What condition must the declination satisfy. To help the teacher of astronomy (for physical and mathematical schools). Problem solution example
A- the azimuth of the luminary, is measured from the point of the South along the line of the mathematical horizon clockwise in the direction of west, north, east. It is measured from 0 o to 360 o or from 0 h to 24 h.
h- the height of the luminary, measured from the point of intersection of the circle of height with the line of the mathematical horizon, along the circle of height up to the zenith from 0 o to +90 o, and down to the nadir from 0 o to -90 o.
http://www.college.ru/astronomy/course/shell/images/Fwd_h.gifhttp://www.college.ru/astronomy/course/shell/images/Bwd_h.gif Equatorial coordinates
Geographic coordinates help determine the position of a point on Earth - latitude and longitude . Equatorial coordinates help determine the position of stars on the celestial sphere - declination and right ascension .For equatorial coordinates, the main planes are the plane of the celestial equator and the declination plane.
The right ascension is counted from the vernal equinox in the direction opposite to the daily rotation of the celestial sphere. Right ascension is usually measured in hours, minutes and seconds of time, but sometimes in degrees.
Declination is expressed in degrees, minutes and seconds. The celestial equator divides the celestial sphere into northern and southern hemispheres. The declinations of stars in the northern hemisphere can be from 0 to 90°, and in the southern hemisphere - from 0 to -90°.
Equatorial coordinates take precedence over horizontal coordinates:
1) Created star charts and catalogs. The coordinates are constant.
2) Compilation of geographical and topological maps of the earth's surface.
3) Implementation of orientation on land, sea space.
4) Checking the time.
Exercises.
Horizontal coordinates.
1. Determine the coordinates of the main stars of the constellations included in the autumn triangle.
2. Find the coordinates of Virgo, Lyra, Canis Major.
3. Determine the coordinates of your zodiac constellation, at what time is it most convenient to observe it?
equatorial coordinates.
1. Find on the star map and name the objects that have coordinates:
1) \u003d 15 h 12 m, \u003d -9 o; 2) \u003d 3 h 40 m, \u003d +48 o.
2. Determine the equatorial coordinates of the following stars from the star map:
1) Ursa Major; 2) China.
3. Express 9 h 15 m 11 s in degrees.
4. Find on the star map and name the objects that have coordinates
1) = 19 h 29 m, = +28 o; 2) = 4 h 31 m, = +16 o 30 / .
5. Determine the equatorial coordinates of the following stars from the star map:
1) Libra; 2) Orion.
6. Express 13 hours 20 meters in degrees.
7. What constellation is the Moon in if its coordinates are = 20 h 30 m, = -20 o.
8. Determine the constellation in which the galaxy is located on the star map M 31, if its coordinates are 0 h 40 m, = 41 o.
4. The culmination of the luminaries.
Theorem about the height of the celestial pole.
Key questions: 1) astronomical methods for determining geographic latitude; 2) using a moving chart of the starry sky, determine the condition of visibility of the stars at any given date and time of day; 3) solving problems using relationships that connect the geographical latitude of the place of observation with the height of the luminary at the climax.
The culmination of the luminaries. Difference between upper and lower climax. Working with the map determining the time of culminations. Theorem about the height of the celestial pole. Practical ways to determine the latitude of the area.
Using the drawing of the projection of the celestial sphere, write down the height formulas in the upper and lower culmination of the luminaries if:
a) the star culminates between the zenith and the south point;
b) the star culminates between the zenith and the celestial pole.
Using the celestial pole height theorem:
- the height of the pole of the world (Polar Star) above the horizon is equal to the geographical latitude of the place of observation
.
Corner 
- both vertical and 
. Knowing that 
is the declination of the star, then the height of the upper culmination will be determined by the expression:
For the bottom climax of a star M 1:
Give home the task to get a formula for determining the height of the upper and lower culmination of a star M 2 .
Assignment for independent work.
1. Describe the conditions for the visibility of stars at 54° north latitude.
|
Star |
visibility condition |
|
Sirius ( \u003d -16 about 43 /) |
|
|
Vega ( = +38 o 47 /) |
never setting star |
|
Canopus ( \u003d -52 about 42 /) |
rising star |
|
Deneb ( = +45 o 17 /) |
never setting star |
|
Altair ( = +8 o 52 /) |
Rising and setting star |
|
Centauri ( \u003d -60 about 50 /) |
rising star |
2. Install a mobile star map for the day and hour of classes for the city of Bobruisk ( = 53 o).
Answer the following questions:
a) which constellations are above the horizon at the time of observation, which constellations are below the horizon.
b) which constellations are rising at the moment, setting at the moment.
3. Determine the geographical latitude of the observation site if:
a) the star Vega passes through the zenith point.
b) the star Sirius at its upper culmination at an altitude of 64° 13/ south of the zenith point.
c) the height of the star Deneb at its upper climax is 83 o 47 / north of the zenith.
d) the star Altair passes at the lower culmination through the zenith point.
On one's own:
Find the intervals of declination of stars that are at a given latitude (Bobruisk):
a) never rise b) never enter; c) can ascend and set.
Tasks for independent work.
1. What is the declination of the zenith point at the geographical latitude of Minsk ( = 53 o 54 /)? Accompany your answer with a picture.
2. In what two cases does the height of the star above the horizon not change during the day? [Either the observer is at one of the poles of the Earth, or the luminary is at one of the poles of the world]
3. Using the drawing, prove that in the case of the upper culmination of the luminary north of the zenith, it will have a height h\u003d 90 o + - .
4. The azimuth of the luminary is 315 o, the height is 30 o. In what part of the sky is this luminary visible? In the southeast
5. In Kyiv, at an altitude of 59 o, the upper culmination of the star Arcturus was observed ( = 19 o 27 /). What is the geographical latitude of Kyiv?
6. What is the declination of the stars culminating in a place with a geographical latitude at the north point?
7. The polar star is 49/46 from the north celestial pole // . What is its declination?
8. Is it possible to see the star Sirius ( \u003d -16 about 39 /) at meteorological stations located on about. Dikson ( = 73 o 30 /) and in Verkhoyansk ( = 67 o 33 /)? [On about. Dixon is not present, not in Verkhoyansk]
9. A star that describes an arc of 180 o above the horizon from sunrise to sunset, during the upper climax, is 60 o from the zenith. At what angle in this place Is the celestial equator tilted towards the horizon?
10. Express the right ascension of the star Altair in arc meters.
11. The star is 20 o from the north celestial pole. Is it always above the horizon of Brest ( = 52 o 06 /)? [Is always]
12. Find the geographical latitude of the place where the star at the top culmination passes through the zenith, and at the bottom it touches the horizon at the north point. What is the declination of this star? = 45 o; [ \u003d 45 about]
13. Azimuth of the star 45 o, height 45 o. In which side of the sky should you look for this luminary?
14. When determining the geographical latitude of the place, the desired value was taken equal to the height of the Polar Star (89 o 10 / 14 / /), measured at the time of the lower climax. Is this definition correct? If not, what is the error? What correction (in magnitude and sign) must be made to the measurement result in order to obtain the correct latitude value?
15. What condition must the declination of a luminary satisfy in order for this luminary not to set at a point with latitude ; so that it is not ascending?
16. The right ascension of the star Aldebaran (-Taurus) is equal to 68 about 15 /. Express it in units of time.
17. Does the star Fomalhaut (-Golden Fish) rise in Murmansk ( = 68 o 59 /), the declination of which is -29 o 53 / ? [Does not rise]
18. Prove from the drawing, from the lower culmination of the star, that h\u003d - (90 o - ).
Homework: § 3. q.v.
5. Measurement of time.
Definition of geographic longitude.
Key issues: 1) differences between the concepts of sidereal, solar, local, zone, seasonal and universal time; 2) the principles of determining time according to astronomical observations; 3) astronomical methods for determining the geographical longitude of the area.
Students should be able to: 1) solve problems for calculating the time and dates of the chronology and transferring time from one counting system to another; 2) determine the geographical coordinates of the place and time of observation.
At the beginning of the lesson, independent work 20 minutes.
1. Using a moving map, determine 2 - 3 constellations visible at a latitude of 53 o in the Northern Hemisphere.
|
patch of sky |
Option 1 15. 09. 21 h |
Option 2 25. 09. 23 h |
|
Northern part |
B. Bear, Charioteer. Giraffe |
B. Bear, Hounds Dogs |
|
southern part |
Capricorn, Dolphin, Eagle |
Aquarius, Pegasus, Y. Pisces |
|
Western part |
Bootes, S. Crown, Snake |
Ophiuchus, Hercules |
|
East End |
Aries, Pisces |
Taurus, Charioteer |
|
Constellation at its zenith |
Swan |
Lizard |
2. Determine the azimuth and height of the star at the time of the lesson:
1 option. B. Ursa, Leo.
Option 2. Orion, Eagle.
3. Using a star map, find the stars by their coordinates.
Main material.
To form concepts about days and other units of measurement of time. The occurrence of any of them (day, week, month, year) is associated with astronomy and is based on the duration of cosmic phenomena (the rotation of the Earth around its axis, the revolution of the Moon around the Earth and the revolution of the Earth around the Sun).
Introduce the concept of sidereal time.
Pay attention to the following; moments:
- the length of the day and year depends on the frame of reference in which the movement of the Earth is considered (whether it is associated with fixed stars, the Sun, etc.). The choice of reference system is reflected in the name of the unit of time.
- the duration of time counting units is associated with the conditions of visibility (culminations) of celestial bodies.
- the introduction of the atomic time standard in science was due to the uneven rotation of the Earth, discovered with increasing clock accuracy.
The introduction of standard time is due to the need to coordinate economic activities in the territory defined by the boundaries of time zones.
Explain the reasons for the change in the length of the solar day throughout the year. To do this, it is necessary to compare the moments of two successive climaxes of the Sun and any star. Mentally choose a star that for the first time culminates simultaneously with the Sun. The next time the culmination of the star and the Sun will not happen at the same time. The sun will culminate at about 4 min later, because against the background of stars it will move about 1 // due to the movement of the Earth around the Sun. However, this movement is not uniform due to the uneven movement of the Earth around the Sun (students will learn about this after studying Kepler's laws). There are other reasons why the time interval between two successive climaxes of the Sun is not constant. There is a need to use the average value of solar time.
Give more precise data: the average solar day is 3 minutes 56 seconds shorter than the sidereal day, and 24 hours 00 minutes 00 from sidereal time is equal to 23 hours 56 minutes 4 from the average solar time.
Universal time is defined as local mean solar time at the zero (Greenwich) meridian.
The entire surface of the Earth is conditionally divided into 24 sections (time zones), limited by meridians. The zero time zone is located symmetrically with respect to the zero meridian. Time zones are numbered from 0 to 23 from west to east. The real boundaries of time zones coincide with the administrative boundaries of districts, regions or states. The central meridians of time zones are 15 o (1 h) apart, so when moving from one time zone to another, time changes by an integer number of hours, and the number of minutes and seconds does not change. A new calendar day (as well as a new calendar year) begins on the date change line, which runs mainly along the 180 o meridian. e. near the northeastern border Russian Federation. To the west of the date line, the day of the month is always one more than to the east of it. When crossing this line from west to east, the calendar number decreases by one, and when crossing from east to west, the calendar number increases by one. This eliminates the error in the calculation of time when moving people traveling from the Eastern to the Western hemisphere of the Earth and back.
Calendar. Limit yourself to consideration brief history calendar as part of culture. It is necessary to single out three main types of calendars (lunar, solar and lunisolar), tell what they are based on, and dwell in more detail on the Julian solar calendar of the old style and the Gregorian solar calendar of the new style. After recommending relevant literature, invite the students to prepare short reports about different calendars for the next lesson or organize a special conference on this topic.
After presenting the material on the measurement of time, it is necessary to move on to generalizations related to the definition of geographic longitude, and thereby summarize the questions about the definition geographical coordinates through astronomical observations.
Modern society cannot do without knowing the exact time and coordinates of points on the earth's surface, without accurate geographical and topographic maps necessary for navigation, aviation and many other practical issues of life.
Due to the rotation of the Earth, the difference between the moments of noon or the culmination of stars with known equatorial coordinates at two points on the earth surface is equal to the difference between the values of the geographical longitude of these points, which makes it possible to determine the longitude of a particular point from astronomical observations of the Sun and other luminaries and, conversely, local time at any point with a known longitude.
To calculate the geographic longitude of the area, it is necessary to determine the moment of climax of any luminary with known equatorial coordinates. Then, using special tables (or a calculator), the observation time is converted from mean solar to stellar. Having learned from the reference book the time of the culmination of this luminary on the Greenwich meridian, we can determine the longitude of the area. The only difficulty here is the exact conversion of units of time from one system to another.
The moments of the climax of the luminaries are determined with the help of a transit instrument - a telescope, strengthened in a special way. The spotting scope of such a telescope can only be rotated around a horizontal axis, and the axis is fixed in the west-east direction. Thus, the instrument turns from the south point through the zenith and the celestial pole to the north point, i.e. it traces the celestial meridian. The vertical thread in the field of view of the telescope tube serves as a mark of the meridian. At the time of the passage of a star through the celestial meridian (in the upper climax), sidereal time is equal to right ascension. The first passage instrument was made by the Dane O. Roemer in 1690. For more than three hundred years, the principle of the instrument has not changed.
Note the fact that the need to accurately determine the moments and intervals of time stimulated the development of astronomy and physics. Up to the middle of the 20th century. astronomical methods of measuring, keeping time and time standards underlay the activities of the World Time Service. The accuracy of the clock was controlled and corrected by astronomical observations. At present, the development of physics has led to the creation of more accurate methods for determining and standards of time. Modern atomic clocks give an error of 1 s in 10 million years. With the help of these watches and other instruments, many characteristics of the visible and true movement of cosmic bodies were refined, new cosmic phenomena were discovered, including changes in the speed of the Earth's rotation around its axis by approximately 0.01 s during the year.
- average time.
- standard time.
- summer time.
Messages for students:
1. Arabic lunar calendar.
2. Turkish lunar calendar.
3. Persian solar calendar.
4. Coptic solar calendar.
5. Projects of ideal perpetual calendars.
6. Counting and keeping time.
6. Heliocentric system of Copernicus.
Key questions: 1) the essence of the heliocentric system of the world and the historical prerequisites for its creation; 2) the causes and nature of the apparent motion of the planets.
Frontal conversation.
1. A true solar day is the time interval between two successive climaxes of the same name of the center of the solar disk.
2. A sidereal day is the time interval between two successive culminations of the same name of the vernal equinox, equal to the period of the Earth's rotation.
3. The mean solar day is the time interval between two culminations of the same name of the mean equatorial Sun.
4. For observers located on the same meridian, the culmination of the Sun (as well as any other luminary) occurs simultaneously.
5. A solar day differs from a stellar day by 3 m 56 s.
6. The difference in the values of local time at two points on the earth's surface at the same physical moment is equal to the difference in the values of their geographical longitudes.
7. When crossing the border of two neighboring belts from west to east, the clock must be moved one hour ahead, and from east to west - one hour ago.
Consider an example solution tasks.
The ship, which left San Francisco on the morning of Wednesday, October 12 and headed west, arrived in Vladivostok exactly 16 days later. What date of the month and on what day of the week did he arrive? What should be taken into account when solving this problem? Who and under what circumstances faced this for the first time in history?
When solving the problem, it must be taken into account that on the way from San Francisco to Vladivostok, the ship will cross a conditional line called the international date line. It passes along the earth's meridian with a geographic longitude of 180 o, or close to it.
When crossing the date change line in the direction from east to west (as in our case), one calendar date is discarded from the account.
For the first time, Magellan and his companions encountered this during their trip around the world.
The branch of astronomy whose main task is to study the geometric, kinematic and dynamic properties of celestial bodies is called ...
A) astrometry
B) Astrophysics
C) Fundamentals of celestial mechanics
D) Cosmology
D) Cosmogony
The science at the intersection of astronomy and physics, which studies the physical processes in astronomical objects, such as stars, galaxies, is called ...
A) astrometry
B) Astrophysics
C) Fundamentals of celestial mechanics
D) Cosmology
D) Cosmogony
A) north point
D) east point
D) there is no correct answer
A) noon line.
B) true horizon
B) right ascension
D) declination
D) there is no correct answer
The angle between the planes of great circles, one of which passes through the poles of the world and the given luminary, and the other through the poles of the world and the vernal equinox, is called ...
A) right ascension.
B) stellar magnitude.
B) declination.
D) climb
D) there is no correct answer
What is the declination of the Sun at the equinoxes?
The third planet from the Sun is...
A) Saturn.
B) Venus.
D) Jupiter
What orbits do the planets take around the sun?
A) in circles
B) ellipses. close to circles.
B) along the branches of parabolas
D) by hyperbole
D) there is no correct answer
The closest point in a planet's orbit to the Sun is called...
A) perihelion.
B) aphelion
B) eccentricity
A telescope is needed to...
A) collect light and create an image of the source
B) collect light from a celestial object and increase the angle of view. under which the object is visible.
C) get an enlarged image of a celestial body
D) to receive sunlight
D) there is no correct answer
All giant planets are...
A) fast rotation.
B) slow rotation
B) super fast rotation
D) reverse rotation
D) there is no correct answer
Asteroids revolve between orbits...
A) Venus and Earth
B) Mars. and Jupiter.
C) Neptune and Pluto
D) Only Mars
D) Only Jupiter
What substances dominate in the atmospheres of stars?
A) helium and oxygen
B) nitrogen and helium
B) hydrogen. and helium.
D) oxygen and nitrogen
D) only hydrogen
What class of stars does the Sun belong to?
A) supergiant
B) a yellow dwarf.
B) white dwarf
D) red giant
D) dwarf
How many constellations is the sky divided into?
D) there is no correct answer
Who discovered the laws of planetary motion around the sun?
A) Ptolemy
B) Copernicus
B) Kepler.
D) Newton
What layer of the Sun is the main source of visible radiation?
A) chromosphere
B) .Photosphere.
B) solar corona
D) Atmosphere
D) Troposphere
Express 9 h 15 m 11 s in degrees.
B) 1380.47.45
D) 90̊ 00ʹ 01ʹʹ
D) there is no correct answer
Parallax Altair 0.20. What is the distance to this star in light years?
A) 20 St. years
B) 0.652 St. of the year
C) 16.3 St. years
D) 1400 St. years
D) there is no correct answer
How many times is a star of magnitude 3.4 fainter than Sirius, which has an apparent magnitude of 1.6?
A) 1.8 times
B) 0.2 times
C) 100 times.
D) 10 times
D) there is no correct answer
The branch of astronomy that studies the properties and evolution of the universe as a whole is called ...
A) astrometry
B) Astrophysics
C) Fundamentals of celestial mechanics
D) Cosmology
D) Cosmogony
a science that studies the origin and development of cosmic bodies and their systems: stars and star clusters, galaxies, nebulae, the solar system including the Sun, planets with satellites, asteroids, comets, meteorites is called ...
A) astrometry
B) Astrophysics
C) Fundamentals of celestial mechanics
D) Cosmology
D) Cosmogony
The branch of astronomy that studies the stars is called...
A) astrometry
B) Astrophysics
B) stellar astronomy
D) Cosmology
D) Cosmogony
What is the name of the 12 zodiac constellations through which the annual path of the Sun passes:
a) the milky way
b) the ecliptic;
c) right ascension;
d) the universe.
D) signs of the zodiac
All planets have moons except...
A) Saturn B) Venus C) Earth D) Mars
D) Jupiter
The diameter of the Sun is greater than the diameter of the Earth
A) 109 times B) 218 times C) 312 times D) 100 times E) 1000 times
Annual parallax is used for:
A) determining the distance to the nearest stars;
B) determining the distance to the planets;
C) distances passing by the Earth in a year;
D) proof of the finiteness of the speed of light;
D) there is no correct answer
Watching the starry sky at night for an hour, you notice that the stars move across the sky. This happens because:
A) the earth moves around the sun
b) the sun moves along the ecliptic
C) the earth rotates on its axis
D) stars move around the earth
D) there is no correct answer
The cube of the semi-major axis of the body's orbit, divided by the square of the period of its revolutions and the sum of the masses of the bodies, is a constant value. What is Kepler's law?
a) Kepler's first law;
b) Kepler's second law;
c) Kepler's third law;
d) Kepler's fourth law.
D) there is no correct answer
The distance from the earth to the sun is called:
a) a light year
b) parsec
c) astronomical unit
d) annual parallax
d) there is no correct answer
What are the main reasons for the change of seasons?
A) a change in the distance to the Sun due to the movement of the Earth in an elliptical orbit;
B) the inclination of the earth's axis to the plane of the earth's orbit;
C) the rotation of the Earth around its axis;
D) temperature changes
D) there is no correct answer
The ratio of the cubes of the semi-major axes of the planets is 64. What is the ratio of their periods of revolution around the Sun?
A) 8 B) 4 C) 16 D) 2 E) 10
When is the Earth closest to the Sun due to its annual orbit?
A) in summer B) at perihelion C) in winter D) at aphelion e) in spring
The terrestrial planets are:
A) Venus B) Jupiter; B) Saturn D) Neptune. D) Uranus
The third refined I. Kepler's Law is used mainly to determine the stars:
A) distance B) period C) mass D) radius E) all of the above
The period of time between two new moons is called:
A) synodic month
B) sidereal month
B) a full lunar month
D) calendar month
D) there is no correct answer
It is known that the orbit of any planet is an ellipse, in one of the focuses of which is the Sun. The point in the orbit closest to the Sun is called:
A) apogee B) perigee C) apogee D) perihelion E) no correct answer
The reference system associated with the Sun, proposed by Nicolaus Copernicus, is called:
a) geocentric;
b) heliocentric;
c) centric;
d) Copernic.
D) there is no correct answer
The highest point in the sky is called...
A) north point B) zenith
B) nadir D) East point E) South point
Sun age:
A) 2 billion years
B) 5 billion. years
C) 500 million years
D) 100 million years
D) 10 billion years
Plane intersection line sky horizon and the meridian is called...
A) noon line.
B) true horizon.
B) right ascension.
D) climb
D) there is no correct answer
Find the location of the giant planets in order of distance from the Sun:
A) Uranus, Saturn, Jupiter, Neptune
B) Neptune, Saturn, Jupiter, Uranus
B) Jupiter, Saturn, Uranus, Neptune
D) Saturn, Uranus, Neptune, Jupiter
D) there is no correct answer
What is the value of the astronomical unit?
A) 160 million km. B) 149.6 million km.
C) 135 million km. D) 143.6 million km. e) 150 million km.
A) circular B) hyperbolic
C) elliptical D) parabolic E) spherical
What can explain the lack of a magnetic field on the Moon?
A) weak attraction
B) slow axial rotation
B) large temperature fluctuations
D) poor electrical conductivity of the mantle
The ratio of the cubes of the semiaxes of the orbits of the two planets is 16. Therefore, the period of revolution of one planet is greater than the period of revolution of the other:
A) 8 times B) 2 times C) 4 times D) 16 times E) the period will not change
The following are the bodies that make up the solar system. Choose an exception.
A) Sun B) major planets and their satellites C) asteroids D) comets E) meteors
Small bodies in the solar system include:
A) stars B) large planets and their satellites C) asteroids D) planets E) the Sun
How long does it take light from the Sun to reach the Earth?
A) comes instantly B) Approximately 8 min
C) 1 light year D) about a day E) 12 hours
The planets are located relative to the Sun:
a) Venus, Earth, Mars, Mercury, Neptune, Saturn, Uranus, Jupiter.
b) Mercury, Venus, Earth, Mars, Neptune, Saturn, Jupiter, Uranus.
c) Mercury. Venus,. Earth,. Mars, Jupiter, Saturn, Uranus, Neptune,
D) Earth, Mars, Venus, Mercury, Jupiter, Saturn, Uranus, Neptune
D) Neptune, Uranus, Saturn, Jupiter, Mercury, Venus, Mars, Earth
Determine the relative position of the planes of the celestial equator and the Earth's equator?
BUT). Tangent
AT). Perpendicular
FROM). Parallel
D). at an angle
E). Forms an angle of 23"27"
Indicate the points of intersection of the circle of the mathematical horizon with the circle of the celestial equator?
BUT). North South
AT). Zenith nadir
FROM). East West
D). Celestial pole
E). equinoxes
Determine the relative position of the axis of the world and the axis of the Earth?
BUT). Angled 30°
AT). 90° angle
FROM). Parallel
D). Floor angle 23°27"
E). Crosses
What is the position of the Sun in the Galaxy?
BUT). At the center of the galaxy
AT). Located in the core of the galaxy
FROM). The Sun is closer to the main plane, at a distance of 10 kpc from the center of the Galaxy.
D). The Sun is closer to the edge of the Galaxy, at a distance of 30 kpc from the center of the Galaxy
E) The Sun is on the main plane of the Galaxy, at a distance of 15 kpc from the center of the Galaxy.
In what direction does the Sun move in our Galaxy at a speed of 20 km/sec?
BUT). towards the constellation Draco
B) in the direction of the constellation Leo
FROM). towards the constellation Hercules
D). towards the constellation Orion
E). towards the constellation Aquila
What condition must the declination of a star satisfy in order for it to be non-ascending under geographic latitude (φ).
BUT). δ< (90°-φ)
AT). | δ | ≥ (90-φ)
FROM). δ ≥-(90- φ)
D). δ< -(90- φ)
E). no correct answer
What is called a stellar year?
E). Difficult to answer
Specify the correct list of giant planets
BUT). Mars, Earth, Jupiter, Saturn
AT). Mars, Mercury, Neptune, Pluto
C). Venus, Uranus, Saturn, Neptune
D). Jupiter, Saturn, Uranus, Neptune
e). Uranus, Saturn, Neptune, Pluto
In what direction does the daily rotation of the celestial sphere occur?
A). If you stand facing south, then from east to west along the “hand of the clock”
B). If you stand facing south, then from west to east along the "hand of the clock"
C). If you face south, then from east to west against the "hand of the clock"
D). If you face south, then from west to east against the "hand of the clock"
e). I find it difficult to answer.
Which of the following planets does not have a satellite?
AT). Neptune
C). Venus
D). Jupiter
Which of the following planets has two moons?
BUT). Earth, Jupiter
AT). Mars, Neptune
C). Venus, Uranus
D). Jupiter, Saturn
e). Uranus, Saturn
When was the Gregorian calendar introduced?
On what day and for what point on the celestial sphere are both right ascension and declination equal to zero?
If a certain star culminated at 8pm today, when will it culminate in 15 days?
BUT). 8:15 p.m.
AT). 7:54 p.m.
FROM). 7 pm
D). 7h. 40m. evenings
E). 9 pm
What explains the existence of different seasons on Earth and the formation of different thermal zones?
BUT). The rotation of the earth
AT). Earth's annual motion
FROM). The tilt of the Earth's axis to the plane of its orbit and the movement of the Earth around the Sun
D). The movement of the sun along the ecliptic
E). There is no correct answer
What is Universal Time?
A). Time equal to the right ascension of the luminary, located in the upper climax.
E. Difficult to answer
In what constellation is the bright star Arcturus located?
FROM). South Cross
D). Bootes
E). southern fish
In what constellation is the bright star Regulus located?
FROM). South Cross
E). southern fish
What is the magnification of the telescope?
Chcm differs from an astrograph from a conventional telescope
A) the increase is small
B) high magnification
C) no eyepiece
D) no lens
E) gives a photograph of a celestial object
What is a telescope lens for?
A) To get a magnification of the image of celestial bodies
B) Collect light emitted by celestial bodies
C) To increase the angle of view
D) Collect the light emitted by celestial bodies and obtain an increase in the image of celestial bodies
E) No correct answer
A) at the equator
B) At the middle latitude of the Earth
C) at the South Pole
D) in the southeast
E) in the northwest
A) at the equator
B) At the middle latitude of the Earth
C) at the South Pole
D) in the southeast
E) in the northwest
At what mutual arrangement of the Sun, Earth and Moon the phases are explained
new moon?
A) When the Sun is between the Moon and the Earth
B) When the Earth is between the Sun and the Moon
C) When the Magnifier is between the Sun and the Earth
D) When the Moon is in opposition to the Sun
E) When the Moon is in opposition to the Earth
In how many days will the last quarter phase of the moon occur? (Counting from
new moon)
A) after 7.5 days
B) after 29.5 days
C) after 15 days
D) after 22.5 days
E) After 27.5 days
What is the period of rotation of the moon about its axis?
A) 29.5 days
B) 30 days
C) 27.32 days
D) 22.5 days
E) 25.5 days
What phase must the moon be in for a lunar eclipse to occur?
A) In the phase of the full moon
C) In the first quarter phase
C) in the new moon phase
])) In the phase of the last quarter
E) In the phase before the new moon
How long does it take for a beam of light to travel from the Sun to the Earth?
A) 3 min 20 sec
B) 57 minutes
C) 10.5 minutes
D) 8 min 18 sec
E) 15 minutes
In what constellation is the bright star Vega located?
FROM). South Cross
E). southern fish
Do sunspots form?
A) In the crown
B) In the chromosphere
C) In the photosphere
D) In the convective zone
E) In the radiation zone
Solar prominences appear?
A) in the crown
B) in the chromosphere
C) In the photosphere
D) In the convective zone
E) In the radiation zone
The division of stars into supergiants and dwarfs is associated with a large difference between them.
a) Dimensions
B) temperature
C) luminosity
EJ chemical composition
Are stars like the Sun related to?
A) supergiants
B) giants
C) yellow dwarfs
D) subgiants
E) red dwarfs
What is the order of the letter designation of spectral classes in order of decreasing temperature from hot to coldest?
A) V.O.A.F.K.G.M.
B) O. A. V. F. K. M. G.
C) O.V.F.A.M.K. G.
D) O.V.A.F. G.K..M.+
E) A.V.O.S.K.M.G.
Which of the following spectral designations for the Sun is correct?
The sequence of supergiants in the G-R diagram is characterized by
A) They are main sequence stars.
B) significantly surpasses the Sun in luminosity
C) they are white stars
The sequence of white dwarfs in the G-R diagram is characterized by
A) Relate to main sequence stars
B) significantly surpasses the Sun in luminosity
C) they are very dense stars
D) Are characterized by the highest luminosities
E) characterized by the largest dimensions
How many stars are in our galaxy?
A) More than 100 million
B) As many as there are in the largest globular clusters
C) more than 100 billion
D) more than 1 billion
E) about 3 billion
Who is the creator of the heliocentric system of the world?
A) N. Copernicus
B) G. Galileo
C) Ptolemy
D) D. Bruno
E) I.Kepler
A) At the North Pole (for residents of the northern hemisphere)
B) At the middle latitude of the Earth
C) at the South Pole
D) in the southeast
E) in the northwest
Is it located near the center of the sun?
A) nuclear reaction zone
B) chromosphere
C) photosphere
D) convective zone
E) radiant energy zone
In what constellation is the bright star Fomalhaut located?
FROM). South Cross
E). southern fish
In what constellation is the bright star Spica located?
BUT). Bootes
AT). Auriga
E) Aldebaran
What is the name of the brightest star in the constellation Bootes?
A) Aldebaran
E) Betelgeuse
What is the name of the brightest star in the constellation Auriga?
C) chapel
E) Caster
Having just risen, the star rises at right angles to the horizon. Where on earth can this be seen?
A) At the North Pole
B) Beyond the Arctic Circle
C) at the equator
D) At any latitude of the northern hemisphere of the Earth, except for the equator and the pole
In what constellation is the bright star Antares located?
A). Perseus
FROM). Scorpion
E). southern fish
Having just culminated, the star is moving downward. In which side of the sky is it?
A) in the east
B) in the south
C) in the west
D) In the northern
E) On the northwestern
Having just culminated, the star moves upward. In which side of the sky is it?
A) in the east
B) in the west
C) in the north
D) In the south
E) On the northeast
All stars visible to the observer move parallel to the horizon from left to right. Where on Earth will this happen?
A) At the equator
B) At any latitude of the northern hemisphere of the Earth, except for the equator and the pole.
C) beyond the Arctic Circle
D) At the North Pole
E) At latitude 23° 27!
We live in some point of the second time zone N1=2n . We now have standard time T1n = 14h23m15S. What is the standard time in Novosibirsk at this moment N2 =6 n
In Mockbe Ni = 2n it's now 10am Standard Time. What time is it in Vladivostok N2=9n also on maternity leave?
For Aizat
Determine the local time at the point, the geographical longitude is 7h46m, if the clock exactly following Moscow standard time shows 18h36m (for Moscow n = 2)
At 18:32 local time, the ship's navigator received the Moscow standard time signals transmitted at 11:00 (determine the ship's longitude).
In Kharkov it is noon, and in Kazan at the same time the clock shows 12h46. What is the longitude of Kazan? (if the longitude of Kharkov is 2.25).
On the shortest day, (for an inhabitant of the northern hemisphere) the Sun rises at what point on the horizon?
A) due east
B) in the southeast
C) Due south
D) In the northeast
C) in the middle of the horizon
On the longest day, (for an inhabitant of the northern hemisphere) the Sun rises at what point on the horizon?
A) in the southeast
B) due east
C) due south
D) In the northeast
E) in the east
Where on Earth is the pole star visible above the observer's head?
A) at the equator
B) At the middle latitude of the Earth
C) On the northern pole (for a resident of the northern hemisphere)
D) South Pole
E) At latitude 550.
Where on Earth is the polar star visible at the foot of the observer?
A) On the northern pole (for a resident of the northern hemisphere)
B) at the middle latitude of the Earth
C) at the equator
D) South Pole
E) At latitude 450
Where on Earth is the polar star visible at an angle to the horizon?
A) at the equator
B) at the middle latitude of the Earth
C) On the northern pole (for a resident of the northern hemisphere)
D) South Pole
E) At latitude 900
A few days after the new moon, a crescent-shaped bright part of the moon is observed with a bulge to the right. On which side of the celestial sphere is such a phase of the moon visible?
A) Before sunrise the Sun is in the east
B) On the south side of the sky, above the horizon after sunset
C) After sunset, on the western side of the sky, closer to the horizon
D) After sunset, on north side sky a little above the horizon
E) After sunset, in the west above the horizon
What phase must the Moon be in for a solar eclipse to occur?
A) In the phase of the full moon
C) In the first quarter phase
C) in the new moon phase
])) In the phase of the last quarter
E) In the phase before the new moon
Why does the Moon always face the Earth with the same side?
A) the moon revolves around the earth
B) The period of revolution of the Moon around the Earth is 27.32 days
C) The period of revolution of the Moon around its axis and around the Earth is 27.32 days
D) The period of revolution of the Moon around its axis is 29.5 days.
E) The moon rotates on its axis.
How many movements of the Loupe do you know?
When does an annular eclipse of the Sun occur?
A) When the Moon is closer to the Earth
B) When the Moon is at a great distance from the Earth
C) When the Moon is at some distance from the Sun-Earth line
D) When the Moon is at a great distance from the Sun, and the Earth is closer to the Sun.
E) When the Moon is between the Earth and the Sun
Determine the correct order of the planets according to the Ptolemaic system of the world?
A) Mars. Mercury. Moon. Jupiter. Saturn, Venus, Sun
B) Mercury. Mars. Moon. Jupiter. Saturn. Venus. Sun
C) the moon. Mars. Jupiter. Saturn. Venus. Sun, Mercury
D) the moon. Mercury. Venus. Sun. Mars. Jupiter. Saturn +
E) Jupiter, Saturn, Venus. Sun. Moon. Mars. Mercury
What law determines the mass of planets with satellites?
A) According to the law of universal gravitation
B) According to Kepler's first law
C) By the perturbation of this planet by others
D) By Kepler's third law augmented by Newton
E) None of the answers A-D are correct
Which moon of Jupiter is volcanic?
A) Ganymede
C) Callisto
E) Among the answers A-D there is no correct answer.
Which planets in the solar system rotate around their axis in reverse
direction, i.e. from east to west?
A) Jupiter and Saturn
B) Mars and Mercury
C) Venus and Uranus
D) Neptune and Pluto
E) Saturn and Neptune
Which of the 9 major planets in the solar system revolves around the sun "lying on its side"
A) Jupiter
B) Mercury
C) Neptune
E) Pluto
Which of the major satellites of the solar system is the only one surrounded by a dense atmosphere?
B) Jupiter's moon Ganymede
C) Iapetus moon of Saturn
D) Titan is a satellite of Saturn
E) Phobos moon of Mars
What is known in astronomy in 1543?
A) By decision of the Catholic Church, burn Giordano Bruno at the stake
c) Galileo invented the telescope
C) Discovered the planet Neptune (Galileo)
D) A book by N. Copernicus was published, which outlines the heliocentric system of the world
What is known in astronomy in 1846?
A) A book by N. Copernicus was published, which outlines the heliocentric system of the world
C) By decision of the Catholic Church, burn Giordano Bruno at the stake
C) Galileo invented the telescope
D) Discovered the planet Neptune (Galileo)
E) I. Newton discovered the law of universal gravitation
What point is called the "middle sun"
A) a fictitious point moving uniformly along the celestial equator
B) a fictitious point moving unevenly along the celestial equator
C) a fictitious point moving uniformly along the ecliptic
D) the sun moving uniformly along the ecliptic
E) the sun moving unevenly along the ecliptic
Which expression defines the aperture ratio of a telescope?
What is a tropical year?
A). Time equal to the right ascension of the luminary, located in the upper climax.
B). The time during which the Sun completes a circle on the celestial sphere
C). The time between two successive passages of the center of the Sun through the vernal equinox
D). Mean time of the Greenwich meridian, counted from midnight.
E). Difficult to answer
What is Civil Time?
A). Time equal to the right ascension of the luminary, located in the upper climax.
B). Time measured by the hour angle of the center of the Sun.
C). Time equal to the hourly angle of the "mean sun"
D). Mean time of the Greenwich meridian, counted from midnight.
E. Difficult to answer
How many times greater is the radius of the sun than the radius of the earth?
What days does the equation of time equal zero?
When was Universal Time introduced?
The ratio of the semi-major axes of the planets is 64, what is the ratio of their rotation periods of the Sun?
The horizontal parallax of the moon is 57' if the equatorial radius of the earth is 6378 km, what is the distance from the moon to the earth?
In what year was the planet Neptune discovered?
What is the magnitude scale called?
A) logarithmic scale
B) algorithmic scale
C) Density
D) equator
How many times the volume of the Sun is larger than the volume of the Earth?
What is the mass of the earth?
A) Мᶿ=5.98*1024 kg
C) Мᶿ=1.76*1016 kg
С) Мᶿ=7.76*1023 kg
D) Мᶿ=3.56*1015 kg
E) Мᶿ=90.7*1012 kg
What is the average temperature of the Sun?
What constellation is the winter solstice in?
B) Sagittarius and Capricorn
C) Capricorn
D) Sagittarius
E) Aquarius
In what year was the planet Uranus discovered?
How many meteorites are there on the surface of the Earth?
A) 234 large meteorite
B) 5609 large meteorite
C) 115 large meteorite
D) 78 large meteorite
E) 183 large meteorite
What point is sidereal time measured from?
A) vernal equinoxes
B) the points of the autumnal equinox
C) the points of the summer solstice
D) winter solstice points
E) points of the summer solstice of the pole of the world
Specify the day of the summer solstice
Specify the day of the winter solstice
Specify the day of the vernal equinox
Specify the day of the autumnal equinox
What is the rotation of the earth around its axis in 24 hours called?
A) climax
B) eclipse
C) Daily rotation of the Earth
D) Earth's annual rotation
E) there is no correct answer
Number of zodiac stars
On which day does the sun rise above the horizon?
Who discovered the laws of planetary motion?
A) Ptolemy
B) Copernicus
E) Galileo
What is the time between two passages through the vernal equinox called?
A) sidereal year
B) Sagittarius
C) twins
E) Capricorn
If the sider period of Mars is 1.9 years, how long does the opposition of Mars repeat?
A) 1.9 g.
In what orbits do the planets move?
A) circular
B) by hyperbole
C) by ellipse
D) along a parabola
E) rectilinear
What is the point at which the Earth is closest to the Sun called?
A) autumn.
B) to perihelion
Let on rps. 11 the semicircle represents the meridian, P is the north celestial pole, OQ is the trace of the equatorial plane. The angle PON, equal to the angle QOZ, is the geographical sprat of the place ip (§ 17). These angles are measured by the arcs NP and QZ, which are therefore also yes; the declination of the luminary Mi, which is in the upper culmination, is measured by the arc QAlr. Denoting its zenith distance as r, we obtain for the luminary, culminating - 1, k, increasing (, * south of the zenith:
For such luminaries, obviously, "
If the luminary passes through the meridian north of the zenith (point M /), then its declination will be QM (\ n we get
I! In this case, taking the complement to 90°, we get the height
stars h at the time of the upper cul-,
minacpp. p M, Z
Finally, if b - e, then the star in the upper culmination passes through the zenith.
It is just as easy to determine the height of the luminary (UM,) at the lower M, the climax, i.e., at the moment of its passage through the meridian between the pole of the world (P) and the north point (N).
From fig. 11 it can be seen that the height h2 of the luminary (M2) is determined by the arc LH2 and is equal to h2 - NP-M2R. Arc arc M2R-r2,
i.e., the distance of the luminary from the pole. Since p2 \u003d 90 - 52> then
h2 = y-"ri2 - 90°. (3)
Formulas (1), (2) and (3) have extensive applications.
Exercises for the chapter /
1. Prove that the equator intersects the horizon at points 90° away from the north and south points (at the east and west points).
2. What are the hour angle and zenith azimuth?
3. What are the declination and hourly angle of the west point? East point?
4. What \thol with the horizon forms the equator with a latitude of - (-55 °? -) -40 °?
5. Is there a difference between the north celestial pole and the north point?
6. Which of the points of the celestial equator is above all above the horizon? Why paRiio the zenith distance of this point for latitude<р?
7. If a star rose at a point in the northeast, then at what point on the horizon will it set? What are the azimuths of the points eb of sunrise and sunset?
8. What is the azimuth of the star at the time of the upper culmination for a place under the latitude cp? Is it the same for all stars?
9. What is the declination of the north celestial pole? south pole?
10. What is the declination of the zenith for a place with latitude o? north point declination? south points?
11. In what direction does the star move in the lower climax?
12. The North Star is 1° away from the celestial pole. What is its declination?
13. What is the height of the North Star at the upper culmination for a place under the latitude cp? Same for the bottom climax?
14. What condition must the declination S of a star satisfy in order for it not to set under latitude 9? to make it non-ascending?
15. What hurts the angular radius of the circle of setting stars in Leningrad (“p = - d9°57”)?” In Tashkent (srg-41b18")? "
16. What is the declination of the stars passing through the zenith in Leningrad and Tashkent? Are they visiting for these cities?
17. At what zenith distance does the star Capella (i - -\-45°5T) pass through the upper culmination in Leningrad? in Tashkent?
18. Up to what declination are the stars of the southern hemisphere visible in these cities?
19. Starting from what latitude can you see Canopus, the brightest star in the sky after Sirius (o - - 53 °) when traveling south? Is it necessary to leave the territory of the USSR for this (check the map)? At what latitude will Kapoius become a non-setting star?
20. What is the height of the Chapel at the lower climax in Moscow = + 5-g<°45")? в Ташкенте?
21. Why is the right ascension counting from west to east, and not in the opposite direction?
22. The two brightest stars in the northern sky are Vega (a = 18ft 35m) and Capella (r -13da). In which side of the sky (western or eastern) and what hour angles are they at the time of the upper climax of the vernal equinox? At the moment of the lower climax of the same point?
23. What interval of sidereal time passes from the lower culmination of the Chapel to the upper climax of Bern?
24. What is the hour angle of the Chapel at the moment of the upper climax of the Run? At the moment of her lower climax?
25. At what hour in sidereal time does the vernal equinox point rise? comes in?
26. Prove that for an observer at the earth's equator, the azimuth of a star at the time of sunrise (AE) and at the time of setting (A^r) is very simply related to the declination of the star (i).
Let's turn to Figure 12. We see that the height of the celestial pole above the horizon is h p =∠PCN, and the geographical latitude of the place is φ=∠COR. These two angles (∠PCN and ∠COR) are equal as angles with mutually perpendicular sides: ⊥, ⊥. The equality of these angles gives the simplest way to determine the geographical latitude of the area φ: the angular distance of the celestial pole from the horizon is equal to the geographic latitude of the area. To determine the geographic latitude of the area, it is enough to measure the height of the celestial pole above the horizon, since:
2. Daily movement of luminaries at different latitudes
Now we know that with a change in the geographical latitude of the place of observation, the orientation of the axis of rotation of the celestial sphere relative to the horizon changes. Let us consider what will be the visible motions of celestial bodies in the region of the North Pole, at the equator and at the middle latitudes of the Earth.
At the pole of the earth the pole of the world is at its zenith, and the stars move in circles parallel to the horizon (Fig. 14, a). Here the stars do not set and do not rise, their height above the horizon is unchanged.
At middle geographic latitudes exist as ascending and incoming stars, as well as those that never fall below the horizon (Fig. 14, b). For example, circumpolar constellations (see Fig. 10) never set at the geographical latitudes of the USSR. Constellations farther from the north celestial pole appear briefly above the horizon. And the constellations lying near the south pole of the world are non-ascending.
But the further the observer moves south, the more southern constellations he can see. At the earth's equator, if the Sun did not interfere during the day, the constellations of the entire starry sky could be seen in a day (Fig. 14, c).
To an observer at the equator, all stars rise and set perpendicular to the horizon plane. Each star here passes over the horizon exactly half of its path. The north pole of the world for him coincides with the point of the north, and the south pole of the world coincides with the point of utah. The axis of the world is located in the plane of the horizon (see Fig. 14, c).
Exercise 2
1. How can you determine by the appearance of the starry sky and its rotation that you have arrived at the North Pole of the Earth?
2. How are the daily paths of stars relative to the horizon for an observer located at the Earth's equator? How do they differ from the daily paths of stars visible in the USSR, i.e., in middle geographical latitudes?
Task 2
Measure the geographic latitude of your area using the eclimeter using the height of the North Star and compare it with the latitude reading on the geographic map.
3. The height of the luminaries at the climax
During the apparent rotation of the sky, which reflects the rotation of the Earth around its axis, the pole of the world occupies a constant position above the horizon at a given latitude (see Fig. 12). During the day, the stars describe circles above the horizon around the axis of the world, parallel to the celestial equator. Moreover, each luminary crosses the celestial meridian twice a day (Fig. 15).
The phenomena of the passage of luminaries through the celestial meridian relative to the horizon for are called culminations. In the upper climax, the height of the luminary is maximum, and in the lower climax, it is minimal. The time interval between climaxes is equal to half a day.
At not setting at a given latitude φ of the luminary M (see Fig. 15), both culminations are visible (above the horizon), for the stars that rise and set (M 1, M 2, M 3), the lower culmination occurs under the horizon, below the north point. At the luminary M 4, located far south of the celestial equator, both climaxes can be invisible (the luminary non-ascending).
The moment of the upper climax of the center of the Sun is called true noon, and the moment of the lower climax is called true midnight.
Let us find the relationship between the height h of the star M at the upper culmination, its declination δ and the latitude of the area φ. To do this, we will use Figure 16, which shows the plumb line ZZ", the world axis PP" and the projections of the celestial equator QQ" and the horizon line NS onto the plane of the celestial meridian (PZSP"N).
We know that the height of the world pole above the horizon is equal to the geographical latitude of the place, i.e. h p =φ. Therefore, the angle between the noon line NS and the axis of the world PP "is equal to the latitude of the area φ, i.e. ∠PON=h p = φ. It is obvious that the inclination of the plane of the celestial equator to the horizon, measured by ∠QOS, will be equal to 90 ° -φ, since ∠QOZ= ∠PON as angles with mutually perpendicular sides (see Fig. 16) Then the star M with declination δ, culminating south of the zenith, has an altitude at its upper culmination
From this formula it can be seen that the geographical latitude can be determined by measuring the height of any luminary with a known declination δ at the upper climax. In this case, it should be borne in mind that if the luminary at the moment of climax is located south of the equator, then its declination is negative.
Problem solution example
A task. Sirius (α B. Psa, see appendix IV) was at its upper climax at 10°. What is the latitude of the observation point?
Pay attention to the fact that the drawing exactly matches the condition of the problem.
Exercise 3
When solving problems, the geographical coordinates of cities can be counted on a geographical map.
1. At what height in Leningrad does the upper climax of Antares (α Scorpio, see Appendix IV) occur?
2. What is the declination of the stars that culminate at the zenith in your city? at a point south?
3. Prove that the height of the luminary at the lower culmination is expressed by the formula h=φ+δ-90°.
4. What condition must satisfy the declination of a star so that it is not setting for a place with a geographical latitude φ? non-ascending?
