. The constellation Aries consists mainly of faint stars, but if nothing interferes with its observation, everyone can safely see at least 50 stars in its composition even with the naked eye. The main stars of this constellation are Hamal, Sheratan and Mezarthim, which in astronomy are called stars of the second, third and fourth magnitudes.

How to find this constellation in the sky? “Territorially” it is located between the constellations Taurus and Pisces. It's even easier to find your way if you look down at the star map a little south of the constellation Triangulum.

However, it is not so easy for uninitiated people to recognize this constellation, because Aries does not represent any special geometric figure. The three main stars Hamal, Sheratan and Mezarthim simply form an arc, and the remaining weak stars are scattered so randomly that one can only envy the imagination of the ancient Greeks, who saw in such a chaotic scattering the image of a mythical ram, and in the arc of the three main stars - its long horns with curls. This is exactly what the constellation was depicted on ancient star charts.

When can we see the constellation? With its arrival comes the best time to observe it in the southern part of the horizon. You can see it without problems anywhere in Russia, especially on long November nights. As for the location of the Sun in this constellation, it is generally accepted that the Sun is currently in Aries from April 19 to May 13.

The main characters of the constellation

The constellation Aries occupies an area of ​​441.1 square degrees of the starry sky. Only three of them deserve special attention. Let's go through them in order, starting with the brightest - the Hamal star.

Hamal

Hamal, which translated from Arabic means “ram’s head” or “grown lamb.” Its apparent magnitude is 2.00m and belongs to the spectral class K2 III. Ptolemy also noted that this star is not included in the constellation drawing, however, he also gave the following comment: “The star is above your head.” That is why in the constellation figure it is placed “on the face” or “above the head” of Aries.

Sheratan

The next bright star from the constellation is Sheratan. She is called the beta of Aries, she is also his second or northern horn. From Arabic Sheratan can be translated as “two marks” or “two signs”. Beta Aries is classified as spectral class A5V, meaning it is a main sequence star. Sheratan is also a double star and therefore has a gravitational companion. The rotation period of the latter is 107 days, and the mass estimate suggests that it belongs to a slightly different spectral class - G. The apparent magnitude of Sheratan is within 2.64m.

Mezarthim

The third brightest star in the constellation in question is traditionally called Mesarthim, also known as Gamma Aries. Mezarthim is interesting because it was perhaps the first star whose duality was discovered with the help of a telescope back in 1664. This circumstance was established by Robert Hooke. Speaking about its apparent magnitude, scientists call the value 3.88m. The spectral class of this triple star, located 204 light years from Earth, is B9 V.

It’s curious: even at the beginning of our era, the location of the zodiac signs in the sky coincided with similar zodiac constellations. Then the vernal equinox point was located in this constellation. From an astronomy perspective, this is the place where the equator intersects the ecliptic. For the common man, this means that when the Sun hits this point, the duration of daylight is equal to the duration of night. However, today the point of the vernal equinox is no longer located in Aries - over the past 2000 years it has migrated to neighboring Pisces. However, the constellation sign (original horns) has since been preserved to indicate both the constellation and the equinox.

Precession

Today there has been a shift in absolutely all characteristic points. Thus, the point of the autumn equinox is now located in the constellation Virgo, the point of the winter solstice lives in Sagittarius, and the summer solstice lives in Taurus. Why did such a change occur? The reason for it was the precession of the earth's axis - a phenomenon discovered by Hipparchus of Rhodes back in the second century BC. This phenomenon is a shift in the direction of the earth's axis under the influence of lunar gravity. It occurs towards the annual movement of our hottest star and is about 50 arc minutes per year, due to which the spring equinox occurs a little earlier each year than the previous one.

History of the constellation

Drawing by John Hevelius from his constellation atlas

Speaking about the history of the constellation, one cannot fail to mention the well-known Golden Fleece. Even the Sumerian tribes called Aries the “constellation of the ram,” the same golden-fleece that saved the mythological Phrixus and Galla from their stepmother Ino. On this ram, the brother and sister reached Colchis by air, but the sister, frightened by heights, fell and drowned in the strait. Phrixus managed to reach his destination, then he sacrificed rams, and gave his fleece to Zeus. Another version says that the constellation is named after Aries, who showed the way to the god Bacchus wandering in the desert. Then he not only placed the ram in the sky, but placed it where the passage of the Sun causes the whole of nature to flourish.

Autumn has come to our world. True autumn, which comes not according to the calendar created by people, but according to the sidereal calendar. Therefore, this Autumn is sometimes called stellar or astronomical. Its beginning is celebrated by the Autumn Equinox Festival.

On the day of the Equinox, the Sun rises exactly at the geographical point of the East and sets at the geographical point of the West.
However, we should not forget that the starry Autumn has come only for residents of the Northern Hemisphere, that is, for everyone who lives north of the earth’s Equator.

But for the southerners (those in the Southern Hemisphere) the stellar Spring came at exactly the same time.
And so year after year, everything is exactly the opposite.

However, in any case, on this day the Earth is evenly illuminated by sunlight and the Sun is at its zenith above the Equator line.

The Autumn Equinox is one of the four sacred holidays that have been revered and solemnly celebrated since ancient times.
In addition to the Autumn Equinox, these are the Winter Solstice, Spring Equinox and Summer Solstice. Eternal cycle.
And so every year in all cultures of the world in all centuries and times.

This is the time when day equals night.
From this moment until the moment of the Spring Equinox, the night will surpass the day. It will be the longest during the Winter Solstice...

In the modern era, at the moment of the Autumn Equinox, the daylight is located in the constellation Virgo.

About 4000 years ago and earlier, the sacred point of the Autumn Equinox was located in the constellation Libra. This is actually why the star figure near this point is called Libra. Here the Sun appeared at the moment when on the whole Earth day was equal to night.

Then, as a result of the phenomenon of precession (cone-shaped movement of the earth's axis), the point of the Autumn Equinox moved to Virgo, but to this day is designated by scientists precisely as the symbol of Libra.

Of course, the Autumn Equinox is not as fun and joyful a holiday as the Spring Equinox. Still, nature is falling asleep, cold weather is approaching. But it is especially solemn, imbued with wisdom and a special philosophy.

The symbol of this wisdom is the Cross. After all, the Equinox is associated with the Sun crossing the celestial Equator.

Two imaginary lines intersect in the skies - the celestial Equator and the solar path - the Ecliptic. So, the Sun seems to cross a special border, a line dividing two mirror-imaged worlds, two hemispheres, which means at this moment it comes to the Cross.

The most famous embodiment of this archetype today is in the Christian tradition. That is why it is no coincidence that the Feast of the Exaltation of the Holy Cross is close to the day of the Autumn Equinox.

The Resurrection, as is known, was preceded by the Crucifixion, that is, the ascent to the Cross. In one of the keys, this is the image of the Sun crucified on the Cross of the Equinox, the Sun located at the intersection of the Ecliptic and the celestial Equator. It is no coincidence that in prayers Christ is sometimes called the Sun of Truth.

In autumn, the Cross becomes a symbol of the sun's descent. And in the Spring, the Sun must pass through the Cross in order to rise again.

It is interesting that the period of the Autumn Equinox was often marked on ancient calendars in the form of such a symbol. It is considered a sheaf laid down for threshing. This is certainly true, because Autumn is the time when the summer harvest has already been harvested.

But in this symbol the Cross is clearly visible - the Cross of the Equinox!

And this is also the DAGAZ rune, the so-called Transformation rune.

The Sun faces transformation, transformation, difficult trials, a thorny path, which should end with the spring Resurrection.
It is no coincidence that in ancient Hellas the famous Eleusinian mysteries were timed to coincide with the Equinoxes, with the Small Mysteries dedicated to the Spring Equinox and the Great Mysteries to the Autumn Equinox.

After all, the myth associated with the abduction by the ruler of the kingdom of the dead, Hades, of the beautiful Persephone, the daughter of the fertility goddess Demeter, perfectly correlates with the change of calendar seasons and the solar annual path. It is also known that before descending into Hades for Cerberus, Hercules went through the Eleusinian Mysteries.

And so, as in ancient times, Autumn Equinox came to us again.
Day is equal to night again...
Time to stop, forget about the bustle, calm your thoughts, think, look at the setting star, partake of the breath of Mother Nature, the measured rhythm of the great Universe, as our wise ancestors once did...