The units of the hour measure of angles should not be confused with units of the measure of time that are identical in name and designation, since angles and time intervals are dissimilar quantities. The hour measure of angles has simple relationships with the degree measure:

	corresponds to 15°;		1° corresponds to 4Ш;
\ T
						1/15s.
For translate		quantities				hourly measures in

degree and	back there are tables (Table V in
AE or adj.	1 of this book).
Geographical			coordinates		sometimes called
ronomic					definitions.
§ 2. Equatorial coordinates of luminaries
Position		celestial bodies		convenient to define

vatorial coordinate system. Let's imagine that

the sky is			huge			sphere, in the center of which is
for the sphere, we can we-
too hard to build
coordinate
			parallels
globe. If pro-
passing through the Northern
before crossing with the imagination
		heavenly
then you will get diametrically
	opposite
ki of Northern R and South
called
is		geometric axis						equatorial
	coordinates Continuing the plane of the earth

ra, until it crosses the celestial sphere, we get the line of the celestial equator on the sphere.

The earth rotates around its axis from west to east

drain, and its full turnover takes one day. To an observer on Earth it seems that the celestial sphere is

rotates with all visible luminaries
in the opposite	direction, i.e. from the east
west. It seems to us that the Sun is every day
around the Earth: in the morning it		rises		eastern
part of the horizon, and			Over the horizon

west. In the future, instead of the actual rotation of the Earth around its axis, we will consider the daily rotation of the celestial sphere. It occurs clockwise when viewed from the North Pole.

It is easier to visually imagine the celestial sphere if you look at it from the outside, as shown in Fig. 2. In addition, it shows the trace of the intersection of the plane of the earth's orbit, or the plane of the ecliptic, with the celestial sphere. The earth commits full turn orbit around the Sun in one year. A reflection of this annual revolution is the apparent annual movement of the Sun along celestial sphere in the same plane, i.e. along the ecliptic J F JL - F J T . Every day, the Sun moves among the stars along the ecliptic to the east by about one degree of arc, completing a full revolution in a year. The ecliptic intersects with the celestial equator at two diametrically opposite points, called equinox points: T - the vernal equinox and - the autumn equinox. When the Sun is at these points, then everywhere on Earth it rises exactly in the east, sets exactly in the west, and day and night are equal to 12 hours. Such days are called equinoxes, and they fall on March 21 and September 23 with no deviation from these dates less than one day.

The planes of geographic meridians, extended until they intersect with the celestial sphere, form celestial meridians at the intersection with it. There are countless celestial meridians. Among them, it is necessary to select the initial one in the same way as on Earth the meridian passing through the Greenwich Observatory is accepted as the zero one. In astronomy, such a reference line is taken to be the celestial meridian passing through the point of the vernal equinox and called the circle of declination of the point of the vernal equinox. Celestial meridians passing through the positions of the luminaries are called the circles of declination of these luminaries,

In the equatorial coordinate system, the main circles are the celestial equator and the declination circle of the Y point. The position of any luminary in this coordinate system is determined by right ascension and declination.

Rectal descent is the spherical angle at the celestial pole between the circle of declination of the vernal equinox and the circle of declination of the luminary, calculated in the direction opposite to the daily rotation of the celestial sphere.

Right ascension is measured by the arc of the celestial

niya of the celestial sphere, therefore a does not depend on the daily rotation of the celestial sphere.

and the direction towards the luminary. The declination is measured by the corresponding arc of the declination circle from the celestial equator to the place of the luminary. If the luminary is in the northern hemisphere (north of the celestial equator), its declination is assigned the name N, and if it is in the southern hemisphere, the name 5. When solving astronomical problems, the plus sign is assigned to the declination value, which is the same as the latitude of the observation site. In the Northern Hemisphere of the Earth, the northern declination is considered positive, and the southern declination is considered negative. The declination of the luminary can vary from 0 to ±90°. The declination of each point on the celestial equator is 0°. The declination of the North Pole is 90°.

Any luminary makes a complete revolution around the celestial pole during the day along its daily parallel together with the celestial sphere, therefore b, like a, does not depend on its rotation. But if the luminary has additional movement (for example, the Sun or a planet) and moves across the celestial sphere, then its equatorial coordinates change.

The values ​​of a and b are related to the observer, as if located at the center of the Earth. This allows you to use the equatorial coordinates of luminaries anywhere on Earth.

§ 3. Horizontal coordinate system

The center of the celestial sphere can be moved to any

point in space.

in particular,

fit with the point of intersection of the main axes

ta. In this case, vertical

tool (Fig.

geometric

horizontal

coordinates

At the intersection with the sky

sheer

forms

observer.

passing

heavenly

perpendicular-

direction

called

plane

true

horizon and at the intersection

surface

heavenly

true

horizon

designations

countries of the world adopted traditional

transcription: N (north), S (south), W (west)

Through a plumb line you can draw

countless

new set

vertical

planes. At the intersection

with surface

celestial sphere

form

circles called verticals. Any vertical

that passes through the location of the luminary is called the vertical of the luminary.

		RRH					characterize
	as a line parallel to the axis of rotation
Then the plane of the celestial equator QQ\ will be parallel
	plane		earth's equator. vertical,
					PZP\ZX ,	is
temporarily heavenly				meridian			observations,
or meridian			observer. Meridian				observer

The observer's meridian with the plane of the true horizon is called the noon line. The closest point of intersection of the midday to the North Pole

through the points of east and west is called the first vertical. Its plane is perpendicular to the plane of the observer's meridian. The celestial sphere is usually

				meridian plane				observer
coincides with the drawing plane.
The main coordinate circles in the horizontal
the system is served by the true horizon and							meridian
giver. According to the first of these circles							the system received
its name.		Coordinates
	are				and anti-aircraft		distance.
A z i m u t		s v e t i l a			A - spherical
zenith point between the observer's meridian
				astronomy				count down
					meridian		observer, but

Since, ultimately, astronomical azimuths of directions are determined for geodetic purposes, it is more convenient to immediately adopt a geodetic account of azimuths in this book. They are measured by arcs of the true horizon from the point of north to the vertical of the luminary along the course of the

the center of the sphere between the direction to the zenith and the direction to the luminary. The zenith distance is measured by the vertical arc of the luminary from the zenith point to the place of the luminary. The zenith distance is always positive and varies in value from 0 to 180°.

The rotation of the Earth around its axis from west to east causes the visible daily rotation of the luminaries around the celestial pole along with the entire celestial sphere. This

To make a star map depicting constellations on a plane, you need to know the coordinates of the stars. The coordinates of stars relative to the horizon, for example altitude, although visual, are unsuitable for making maps, since they change all the time. It is necessary to use a coordinate system that would rotate with starry sky. It is called the equatorial system. In it, one coordinate is the angular distance of the luminary from the celestial equator, called declination (Fig. 19). It varies within ±90° and is considered positive north of the equator and negative south. Declination is similar to geographic latitude.

The second coordinate is similar to geographic longitude and is called right ascension a.

Rice. 18. Daily paths of the Sun above the horizon at different times of the year during observations: a - in mid-latitudes; b - at the Earth's equator.

Rice. 19. Equatorial coordinates.

Rice. 20. The height of the luminary at the upper culmination.

The right ascension of the luminary M is measured by the angle between the planes of the great circle drawn through the poles of the world and the given luminary and the great circle passing through the poles of the world and the point of the vernal equinox (Fig. 19). This angle is measured from the vernal equinox point T counterclockwise when viewed from north pole. It varies from 0 to 360° and is called right ascension because the stars located on the celestial equator rise in order of increasing right ascension. In the same order they culminate one after another. Therefore, a is usually expressed not in angular measure, but in time, and it is assumed that the sky rotates by 15°, and by 1° in 4 minutes. Therefore, right ascension is 90°, otherwise it will be 6 hours, and 7 hours 18 minutes. In units of time, right ascensions are written along the edges of the star chart.

There are also star globes, where the stars are depicted on the spherical surface of the globe.

On one map, only part of the starry sky can be depicted without distortion. It is difficult for beginners to use such a map, because they do not know which constellations are visible at a given time and how they are located relative to the horizon. A moving star map is more convenient. The idea of ​​its device is simple. Superimposed on the map is a circle with a cutout representing the horizon line. The horizon cutout is eccentric, and when you rotate the overlay circle in the cutout, constellations located above the horizon at different time. How to use such a card is described in Appendix VII.

(see scan)

2. The height of the luminaries at the culmination.

Let's find the relationship between the height of the luminary M at the upper culmination, its declination 6 and the latitude of the area

Figure 20 shows the plumb line of the celestial axis and the projection of the celestial equator and the horizon line (noon line) onto the plane of the celestial meridian. The angle between the noon line and the celestial axis is equal, as we know, to the latitude of the area. Obviously, the inclination of the plane of the celestial equator to the horizon, measured by the angle, is equal to 90° - (Fig. 20). The star M with declination 6, culminating south of the zenith, has a height of

From this formula it can be seen that geographic latitude can be determined by measuring the altitude of any star with a known declination of 6 at its upper culmination. It should be taken into account that if the star at the moment of culmination is located south of the equator, then its declination is negative.

(see scan)

3. Exact time.

For measuring short periods of time in astronomy, the basic unit is the average length of the solar day, that is, the average period of time between the two upper (or lower) culminations of the center of the Sun. The average value must be used because the length of the sunny day fluctuates slightly throughout the year. This is due to the fact that the Earth revolves around the Sun not in a circle, but in an ellipse, and the speed of its movement changes slightly. This causes slight irregularities in the apparent movement of the Sun along the ecliptic throughout the year.

The moment of the upper culmination of the center of the Sun, as we have already said, is called true noon. But to check the clock, to determine the exact time, there is no need to mark on it exactly the moment of the culmination of the Sun. It is more convenient and accurate to mark the moments of the culmination of stars, since the difference between the moments of the culmination of any star and the Sun is precisely known for any time. Therefore, to determine the exact time, using special optical instruments, they mark the moments of the culminations of the stars and use them to check the correctness of the clock that “stores” time. The time determined in this way would be absolutely accurate if the observed rotation of the sky occurred with a strictly constant angular velocity. However, it turned out that the speed of the Earth’s rotation around its axis, and therefore the apparent rotation of the celestial

sphere, experiences very small changes over time. Therefore, to “save” exact time, special atomic clocks are now used, the course of which is controlled by oscillatory processes in atoms that occur at a constant frequency. The clocks of individual observatories are checked against atomic time signals. Comparing time determined from atomic clocks and the apparent motion of stars makes it possible to study the irregularities of the Earth's rotation.

Determining the exact time, storing it and transmitting it by radio to the entire population is the task of the exact time service, which exists in many countries.

Precise time signals via radio are received by navigators of the navy and air force, and many scientific and industrial organizations that need to know the exact time. Knowing the exact time is necessary, in particular, to determine the geographical longitudes of different points on the earth's surface.

4. Counting time. Determination of geographic longitude. Calendar.

From the course of physical geography of the USSR, you know the concepts of local, zone and maternity time, and also that the difference in geographical longitude of two points is determined by the difference in the local time of these points. This problem is solved by astronomical methods using stellar observations. Based on determining the exact coordinates of individual points, the earth's surface is mapped.

To count large periods of time, people since ancient times have used the duration of either a lunar month or a solar year, i.e., the duration of the Sun's revolution along the ecliptic. The year determines the frequency of seasonal changes. A solar year lasts 365 solar days, 5 hours 48 minutes 46 seconds. It is practically incommensurate with the day and with the length of the lunar month - the period of change of lunar phases (about 29.5 days). This is the difficulty of creating a simple and convenient calendar. Behind centuries-old history Throughout humanity, many different calendar systems have been created and used. But all of them can be divided into three types: solar, lunar and lunisolar. Southern pastoral peoples usually used lunar months. A year consisting of 12 lunar months contained 355 solar days. To coordinate the calculation of time by the Moon and the Sun, it was necessary to establish either 12 or 13 months in the year and insert additional days into the year. Simpler and more convenient was the solar calendar, which was used back in Ancient Egypt. Currently, most countries in the world also adopt a solar calendar, but a more advanced one, called the Gregorian calendar, which is discussed below.

When compiling a calendar, it is necessary to take into account that the duration of the calendar year should be as close as possible to the duration of the Sun's revolution along the ecliptic and that the calendar year should contain a whole number of solar days, since it is inconvenient to start the year at different times of the day.

These conditions were satisfied by the calendar developed

by the Alexandrian astronomer Sosigenes and introduced in 46 BC. e. in Rome by Julius Caesar. Subsequently, as you know from the course of physical geography, it received the name Julian or old style. In this calendar, the years are counted three times in a row for 365 days and are called simple, the year following them is 366 days. It's called a leap year. Leap years in the Julian calendar are those years whose numbers are divisible by 4 without a remainder.

The average length of the year according to this calendar is 365 days 6 hours, i.e. it is approximately 11 minutes longer than the true one. Due to this old style lagged behind the actual flow of time by about 3 days every 400 years.

IN Gregorian calendar(new style), introduced in the USSR in 1918 and even earlier adopted in most countries, years ending in two zeros, with the exception of 1600, 2000, 2400, etc. (i.e. those with hundreds divisible by 4 without remainder) are not considered leap days. This corrects the error of 3 days, which accumulates over 400 years. Thus, the average length of the year in the new style turns out to be very close to the period of revolution of the Earth around the Sun.

By the 20th century the difference between the new style and the old (Julian) reached 13 days. Because in our country a new style was introduced only in 1918, then the October Revolution, committed in 1917 on October 25 (old style), is celebrated on November 7 (new style).

The difference between the old and new styles of 13 days will remain in the 21st century, and in the 22nd century. will increase to 14 days.

The new style, of course, is not completely accurate, but an error of 1 day will accumulate according to it only after 3300 years.

A constellation is an area of ​​the sky within certain established boundaries. The entire sky is divided into 88 constellations, which can be found by their characteristic arrangement of stars.
Some constellation names are associated with Greek mythology, for example Andromeda, Perseus, Pegasus, some - with objects that resemble the figures formed by the bright stars of the constellations: Arrow, Triangulum, Libra, etc. There are constellations named after animals, for example Leo, Cancer, Scorpion.
Constellations in the sky are found by mentally connecting their brightest stars with straight lines into a certain figure. In each constellation, the bright stars have long been designated by Greek letters, most often the brightest star of the constellation - by the letter, then by the letters, etc. in alphabetical order in descending order of brightness; For example, polar Star there are constellations Ursa Minor.
Stars have different brightness and color: white, yellow, reddish. The redder the star, the cooler it is. Our Sun is a yellow star.
To the bright stars the ancient Arabs gave proper names. White stars: Vega in the constellation Lyra, Altair in the constellation Aquila (visible in summer and autumn), Sirius- the brightest star in the sky (visible in winter); red stars: Betelgeuse in the constellation Orion and Aldebaran in the constellation Taurus (visible in winter), Antares in the constellation Scorpio (visible in summer); yellow Chapel in the constellation Auriga (visible in winter).
Accurate measurements show that stars have both fractional and negative magnitudes, for example: for Aldebaran the magnitude m=1.06, for Vega m=0.14, for Sirius m= -1.58, for the Sun m = - 26,80.
The phenomena of the daily movement of stars are studied using a mathematical construction - the celestial sphere, that is, an imaginary sphere of arbitrary radius, the center of which is at the observation point.
The axis of apparent rotation of the celestial sphere, connecting both poles of the world (P and P") and passing through the observer, is called axis mundi. The axis of the world for any observer will always be parallel to the axis of rotation of the Earth.
To make a star map depicting constellations on a plane, you need to know the coordinates of the stars. In the equatorial system, one coordinate is the distance of the star from the celestial equator, called declination. It varies within ±90° and is considered positive north of the equator and negative south. Declination is similar to geographic latitude. The second coordinate is similar to geographic longitude and is called right ascension.
The right ascension of a luminary is measured by the angle between the planes of great circles, one passing through the poles of the world and the given luminary, and the other through the poles of the world and the point of the vernal equinox lying on the equator. This point was named so because the Sun appears there (on the celestial sphere) in the spring of March 20-21, when day is equal to night.

Determination of geographic latitude

The phenomena of the passage of luminaries through the celestial meridian are called culminations. At the upper culmination the height of the luminary is maximum, at the lower culmination it is minimum. The time interval between climaxes is half a day.
Geographic latitude can be determined by measuring the altitude of any star with a known declination at its upper culmination. It should be taken into account that if the star at the moment of culmination is located south of the equator, then its declination is negative.

EXAMPLE OF SOLVING A PROBLEM

Task. Sirius was at its highest climax at 10°. What is the latitude of the observation site?

Ecliptic. Apparent motion of the Sun and Moon

The Sun and Moon change the altitude at which they culminate. From this we can conclude that their position relative to the stars (declination) changes. It is known that the Earth moves around the Sun, and the Moon around the Earth.
When determining the height of the Sun at noon, we noticed that twice a year it occurs on the celestial equator, in the so-called equinoctial points. This happens in days spring And autumn equinox(around March 21 and around September 23). The horizon plane divides the celestial equator in half. Therefore, on the days of the equinoxes, the paths of the Sun above and below the horizon are equal, therefore, the lengths of day and night are equal. Moving along the ecliptic, the Sun on June 22 moves farthest from the celestial equator towards the north pole of the world (at 23°27"). At noon for the northern hemisphere of the Earth it is highest above the horizon (this value above the celestial equator). The day is the longest, it's called day summer solstice.
The path of the Sun runs through 12 constellations, called zodiacal (from the Greek word zoon - animal), and their totality is called the zodiac belt. It includes the following constellations: Pisces, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius. The Sun travels through each zodiac constellation for about a month. The vernal equinox point (one of the two intersections of the ecliptic with the celestial equator) is located in the constellation Pisces.

EXAMPLE OF SOLVING A PROBLEM

Task. Determine the midday height of the Sun in Arkhangelsk and Ashgabat on the days of the summer and winter solstice

Given 1=65° 2=38° l=23.5° z=-23.5°	SOLUTION We find the approximate latitudes of Arkhangelsk (1) and Ashgabat (2) from a geographical map. The declinations of the Sun on the days of the summer and winter solstices are known. According to the formula we find: 1l =48.5°, 1z = 1.5°, 2l = 75.5°, 2z =28.5°.
1l -? 2l -? 1z -? 2z -?

Movement of the Moon. Solar and lunar eclipses

Without being self-luminous, the Moon is visible only in the part where it falls Sun rays, or rays reflected by the Earth. This explains the phases of the moon. Every month, the Moon, moving in orbit, passes between the Earth and the Sun and faces us with its dark side, at which time the new moon occurs. 1 - 2 days after this, a narrow bright crescent of the young Moon appears in the western sky. The rest of the lunar disk is at this time dimly illuminated by the Earth, which is turned toward the Moon with its daytime hemisphere. After 7 days, the Moon moves away from the Sun by 90°, the first quarter begins, when exactly half of the Moon’s disk is illuminated and the “terminator,” that is, the dividing line between the light and dark sides, becomes straight - the diameter of the lunar disk. In the following days, the “terminator” becomes convex, the appearance of the Moon approaches a bright circle, and after 14 - 15 days the full moon occurs. On the 22nd day the last quarter is observed. The angular distance of the Moon from the Sun decreases, it again becomes a crescent and after 29.5 days the new moon occurs again. The interval between two successive new moons is called the synodic month, which has an average length of 29.5 days. The synodic month is longer than the sidereal month. If a new moon occurs near one of the nodes of the lunar orbit, a solar eclipse occurs, and a full moon near a node is accompanied by a lunar eclipse.

Lunar and solar eclipses

Due to a slight change in the distances of the Earth from the Moon and the Sun, the apparent angular diameter of the Moon is sometimes slightly larger, sometimes slightly smaller than the solar one, sometimes equal to it. In the first case, a total eclipse of the Sun lasts up to 7 minutes. 40 s, in the third - only one instant, and in the second case, the Moon does not completely cover the Sun, it is observed annular eclipse. Then around the dark disk of the Moon the shining rim of the solar disk is visible.
Based on precise knowledge of the laws of motion of the Earth and the Moon, the moments of eclipses and where and how they will be visible are calculated hundreds of years in advance. Maps have been compiled that show the strip of total eclipse, lines (isophases) where the eclipse will be visible in the same phase, and lines relative to which the moments of the beginning, end and middle of the eclipse can be counted for each area.
There can be from two to five solar eclipses per year for the Earth, in the latter case they are certainly partial. On average, a total solar eclipse is seen extremely rarely in the same place - only once every 200-300 years.
If the Moon comes between the Sun and the Earth at new moon, then solar eclipses occur. During a total eclipse, the Moon completely covers the solar disk. In broad daylight, twilight suddenly sets in for a few minutes and the faintly glowing corona of the Sun and the brightest stars become visible to the naked eye.

Total solar eclipse

Exact time and determination of geographic longitude

For measuring short periods of time in astronomy, the basic unit is average duration of sunny day, i.e., the average time interval between the two upper (or lower) culminations of the center of the Sun. This is due to the fact that the Earth revolves around the Sun not in a circle, but in an ellipse, and the speed of its movement changes slightly.
The moment of the highest culmination of the center of the Sun is called true noon. But to check the clock, to determine the exact time, there is no need to mark on it exactly the moment of the culmination of the Sun. It is more convenient and accurate to mark the moments of the culmination of stars, since the difference between the moments of the culmination of any star and the Sun is precisely known for any time.
Determining the exact time, storing it, and transmitting it by radio to the entire population is the task time services, which exists in many countries.
To count large periods of time, people since ancient times have used the duration of either a lunar month or a solar year, i.e., the duration of the Sun's revolution along the ecliptic. The year determines the frequency of seasonal changes. A solar year lasts 365 solar days 5 hours 48 minutes 46 seconds.
When compiling a calendar, it is necessary to take into account that the duration of the calendar year should be as close as possible to the duration of the Sun's revolution along the ecliptic, and that the calendar year should contain an integer number of solar days, since it is inconvenient to start the year at different times of the day.

Astronomy is a whole world full of beautiful images. This amazing science helps to find answers to the most important questions of our existence: learn about the structure of the Universe and its past, about the Solar system, about how the Earth rotates, and much more. There is a special connection between astronomy and mathematics, because astronomical predictions are the result of rigorous calculations. In fact, many problems in astronomy became possible to solve thanks to the development of new branches of mathematics.

From this book the reader will learn about how the position of celestial bodies and the distance between them is measured, as well as about astronomical phenomena during which space objects occupy a special position in space.

If the well, like all normal wells, was directed towards the center of the Earth, its latitude and longitude did not change. The angles that determine Alice's position in space remained unchanged, only her distance to the center of the Earth changed. So Alice didn't have to worry.

Option one: altitude and azimuth

The most understandable way to determine coordinates on the celestial sphere is to indicate the angle that determines the height of the star above the horizon, and the angle between the north-south straight line and the projection of the star onto the horizon line - azimuth (see the following figure).

HOW TO MEASURE ANGLES MANUALLY

A device called a theodolite is used to measure the altitude and azimuth of a star.

However, there is a very simple, although not very accurate, way to measure angles manually. If we extend our hand in front of us, the palm will indicate an interval of 20°, the fist - 10°, the thumb - 2°, the little finger -1°. This method can be used by both adults and children, since the size of a person’s palm increases in proportion to the length of his arm.

Option two, more convenient: declination and hour angle

Determining the position of a star using azimuth and altitude is not difficult, but this method has a serious drawback: the coordinates are tied to the point at which the observer is located, so the same star, when observed from Paris and Lisbon, will have different coordinates, since the horizon lines in these cities will be located differently. Consequently, astronomers will not be able to use this data to exchange information about their observations. Therefore, there is another way to determine the position of the stars. It uses coordinates reminiscent of the latitude and longitude of the earth's surface, which can be used by astronomers anywhere on the globe. This intuitive method takes into account the position of the Earth's rotation axis and assumes that the celestial sphere rotates around us (for this reason, the Earth's rotation axis was called the axis mundi in Antiquity). In reality, of course, the opposite is true: although it seems to us that the sky is rotating, in fact it is the Earth that is rotating from west to east.

Let us consider a plane cutting the celestial sphere perpendicular to the axis of rotation passing through the center of the Earth and the celestial sphere. This plane will intersect the earth's surface along a great circle - the earth's equator, and also the celestial sphere - along its great circle, which is called the celestial equator. The second analogy with earthly parallels and meridians would be the celestial meridian, passing through two poles and located in a plane perpendicular to the equator. Since all celestial meridians, like terrestrial ones, are equal, the prime meridian can be chosen arbitrarily. Let us choose as the zero meridian the celestial meridian passing through the point at which the Sun is located on the day of the vernal equinox. The position of any star and celestial body is determined by two angles: declination and right ascension, as shown in the following figure. Declination is the angle between the equator and the star, measured along the meridian of a place (from 0 to 90° or from 0 to -90°). Right ascension is the angle between the vernal equinox and the meridian of the star, measured along the celestial equator. Sometimes, instead of right ascension, the hour angle, or the angle that determines the position of the celestial body relative to the celestial meridian of the point at which the observer is located, is used.

The advantage of the second equatorial coordinate system (declination and right ascension) is obvious: these coordinates will be unchanged regardless of the position of the observer. In addition, they take into account the rotation of the Earth, which makes it possible to correct the distortions it introduces. As we have already said, the apparent rotation of the celestial sphere is caused by the rotation of the Earth. A similar effect occurs when we are sitting on a train and see another train moving next to us: if you do not look at the platform, you cannot determine which train has actually started moving. We need a starting point. But if instead of two trains we consider the Earth and the celestial sphere, finding an additional reference point will not be so easy.

In 1851 a Frenchman Jean Bernard Leon Foucault (1819–1868) conducted an experiment demonstrating the motion of our planet relative to the celestial sphere.

He suspended a load weighing 28 kilograms on a 67-meter-long wire under the dome of the Parisian Pantheon. The oscillations of the Foucault pendulum lasted 6 hours, the oscillation period was 16.5 seconds, the pendulum deflection was 11° per hour. In other words, over time, the plane of oscillation of the pendulum shifted relative to the building. It is known that pendulums always move in the same plane (to verify this, just hang a bunch of keys on a rope and watch its vibrations). Thus, the observed deviation could be caused by only one reason: the building itself, and therefore the entire Earth, rotated around the plane of oscillation of the pendulum. This experiment became the first objective evidence of the rotation of the Earth, and Foucault pendulums were installed in many cities.

The Earth, which appears to be motionless, rotates not only on its own axis, making a complete revolution in 24 hours (equivalent to a speed of about 1600 km/h, that is, 0.5 km/s if we are at the equator), but also around the Sun , making a full revolution in 365.2522 days (with an average speed of approximately 30 km/s, that is, 108000 km/h). Moreover, the Sun rotates relative to the center of our galaxy, completing a full revolution every 200 million years and moving at a speed of 250 km/s (900,000 km/h). But that’s not all: our galaxy is moving away from the rest. Thus, the movement of the Earth is more like a dizzying carousel in an amusement park: we spin around ourselves, move through space and describe the spiral at breakneck speed. At the same time, it seems to us that we are standing still!

Although other coordinates are used in astronomy, the systems we have described are the most popular. It remains to answer the last question: how to convert coordinates from one system to another? The interested reader will find a description of all the necessary transformations in the application.

MODEL OF THE FOUCAULT EXPERIMENT

We invite the reader to conduct a simple experiment. Let's take a round box and glue a sheet of thick cardboard or plywood onto it, onto which we will attach a small frame in the shape of a football goal, as shown in the figure. Let's place a doll in the corner of the sheet, which will play the role of an observer. We tie a thread to the horizontal bar of the frame, on which we attach the sinker.

Let's move the resulting pendulum to the side and release it. The pendulum will oscillate parallel to one of the walls of the room in which we are located. If we begin to smoothly rotate the sheet of plywood together with the round box, we will see that the frame and the doll will begin to move relative to the wall of the room, but the plane of oscillation of the pendulum will still be parallel to the wall.

If we imagine ourselves as a doll, we will see that the pendulum moves relative to the floor, but at the same time we will not be able to feel the movement of the box and the frame on which it is attached. Similarly, when we observe a pendulum in a museum, it seems to us that the plane of its oscillations is shifting, but in fact we ourselves are shifting along with the museum building and the entire Earth.

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Key questions: 1. The concept of constellation. 2. Difference between stars in brightness (luminosity), color. 3. Magnitude. 4. Visible diurnal movement stars 5. celestial sphere, its main points, lines, planes. 6. Star map. 7. Equatorial SC.

Demonstrations and TSO: 1. Demonstration moving sky map. 2. Model of the celestial sphere. 3. Star atlas. 4. Transparencies, photographs of constellations. 5. Model of the celestial sphere, geographical and star globes.

For the first time, stars were designated by letters of the Greek alphabet. In the constellation atlas of Baiger in the 18th century, the drawings of the constellations disappeared. The magnitudes are indicated on the map.

Ursa Major - (Dubhe), (Merak), (Fekda), (Megrets), (Aliot), (Mizar), (Benetash).

Lyra - Vega, Lebedeva - Deneb, Bootes - Arcturus, Auriga - Capella, B. Canis - Sirius.

The Sun, Moon and planets are not indicated on the maps. The path of the Sun is shown on the ecliptic in Roman numerals. Star maps display a grid of celestial coordinates. The observed daily rotation is an apparent phenomenon - caused by the actual rotation of the Earth from west to east.

Proof of Earth's rotation:

1) 1851 physicist Foucault - Foucault pendulum - length 67 m.

2) space satellites, photographs.

Celestial sphere- an imaginary sphere of arbitrary radius used in astronomy to describe the relative positions of luminaries in the sky. The radius is taken as 1 Pc.

88 constellations, 12 zodiac. It can be roughly divided into:

1) summer - Lyra, Swan, Eagle 2) autumn - Pegasus with Andromeda, Cassiopeia 3) winter - Orion, B. Canis, M. Canis 4) spring - Virgo, Bootes, Leo.

Plumb line intersects the surface of the celestial sphere at two points: at the top Z - zenith- and at the bottom Z" - nadir.

Mathematical horizon- a large circle on the celestial sphere, the plane of which is perpendicular to the plumb line.

Dot N mathematical horizon is called north point, dot S - point south. Line N.S.- called noon line.

Celestial equator called a great circle perpendicular to the axis of the world. The celestial equator intersects the mathematical horizon at points of the east E And west W.

Heavenly meridian called the great circle of the celestial sphere passing through the zenith Z, celestial pole R, south celestial pole R", nadir Z".

Homework: § 2.

Constellations. Star cards. Celestial coordinates.

1. Describe what daily circles the stars would describe if astronomical observations were carried out: at the North Pole; at the equator.

The apparent motion of all stars occurs in a circle parallel to the horizon. The North Pole of the world when observed from the North Pole of the Earth is at the zenith.

All stars rise at right angles to the horizon in the eastern part of the sky and also set below the horizon in the western part. The celestial sphere rotates around an axis passing through the poles of the world, located exactly on the horizon at the equator.

2. Express 10 hours 25 minutes 16 seconds in degrees.

The Earth makes one revolution in 24 hours - 360 degrees. Therefore, 360 o corresponds to 24 hours, then 15 o - 1 hour, 1 o - 4 minutes, 15 / - 1 minute, 15 // - 1 s. Thus,

1015 o + 2515 / + 1615 // = 150 o + 375 / +240 / = 150 o + 6 o +15 / +4 / = 156 o 19 / .

3. Determine the equatorial coordinates of Vega from the star map.

Let's replace the name of the star with a letter designation (Lyra) and find its position on the star map. Through an imaginary point we draw a circle of declination until it intersects with the celestial equator. The arc of the celestial equator, which lies between the point of the vernal equinox and the point of intersection of the circle of declination of a star with the celestial equator, is the right ascension of this star, measured along the celestial equator towards the apparent daily rotation of the celestial sphere. The angular distance measured along the declination circle from the celestial equator to the star corresponds to the declination. Thus, = 18 h 35 m, = 38 o.

We rotate the overlay circle of the star map so that the stars cross the eastern part of the horizon. On the limb, opposite the mark of December 22, we find the local time of its sunrise. By placing the star in the western part of the horizon, we determine the local time of sunset of the star. We get

5. Determine the date of the upper culmination of the star Regulus at 21:00 local time.

We install the overhead circle so that the star Regulus (Leo) is on the line of the celestial meridian (0 h - 12 h scale of the overhead circle) south of the north pole. On the dial of the applied circle we find the mark 21 and opposite it on the edge of the applied circle we determine the date - April 10.

6. Calculate how many times brighter Sirius is North Star.

It is generally accepted that with a difference of one magnitude, the apparent brightness of stars differs by approximately 2.512 times. Then a difference of 5 magnitudes will amount to a difference in brightness of exactly 100 times. So stars of the 1st magnitude are 100 times brighter than the stars 6th magnitude. Consequently, the difference in the apparent magnitudes of two sources is equal to unity when one of them is brighter than the other (this value is approximately equal to 2.512). In general, the ratio of the apparent brightness of two stars is related to the difference in their apparent magnitudes by a simple relationship:

Luminaries whose brightness exceeds the brightness of stars 1 m, have zero and negative magnitudes.

Magnitudes of Sirius m 1 = -1.6 and Polaris m 2 = 2.1, we find in the table.

Let us take logarithms of both sides of the above relationship:

Thus, . From here. That is, Sirius is 30 times brighter than the North Star.

Note: using the power function, we will also get the answer to the question of the problem.

7. Do you think it is possible to fly on a rocket to any constellation?

A constellation is a conventionally defined area of ​​the sky within which there are luminaries located at different distances from us. Therefore, the expression “fly to a constellation” is meaningless.