• A dull time, eyes charm ... Autumn is beautiful to me your farewell beauty
• There are four different types of man on earth. The appearance of modern man: the time and place of the appearance of man
• A poem by A.A. Akhmatova “I am not with those who abandoned the earth…” (perception, interpretation, evaluation). Anna Andreevna Akhmatova. “I am not with those who threw the earth ... I am not with those who threw the earth to be torn to pieces by enemies
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• Semiconductor resistors
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• History of Journalism The 26th Congress of the CPSU was held in
• Correct chronology in Rus'
• Scientific writings by James Maxwell
• Oleg Mityaev Oleg Mityaev biography briefly about the main thing

Checking d.z

• How many constellations are there in the sky? Write down the name of the circumpolar constellations you know. Draw its view of any circumpolar constellation. What letter denotes the brightest star in the constellation? Which constellation contains the North Star? Name the brightest star in the sky. What characterizes a star in the sky, depending on the apparent brightness. How to determine the direction to the north? What is the ecliptic. How many zodiac constellations are there? What about zodiac signs?
• How many constellations are there in the sky?
• Write down the name of the circumpolar constellations you know.
• Draw its view of any circumpolar constellation
• What letter represents the brightest star in the constellation?
• Which constellation contains the North Star?
• Name the brightest star in the sky.
• What characterizes a star in the sky, depending on the apparent brightness.
• How to determine the direction to the north?
• What is the ecliptic.
• How many zodiac constellations are there? What about zodiac signs?

Practical work#1

Constellation

Constellation diagram, alpha

Big Dipper

Constellation

Ursa Minor

constellation diagram

Cassiopeia

Auriga

Practical work#1

• Using a star map, enter constellation schemes with bright stars into the appropriate columns of the table. In each constellation, highlight the brightest star and write its name.

Constellation

Constellation diagram, alpha

Big Dipper

Ursa Minor

Constellation

polar Star

Cassiopeia

constellation diagram

Auriga

Mirfak(Alpha Perseus / α Per) is the brightest star in the constellation Perseus. Translated from Arabic Mirfak as-Suraya- elbow,

Shedar(Alpha Cassiopeia)

Chapel(α Aur / α Aurigae / Alpha Aurigae)

Working with a mobile map of the starry sky

• 1. What constellations will be visible on February 17 at 10 p.m.
• 2. Will the constellation of Orion be visible on March 30 at midnight.
• 3. Is it possible to see the constellation Virgo on the night of February 17-18?

The position of a point on Earth is uniquely determined by geographical coordinates - longitude (λ) and latitude (φ).

The position of the star in the sky is uniquely determined by equatorial coordinates - right ascension (α) and declination (δ)

Basic points and lines

• Celestial sphere - an imaginary sphere of arbitrary radius, described around an observer on Earth, on the inner surface of which luminaries are applied.
• The axis of the world is the axis around which the Earth rotates, moving in world space
• The poles of the world are the imaginary axis of the visible rotation of the celestial sphere.
• celestial equator called a great circle perpendicular to the axis of the world. heavenly meridian called the great circle of the celestial sphere, passing through the celestial pole P, the south celestial pole R.

Equatorial coordinate system - the system used to determine the stellar coordinates and compiling catalogs. Determines the annual movement of the Sun and other luminaries.

• declination-arc mm hour circle from the celestial equator to the luminary. They are counted from 0 to +90 to the north pole and from 0 to -90 to the south. p+=90.

• Right ascension α- called the arc of the celestial equator ♈ from the point spring equinox♈ to the hour circle passing through the luminary (counterclockwise) from 0 to 360 or from 0 to 24 hours.

The position of the star X is indicated by coordinates - right ascension α (angular distance along the celestial equator from the vernal equinox point ϓ to the direction to the star) and declination δ (angular distance from the celestial equator along the great circle passing through the poles of the world).

Right ascension is measured in hours and can only be a positive value, declination is in degrees and can take both positive and negative values.

The magnitude of the right ascension of the same luminary does not change due to the daily rotation of the sky and does not depend on the place of observation on the surface of the Earth.

Due to the Earth's rotation, 15° corresponds to 1 hour and 1° to 4 minutes, so a right ascension of 12 hours is 180° and 7 hours 40 minutes is 115°.

The equatorial coordinates of the stars do not change for centuries,

so the equatorial coordinate system is used

when creating star globes, maps and atlases.

On a star globe, not only stars are depicted,

but also a grid of equatorial coordinates.

• Alpha southern fish
• betta andromeda
• Alpha Taurus (Aldebaran)
• Alpha Libra

Horizontal coordinate system used for direct determination of the apparent positions of the luminaries using goniometric instruments

h - height- the angular distance of the luminary from the horizon (Р MOA, measured in degrees, minutes, seconds; from 0 o to 90 o)

A - azimuth is the angular distance of the luminary’s vertical from the south point (Ð SOА) in the direction of the luminary’s daily motion, i.e. clockwise; It is measured in degrees minutes and seconds from 0° to 360°).

climax - the phenomenon of crossing the heavenly meridian by the luminary

• According to the daily movement of the luminaries are divided into:
• 1 - non-ascending
• 2 - (ascending - setting ) ascending and setting
• 3 - non-approaching .

Practical work №2

Spica -a Virgo +1.04

• What is the celestial sphere?
• What lines and points of the celestial sphere do you know?
• What observations prove the daily rotation of the celestial sphere (does this serve as proof of the rotation of the Earth around its axis).
• Is it possible, using a horizontal coordinate system, to create maps of the starry sky?
• What is a climax?
• Based on the climax, give the concept of non-setting, not ascending, - ascending-setting luminaries.

House. Exercise

• par.4, learn the main points and lines of the celestial sphere, coordinate systems

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Slides captions:

Celestial sphere. An imaginary sphere of large radius, the center of which is the observer.

On the celestial sphere, we see objects as points of light. Only the Sun and Moon we see as disks.

Blank No. 1. We work with this blank, mark the main points, lines and circles on it.

As a result, we get such a celestial sphere with the parameters marked on it.

The main lines, circles and points of the celestial sphere (to know and be able to show). Vertical of the observer (plumb line). Zenith, nadir. True (mathematical) horizon. Axis of the world. Poles of the world. Celestial meridian. Celestial equator. Almukantarat. Spring equinox point.

Celestial coordinate systems are used to determine the position of the luminaries on the celestial sphere. Horizontal coordinate system - indicates the position of the star relative to the true horizon. Azimuth - part of the arc from the point of the south to the vertical of the star. Denoted by the letter A, measured in degrees (from 0 to 360), counted clockwise. The height of the luminary is the angle (part of the arc) between the plane of the true horizon and the straight line drawn from the center of the celestial sphere to the luminary. Denoted by the letter h, measured in degrees (from 0 to 90).

On the workpiece No. 2, we will build the azimuth and height of the luminary.

Celestial coordinate systems are used to determine the position of the luminaries on the celestial sphere. Equatorial coordinate system - indicates the position of the star relative to the celestial equator. Declination is the angular distance from the luminary to the celestial equator. It is counted in a circle drawn through the star and the poles of the world. It is considered positive for luminaries located north of the celestial equator, and negative for luminaries located south of the celestial equator.

Celestial coordinate systems are used to determine the position of the luminaries on the celestial sphere. Equatorial coordinate system - indicates the position of the star relative to the celestial equator. Right ascension is measured along the celestial equator from the vernal equinox. The right ascension is counted in the direction opposite to the rotation of the celestial sphere. In astronomy, right ascension is expressed not in degrees, but in hours.

Astronomy lesson
Topic: "Celestial coordinates" (technological map of the lesson)

Planned educational outcomes

Lesson summary

Choose a picture and answer a question. We check the correctness and completeness of the answer.
1. What is the name of this constellation? What is called a constellation and how many constellations are there in the celestial sphere?
constellation called a section of the celestial sphere, the boundaries of which are determined by a special decision of the International Astronomical Union (IAU). In total, there are 88 constellations in the celestial sphere.

2. What is the name of this constellation?
Constellation Aquarius.

3. What is the name of the constellation? And what is its origin?
Scales. One of the non-living zodiac constellations. The origin of the name of this constellation is also associated with the myth of the goddess Themis. Not only the Thunderer Zeus keeps the laws of Olympus, but also the mother of Prometheus, the goddess Themis. She convenes meetings of the gods on the eternal Olympus and monitors order and law. She holds scales in her hands - a sign of justice.
4. What is the celestial sphere?
An imaginary sphere of arbitrary radius centered at an arbitrary point, on the surface of which the positions of the luminaries are plotted as they are visible in the sky at some point in time from a given point.

5. What is the apparent phenomenon called? What is the axis of the world?
The apparent phenomenon of the rotation of the celestial sphere around the polar star reflects the actual rotation of the globe around its axis. The axis parallel to the axis of the visible rotation of the celestial sphere is called the axis of the world.

6 . What is the name of the brightest star in the constellation Bootes? .
The constellation Bootes, the brightest star of this constellation Arcturus. It can be found along the continuation of the tail of the Big Dipper.

7. What is called the ecliptic?
The annual path of the Sun passing through the 12 zodiac constellations.

8. How do planets differ from stars when viewed with the naked eye?
Both the planet and the star are characterized by luminescence, by which they can be seen from the Earth. However, a star is a self-luminous object. While the planet glows due to the light reflected from the stars. Therefore, the radiation of the planets is many times weaker than the stellar radiation. For stars, the twinkling caused by the fluctuation of the air is more characteristic. The planets, in turn, shine evenly, albeit more dimly.

9. What is apparent stellar magnitude?
Apparent magnitudemindicates the radiation flux near the observer, i.e., the observed brightness of a celestial source, which depends not only on the real power of the object, but also on the distance to it.

Main part:
How to accurately describe the position of the star in the sky? Where to direct your eye or telescope to see what interests the observer.
Mathematicians have long used a way to describe a point in space using a coordinate system. There are such coordinate systems in which the position of the object is characterized not by linear, but by angular ones. (Geographic coordinates - latitude and longitude - are the angles that determine the position of a point on the surface of the Earth.
To describe the mutual positions of the visible movements of the luminaries, it is convenient to place all the luminaries on the inner surface of an imaginary sphere in the center of the observer. Such a sphere is called the celestial.
The axis parallel to the axis of apparent rotation of the celestial sphere is called the axis of the world.
The axis of the world crosses the celestial sphere at two points - the poles of the world.

From the "Celestial Atlas" by A. Cellarius 1660 Tycho Brahe's armillary sphere

Celestial equator and celestial meridian.
celestial equator called a great circle perpendicular to the axis of the world.
heavenly meridian called the great circle of the celestial sphere, passing through the celestial pole P, the south celestial pole R.

Horizontal coordinate system: Main planehorizontal systemcoordinates ismathematical horizon NWSE, and the report is from Z zenith and from one of the points of the mathematical horizon. One coordinate iszenith distance z (Zenith distance to south zv = φ - δ; To north zн = 180 - φ - δ) orthe height of the sun above the horizon h . Height h luminaries M called the height of the vertical circle mM frommathematical horizonbefore luminaries, or center corner mOM between planemathematical horizonand direction to luminary M . Heights are counted from 0 to 90 k zenith and from 0 to -90 Nadir. The zenith distance of the luminary is called the arc of the vertical circle ZM from light to zenith . z + h = 90 (1). The position of the vertical circle itself is determined by the coordinate arc - azimuth A . Azimuth A called an arcmathematical horizon sm from the point south S to a vertical circle passing through the luminary. Azimuths counted in the direction of rotation celestial sphere , i.e. west of the south point, ranging from 0 to 360. The coordinate system is used to directly determine the apparent positions of the luminaries using goniometric tools.

First equatorial coordinate system: Countdown start -celestial equator Q. One coordinate isdeclination. declinationcalled an arc mm hour circle PMmP′ from the celestial equator to the luminary. They are counted from 0 to +90 to the north pole and from 0 to -90 to the south. p+=90. The position of the hour circle is determined hour angle t . hour angle luminaries M called the arc of heaven Equator Qm from the top Q celestial equator to hour circle PMmP′, passing through the light. Hourly angles are measured in the direction of the daily rotation of the celestial sphere, to the west of Q in the range from 0 to 360 or from 0 to 24 hours. The coordinate system is used in practical astronomy to determine the exact time and daily rotation of the sky. Determines the daily movement of the Sun, Moon and other luminaries.

Second equatorial coordinate system: One coordinate is declination , anotherright ascension α. direct ascent α luminaries M called the arc of the celestial equator ♈ m from the pointspring equinox♈ to the hour circle passing through the luminary. It is counted in the direction opposite to the daily rotation in the range from 0 to 360 or from 0 to 24 hours. The system is used for determining star coordinates and compiling catalogs. Determines the annual movement of the Sun and other luminaries.

The height of the celestial pole above the horizon, the height of the luminary in the meridian
The height of the celestial pole above the horizon is always equal to the astronomical latitude of the observer's place:
If the declination of the star is less than the geographic latitude, then it culminates south of the zenith at z = φ - δ or at a height h = 90 - φ + δ
If the declination of the star is equal to the geographic latitude, then it culminates at the zenith and z = 0, and h = + 90
If the declination of the star is greater than the geographic latitude, then it culminates north of the zenith at z = c - φ or at a height h = 90 + φ - c

Task 1.
The stars with what declination will culminate at the zenith at the latitude of Moscow (55° 45′ N 37° 37′ E)?

We recall the most necessary formulas for solving problems on the relationship of latitude, altitude and declination:
South of the zenith -hVC=90 ∘ −φ+δ , or elsehVC=90 ∘ +(δ−φ) &
hnk=δ−(90∘ −φ) , or elsehnk=δ+φ−90∘ .
north of the zenithhVC=90 ∘ −δ+φ , or elsehVC=90 ∘ −(δ−φ) .
hnk=δ−(90∘ −φ) , or elsehnk=δ+φ−90∘ .
At the zenith at the latitude of Moscow, the luminaries will be in the upper climax. Think, maybe at the bottom? Therefore, we apply the formula for the upper climax. What? South or north of the zenith? It is obvious that the formulas for the height of the upper culmination to the south or north of the zenith should not have a break at the transition point (h = 90°). From the formulas it can be seen that any can be used.
hYu=90 ∘ +(δ−φ)=hWith=90 ∘ −(δ−φ)=90∘ is the height of the zenith. It can be seen from the formulas thatδ = φ . Answer 55° 45′
Task 2.
At what height is the Pole of Peace at the latitude of Moscow (55° 45′ N 37° 37′ E)?

The pole of the world is remarkable in that it has a declinationδ = 90 ∘ .
A star located at the celestial pole will have a constant height h =φ .
Try to deduce this from the formulas of the upper and lower culmination. What formula should be chosen? Will any formula work and why?
Task 3.
What is the declination of a non-setting star that barely touches the horizon at the latitude of Moscow (55° 45′ N 37° 37′ E)? Ignore optical effects.

According to the condition, the star at the latitude of Moscow is not setting, but nevertheless sometimes touches the horizon. At what point can this happen? It can be seen that at the time of the lower climax, since at the moment of the upper climax, its height will be no less. Let's write down the height formula in the lower climax: h nk=δ+φ−900
What is the height on the horizon? That's right, zero. Hence declination and latitude are complementary up to 900 (δ+φ=900 ). Answer: 37° 37′

D.Z. § 4
Card 1. What is the declination of the zenith point at the geographical latitude of Minsk (ᵠ = 53 O54 / )?
Card 2. In what constellation is the Pole of the Ecliptic located today?At what geographical parallels does the star Capella (δ = + 45 ° 58 ") go beyond the horizon, is never visible, and passes in the nadir at the lower culmination?

3 Card Arctic Circle (φ=+66°33"). Capella Declination δ=+45°58".

slide 2

The branch of astronomy in which systems of astronomical coordinates are introduced and the positions and speeds of movement of celestial bodies in relation to these systems are determined is called astrometry. This is the oldest part of astronomy.

slide 3

− rectangular coordinates of the point Р

− spherical coordinates of the point Р

slide 4

Horizontal coordinate system

When constructing any celestial coordinate system on the celestial sphere, a large circle (the main circle of the coordinate system) and two diametrically opposite points on an axis perpendicular to the plane of this circle (the poles of the coordinate system) are selected.

slide 5

The true horizon is taken as the main circle of the horizontal coordinate system, the zenith (Z) and nadir (Z1) serve as poles, through which large semicircles are drawn, called height circles or verticals.

• vertical
• Zenith
• Nadir
• heavenly body
• True horizon

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