Practical work and thematic assignments in astronomy. The simplest practical work on astronomy in high school

The simplest practical work on astronomy in high school.

1. Observations of the visible daily rotation of the starry sky.

a) Conduct an observation for one evening and note how the position of the constellations Ursa Minor and Ursa Major changes.

b) Determine the rotation of the sky by the passage of stars through the field of view of a fixed telescope. Knowing the field of view of the telescope, use a stopwatch to determine the speed of rotation of the sky (in degrees per hour).

2. Observation of the annual change of the starry sky.

3. Observation of changes in the midday height of the Sun.

Within a month, once a week at true noon, measure the height of the Sun. Enter the measurement results in the table:

Construct a graph of the change in the noon height of the Sun, plotting the dates on the X axis, and the noon height on the Y axis.

To determine the time of true noon, you need to use the formula:

T ist.pold. = 12 + h + (n - l).

In this case, you need to enter an amendment of 1 hour for summer time.

4. Observation of the apparent position of the planets relative to the stars.

5. Observation of the satellites of Jupiter.

It is necessary to conduct observations of Jupiter's satellites through a telescope and sketch their position relative to the planet's disk. The absence of some satellites means their eclipse or occultation.

6. Determination of the geographical latitude of a place.

6.1 According to the height of the Sun at noon.

A few minutes before the onset of true noon, install the theodolite in the plane of the meridian. Calculate the time of noon in advance.

At or near noon, measure the height h of the lower edge of the disc. Correct the found height by the value of the radius of the Sun (16 ').

Calculate the latitude of a place using the dependence

j \u003d 90 0 - h c + d c,

where h c is the height of the center of the Sun, d c is the declination of the Sun per hour of observation, interpolated taking into account its hourly change.

6.2 According to the height of the North Star.

Using a theodolite or other goniometric instrument, measure the height of the North Star above the horizon. This will be the approximate value of the latitude with an error of about 1 0 .

7. Determination of the geographical longitude of a place.

7.1 Install the theodolite in the plane of the meridian and determine the moment of the culmination of the Sun by the clock (the moment the Sun passes through the vertical thread of the theodolite). This will be the moment T p expressed in standard time.

7.2 Calculate the local solar time at the moment on the zero meridian T 0 if the number of this zone is 2.

T 0 \u003d T p - n.

7.3 Determine the local average time T m at the moment of the culmination of the Sun, which is equal to 12 + h.

7.4 Calculate the longitude of a place as the difference between local times:

l \u003d T m - T 0.

8. Observation of the surface of the moon through a telescope.

On the map of the Moon, get acquainted with some well-observed lunar formations.

Compare the observation results with the available map.

MATERIALS FOR PRACTICAL
(LABORATORY) STUDIES
Astronomy
Grade 11
Full-time form of education)
Lecturer: Demenin L.N.
Vladivostok

Explanatory note
The main purpose of practical training is to solve various kinds of problems.
Along with the formation of skills and abilities in the process of practical training
generalize, systematize, deepen and concretize theoretical knowledge,
the ability and readiness to use theoretical knowledge in practice is developed,
intellectual skills develop.
To improve the effectiveness of practical training, it is recommended:
use of active teaching methods in the practice of teaching;
use of collective and group forms of work, maximum
use of individual forms in order to increase the responsibility of each
student for independent performance of the full scope of work;
conducting classes at an increased level of difficulty with the inclusion of tasks in them,
related to the choice by students of the conditions for the performance of work, the specification of goals,
independent selection of the necessary methods and means of solving problems;
selection of additional tasks and assignments for students working in more
at a fast pace, to effectively use the time allotted in the lesson, etc.
Practical block for the discipline "Astronomy"
Practical work No. 1
(with a plan of the solar system)

Target:
Scale drawing of a plan of the solar system showing the real
positions of the planets on the date of the work.

Compass, "School astronomical calendar" for the current academic year.
Working process:
1. Familiarize yourself with the content of task 12 of the textbook.
3

2. Complete item 1 of task 12. To do this, use Appendix IV of the textbook and
pre-fill the table (in place of gaps in the first row of the table, indicate
parameter that is needed for the build).
On a separate sheet in the center, you need to place the Sun as a point
Light source. Taking the orbits of the planets as circles, you need to mark them with a dotted line
(the centers of the circles will coincide and be at the point that denotes
position of the sun).
Draw a beam from the center (the position of the Sun) in an arbitrary direction,
taking it as the direction to the vernal equinox.
3. Familiarize yourself with the contents of the "School Astronomical Calendar".
4. Fill in the gaps by giving definitions:
Heliocentric longitude is the central angle between the direction
_________.
Ephemeris _____________________________________________________.
5. Complete item 2 (b) of task 12. Record the results in the table.
6. Complete item 2 (c) of task 12. Enter the results in the table (in the absence of
put a dash in the corresponding cell of the specified configuration for the planet).
7. Find in the "School astronomical calendar" for the current academic year
table of heliocentric longitudes of the planets. Carefully read paragraph 3 of task 12.
Put on the plan of the solar system the position of Mercury, Venus, Earth, Mars.
Main literature:

5358194625;
2. Kunash M.A. Astronomy. Grade 11. Methodological guide to the textbook B.A.
Vorontsova Velyaminova, E.K. Strout, Astronomy. A basic level of. Grade 11 / M.A.
Kunash. - M.: Bustard, 2018. - 217, (7) 7s. ISBN 9785358178052.
Internet resources:
− http://www.afportal.ru/astro/model – Astrophysical portal. Interactive Plan
solar system.
Practical work No. 2
(two groups of planets in the solar system)
4

Target:
Explore the characteristics of the planets in the solar system.
Used tools and materials:
"School astronomical calendar" for the current academic year.
Working process:
1. Familiarize yourself with the contents of §15 of the textbook.
2.
Specify the basis according to which the division of the planets into two occurs
groups.
3.
Using the data of §15 and appendix VI of the textbook, characterize the groups
planets according to their physical characteristics. Parse the specified values ​​by answering
to questions:
A) by what criteria do the planets of the two groups have the most significant differences?
B) the density of the planets of which group is greater? What can explain the differences in
density of physical bodies?
4. Using the data of §15 of the textbook, characterize the physicochemical properties
each group of planets in the solar system. Parse the indicated values,
by answering the following questions:
A) What is the similarity of the chemical composition of the planets of the two groups?
B) What is the difference in the chemical composition of the planets of the two groups?
C) At what stage the formation of the bodies of the solar system. According to the reviewed
earlier hypothesis, there was a difference in the chemical composition of the planets of the two groups?
5. Using the data from Appendix VI of the textbook and the "School Astronomical
calendar" for the current academic year, explore the features of interaction between groups
planets in a gravitationally interconnected system of bodies. Analyze the specified
values, answering the question: “By what criteria the planets of the two groups have the most
significant differences?
6. Formulate a conclusion about the features of the groups of planets in the solar system,
the physical foundations of their differences and similarities.
Main literature:
1. Vorontsov Velyaminov B.A., Strout E.K. Astronomy. A basic level of. Grade 11:
textbook - 5th edition, revision. - M.: Bustard, 2018. - 238, (2) p.: ill., 8 p. col. incl. ISBN 978
5358194625;

Foreword
Observations and practical work on astronomy play an important role in the formation of astronomical concepts. They increase interest in the subject being studied, connect theory with practice, develop such qualities as observation, attentiveness, and discipline.
This manual describes the author's experience in organizing and conducting practical work on astronomy in high school.
The manual consists of two chapters. The first chapter gives some specific remarks on the use of instruments such as a telescope, theodolite, sundial, etc. The second chapter describes 14 practical works, which basically correspond to the astronomy program. The teacher can conduct observations not provided for by the program in extracurricular activities. Due to the fact that not all schools have the required number of telescopes and theodolites, some observations
activities can be combined into one session. At the end of the work, methodological instructions for their organization and implementation are given.
The author considers it his duty to express his gratitude to the reviewers M. M. Dagaev and A. D. Marlensky for valuable suggestions made in preparing the book for publication.
Author.

Chapter I
EQUIPMENT FOR ASTRONOMICAL OBSERVATIONS AND PRACTICAL WORKS
TELESCOPES AND THEODOLITES
The description and instructions for the use of these devices are quite fully set out in other textbooks and in the appendices to the devices. Here are just a few guidelines for their use.
telescopes
As you know, for the exact installation of the equatorial tripod of the telescope, its eyepiece must have a cross of threads. One of the ways to make a cross of threads is described in P. G. Kulikovsky's "Amateur's Handbook" and is as follows.
On the ocular diaphragm or a light ring made according to the diameter of the eyepiece sleeve, two hairs or two cobwebs should be glued mutually perpendicular with the help of alcohol varnish. In order for the threads to be well stretched when gluing, it is necessary to attach light weights (for example, plasticine balls or pellets) to the ends of the hairs (about 10 cm long). Then put the hairs in diameter on a horizontally located ring perpendicular to each other and drop a drop of oil in the right places, letting it dry for several hours. After the varnish has dried, carefully cut off the ends with weights. If the crosshair is glued to the ring, it must be inserted into the eyepiece sleeve so that the cross of threads is located at the very ocular diaphragm.
You can make a crosshair and photographic method. To do this, you need to photograph two mutually perpendicular lines, clearly drawn in ink on white paper, and then get a positive picture from the negative on another film. The resulting "crosshair" should be cut to the size of the tube and fixed in the ocular diaphragm.
A big inconvenience of a school refractor telescope is its poor stability on a tripod that is too light. Therefore, if the telescope is mounted on a permanent stable pole, the observation conditions are greatly improved. The base bolt on which the telescope is mounted, which is the so-called Morse cone No. 3, can be made in school workshops. You can also use the stand bolt from the tripod supplied with the telescope.
Although the latest models of telescopes have finder sights, it is much more convenient to have a finder tube with a low magnification on the telescope (for example, an optical sight). The seeker is mounted in special rings-stands so that its optical axis is strictly parallel to the optical axis of the telescope. In telescopes that do not have a finder scope, when aiming at weak objects, the eyepiece with the lowest magnification should be inserted, in this case the field of view is the largest.
neck. After aiming, carefully remove the eyepiece and replace it with another one with a higher magnification.
Before pointing the telescope at faint objects, it is necessary to set the eyepiece to focus (this can be done by a distant terrestrial object or a bright star). In order not to repeat aiming every time, it is better to mark this position on the eyepiece tube with a noticeable line.
When observing the Moon and the Sun, it should be borne in mind that their angular dimensions are about 32", and if you use an eyepiece that gives 80x magnification, then the field of view will be only 30". To observe planets, binary stars, as well as individual details of the lunar surface and the shape of sunspots, it is advisable to use the highest magnifications.
When making observations, it is useful to know the duration of the movement of celestial bodies through the field of view of a fixed telescope at different magnifications. If the luminary is located near the celestial equator, then due to the rotation of the Earth around its axis, it will move in the field of view of the pipe at a speed of 15 "per 1 min. min. The field of view of 1°07" and 30" will pass in 4.5 minutes and 2 minutes, respectively.
In schools where there is no telescope, you can make a homemade refractor telescope from a large lens from an epidiascope and an eyepiece from a school microscope. According to the diameter of the lens, a pipe about 53 cm long is made from roofing iron. A wooden disk with a hole for the eyepiece is inserted into its other end.
1 A description of such a telescope is given in an article by B. A. Kolokolov in the journal Physics at School, 1957, No. 1.
When making a telescope, you should pay attention to the fact that the optical axes of the objective and the eyepiece coincide. To improve the clarity of the image of such bright bodies as the Moon and the Sun, the lens must be apertured. The magnification of such a telescope is approximately 25. It is not difficult to make a home-made telescope from spectacle glasses1.
To judge the capability of any telescope, you need to know about it such data as the magnification, the limiting angle of resolution, penetrating power and field of view.
The magnification is determined by the ratio of the focal length of the lens F to the focal length of the eyepiece f (each of which is easy to determine by experience):
This magnification can also be found from the ratio of the lens diameter D to the diameter of the so-called exit pupil d:
The exit pupil is defined as follows. The tube focuses "to infinity", i.e., almost to a very distant object. Then it is directed to a light background (for example, to a clear sky), and on graph paper or on tracing paper, holding it at the very eyepiece, a clearly defined circle is obtained - the image of the lens given by the eyepiece. This will be the exit pupil.
1 I. D. Novikov and V. A. Shishakov, Homemade Astronomical Instruments and Observations with Them, Nauka, 1965.
The limiting resolution angle r characterizes the minimum angular distance between two stars or details of the planet's surface, at which they are visible separately. The theory of light diffraction gives a simple formula for determining r in arcseconds:
where D is the lens diameter in millimeters.
In practice, the value of r can be estimated from observations of close binary stars using the table below.
Star Coordinates Magnitudes of components Angular distance between components
To find the stars listed in the table, the star atlas of A. A. Mikhailov1 is convenient.
The location of some double stars is shown in Figure 1.
1 You can also use the "Educational Star Atlas" by A. D. Mogilko, in which the position of the stars is given on 14 large-scale maps.
Theodolites
With angular measurements using a theodolite, a well-known difficulty is the reading of the readings on the limbs. Therefore, let us consider in more detail an example of a reference using a vernier on a TT-50 theodolite.
Both limbs, vertical and horizontal, are divided into degrees, each degree, in turn, is subdivided into 3 more parts, 20 "in each. The reference pointer is the zero stroke of the vernier (vernier) placed on the alidade. any stroke of the limb, then the proportion of division of the limb, to which the strokes do not coincide, is determined by the vernier scale.
Vernier usually has 40 divisions, which in their length capture 39 divisions of the limbus (Fig. 2)1. This means that each division of the vernier is 39/4 of the division of the limb, or, in other words, U40 less than it. Since one division of the limb is 20", then the division of the vernier is less than the division of the limb by 30".
Let the zero stroke of the vernier occupies the position indicated by the arrow in Figure 3. Note that exactly
1 For convenience, the scales of the circles are depicted as rectilinear.
the ninth division of vernier coincided with the stroke of the limbus. The eighth division does not reach the corresponding stroke of the limbus by 0.5, the seventh - by G, the sixth - by G.5, and the zero stroke does not reach the corresponding stroke of the limb (to its right) by 0.5-9 \u003d 4 " , 5. Hence, the reading will be written as follows1:
Rice. 3. Reading with a vernier
For a more accurate reading, two verniers are installed on each of the limbs, located at 180 ° from one another. On one of them (which is taken as the main one), degrees are counted, and minutes are taken as the arithmetic average of the readings of both verniers. However, for school practice, it is quite enough to count one vernier.
1 Digitization of the vernier is done so that the reading can be done immediately. Indeed, the matching stroke corresponds to 4.5; therefore, 4.5 must be added to the number 6-20.
In addition to sighting, ocular filaments are used to determine distances using a rangefinder rod (a ruler on which equal divisions are clearly visible from a distance). The angular distance between the extreme horizontal threads a and b (Fig. 4) is chosen so that 100 cm of the rail is placed just between these threads when the rail is exactly 100 m from the theodolite. In this case, the rangefinder coefficient is 100.
Eyepiece threads can also be used for approximate angular measurements, given that the angular distance between the horizontal threads a i b p. is 35 ".

SCHOOL GONITOR
For such astronomical measurements as determining the noon altitude of the Sun, the geographical latitude of a place from the observations of the North Star, distances to distant objects, carried out as an illustration of astronomical methods, you can use a school goniometer, which is available in almost every school.
The device device can be seen from Figure 5. On the reverse side of the goniometer base, in the center on the hinge, a tube is fixed for mounting the goniometer on a tripod or on a stick that can be stuck into the ground. Thanks to the hinged fastening of the tube, the goniometer limb can be installed in vertical and horizontal planes. A plumb-line arrow 1 serves as an indicator of vertical angles. An alidade 2 with diopters is used to measure horizontal angles, and the installation of the device base is controlled by two levels 3. A viewing tube 4 is attached to the upper edge for ease of viewing.
Yoodki on the subject. To determine the height of the Sun, a folding screen 5 is used, on which a bright spot is obtained when the tube is directed to the Sun.

SOME INSTRUMENTS OF THE ASTRONOMICAL SITE
An instrument for determining the noon altitude of the Sun
Among the various types of this device, in our opinion, the quadrant altimeter is the most convenient (Fig. 6). It consists of a right angle (two planks) attached
to it in the form of an arc of a metal ruler and a horizontal rod A, reinforced with wire racks in the center of the circle (of which the ruler is a part). If you take a metal ruler 45 cm long with divisions, then you do not need to make markings for degrees. Each centimeter of the ruler will correspond to two degrees. The length of the wire racks in this case should be equal to 28.6 cm. Before measuring the midday height of the Sun, the device must be set to a level or plumb line and oriented with the lower base along the noon line.
World Pole Pointer
Usually, on a school geographical site, an inclined pole or pole is dug into the ground to indicate the direction of the axis of the world. But for the lessons of astronomy this is not enough, here it is necessary to take care of the measurement
the angle formed by the axis of the world with the plane of the horizon. Therefore, we can recommend a pointer in the form of a bar about 1 m long with a fairly large eclimeter, made, for example, from a school protractor (Fig. 7). This provides both greater clarity and sufficient accuracy in measuring the height of the pole.
The simplest passage instrument
To observe the passage of luminaries through the celestial meridian (which is associated with many practical problems), you can use the simplest thread passage instrument (Fig. 8).
To mount it, it is necessary to draw a midday line on the site and dig two pillars at its ends. The southern pillar must be of sufficient height (about 5 m) so that the plumb line lowered from it covers
a larger area of ​​the sky. The height of the northern pillar, from which the second plumb line descends, is about 2 m. The distance between the pillars is 1.5-2 m. At night, the threads must be illuminated. Such an installation is convenient in that it provides observation of the culmination of the luminaries by several students at once.
star pointer
The star pointer (Fig. 9) consists of a light frame with parallel bars on a hinged device. By aiming one of the bars at the star, we orient the others in the same direction. When making such a pointer, it is necessary that there are no backlashes in the hinges.
Rice. 9. Star Pointer
1 Another model of the passage instrument is described in the collection New School Instruments in Physics and Astronomy, ed. APN RSFSR, 1959.
Sundial indicating local, standard and standard time1
Conventional sundials (equatorial or horizontal), which are described in many textbooks, have the disadvantage that they show
Rice. 10. Sundial with a graph of the equation of time
They call true solar time, which we almost never use in practice. The sundial described below (Fig. 10) is free from this drawback and is a very useful device in the study of issues related to the concept of time, as well as for practical work.
1 The model of this clock was proposed by A. D. Mogilko and described in the collection “New School Instruments in Physics and Astronomy”, ed. APN RSFSR, 1959,
The hour circle 1 is installed on a horizontal stand in the plane of the equator, i.e. at an angle of 90 ° -av, where f is the latitude of the place. The alidade 2, which rotates on the axis, has a small round hole 3 at one end, and at the other, on the bar 4, a graph of the equation of time in the form of a figure eight. The time indicator is three arrows printed on the alidade bar under hole 3. When the clock is set correctly, the hand M shows the local time, the arrow I shows the standard time and the arrow D shows the standard time. Moreover, the arrow M is applied exactly under the middle of the hole 3 perpendicular to the dial. To draw the arrow R, you need to know the correction% -n, where X is the longitude of the place, expressed in hours, n is the number of the time zone. If the correction is positive, then the arrow I is set to the right of the arrow M, if negative - to the left. The arrow D is set from the arrow I to the left by 1 hour. The height of the hole 3 from the alidade is determined by the height h of the equator line on the graph of the equation of time, printed on the bar 4.
To determine the time, the clock is carefully oriented along the meridian by the “0-12” line, the base is set horizontally by levels, then the alidade is rotated until the ray of the Sun that has passed through hole 3 falls on the graph branch corresponding to the date of observation. The hands at this point will give the timing.
Astronomical corner
To solve problems in astronomy lessons, to perform a number of practical work (determining the latitude of a place, determining time from the Sun and stars, observing Jupiter's satellites, etc.), as well as to illustrate the material presented in the lessons, in addition to published tables on astronomy, it is useful to have large scale reference tables, graphs, drawings, results of observations, samples of students' practical work and other materials that make up the astronomical corner. In the astronomical corner, Astronomical calendars (an annual published by VAGO and the School Astronomical Calendar) are also needed, which contain information necessary for classes, indicate the most important astronomical events, and provide data on the latest achievements and discoveries in astronomy.
In the event that there are not enough calendars, it is desirable to have the following from reference tables and graphs in the astronomical corner: declination of the Sun (every 5 days); equation of time (table or graph), change in the phases of the moon and its declinations for a given year; configurations of Jupiter's satellites and satellite eclipse tables; the visibility of the planets in a given year; information about eclipses of the Sun and Moon; some constant astronomical quantities; coordinates of the brightest stars, etc.
In addition, a movable star chart and a study star atlas by A. D. Mogilko, a silent star chart, and a model of the celestial sphere are needed.
To register the moment of true noon, it is convenient to have a photorelay specially installed along the meridian (Fig. 11). The box in which the photorelay is placed has two narrow slots oriented exactly along the meridian. Sunlight passing through the outer slot (the width of the slots is 3-4 mm) exactly at noon, enters the second, inner slot, falls on the photocell and turns on the electric bell. As soon as the beam from the outer slot shifts and stops illuminating the photocell, the bell is turned off. With a distance between the slots of 50 cm, the duration of the signal is about 2 minutes.
If the device is installed horizontally, then the top cover of the chamber between the outer and inner slot must be made with an inclination to ensure that sunlight hits the inner slot. The angle of inclination of the top cover depends on the highest noon altitude of the Sun at a given location.
In order to use the given signal to check the clock, it is necessary to have a table on the photo relay box indicating the moments of true noon with an interval of three days1.
Since the armature of the electromagnetic relay is attracted when darkened, the contact plates I, through which the bell circuit is switched on, must be normally closed, i.e., closed when the armature is depressed.
1 The calculation of the moment of true noon is given in work No. 3 (see page 33).

Chapter II.
OBSERVATIONS AND PRACTICAL WORKS

Practical exercises can be divided into three groups: a) observations with the naked eye, b) observations of celestial bodies with a telescope and other optical instruments, c) measurements with theodolite, the simplest goniometers and other equipment.
The work of the first group (observation of the starry sky, observation of the movement of the planets, observation of the movement of the moon among the stars) is performed by all students of the class under the guidance of a teacher or individually.
When performing observations with a telescope, difficulties arise due to the fact that, as a rule, there are only one or two telescopes at school, and there are many students. If, however, we take into account that the duration of observation by each schoolchild rarely exceeds one minute, then the need to improve the organization of astronomical observations becomes obvious.
Therefore, it is advisable to divide the class into links of 3-5 people and each link, depending on the availability of optical instruments in the school, determine the time of observation. For example, in the autumn months, observations can be scheduled from 20:00. If each link is given 15 minutes, then even if one instrument is available, the entire class will be able to observe in 1.5-2 hours.
Given that the weather often interferes with observation plans, surveys should be carried out during the months when the weather is most stable. Each link in this case must perform 2-3 work. This is quite possible if the school has 2-3 instruments and the teacher has the opportunity to involve an experienced laboratory assistant or an amateur astronomer from the class asset to help.
In some cases, optical instruments can be borrowed from neighboring schools to conduct classes. For some work (for example, the observation of Jupiter's satellites, determining the size of the Sun and Moon, and others), various spotting scopes, theodolites, prism binoculars, home-made telescopes are suitable.
The work of the third group can be carried out both by links and by the whole class. To perform most of this type of work, you can use simplified instruments available at school (goniometers, eclimeters, gnomon, etc.). (...)

Work 1.
OBSERVATION OF THE VISIBLE DAILY ROTATION OF THE STARRY SKY
I. According to the position of the circumpolar constellations Ursa Minor and Ursa Major
1. During the evening, observe (after 2 hours) how the position of the constellations Ursa Minor and Ursa Major changes. "
2. Enter the results of observations in the table, orienting the constellations relative to the plumb line.
3. Draw a conclusion from the observation:
a) where is the center of rotation of the starry sky;
b) in what direction it rotates;
c) how many degrees does the constellation approximately rotate in 2 hours.
II. By the passage of the luminaries through the field of view
fixed optical tube
Equipment: telescope or theodolite, stopwatch.
1. Point the telescope or theodolite tube at some star located near the celestial equator (in the autumn months, for example, at a Eagle). Set the pipe in height so that the star passes through the field of view in diameter.
2. Observing the apparent movement of the star, use a stopwatch to determine the time it takes for it to pass through the field of view of the tube1.
3. Knowing the size of the field of view (from the passport or from reference books) and the time, calculate with what angular velocity the starry sky rotates (by how many degrees in every hour).
4. Determine in which direction the starry sky rotates, given that tubes with an astronomical eyepiece give an inverse image.

Work 2.
OBSERVATION OF THE ANNUAL CHANGE IN THE APPEARANCE OF THE STARRY SKY
1. At the same hour, once a month, observe the position of the circumpolar constellations Ursa Major and Ursa Minor, as well as the position of the constellations in the southern side of the sky (make 2 observations).
2. Enter the results of observations of circumpolar constellations into the table.
1 If the star has declination b, then the time found should be multiplied by cos b.
3. Draw a conclusion from observations:
a) whether the position of the constellations remains unchanged at the same hour in a month;
b) in what direction the circumpolar constellations move and by how many degrees per month;
c) how the position of the constellations in the southern side of the sky changes: in what direction do they move and by how many degrees.
Methodological notes to the work No. 1 and 2
1. For the speed of drawing constellations in works No. 1 and 2, students should have a ready-made template of these constellations, chipped from a map or from figure 5 of a school astronomy textbook. Pinning the template to point a (Polar) on a vertical line, rotate it until the line "a-r" Ursa Minor takes the appropriate position relative to the plumb line, and transfer the constellations from the template to the drawing.
2. The second way to observe the daily rotation of the sky is faster. However, in this case, students perceive the movement of the starry sky from west to east, which requires additional explanation.
For a qualitative assessment of the rotation of the southern side of the starry sky without a telescope, this method can be recommended. It is necessary to stand at some distance from a vertically placed pole, or a well-visible plumb line, projecting a pole or thread near a star. After 3-4 minutes, the movement of the star to the west will be clearly visible.
3. The change in the position of the constellations in the southern side of the sky (work No. 2) can be established by the displacement of the stars from the meridian in about a month. As an object of observation, you can take the constellation Aquila. Having the direction of the meridian (for example, 2 plumb lines), they note at the beginning of September (at about 20 o'clock) the moment of the climax of the star Altair (a Eagle). A month later, at the same hour, a second observation is made and, with the help of goniometric instruments, it is estimated how many degrees the star has shifted west of the meridian (the shift should be about 30 °).
With the help of a theodolite, the displacement of a star to the west can be noticed much earlier, since it is about 1 ° per day.
4. The first lesson on familiarization with the starry sky is held at the astronomical site after the first introductory lesson. After getting acquainted with the constellations Ursa Major and Ursa Minor, the teacher introduces students to the most characteristic constellations of the autumn sky, which must be firmly known and able to be found. From Ursa Major, students make a "journey" through the North Star to the constellations of Cassiopeia, Pegasus and Andromeda. Pay attention to the large nebula in the constellation Andromeda, which is visible on a moonless night with the naked eye as a faint blur. Here, in the northeastern part of the sky, the constellations Auriga with the bright star Capella and Perseus with the variable star Algol are noted.
Again we return to the Big Dipper and look where the break in the handle of the "bucket" points. Not high above the horizon in the western side of the sky we find the bright orange star Arcturus (and Bootes), and then above it in the form of a wedge and the whole constellation. To the left of Volop-
a semicircle of dim stars stands out - the Northern Crown. Almost at its zenith, a Lyra (Vega) shines brightly, to the east along the Milky Way lies the constellation Cygnus, and from it directly to the south - the Eagle with the bright star Altair. Turning to the east, we again find the constellation Pegasus.
At the end of the lesson, you can show where the celestial equator and the initial circle of declinations pass. Students will need this when they become familiar with the main lines and points of the celestial sphere and equatorial coordinates.
In subsequent classes in winter and spring, students get acquainted with other constellations, conduct a series of astrophysical observations (colors of stars, changes in the brightness of variable stars, etc.).

Work 3.
OBSERVATION OF CHANGES IN THE NOON HEIGHT OF THE SUN
Equipment: quadrant altimeter, or school goniometer, or gnomon.
1. Within a month, once a week at true noon, measure the height of the Sun. The results of measurements and data on the declination of the Sun in the remaining months of the year (taken a week later) are entered in the table.
2. Construct a graph of the change in the noon height of the Sun, plotting the dates along the X axis, and the noon height along the Y axis. On the graph, draw a straight line corresponding to the height of the equatorial point in the meridian plane at a given latitude, mark the points of equinoxes and solstices and draw a conclusion about the nature of the change in the height of the Sun during the year.
Note. You can calculate the midday height of the Sun from declination in the remaining months of the year using the equation
Methodical remarks
1. To measure the height of the Sun at noon, you must either have the direction of the noon line drawn in advance, or know the moment of true noon according to standard time. You can calculate this moment if you know the equation of time for the day of observation, the longitude of the place and the number of the time zone (...)
2. If the windows of the class face south, then the quadrant altimeter installed, for example, on the windowsill along the meridian, makes it possible to immediately receive the height of the Sun at true noon.
When measuring with a gnomon, it is also possible to prepare a scale on a horizontal base in advance and immediately obtain the value of the angle Iiq from the length of the shadow. The ratio is used to mark the scale
where I is the height of the gnomon, r is the length of its shadow.
You can also use the method of a floating mirror placed between the window frames. A bunny, thrown onto the opposite wall, at true noon will cross the meridian marked on it with the scale of the Sun's heights. In this case, the whole class, watching the bunny, can mark the midday height of the Sun.
3. Taking into account that this work does not require high measurement accuracy and that near the culmination the height of the Sun changes insignificantly with respect to the moment of culmination (about 5 "in the interval ± 10 min), the measurement time may deviate from the true noon by 10-15 min .
4. It is useful in this work to make at least one measurement using a theodolite. It should be noted that when pointing the middle horizontal thread of the crosshair under the lower edge of the solar disk (in fact, under the upper one, since the theodolite tube gives an inverse image), it is necessary to subtract the angular radius of the Sun from the result obtained (about 16 ") to obtain the height of the center of the solar disk.
The result obtained with the help of a theodolite can later be used to determine the geographical latitude of a place, if for some reason this work cannot be delivered.

Work 4.
DETERMINATION OF THE DIRECTION OF THE SKY MERIDIAN
1. Choose a point convenient for observing the southern side of the sky (you can in the classroom if the windows face south).
2. Install the theodolite and under its plumb line, lowered from the upper base of the tripod, make a permanent and clearly visible mark of the selected point. When observing at night, it is necessary to slightly illuminate the field of view of the theodolite tube with diffused light so that the ocular filaments are clearly visible.
3. Having approximately estimated the direction of the south point (for example, using a theodolite compass or pointing the pipe at the North Star and turning it 180 °), point the pipe at a fairly bright star, slightly east of the meridian, fix the alidade of the vertical circle and the pipe. Take three readings on the horizontal limb.
4. Without changing the height of the pipe, follow the movement of the star until it is at the same height after passing the meridian. Make a second reading of the horizontal limb and take the arithmetic mean of these readings. This will be the reference to the south point.
5. Point the pipe in the direction of the south point, i.e. set the zero stroke of the vernier to the number corresponding to the reading found. If no terrestrial objects that would serve as a reference point for the south point fall into the field of view of the pipe, then it is necessary to “bind” the found direction to a clearly visible object (east or west of the meridian).
Methodical remarks
1. The described method of determining the direction of the meridian by equal heights of any star is more accurate. If the meridian is determined by the Sun, then it must be borne in mind that the declination of the Sun is constantly changing. This leads to the fact that the curve along which the Sun moves during the day is not symmetrical with respect to the meridian (Fig. 12). This means that the found direction, as a half-sum of reports at equal heights of the Sun, will differ somewhat from the meridian. The error in this case can reach up to 10".
2. For a more accurate determination of the direction of the meri-
diana take three readings using the three horizontal lines present in the eyepiece of the tube (Fig. 13). Pointing the pipe at the star and acting with micrometer screws, the star is placed slightly above the upper horizontal line. Acting only with the micrometer screw of the alidade of the horizontal circle and maintaining the height of the theodolite, the star is kept on a vertical thread all the time.
As soon as it touches the upper horizontal thread a, the first count is taken. Then the star is passed through the middle and lower horizontal threads b and c and the second and third readings are taken.
After passing the star through the meridian, catch it at the same height and again take readings on the horizontal limb, only in the reverse order: first the third, then the second and first readings, since the star will descend after passing the meridian, and in the pipe giving the opposite image, she will rise. When observing the Sun, they proceed similarly, passing the lower edge of the solar disk through the horizontal threads.
3. To bind the found direction to a noticeable object, you need to point the pipe at this object (world) and record the reading of the horizontal circle. Subtracting from it the reading of the south point, the azimuth of the earth object is obtained. When re-installing the theodolite at the same point, it is necessary to point the pipe at the earthly object and, knowing the angle between this direction and the direction of the meridian, install the theodolite pipe in the plane of the meridian.
KOHETS FRAGMEHTA TEXTBOOK

LITERATURE
Astronomical calendar VAGO (yearbook), ed. Academy of Sciences of the USSR (since 1964 "Science").
Barabashov N.P., Instructions for observing Mars, ed. Academy of Sciences of the USSR, 1957.
BronshtenV. A., Planets and their observations, Gostekhizdat, 1957.
Dagaev M. M., Laboratory workshop on general astronomy, Higher School, 1963.
Kulikovsky P. G., Reference book for amateur astronomy, Fizmatgiz, 1961.
Martynov D. Ya., Course of practical astrophysics, Fizmatgiz, 1960.
Mogilko A. D., Educational Star Atlas, Uchpedgiz, 1958.
Nabokov M. E., Astronomical observations with binoculars, ed. 3, Uchpedgiz, 1948.
Navashin M.S., Telescope of an amateur astronomer, Fizmatgiz, 1962.
N ovikov I. D., Shishakov V. A., Self-made astronomical instruments and instruments, Uchpedgiz, 1956.
"New school instruments in physics and astronomy". Collection of articles, ed. A. A. Pokrovsky, ed. APN RSFSR, 1959.
Popov P. I., Public practical astronomy, ed. 4, Fizmatgiz, 1958.
Popov P. I., Baev K. L., Vorontsov-Velyaminov B. A., Kunitsky R. V., Astronomy. Textbook for pedagogical universities, ed. 4, Uchpedgiz, 1958.
"Teaching Astronomy at School". Collection of articles, ed. B. A. Vorontsova-Velyaminova, ed. APN RSFSR, 1959.
Sytinskaya N.N., The Moon and Its Observation, Gostekhizdat, 1956.
Tsesevich V.P., What and how to observe in the sky, ed. 2, Gostekhizdat, 1955.
Sharonov VV, The sun and its observation, ed. 2, Gostekhizdat, 1953.
School astronomical calendar (yearbook), "Enlightenment".

Tasks for independent work on astronomy.

Topic 1. Studying the starry sky using a moving map:

1. Set the mobile map for the day and hour of observations.

date of observation __________________

observation time ___________________

2. List the constellations that are located in the northern part of the sky from the horizon to the celestial pole.

_______________________________________________________________

5) Determine whether the constellations Ursa Minor, Bootes, Orion will set.

Ursa Minor___

Bootes___

______________________________________________

7) Find the equatorial coordinates of the star Vega.

Vega (α Lyrae)

Right ascension a = _________

Declension δ = _________

8) Specify the constellation in which the object is located with coordinates:

a=0 hours 41 minutes, δ = +410

9. Find the position of the Sun on the ecliptic today, determine the length of the day. Sunrise and sunset times

Sunrise____________

Sunset _____________

10. The residence time of the Sun at the moment of the upper climax.

________________

11. In what zodiac constellation is the Sun located during the upper climax?

12. Determine your zodiac sign

Date of Birth___________________________

constellation __________________

Topic 2. The structure of the solar system.

What are the similarities and differences between the terrestrial planets and the giant planets. Fill in the form of a table:

2. Select a planet by option in the list:

Make a report about the planet of the solar system according to the option, focusing on the questions:

How is the planet different from others?

What is the mass of this planet?

What is the position of the planet in the solar system?

How long is a planetary year and how long is a sidereal day?

How many sidereal days fit into one planetary year?

The average life expectancy of a person on Earth is 70 Earth years, how many planetary years can a person live on this planet?

What details can be seen on the surface of the planet?

What are the conditions on the planet, is it possible to visit it?

How many satellites does the planet have and which ones?

3. Select the appropriate planet for the corresponding description:

Topic 3. Characteristics of stars.

Choose a star according to the option.

Indicate the position of the star on the spectrum-luminosity diagram.

Required formulas:

Average density:

Luminosity:

Lifetime:

Star distance:

Topic 4. Theories of origin and evolution of the Universe.

Name the galaxy we live in:

Classify our galaxy according to the Hubble system:

Draw schematically the structure of our galaxy, sign the main elements. Determine the position of the Sun.

What are the names of the satellites of our galaxy?

How long does it take for light to pass through our galaxy along its diameter?

What objects are the constituent parts of galaxies?

Classify the objects of our galaxy by photographs:

What objects are the constituent parts of the universe?

Universe

Which galaxies make up the population of the Local Group?

What is the activity of galaxies?

What are quasars and how far from Earth are they?

Describe what is seen in the photographs:

Does the cosmological expansion of the Metagalaxy affect the distance from the Earth...

to the moon; □

To the center of the Galaxy; □

To the galaxy M31 in the constellation Andromeda; □

To the center of the local cluster of galaxies □

Name three possible variants of the development of the Universe according to Friedman's theory.

Bibliography

Main:

Klimishin I.A., "Astronomy-11". - Kyiv, 2003

Gomulina N. "Open Astronomy 2.6" CD - Physicon 2005

Workbook on astronomy / N.O. Gladushina, V.V. Kosenko. - Lugansk: Educational book, 2004. - 82 p.

Additional:

Vorontsov-Velyaminov B. A.
"Astronomy" Textbook for the 10th grade of high school. (Ed. 15th). - Moscow "Enlightenment", 1983.

Perelman Ya. I. "Entertaining astronomy" 7th ed. - M, 1954.

Dagaev M. M. "Collection of problems in astronomy." - Moscow, 1980.

Complex of practical works

in the discipline Astronomy

LIST OF PRACTICAL WORKS

Practical work No. 1

Subject:Starry sky. Celestial coordinates.

Objective:Acquaintance with the starry sky, solving problems under the conditions of visibility of constellations and determining their coordinates.

Equipment: mobile map of the starry sky.

Theoretical justification

celestial sphere an imaginary auxiliary sphere of arbitrary radius is called, on which all the luminaries are projected as they are seen by the observer at a certain moment in time from a certain point in space.

Points of intersection of the celestial sphere with plumb line passing through its center are called: the upper point - zenith (z), bottom point - nadir (z¢). The great circle of the celestial sphere, the plane of which is perpendicular to the plumb line, is called mathematical, or true horizon(Fig. 1).

Tens of thousands of years ago, it was noticed that the apparent rotation of the sphere occurs around some invisible axis. In fact, the apparent rotation of the sky from east to west is a consequence of the rotation of the Earth from west to east.

The diameter of the celestial sphere around which it rotates is called axis of the world. The axis of the world coincides with the axis of rotation of the Earth. The points of intersection of the axis of the world with the celestial sphere are called the poles of the world(Fig. 2).

Rice. 2 . Celestial sphere: geometrically correct image in orthogonal projection

The angle of inclination of the axis of the world to the plane of the mathematical horizon (the height of the pole of the world) is equal to the angle of the geographic latitude of the area.

The great circle of the celestial sphere, the plane of which is perpendicular to the axis of the world, is called celestial equator (QQ¢).

The great circle passing through the celestial poles and zenith is called celestial meridian (PNQ¢ Z¢ P¢ SQZ).

The plane of the celestial meridian intersects with the plane of the mathematical horizon along a straight noon line, which intersects with the celestial sphere at two points: north (N) and south (S).

The celestial sphere is divided into 88 constellations, differing in area, composition, structure (the configuration of bright stars that form the main pattern of the constellation) and other features.

Constellation- the main structural unit of the division of the starry sky - a section of the celestial sphere within strictly defined boundaries. The composition of the constellation includes all the luminaries - projections of any space objects (Sun, Moon, planets, stars, galaxies, etc.) observed at a given time in a given section of the celestial sphere. Although the position of individual bodies on the celestial sphere (the Sun, Moon, planets and even stars) changes over time, the mutual position of the constellations on the celestial sphere remains constant.

ecliptic ( rice. 3). The direction of this slow movement (about 1 per day) is opposite to the direction of the daily rotation of the Earth.

Fig.3 . The position of the ecliptic on the celestial sphere

e points of spring(^) and autumn(d) equinoxes

solstice points

On the map, the stars are shown as black dots, the sizes of which characterize the brightness of the stars, the nebulae are indicated by dashed lines. The North Pole is shown in the center of the map. Lines emanating from the north celestial pole show the location of the circles of declination. On the map, for the two nearest declination circles, the angular distance is 2 hours. The celestial parallels are plotted through 30. With their help, the declination of the luminaries is counted. The points of intersection of the ecliptic with the equator, for which the right ascension is 0 and 12 hours, are called the points of the spring and autumn equinoxes, respectively. Months and dates are marked along the edge of the star chart, and hours are on the overlaid circle.

To determine the position of the celestial body, it is necessary to combine the month and date indicated on the star chart with the hour of observation on the overlay circle.

On the map, the zenith is located near the center of the notch, at the point of intersection of the thread with the celestial parallel, the declination of which is equal to the geographical latitude of the place of observation.

Working process

1. Install a mobile map of the starry sky for the day and hour of observation and name the constellations located in the southern part of the sky from the horizon to the pole of the world, in the east - from the horizon to the pole of the world.

2. Find the constellations located between the points of the west and north on October 10 at 21 o'clock.

3. Find the constellations on the star map, with the nebulae indicated in them, and check whether they can be observed with the naked eye.

4. Determine if the constellations of Virgo, Cancer, Libra will be visible at midnight on September 15th. Which constellation at the same time will be near the horizon in the north.

5. Determine which of the listed constellations: Ursa Minor, Bootes, Charioteer, Orion - for a given latitude, the places will not be set.

6. Answer the question: can Andromeda be at its zenith for your latitude on September 20?

7. On the map of the starry sky, find five of any of the listed constellations: Ursa Major, Ursa Minor, Cassiopeia, Andromeda, Pegasus, Cygnus, Lyra, Hercules, Northern Crown - determine approximately the coordinates (celestial) - declination and right ascension of the stars of these constellations.

8. Determine which constellation will be near the horizon on May 05 at midnight.

test questions

1. What is called a constellation, how are they depicted on a map of the starry sky?

2. How to find the North Star on the map?

3. Name the main elements of the celestial sphere: horizon, celestial equator, axis of the world, zenith, south, west, north, east.

4. Define the coordinates of the star: declination, right ascension.

Primary Sources (MI)

Practical work No. 2

Subject: Time measurement. Determination of geographic longitude and latitude

Objective: Determination of the geographical latitude of the place of observation and the height of the star above the horizon.

Equipment: model

Theoretical justification

The apparent annual movement of the Sun against the background of stars occurs along a large circle of the celestial sphere - ecliptic ( rice. one). The direction of this slow movement (about 1 per day) is opposite to the direction of the daily rotation of the Earth.

Rice. 1. The position of the ecliptic on the celestial spheres

The axis of rotation of the earth has a constant angle of inclination to the plane of revolution of the earth around the sun, equal to 66 33. As a result, the angle e between the plane of the ecliptic and the plane of the celestial equator for an earthly observer is: e\u003d 23 26 25.5. The points of intersection of the ecliptic with the celestial equator are called points of spring(γ) and autumn(d) equinoxes. The point of the vernal equinox is in the constellation of Pisces (until recently - in the constellation of Aries), the date of the vernal equinox is March 20 (21). The autumnal equinox is in the constellation Virgo (until recently in the constellation Libra); the date of the autumnal equinox is September 22 (23).

Points that are 90° from the vernal equinox are called solstice points. The summer solstice falls on June 22, the winter solstice on December 22.

one. " stellar» the time associated with the movement of stars on the celestial sphere is measured by the hour angle of the vernal equinox point: S = t γ ; t = S - a

2. " solar"Time associated: with the apparent movement of the center of the Sun's disk along the ecliptic (true solar time) or the movement of the "average Sun" - an imaginary point moving uniformly along the celestial equator in the same time interval as the true Sun (average solar time).

With the introduction in 1967 of the atomic time standard and the International SI system, the atomic second is used in physics.

Second- physical quantity numerically equal to 9192631770 periods of radiation corresponding to the transition between hyperfine levels of the ground state of the cesium-133 atom.

Day- the period of time during which the Earth makes one complete rotation around its axis relative to any landmark.

sidereal day- the period of rotation of the Earth around its axis relative to the fixed stars, is defined as the time interval between two successive upper climaxes of the vernal equinox.

true solar day- the period of rotation of the Earth around its axis relative to the center of the solar disk, defined as the time interval between two successive climaxes of the same name of the center of the solar disk.

Mean solar day - the time interval between two successive climaxes of the same name of the mean Sun.

During their daily movement, the luminaries cross the celestial meridian twice. The moment of crossing the celestial meridian is called the culmination of the luminary. At the moment of the upper climax, the luminary reaches its greatest height above the horizon. If we are at northern latitudes, then the height of the pole of the world above the horizon (angle pon): h p = φ. Then the angle between the horizon ( NS ) and the celestial equator ( QQ 1 ) will be equal to 180°- φ - 90°= 90° - φ . if the luminary culminates south of the horizon, then the angle MOS, which expresses the height of the luminary M at the climax, is the sum of two angles: Q 1 OS and MOQ 1 .the value of the first of them we have just determined, and the second is nothing more than the declination of the luminary M equal to δ.

Thus, the height of the luminary at the culmination:

h \u003d 90 ° - φ + δ.

If δ, then the upper climax will occur above the northern horizon at a height

h = 90°+ φ - δ.

These formulas are also valid for the Southern Hemisphere of the Earth.

Knowing the declination of the luminary and determining from observations its height at the culmination, one can find out the geographical latitude of the place of observation.

Working process

1. Learn the basic elements of the celestial sphere.

2. Complete tasks

Exercise 1. Determine the declination of the star whose upper culmination was observed in Moscow (geographic latitude 56°) at an altitude of 47° above the south point.

Task 2. What is the declination of the stars that culminate at the zenith; at a point south?

Task 3. The geographical latitude of Kyiv is 50°. At what height in this city does the upper climax of the star Antares occur, the declination of which is - 26 °?

Task 5. At what latitude is the Sun at noon at its zenith on March 21, June 22?

Task 6. The noon altitude of the sun is 30° and its declination is 19°. Determine the geographic latitude of the observation site.

Task 7. Determine the position of the Sun on the ecliptic and its equatorial coordinates today. To do this, it is enough to mentally draw a straight line from the pole of the world to the corresponding date on the edge of the map. (attach a ruler). The sun should be located on the ecliptic at the point of its intersection with this line.

1. Write the number, topic and purpose of the work.

2. Complete the tasks in accordance with the instructions, describe the results obtained for each task.

3. Answer security questions.

test questions

1. At what points does the celestial equator intersect with the horizon line?

2. what circle of the celestial sphere do all the luminaries cross twice a day?

3. At what point on the globe is not a single star of the Northern celestial hemisphere visible?

4. Why does the midday height of the Sun change throughout the year?

Primary Sources (MI)

OI1 Vorontsov-Velyaminov, B. A. Strout E. K. Textbook “Astronomy. A basic level of. Grade 11". M.: Bustard, 2018

Practical work No. 3

Subject:Determining Mean Solar Time and the height of the Sun at the culminations

Objective: To study the annual movement of the Sun across the sky. Determine the height of the sun at the culmination.

Equipment: model of the celestial sphere, a moving map of the starry sky.

Theoretical justification

The sun, like other stars, describes its path through the celestial sphere. Being in the middle latitudes, we can watch every morning how it appears from behind the horizon in the eastern part of the sky. Then it gradually rises above the horizon and, finally, at noon reaches its highest position in the sky. After that, the Sun gradually descends, approaching the horizon, and sets in the western part of the sky.

Even in ancient times, people who watched the movement of the Sun across the sky discovered that its midday height changes over the course of the year, as does the appearance of the starry sky.

If during the year we daily mark the position of the Sun on the celestial sphere at the moment of its climax (that is, indicate its declination and right ascension), then we will get a large circle representing the projection of the apparent path of the center of the solar disk during the year. This circle was called by the ancient Greeksecliptic , which translates as ‘eclipse ’.

Of course, the movement of the Sun against the background of stars is an apparent phenomenon. And it is caused by the rotation of the Earth around the Sun. That is, in fact, in the plane of the ecliptic lies the path of the Earth around the Sun - its orbit.

We have already talked about the fact that the ecliptic crosses the celestial equator at two points: at the vernal equinox (ram point) and at the autumn equinox (balance point) (Fig. 1)

Figure 1. Celestial sphere

In addition to the equinoxes, two more intermediate points are distinguished on the ecliptic, at which the declination of the Sun is greatest and least. These points are called pointssolstice. AT summer solstice point (it is also called the point of cancer) The sun has a maximum declination - +23 about 26'. AT winter solstice point (point of Capricorn) the declination of the Sun is minimal and is -23 about 26'.

The constellations that the ecliptic passes through are namedecliptic.

Even in Ancient Mesopotamia, it was noticed that the Sun, with its apparent annual movement, passes through 12 constellations: Aries, Taurus, Gemini, Cancer, Leo, Virgo, Libra, Scorpio, Sagittarius, Capricorn, Aquarius and Pisces. Later, the ancient Greeks called this beltBelt of the Zodiac. Literally, it translates as "a circle of animals." Indeed, if you look at the names of the zodiac constellations, it is easy to see that half of them in the classical Greek zodiac are represented in the form of animals (in addition to mythological creatures).

Initially, the ecliptic signs of the zodiac coincided with the zodiac, since there was no clear separation of the constellations yet. The beginning of the countdown of the signs of the zodiac was established from the point of the vernal equinox. And the zodiac constellations divided the ecliptic into 12 equal parts.

Now the zodiac and ecliptic constellations do not coincide: there are 12 zodiac constellations, and 13 ecliptic constellations (the constellation Ophiuchus is added to them, in which the Sun is from November 30 to December 17. In addition, due to the precession of the earth's axis, the points of the spring and autumn equinoxes constantly shifting (Fig. 2).

Figure 2. Ecliptic and zodiac constellations

Precession (or precession of the equinoxes) - this is a phenomenon that occurs due to the slow wobble of the earth's axis of rotation. In this cycle, the constellations go in the opposite direction, compared to the usual annual cycle. In this case, it turns out that the vernal equinox approximately every 2150 years is shifted by one sign of the zodiac in a clockwise direction. So from 4300 to 2150 BC, this point was located in the constellation Taurus (the era of Taurus), from 2150 BC to 1 AD - in the constellation Aries. Accordingly, now, the vernal equinox is in Pisces.

As we have already mentioned, the day of the vernal equinox (around March 21) is taken as the beginning of the movement of the Sun along the ecliptic. The daily parallel of the Sun, under the influence of its annual motion, is continuously shifted by a step of declination. Therefore, the general movement of the Sun in the sky occurs as if in a spiral, which is the result of the addition of daily and annual movement. So, moving in a spiral, the Sun increases its declination by about 15 minutes a day. At the same time, the duration of daylight hours in the Northern Hemisphere is growing, while in the Southern Hemisphere it is decreasing. This increase will continue until the declination of the Sun reaches +23 about 26 ', which will happen around June 22, on the day of the summer solstice (Fig. 3). The name "solstice" is due to the fact that at this time (about 4 days) the Sun practically does not change its declination (that is, it seems to be "standing").

Figure 3. The motion of the Sun as a result of the addition of daily and annual motion

After the solstice, a decrease in the declination of the Sun follows and the long day begins to gradually decrease until day and night are equal (that is, until about September 23).

After 4 days, for an observer in the Northern Hemisphere, the declination of the Sun will begin to gradually increase and, after about three months, the luminary will again come to the vernal equinox.

Now let's move to the North Pole (Fig. 4). Here, the daily motion of the Sun is almost parallel to the horizon. Therefore, for half a year the Sun does not set, describing circles above the horizon - a polar day is observed.

Six months later, the declination of the Sun will change its sign to minus, and the polar night will begin at the North Pole. It will also last about six months. After the solstice, a decrease in the declination of the Sun follows and the long day begins to gradually decrease until day and night are equal (that is, until about September 23).

After passing the autumn equinox, the Sun changes its declination to the south. In the Northern Hemisphere, the day continues to decrease, while in the Southern Hemisphere, on the contrary, it increases. And this will continue until the Sun reaches the winter solstice (until about December 22). Here the Sun again for about 4 days will practically not change its declination. At this time, the northern hemisphere experiences the shortest days and longest nights. In the South, on the contrary, summer is in full swing and the longest day.

Figure 4. Daily movement of the Sun at the pole

Let's move to the equator (Fig. 5). Here our Sun, like all other luminaries, rises and sets perpendicular to the plane of the true horizon. Therefore, at the equator, day is always equal to night.

Figure 5. Daily movement of the Sun at the equator

Now let's turn to the sky map and work with it a little. So, we already know that a star map is a projection of the celestial sphere onto a plane with objects plotted on it in the equatorial coordinate system. Recall that in the center of the map is the north pole of the world. Next to him is the North Star. The grid of equatorial coordinates is represented on the map by rays radiating from the center and concentric circles. On the edge of the map, next to each ray, are written numbers denoting right ascension (from zero to twenty-three hours).

As we said, the apparent annual path of the Sun among the stars is called the ecliptic. On the map, it is represented by an oval, which is somewhat offset relative to the North Pole of the world. The intersection points of the ecliptic with the celestial equator are called the points of the spring and autumn equinoxes (they are indicated by the symbols of the ram and scales). The other two points - the points of the summer and winter solstices - are indicated on our map by a circle and a rhombus, respectively.

In order to be able to determine the time of sunrise and sunset or planets, you must first put their position on the map. For the Sun, this is not a big deal: it is enough to attach a ruler to the North Pole of the world and a stroke of a given date. The point of intersection of the ruler with the ecliptic will show the position of the Sun on that date. Now let's use the mobile map of the starry sky to determine the equatorial coordinates of the Sun, for example, on October 18th. And also find the approximate time of its sunrise and sunset on this date.

Figure 6. The apparent path of the Sun at different times of the year

Due to the changing declination of the Sun and Moon, their daily paths change all the time. The midday height of the sun also changes daily. It is easy to determine by the formula

h = 90° - φ + δ Ͽ

With a change in δ Ͽ, the points of sunrise and sunset also change (Fig. 6). In summer, in the middle latitudes of the northern hemisphere of the Earth, the Sun rises in the northeastern part of the sky and sets in the northwestern part of the sky, and in winter it rises in the southeast and sets in the southwest. The high altitude of the climax of the Sun and the long duration of the day are the cause of the onset of summer.

During the summer in the Earth's southern hemisphere at mid-latitudes, the Sun rises in the southeast, culminates in the northern side of the sky, and sets in the southwest. At this time, it is winter in the northern hemisphere.

Working process

1. Study the movement of the Sun at different times of the year and at different latitudes.

2. Study from pictures 1-6 equinoxes, points at which the declination of the sun is greatest and least (points solstice).

3. Complete tasks.

Exercise 1. Describe the movement of the Sun from March 21 to June 22 at northern latitudes.

Task 2. Describe with duck movement of the Sun at the pole.

Task 3. Where does the Sun rise and set in winter in the southern hemisphere (i.e. when is summer in the northern hemisphere)?

Task 4. Why does the sun rise high above the horizon in summer and low in winter? Explain this, based on the nature of the movement of the Sun along the ecliptic.

Task 5. Solve the problem

Determine the height of the upper and lower culminations of the Sun on March 8 in your city. Sun declination δ Ͽ = -5°. (The latitude of your city φ is determined from the map).

1. Write the number, topic and purpose of the work.

2. Complete the tasks in accordance with the instructions, describe the results obtained for each task.

3. Answer security questions.

test questions

1. How does the Sun move for an observer at the pole?

2. When is the Sun at its zenith at the equator?

3. The northern and southern polar circles have a latitude of ±66.5°. What are these latitudes?

Primary Sources (MI)

OI1 Vorontsov-Velyaminov, B. A. Strout E. K. Textbook “Astronomy. A basic level of. Grade 11". M.: Bustard, 2018

Practical work No. 4

Subject: Application of Kepler's laws in solving problems.

Objective: Determining the sidereal periods of planets using Kepler's laws.

Equipment: model celestial sphere, a moving map of the starry sky.

Theoretical justification

Sidereal(stellar T

synodic S

For the lower (inner) planets:

For the upper (outer) planets:

The length of the mean solar day s for the planets of the solar system depends on the sidereal period of their rotation around its axis t, direction of rotation and sidereal period of revolution around the Sun T.

Figure 1. Movement of the planets around the Sun

The planets move around the Sun in ellipses (Fig. 1). An ellipse is a closed curve, a remarkable property of which is the constancy of the sum of distances from any point to two given points, called foci. The line segment connecting the most distant points of the ellipse is called its major axis. The average distance of the planet from the sun is equal to half the length of the major axis of the orbit.

Kepler's laws

1. All the planets of the solar system revolve around the sun in elliptical orbits, in one of the focuses of which is the sun.

2. Radius - the vector of the planet describes equal areas for equal periods of time, the speed of the planets is maximum at perihelion and minimum at aphelion.

Figure 2. Description of the areas during the movement of the planet

3. The squares of the periods of revolution of the planets around the Sun are related to each other as the cubes of their average distances from the Sun

Working process

1. Study the laws of planetary motion.

2. Indicate the trajectory of the planets in the figure, indicate the points: perihelion and aphelion.

3. Complete tasks.

Exercise 1. Prove that the conclusion follows from Kepler's second law: the planet, moving along its orbit, has a maximum speed at the closest distance from the Sun, and a minimum - at the greatest distance. How does this conclusion agree with the law of conservation of energy.

Task 2. Comparing the distance from the Sun to other planets with their periods of revolution (see Table 1.2), check the fulfillment of Kepler's third law

Task 3. Solve the problem

Task 4. Solve the problem

The synodic period of the outer minor planet is 500 days. Determine the semi-major axis of its orbit and the sidereal period of revolution.

1. Write the number, topic and purpose of the work.

2. Complete the tasks in accordance with the instructions, describe the results obtained for each task.

3. Answer security questions.

test questions

1. Formulate Kepler's laws.

2. How does the speed of the planet change as it moves from aphelion to perihelion?

3. At what point in the orbit does the planet have maximum kinetic energy; maximum potential energy?

Primary Sources (MI)

OI1 Vorontsov-Velyaminov, B. A. Strout E. K. Textbook “Astronomy. A basic level of. Grade 11". M.: Bustard, 2018

The main characteristics of the planets of the solar system Table 1

Diameter (Earth = 1)

0,382

0,949

0,532

11,209

9,44

4,007

3,883

Diameter, km

4878

12104

12756

6787

142800

120000

51118

49528

Mass (Earth = 1)

0,055

0,815

0,107

318

Mean distance from the Sun (AU)

0,39

0.72

1.52

5.20

9.54

19.18

30.06

Orbital period (Earth years)

0.24

0.62

1.88

11.86

29.46

84.01

164,8

Orbital eccentricity

0,2056

0,0068

0,0167

0,0934

0.0483

0,0560

0,0461

0,0097

Orbital speed (km/sec)

47.89

35.03

29.79

24.13

13.06

9.64

6,81

5.43

Period of rotation around its axis (in Earth days)

58.65

243

1.03

0.41

0.44

0.72

0.72

Axis tilt (degrees)

0.0

177,4

23.45

23.98

3.08

26.73

97.92

28,8

Average surface temperature (C)

180 to 430

465

89 to 58

82 to 0

150

170

200

210

Gravity at the equator (Earth = 1)

0,38

0.9

0,38

2.64

0.93

0.89

1.12

Space velocity (km/sec)

4.25

10.36

11.18

5.02

59.54

35.49

21.29

23.71

Average density (water = 1)

5.43

5.25

5.52

3.93

1.33

0.71

1.24

1.67

Composition of the atmosphere

No

CO 2

N 2 + O 2

CO 2

H 2 + Not

H 2 + Not

H 2 + Not

H 2 + Not

Number of satellites

Rings

No

No

No

No

Yes

Yes

Yes

Yes

Some physical parameters of the planets of the solar system Table 2

Distance from the Sun

radius, km

number of earth radii

weight, 10 23 kg

mass relative to the earth

average density, g / cm 3

orbital period, number of Earth days

period of revolution around its axis

number of satellites (moons)

albedo

acceleration of gravity at the equator, m/s 2

separation speed from the planet's gravity, m/s

presence and composition of the atmosphere, %

average surface temperature, °C

million km

a.u.

The sun

695 400

109

1.989×10 7

332,80

1,41

25-36

618,0

Is absent

5500

Mercury

57,9

0,39

2440

0,38

3,30

0,05

5,43

59 days

0,11

3,70

4,4

Is absent

240

Venus

108,2

0,72

6052

0,95

48,68

0,89

5,25

244

243 days

0,65

8,87

10,4

CO 2, N 2, H 2 O

480

Earth

149,6

1,0

6371

1,0

59,74

1,0

5,52

365,26

23 h 56 min 4s

0,37

9,78

11,2

N 2, O 2, CO 2, A r, H 2 O

Moon

150

1,0

1738

0,27

0,74

0,0123

3,34

29,5

27 h 32 min

0,12

1,63

2,4

Very discharged

Mars

227,9

1,5

3390

0,53

6,42

0,11

3,95

687

24 h 37 min 23 s

0,15

3,69

5,0

CO 2 (95.3), N 2 (2.7),
BUT r (1,6),
O 2 (0.15), H 2 O (0.03)

Jupiter

778,3

5,2

69911

18986,0

318

1,33

11.86 years old

9 h 30 min 30 s

0,52

23,12

59,5

H (77), He (23)

128

Saturn

1429,4

9,5

58232

5684,6

0,69

29.46 years old

10 h 14 min

0,47

8,96

35,5

N, Not

170

Uranus

2871,0

19,2

25 362

4

868,3

17

1,29

84.07 years

11 h3

20

0,51

8,69

21,3

H (83),
Not (15), CH 4 (2)

-143

Neptune

4504,3

30,1

24 624

4

1024,3

17

1,64

164.8 years

16h

8

0,41

11,00

23,5

H, He, CH 4

-155

Pluto

5913,5

39,5

1151

0,18

0,15

0,002

2,03

247,7

6.4 days

1

0,30

0,66

1,3

N 2 , CO, NH 4

-210

Practical work No. 5

Subject: Determination of the synodic and sidereal period of revolutions of the luminary

Objective: synodic and sidereal circulation periods.

Equipment: celestial sphere model.

Theoretical justification

Sidereal(stellar) the period of revolution of the planet is the time interval T , for which the planet makes one complete revolution around the Sun in relation to the stars.

synodic The period of revolution of a planet is the period of time S between two successive configurations of the same name.

synodic period is equal to the time interval between any two or any other two identical successive phases. The period of a complete change of all lunar phases from novolu The period before the new moon is called the synodic period of revolution of the moon or the synodic month, which is approximately 29.5 days. It is during this time that the Moon travels such a path along its orbit that it has time to go through the same phase twice.
A full revolution of the Moon around the Earth relative to the stars is called the sidereal period of revolution or sidereal month, it lasts 27.3 days.

The formula for the relationship between the sidereal periods of revolution of two planets (we take the Earth for one of them) and the synodic period S of one relative to the other:

For the lower (inner) planets : - = ;

For upper (outer) planets : - = , where

P is the sidereal period of the planet;

T is the sidereal period of the Earth;

S is the synodic period of the planet.

Sidereal period of circulation (from sidus, star; genus. case sideris) - the period of time during which any celestial satellite body makes a complete revolution around the main body relative to the stars. The concept of "sidereal period of revolution" is applied to bodies circulating around the Earth - the Moon (sidereal month) and artificial satellites, as well as to planets circling the Sun, comets, etc.

The sidereal period is also called . For example, the Mercury year, the Jupiter year, etc. At the same time, one should not forget that several concepts can be called the word "". So, one should not confuse the terrestrial sidereal year (the time of one revolution of the Earth around the Sun) and (the time during which all the seasons change), which differ from each other by about 20 minutes (this difference is mainly due to the earth's axis). Tables 1 and 2 present data on the synodic and sidereal periods of the planets. The table also includes figures for the Moon, main belt asteroids, dwarf planets, and Sedna..

ssyntable 1

Table 1. Synodic period of the planets(\displaystyle (\frac (1)(S))=(\frac (1)(T))-(\frac (1)(Z)))

309.88 years

557 years

12,059 years

Working process

1. Study the laws of the relationship between the synodic and sidereal periods of the planets.

2. Study the trajectory of the Moon in the figure, indicate the synodic and sidereal months.

3. Complete tasks.

Exercise 1. Determine the sidereal period of the planet if it is equal to the synodic period. Which real planet in the solar system is closest to this condition?

Task 2. The largest asteroid, Ceres, has a sidereal orbital period of 4.6 years. Calculate the synodic period and express it in years and days.

Task 3. An asteroid has a sidereal period of about 14 years. What is the synodic period of its circulation?

Report content

1. Write the number, topic and purpose of the work.

2. Complete the tasks in accordance with the instructions, describe the results obtained for each task.

3. Answer security questions.

test questions

1. What period of time is called the sidereal period?

2. What are the synodic and sidereal months of the Moon?

3. After what period of time do the minute and hour hands meet on the watch dial?

Primary Sources (MI)

OI1 Vorontsov-Velyaminov, B. A. Strout E. K. Textbook “Astronomy. A basic level of. Grade 11". M.: Bustard, 2018