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

1. The place of sunrise and sunset, and therefore its azimuth, changes from day to day. Starting from March 21 (when the Sun rises at the point of the east and sets at the point of the west) to September 23, the sun rises in the north-east quarter, and sunset - in the north-west. At the beginning of this time, the sunrise and sunset points move north and then in the opposite direction. On September 23, just like on March 21, the Sun rises at the east point and sets at the west point. Starting from September 23 to March 21, a similar phenomenon will repeat in the southeast and southwest quarters. The movement of sunrise and sunset points has a one-year period.

The stars always rise and set at the same points on the horizon.

2. The meridional altitude of the Sun changes every day. For example, in Odessa (average = 46°.5 N) on June 22 it will be greatest and equal to 67°, then it will begin to decrease and on December 22 it will reach its lowest value of 20°. After December 22, the meridional altitude of the Sun will begin to increase. This is also a one-year phenomenon. The meridional altitude of stars is always constant. 3. The duration of time between the culminations of any star and the Sun is constantly changing, while the duration of time between two culminations of the same stars remains constant. So, at midnight we see those constellations culminating that are currently on the opposite side of the sphere from the Sun. Then some constellations give way to others, and over the course of a year at midnight all the constellations will culminate in turn.

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

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

We will get the most clear idea of ​​this movement of the Sun if we determine its equatorial coordinates every day - right ascension a and declination b. Then, using the found coordinate values, we plot the points on the auxiliary celestial sphere and connect them with a smooth curve. As a result, we obtain a large circle on the sphere, which will indicate the path of the visible annual movement of the Sun. The circle on the celestial sphere along which the Sun moves is called the ecliptic. The plane of the ecliptic is inclined to the plane of the equator at a constant angle g = =23°27", which is called the angle of inclination ecliptic to equator(Fig. 82).

Rice. 82.

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

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

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

The Sun arrives at the vernal equinox on March 21st. The right ascension a and declination b of the Sun are zero. Throughout the globe, the Sun rises at point O st and sets at point W, and day is equal to night. Starting March 21, the Sun moves along the ecliptic towards the summer solstice point. The right ascension and declination of the Sun are continuously increasing. It is astronomical spring in the northern hemisphere, and autumn in the southern hemisphere.

On June 22, approximately 3 months later, the Sun comes to the summer solstice point L. The direct ascension of the Sun is a = 90°, a declination b = 23°27"N. In the northern hemisphere, astronomical summer begins (the longest days and shortest nights), and in the south - winter (the longest nights and shortest days). With the further movement of the Sun, its northern declination begins to decrease, and its right ascension continues to increase.

About three more months later, on September 23, the Sun comes to the point of the autumnal equinox Q. The direct ascension of the Sun is a=180°, declination b=0°. Since b = 0 ° (like March 21), then for all points on the earth’s surface the Sun rises at point O st and sets at point W. Day will be equal to night. The name of the declination of the Sun changes from northern 8n to southern - bS. In the northern hemisphere, astronomical autumn begins, and in the southern hemisphere, spring begins. With further movement of the Sun along the ecliptic to the winter solstice point U, declination 6 and right ascension aO increase.

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

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

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

The peculiarity of changes in the right ascension of the Sun plays an important role when choosing the basic units for measuring time.

The vernal equinox point moves along the ecliptic towards the annual movement of the Sun. Its annual movement is 50", 27 or rounded 50",3 (for 1950). Consequently, the Sun does not reach its original place relative to the fixed stars by an amount of 50",3. For the Sun to travel the indicated path, it will take 20 mm 24 s. For this reason, spring

It occurs before the Sun completes its visible annual motion, a full circle of 360° relative to the fixed stars. The shift in the moment of the onset of spring was discovered by Hipparchus in the 2nd century. BC e. from observations of stars that he made on the island of Rhodes. He called this phenomenon the anticipation of the equinoxes, or precession.

The phenomenon of moving the vernal equinox point caused the need to introduce the concepts of tropical and sidereal years. The tropical year is the period of time during which the Sun makes a full revolution across the celestial sphere relative to the point of the vernal equinox T. “The duration of the tropical year is 365.2422 days. The tropical year is consistent with natural phenomena and precisely contains the full cycle of the seasons of the year: spring, summer, autumn and winter.

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

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

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

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

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

Let's consider these phenomena at some latitudes:

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

Rice. 83.

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

On the days of the equinoxes, polar sunrises or sunsets occur. On the days of the solstices, the height of the Sun reaches its greatest values. The altitude of the Sun is always equal to its declination. The polar day and polar night last for 6 months.

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

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

Temperate zone called the part of the earth's surface in which the Sun rises and sets every day, but is never at its zenith. There are two temperate zones. In the northern hemisphere, between latitudes φ = 23°27"N and φ = 66°33"N, and in the southern hemisphere, between latitudes φ=23°27"S and φ = 66°33"S. Temperate zones occupy 50% of the earth's surface.

Polar belt called the part of the earth's surface in which polar days and nights are observed. There are two polar zones. The northern polar belt extends from latitude φ = 66°33"N to the north pole, and the southern one - from φ = 66°33"S to the south pole. They occupy 10% of the earth's surface.

For the first time, the correct explanation of the visible annual movement of the Sun across the celestial sphere was given by Nicolaus Copernicus (1473-1543). He showed that the annual movement of the Sun across the celestial sphere is not its actual movement, but only an apparent one, reflecting the annual movement of the Earth around the Sun. The Copernican world system was called heliocentric. According to this system, at the center of the solar system is the Sun, around which the planets move, including our Earth.

The Earth simultaneously participates in two movements: it rotates around its axis and moves in an ellipse around the Sun. The rotation of the Earth around its axis causes the cycle of day and night. Its movement around the Sun causes the change of seasons. The combined rotation of the Earth around its axis and the movement around the Sun causes the visible movement of the Sun across the celestial sphere.

To explain the apparent annual motion of the Sun across the celestial sphere, we will use Fig. 84. The Sun S is located in the center, around which the Earth moves counterclockwise. The earth's axis remains unchanged in space and makes an angle with the ecliptic plane equal to 66°33". Therefore, the equator plane is inclined to the ecliptic plane at an angle e=23°27". Next comes the celestial sphere with the ecliptic and the signs of the Zodiac constellations marked on it in their modern location.

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

Rice. 84.

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

On December 22, the Earth comes to position IV. The Sun is projected into the constellation Sagittarius. Declination of the Sun 6=23°.5S. In the southern hemisphere, more of the diurnal parallels are illuminated than in the northern hemisphere, so in the southern hemisphere the day is longer than the night, and in the northern hemisphere it is vice versa. The sun's rays fall almost vertically into the southern hemisphere, and at an angle into the northern hemisphere. Therefore, astronomical summer begins in the southern hemisphere, and winter in the northern hemisphere. The sun illuminates the southern polar zone and does not illuminate the northern one. The southern polar zone experiences polar day, while the northern zone experiences night.

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

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Place a chair in the middle of the room and, facing it, make several circles around it. And it doesn’t matter that the chair is motionless - it will seem to you that it is moving in space, because it will be visible against the background of various objects in the room’s furnishings.

In the same way, the Earth revolves around the Sun, and to us, the inhabitants of the Earth, it seems that the Sun moves against the background of the stars, making a full revolution across the sky in one year. This movement of the Sun is called annual. In addition, the Sun, like all other celestial bodies, participates in the daily movement of the sky.

The path among the stars along which the annual movement of the Sun occurs is called the ecliptic.

The Sun makes a full revolution along the ecliptic in a year, i.e. approximately in 365 days, so the Sun moves by 360°/365≈1° per day.

Since the Sun moves approximately along the same path from year to year, i.e. The position of the ecliptic among the stars changes over time very, very slowly; the ecliptic can be plotted on a star map:

Here the purple line is the celestial equator. Above it is the part of the northern hemisphere of the sky adjacent to the equator, below is the equatorial part of the southern hemisphere.

The thick wavy line represents the annual path of the Sun across the sky, i.e. ecliptic. At the top it is written which season of the year begins in the northern hemisphere of the Earth when the Sun is in the corresponding area of ​​the sky.

The image of the Sun on the map moves along the ecliptic from right to left.

During the year, the Sun manages to visit 12 zodiac constellations and one more - Ophiuchus (from November 29 to December 17),

There are four special points on the ecliptic.

BP is the point of the vernal equinox. The sun, passing through the vernal equinox, falls from the southern hemisphere of the sky to the northern.

LS is the point of the summer solstice, a point on the ecliptic located in the northern hemisphere of the sky and farthest from the celestial equator.

OR is the point of the autumnal equinox. The sun, passing through the autumn equinox, falls from the northern hemisphere of the sky into the southern.

ZS is the winter solstice point, a point on the ecliptic located in the southern hemisphere of the sky and farthest from the celestial equator.

Finally, how do you know that the Sun is actually moving across the sky among the stars?

Currently this is not a problem at all, because... the brightest stars are visible through a telescope even during the day, so the movement of the Sun among the stars with the help of a telescope can, if desired, be seen with your own eyes.

In the pre-telescopic era, astronomers measured the length of the shadow from the gnomon, a vertical pole, which allowed them to determine the angular distance of the Sun from the celestial equator. In addition, they observed not the Sun itself, but stars diametrically opposite to the Sun, i.e. those stars that were highest above the horizon at midnight. As a result, ancient astronomers determined the position of the Sun in the sky and, consequently, the position of the ecliptic among the stars.

Due to the annual revolution of the Earth around the Sun in the direction from West to East, it seems to us that the Sun moves among the stars from West to East along a large circle of the celestial sphere, which is called ecliptic, with a period of 1 year . The plane of the ecliptic (the plane of the earth's orbit) is inclined to the plane of the celestial (as well as the earth's) equator at an angle. This angle is called ecliptic inclination.

The position of the ecliptic on the celestial sphere, that is, the equatorial coordinates of the points of the ecliptic and its inclination to the celestial equator are determined from daily observations of the Sun. By measuring the zenith distance (or height) of the Sun at the moment of its upper culmination at the same geographical latitude,

It can be established that the declination of the Sun throughout the year varies from to . In this case, the direct ascension of the Sun varies throughout the year from to, or from to.

Let's take a closer look at the change in the coordinates of the Sun.

At the point spring equinox^, which the Sun passes annually on March 21, the right ascension and declination of the Sun are zero. Then, every day the right ascension and declination of the Sun increase.

At the point summer solstice a, where the Sun falls on June 22, its right ascension is 6 h, and the declination reaches its maximum value + . After this, the declination of the Sun decreases, but the right ascension continues to increase.

When the Sun comes to point on September 23 autumn equinox d, its right ascension will become equal to , and its declination will again become zero.

Further, right ascension, continuing to increase, at the point winter solstice g, where the Sun hits on December 22, becomes equal, and the declination reaches its minimum value - . After this, the declination increases, and after three months the Sun comes again to the point of the vernal equinox.

Let's consider the change in the location of the Sun in the sky throughout the year for observers located in different places on the Earth's surface.

Earth's north pole, on the day of the vernal equinox (21.03) the Sun circles the horizon. (Recall that at the North Pole of the earth there are no phenomena of rising and setting of luminaries, that is, any luminary moves parallel to the horizon without crossing it). This marks the beginning of polar day at the North Pole. The next day, the Sun, having risen slightly along the ecliptic, will describe a circle parallel to the horizon at a slightly higher altitude. Every day it will rise higher and higher. The Sun will reach its maximum height on the day of the summer solstice (June 22) – . After this, a slow decrease in altitude will begin. On the day of the autumn equinox (September 23), the Sun will again be on the celestial equator, which coincides with the horizon at the North Pole. Having made a farewell circle along the horizon on this day, the Sun descends below the horizon (under the celestial equator) for six months. The polar day, which lasted six months, is over. The polar night begins.

For an observer located on Arctic Circle The Sun reaches its greatest height at noon on the day of the summer solstice -. The midnight height of the Sun on this day is 0°, that is, the Sun does not set on this day. This phenomenon is usually called polar day.

On the day of the winter solstice, its midday height is minimal - that is, the Sun does not rise. It's called polar night. The latitude of the Arctic Circle is the smallest in the northern hemisphere of the Earth, where the phenomena of polar day and night are observed.

For an observer located on northern tropics, The sun rises and sets every day. The Sun reaches its maximum midday height above the horizon on the day of the summer solstice - on this day it passes the zenith point (). The Tropic of the North is the northernmost parallel where the Sun is at its zenith. The minimum midday altitude, , occurs on the winter solstice.

For an observer located on equator, absolutely all the luminaries set and rise. Moreover, any luminary, including the Sun, spends exactly 12 hours above the horizon and 12 hours below the horizon. This means that the length of the day is always equal to the length of the night - 12 hours each. Twice a year - on the days of the equinoxes - the midday altitude of the Sun becomes 90°, that is, it passes through the zenith point.

For an observer located on latitude of Sterlitamak, that is, in the temperate zone, the Sun is never at its zenith. It reaches its greatest height at noon on June 22, on the day of the summer solstice. On the day of the winter solstice, December 22, its height is minimal - .

So, let us formulate the following astronomical signs of thermal belts:

1. In cold zones (from the polar circles to the poles of the Earth) the Sun can be both a non-setting and non-rising luminary. The polar day and polar night can last from 24 hours (at the northern and southern polar circles) to six months (at the northern and southern poles of the Earth).

2. In temperate zones (from the northern and southern tropics to the northern and southern polar circles) the Sun rises and sets every day, but is never at its zenith. In summer, the day is longer than the night, and in winter, the opposite is true.

3. In the hot zone (from the northern tropic to the southern tropic) the Sun is always rising and setting. The Sun is at its zenith from once - in the northern and southern tropics, to twice - at other latitudes of the belt.

The regular change of seasons on Earth is a consequence of three reasons: the annual revolution of the Earth around the Sun, the inclination of the Earth's axis to the plane of the Earth's orbit (the ecliptic plane), and the Earth's axis maintaining its direction in space over long periods of time. Thanks to the combined action of these three reasons, the apparent annual movement of the Sun occurs along the ecliptic, inclined to the celestial equator, and therefore the position of the Sun’s daily path above the horizon of various places on the earth’s surface changes throughout the year, and consequently, the conditions for their illumination and heating by the Sun change.

The unequal heating by the Sun of areas of the earth's surface with different geographic latitudes (or the same areas at different times of the year) is easily determined by simple calculation. Let us denote by the amount of heat transferred to a unit area of ​​the earth's surface by vertically falling solar rays (Sun at zenith). Then, at a different zenith distance of the Sun, the same unit of area will receive the amount of heat

By substituting the values ​​of the Sun at true noon on different days of the year into this formula and dividing the resulting equalities by each other, you can find the ratio of the amount of heat received from the Sun at noon on these days of the year.

Quests:

1. Calculate the inclination of the ecliptic and determine the equatorial and ecliptic coordinates of its main points from the measured zenith distance. The Sun at its highest culmination on the days of the solstices:

2. Determine the inclination of the apparent annual path of the Sun to the celestial equator on the planets Mars, Jupiter and Uranus.

3. Determine the inclination of the ecliptic about 3000 years ago, if, according to observations at that time in some place in the northern hemisphere of the Earth, the midday altitude of the Sun on the day of the summer solstice was +63〫48ʹ, and on the day of the winter solstice +16〫00ʹ south of the zenith.

4. According to the maps of the star atlas of Academician A.A. Mikhailov to establish the names and boundaries of the zodiacal constellations, indicate those of them in which the main points of the ecliptic are located, and determine the average duration of the movement of the Sun against the background of each zodiacal constellation.

5. Using a moving map of the starry sky, determine the azimuths of points and the times of sunrise and sunset, as well as the approximate duration of day and night at the geographic latitude of Sterlitamak on the days of the equinoxes and solstices.

6. Calculate the noon and midnight heights of the Sun for the days of the equinoxes and solstices in: 1) Moscow; 2) Tver; 3) Kazan; 4) Omsk; 5) Novosibirsk; 6) Smolensk; 7) Krasnoyarsk; 8) Volgograd.

7. Calculate the ratio of the amounts of heat received at noon from the Sun on the days of the solstices by identical sites at two points on the earth’s surface located at latitude: 1) +60〫30ʹ and in Maykop; 2) +70〫00ʹ and in Grozny; 3) +66〫30ʹ and in Makhachkala; 4) +69〫30ʹ and in Vladivostok; 5) +67〫30ʹ and in Makhachkala; 6) +67〫00ʹ and in Yuzhno-Kurilsk; 7) +68〫00ʹ and in Yuzhno-Sakhalinsk; 8) +69〫00ʹ and in Rostov-on-Don.

Kepler's laws and planetary configurations

Under the influence of gravitational attraction to the Sun, the planets revolve around it in slightly elongated elliptical orbits. The Sun is located at one of the foci of the planet's elliptical orbit. This movement obeys Kepler's laws.

The magnitude of the semimajor axis of a planet's elliptical orbit is also the average distance from the planet to the Sun. Due to the insignificant eccentricities and small inclinations of the orbits of the large planets, when solving many problems, it is possible to approximately assume that these orbits are circular with a radius and lie practically in the same plane - in the ecliptic plane (the plane of the Earth's orbit).

According to Kepler’s third law, if and are, respectively, the sidereal periods of revolution of a certain planet and the Earth around the Sun, and and are the semimajor axes of their orbits, then

Here, the periods of revolution of the planet and the Earth can be expressed in any units, but the dimensions must be the same. A similar statement is true for the semimajor axes and.

If we take 1 tropical year ( – the period of revolution of the Earth around the Sun) as a unit of measurement of time, and 1 astronomical unit () as a unit of measurement of distance, then Kepler’s third law (7.1) can be rewritten as

where is the sidereal period of the planet’s revolution around the Sun, expressed in average solar days.

Obviously, for the Earth the average angular velocity is determined by the formula

If we take the angular velocities of the planet and the Earth as the unit of measurement, and the orbital periods are measured in tropical years, then formula (7.5) can be written as

The average linear speed of the planet in orbit can be calculated using the formula

The average value of the Earth's orbital speed is known and is . Dividing (7.8) by (7.9) and using Kepler’s third law (7.2), we find the dependence on

The "-" sign corresponds to internal or the lower planets (Mercury, Venus), and “+” – external or upper (Mars, Jupiter, Saturn, Uranus, Neptune). In this formula they are expressed in years. If necessary, the found values ​​can always be expressed in days.

The relative position of the planets is easily determined by their heliocentric ecliptic spherical coordinates, the values ​​of which for various days of the year are published in astronomical yearbooks, in a table called “heliocentric longitudes of the planets.”

The center of this coordinate system (Fig. 7.1) is the center of the Sun, and the main circle is the ecliptic, the poles of which are spaced 90º from it.

Great circles drawn through the poles of the ecliptic are called circles of ecliptic latitude, according to them is measured from the ecliptic heliocentric ecliptic latitude, which is considered positive in the northern ecliptic hemisphere and negative in the southern ecliptic hemisphere of the celestial sphere. Heliocentric ecliptic longitude is measured along the ecliptic from the point of the vernal equinox ¡ counterclockwise to the base of the circle of latitude of the luminary and has values ​​ranging from 0º to 360º.

Due to the small inclination of the orbits of large planets to the ecliptic plane, these orbits are always located near the ecliptic, and as a first approximation, their heliocentric longitude can be considered, determining the position of the planet relative to the Sun only by its heliocentric ecliptic longitude.

Rice. 7.1. Ecliptic celestial coordinate system

Consider the orbits of the Earth and some inner planet (Fig. 7.2), using heliocentric ecliptic coordinate system. In it, the main circle is the ecliptic, and the zero point is the vernal equinox point ^. The ecliptic heliocentric longitude of the planet is counted from the direction “Sun – vernal equinox ^” to the direction “Sun – planet” counterclockwise. For simplicity, we will assume that the orbital planes of the Earth and the planet are coincident, and the orbits themselves are circular. The position of the planet in its orbit is then given by its ecliptic heliocentric longitude.

If the center of the ecliptic coordinate system is aligned with the center of the Earth, then this will be geocentric ecliptic coordinate system. Then the angle between the directions “center of the Earth - point of the vernal equinox ^” and “center of the Earth - planet” is called ecliptic geocentric longitude planets Heliocentric ecliptic longitude of the Earth and geocentric ecliptic longitude of the Sun, as can be seen from Fig. 7.2 are related by the relation:

We will call configuration planets are some fixed relative positions of the planet, the Earth and the Sun.

Let us consider separately the configurations of the inner and outer planets.

Rice. 7.2. Helio- and geocentric systems
ecliptic coordinates

There are four configurations of the inner planets: bottom connection(n.s.), top connection(v.s.), greatest western elongation(n.s.e.) and greatest eastern elongation(n.v.e.).

In inferior conjunction (NC), the inner planet is on the line connecting the Sun and the Earth, between the Sun and the Earth (Fig. 7.3). For an earthly observer, at this moment the inner planet “connects” with the Sun, that is, it is visible against the background of the Sun. In this case, the ecliptic geocentric longitudes of the Sun and the inner planet are equal, that is: .

Near the inferior conjunction, the planet moves in the sky in a retrograde motion near the Sun; it is above the horizon during the day, near the Sun, and it is impossible to observe it by looking at anything on its surface. It is very rare to see a unique astronomical phenomenon - the passage of the inner planet (Mercury or Venus) across the disk of the Sun.

Rice. 7.3. Configurations of the inner planets

Since the angular velocity of the inner planet is greater than the angular velocity of the Earth, after some time the planet will shift to a position where the “planet-Sun” and “planet-Earth” directions differ by (Fig. 7.3). For an observer on Earth, the planet is removed from the solar disk at its maximum angle, or they say that the planet at this moment is at its greatest elongation (distance from the Sun). There are two greatest elongations of the inner planet - western(n.s.e.) and eastern(n.v.e.). At greatest western elongation (), the planet sets below the horizon and rises earlier than the Sun. This means that it can be observed in the morning, before sunrise, in the eastern sky. It's called morning visibility planets.

After passing through the greatest western elongation, the disk of the planet begins to approach the disk of the Sun on the celestial sphere until the planet disappears behind the disk of the Sun. This configuration, when the Earth, the Sun and the planet lie on the same straight line, with the planet behind the Sun, is called top connection(v.s.) planets. Observations of the inner planet cannot be carried out at this moment.

After superior conjunction, the angular distance between the planet and the Sun begins to increase, reaching its maximum value at greatest eastern elongation (CE). At the same time, the heliocentric ecliptic longitude of the planet is greater than that of the Sun (and the geocentric one, on the contrary, is less, that is). The planet in this configuration rises and sets later than the Sun, which makes it possible to observe it in the evening after sunset ( evening visibility).

Due to the ellipticity of the orbits of the planets and the Earth, the angle between the directions to the Sun and to the planet at greatest elongation is not constant, but varies within certain limits, for Mercury - from to , for Venus - from to .

The greatest elongations are the most convenient moments for observing the inner planets. But since even in these configurations Mercury and Venus do not move far from the Sun on the celestial sphere, they cannot be observed throughout the night. The duration of evening (and morning) visibility for Venus does not exceed 4 hours, and for Mercury - no more than 1.5 hours. We can say that Mercury is always “bathed” in the sun’s rays - it must be observed either immediately before sunrise or immediately after sunset, in a bright sky. The apparent brightness (magnitude) of Mercury varies over time, ranging from to . The apparent magnitude of Venus varies from to . Venus is the brightest object in the sky after the Sun and Moon.

The outer planets also have four configurations (Fig. 7.4): compound(With.), confrontation(p.), eastern And western quadrature(Z.Q. and Q.Q.).

Rice. 7.4. Outer planet configurations

In the conjunction configuration, the outer planet is located on the line connecting the Sun and Earth, behind the Sun. At this moment it cannot be observed.

Since the angular velocity of the outer planet is less than that of the Earth, the further relative motion of the planet on the celestial sphere will be retrograde. At the same time, it will gradually shift west of the Sun. When the angular distance of the outer planet from the Sun reaches , it will fall into the “western quadrature” configuration. In this case, the planet will be visible in the eastern sky throughout the second half of the night until sunrise.

In the “opposition” configuration, sometimes also called “opposition”, the planet is located in the sky from the Sun by , then

The planet located in the eastern quadrature can be observed from evening to midnight.

The most favorable conditions for observing the outer planets are during the era of their opposition. At this time, the planet is available for observation throughout the night. At the same time, it is as close as possible to the Earth and has the largest angular diameter and maximum brightness. It is important for observers that all the upper planets reach their greatest height above the horizon during winter oppositions, when they move across the sky in the same constellations where the Sun is in the summer. Summer oppositions at northern latitudes occur low above the horizon, which can make observations very difficult.

When calculating the date of a particular configuration of a planet, its location relative to the Sun is depicted in a drawing, the plane of which is taken to be the plane of the ecliptic. The direction to the vernal equinox point ^ is chosen arbitrarily. If a day of the year is given on which the heliocentric ecliptic longitude of the Earth has a certain value, then the location of the Earth should first be noted on the drawing.

The approximate value of the Earth's heliocentric ecliptic longitude is very easy to find from the date of observation. It is easy to see (Fig. 7.5) that, for example, on March 21, looking from the Earth towards the Sun, we are looking at the vernal equinox point ^, that is, the direction “Sun - vernal equinox point” differs from the direction “Sun - Earth” by , which means that the heliocentric ecliptic longitude of the Earth is . Looking at the Sun on the day of the autumnal equinox (September 23), we see it in the direction of the autumnal equinox point (in the drawing it is diametrically opposite to point ^). At the same time, the ecliptic longitude of the Earth is . From Fig. 7.5 it is clear that on the day of the winter solstice (December 22) the ecliptic longitude of the Earth is , and on the day of the summer solstice (June 22) - .

Rice. 7.5. Earth's ecliptic heliocentric longitudes
on different days of the year, since the Sun and Earth are always at opposite ends of the same radius vector. But geocentric longitude and by difference

determine the conditions for their visibility from Earth, assuming that on average a planet becomes visible when it moves away from the Sun at an angle of about 15º.

In reality, the conditions for the visibility of planets depend not only on their distance from the Sun, but also on their declination and on the geographic latitude of the observation site, which affects the duration of twilight and the altitude of the planets above the horizon.

Since the position of the Sun on the ecliptic is well known for each day of the year, using the star chart and the values ​​it is easy to indicate the constellation in which the planet is located on the same day of the year. The solution to this problem is made easier by the fact that on the lower edge of the maps of the Small Star Atlas A.A. Mikhailov, red numbers indicate the dates on which the declination circles marked by them culminate at the middle midnight. These same dates show the approximate position of the Earth in its orbit according to observations from the Sun. Therefore, having determined from the map the equatorial coordinates and the points of the ecliptic culminating at the middle midnight of a given date, it is easy to find the equatorial coordinates of the Sun for the same date

and using them to show its position on the ecliptic.

Using the heliocentric longitude of the planets, it is easy to calculate the days (dates) of the onset of their various configurations. To do this, it is enough to go to the reference system associated with the planet. This assumes that ultimately we will consider the planet stationary, and the Earth moving in its orbit, but with a relative angular velocity.

Let us obtain the necessary formulas for studying the motion of the upper planet. Let on some day of the year the heliocentric longitude of the upper planet be , and the heliocentric longitude of the Earth be . The upper planet moves slower than the Earth (), which is catching up with the planet, and on some day of the year. Therefore, to calculate the distance the lower planet travels from one configuration to another, assuming a stationary Earth.

All the problems discussed above should be solved approximately, rounding the values ​​to 0.01 astronomical units, and to 0.01 years, and to a whole day.

Annual path of the Sun

The expression “the path of the Sun among the stars” may seem strange to some. After all, you can’t see the stars during the day. Therefore, it is not easy to notice that the Sun slowly, by about 1˚ per day, moves among the stars from right to left. But you can see how the appearance of the starry sky changes throughout the year. All this is a consequence of the Earth’s revolution around the Sun.

The path of the visible annual movement of the Sun against the background of stars is called the ecliptic (from the Greek “eclipse” - “eclipse”), and the period of rotation along the ecliptic is called the sidereal year. It is equal to 265 days 6 hours 9 minutes 10 seconds, or 365.2564 average solar days.

The ecliptic and the celestial equator intersect at an angle of 23˚26" at the points of the spring and autumn equinox. The Sun usually appears at the first of these points on March 21, when it passes from the southern hemisphere of the sky to the northern. At the second - on September 23, when it passes from the northern hemisphere to the south. At the point of the ecliptic most distant to the north, the Sun occurs on June 22 (summer solstice), and to the south - on December 22 (winter solstice). In a leap year, these dates are shifted by one day.

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

Since the point of the vernal equinox moves slowly among the stars due to the precession of the earth's axis, the duration of the tropical year is less than the duration of the sidereal year. It is 365.2422 average solar days.

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

And finally, the last thing is related to the apparent annual movement of the Sun. The Sun passes half of the ecliptic from the spring equinox to the autumn equinox (from March 21 to September 23) in 186 days. The second half, from the autumn and spring equinox, takes 179 days (180 in a leap year). But the halves of the ecliptic are equal: each is 180˚. Consequently, the Sun moves unevenly along the ecliptic. This unevenness is explained by changes in the speed of the Earth's movement in an elliptical orbit around the Sun.

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

SOLAR ECLIPSE

At the moment of the lunar new moon, a solar eclipse can occur - after all, it is during the new moon that the Moon passes between the Sun and the Earth. Astronomers know in advance when and where a solar eclipse will be observed, and report this in astronomical calendars.

The Earth got one and only satellite, but what a satellite! The Moon is 400 times smaller than the Sun and just 400 times closer to the Earth, so in the sky the Sun and Moon appear to be disks of the same size. So during a total solar eclipse, the Moon completely obscures the bright surface of the Sun, leaving the entire solar atmosphere exposed.

Exactly at the appointed hour and minute, through the dark glass you can see how something black creeps onto the bright disk of the Sun from the right edge, and how a black hole appears on it. It gradually grows until finally the solar circle takes the form of a narrow sickle. At the same time, daylight quickly weakens. Here the Sun completely hides behind a dark curtain, the last ray of day goes out, and the darkness, which seems the deeper the more sudden it is, spreads out around, plunging man and all of nature into silent surprise.

English astronomer Francis Bailey talks about the eclipse of the Sun on July 8, 1842 in the city of Pavia (Italy): “When the total eclipse occurred and the sunlight instantly went out, some kind of bright radiance suddenly appeared around the dark body of the Moon, similar to a crown or a halo around the head St. No reports of past eclipses had written about anything like this, and I did not at all expect to see the splendor that was now before my eyes. The width of the crown, based on the circumference of the Moon’s disk, was equal to approximately half the lunar diameter. seemed composed of bright rays. Its light was denser near the very edge of the Moon, and as it moved away, the rays of the crown became weaker and thinner. The weakening of the light proceeded completely smoothly as the distance increased. The crown appeared in the form of beams of straight, weak rays; like a fan; the rays were of unequal length. The crown was not reddish, not pearly, its rays shimmered or flickered like a gas flame. No matter how brilliant this phenomenon was, no matter how much delight it aroused among the spectators, there was still something sinister in this strange, wondrous spectacle, and I fully understand how shocked and frightened people could have been at the time when these phenomena happened completely unexpectedly.

The most surprising detail of the whole picture was the appearance of three large protrusions (prominences), which rose above the edge of the Moon, but obviously formed part of the crown. They looked like mountains of enormous height, like the snowy peaks of the Alps when they are illuminated by the red rays of the setting Sun. Their red color faded into lilac or purple; perhaps a peach blossom shade would be best suited here. The light of the protrusions, in contrast to the rest of the crown, was completely calm, the “mountains” did not sparkle or shimmer. All three protrusions, slightly different in size, were visible until the last moment of the total phase of the eclipse. But as soon as the first ray of the Sun broke through, the prominences, along with the corona, disappeared without a trace, and the bright light of day was immediately restored." This phenomenon, so subtly and colorfully described by Bailey, lasted just over two minutes.

Remember Turgenev's boys on Bezhinsky meadow? Pavlusha talked about how the Sun was no longer visible, about a man with a jug on his head, who was mistaken for the Antichrist Trishka. So this was a story about the same eclipse on July 8, 1842!

But there was no eclipse in Rus' greater than that described in “The Tale of Igor’s Campaign” and the ancient chronicles. In the spring of 1185, the Novgorod-Seversk prince Igor Svyatoslavich and his brother Vsevolod, filled with military spirit, went against the Polovtsians to gain glory for themselves and booty for their squad. On May 1, in the late afternoon, as soon as the regiments of the “Dazhd-God’s grandchildren” (descendants of the Sun) entered the foreign land, it grew dark earlier than expected, the birds fell silent, the horses neighed and did not move, the shadows of the horsemen were unclear and strange, the steppe breathed with cold. Igor looked around and saw that the “sun standing like a moon” was seeing them off. And Igor said to his boyars and his squad: “Do you see? What does this radiance mean??” They looked, and saw, and bowed their heads. And the men said: “Our prince! This radiance does not promise us good!” Igor answered: “Brothers and squad! The secret of God is unknown to anyone. And what God gives us - for our good or for our misfortune - we will see.” On the tenth day of May, Igor’s squad was killed in the Polovtsian steppe, and the wounded prince was captured.