How to determine the midday height of the sun. §5.2

The great circle of the ecliptic intersects the great circle of the celestial
equator at an angle of 23°27" per day summer solstice, 22 June-
nya, the Sun rises at noon above the horizon above the point at
which the celestial equator intersects the meridian by this amount
(Fig. 17). The Sun is the same amount below the equator per day
winter solstice, December 22. Thus, the height of the Sun
Tsa at the upper culmination changes during the year by 46°54".

It is clear that at midnight at the upper climax there is a zodiac-
constellation opposite to the one in which the Sun is located
tse. For example, in March the Sun passes through the constellation Pisces, and in
midnight culminates in the constellation Virgo. Figure 18 shows
daily paths of the Sun above the horizon on the days of the equinoxes and solar
cestoes for mid-latitudes (top) and the Earth's equator (bottom)

Rice. 18. Daily paths of the Sun above
horizon at different times
change of year during observation-
nias: a - in average geo-
graphic latitudes;
b - at the Earth's equator.

Rice. 19. Equatorial coordinates
naty.

2 1. Find the 12 zodiac constellations
on the star map and if possible
find some of them in the sky.
2. Using an eclimeter or gnomon
(known to you from physical geography
fii), measure at least once a month
the height of the Sun above the horizon is about
noon for several months.
By plotting the height change graph
Sun over time, you will get cri-
way, by which you can, for example,
apply part of the ecliptic to the sidereal
map, taking into account that the Sun is per month
shifts in the starry sky to the east
ku approximately 30°.

f .STAR CHARTS,

CELESTIAL COORDINATES
AND TIME

1. Maps and coordinates. To make
make a star map, depict-
finding constellations on a plane, you need
know the coordinates of the stars. Coor-
dinata of stars relative to the horizon
umbrella, for example height, although
visual, but unsuitable for co-
placing cards, since all the time
me are changing. Must be used
such a coordinate system that
would rotate along with the stars -
sky. It's called equa-
torial system. IN
one of its coordinates is
angular distance of the luminary from
celestial equator, called
declination b (Fig. 19). It's me-
varies within ±90° and is considered
positive to the north of the eq-
ator and negative - to the south.
Declination is similar to geo-
graphic breadth

The second coordinate is similar
geographic longitude and name
ascends straight
niem a.

Exactly spring
equinox

Right ascension of the luminary M
measured angle between planes
mi of the great circle drawn by the
rez the poles of the world and the given light
lo M, and a great circle, passing
passing through the poles of the world and the point
spring equinox (Fig. 19).
This angle is measured from the point ve-
autumnal equinox T against the move
clockwise when viewed from the north
the right pole. It changes from O
up to 360° and is called direct reproduction
divergence because the stars, divergence
placed on the celestial equator,
ascend in ascending order
right ascension. In the same
in a row they culminate one after another
homo. Therefore, a is usually expressed
Not V angular measure, and in time,

and proceed from the fact that in 1 hour the sky rotates by 15°, and in 4 minutes -
on G. Therefore, right ascension is 90°, otherwise it will be 6 hours, and
7 hours 18 minutes = 109°30/. In units of time along the edges of the sidereal
maps indicate right ascensions.

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

On one map you can depict only part of it without distortion
starry sky It is difficult for beginners to use such a map,
because they don't know which constellations are visible in given time
and how they are located relative to the horizon. More convenient to move
star map. The idea of ​​its device is simple. To the map
superimposed a circle with a cutout representing the horizon line. Cutout
horizon is eccentric, and when rotating the overhead circle in alignment
The image will show constellations located above the horizon at different
time. How to use such a card is described in Appendix VII.

3 1. Express 9 hours 15 minutes 11 seconds in degrees.

According to the coordinate table bright stars given in Appendix IV, find
on the star map some of the indicated stars.

Using the map, count the coordinates of several bright stars and check yourself:
using the table from Appendix IV.

Using the School Astronomical Calendar, find the coordinates of the planets
at a given time and determine from the map in which constellation they are located.
Find them in the sky in the evening.

Using a moving star chart, determine which zodiac signs
the constellations will be visible above the horizon on the evening of observation.

2. The height of the luminaries at the culmination. Let's find the relationship between you-
the hundredth h of the luminary M at the upper culmination, its declination 6
and latitude of the area f.

Rice. 20. Height of the luminary at the top
climax.

Figure 20 shows the plumb line ZZ", the axis of the world
PP" and projections of the celestial equator EQ and horizon line NS
(noon line) to the plane of the celestial meridian (PZSP"N)
The angle between the noon line NS and the world axis PP" is equal to
we know the latitude of the area

Obviously, the tilt of the plane

celestial equator to the horizon, measured by angle

equal (Fig. 20). Star M with declination 6, culminating
south of the zenith, has a height of + at its upper culmination

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

4 1. Sirius(A B. Psa, see Appendix IV) was at its highest climax on
height 10°. What is the latitude of the observation site?

For the following exercises geographical coordinates cities can
count on a geographical map.

At what altitude in Leningrad is the upper culmination of Antares
(A Scorpio, see Appendix IV)?

What is the declination of the stars that culminate at their zenith in your city?
at the point south?

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

3. Exact time. For measuring short periods of time
in astronomy the basic unit is the average duration
the number of solar days, i.e. the average period of time
between two upper (or lower) center climaxes
Sun. The average value must be used because
During the year, the duration of sunny days fluctuates slightly.
This is due to the fact that the Earth revolves around the Sun in a different direction.
in a circle, but in an ellipse and the speed of its movement is slightly
is changing. This causes slight unevenness in the visible
the movement of the Sun along the ecliptic during the year.

The moment of the upper culmination of the center of the Sun, as we have already said,
rili, is called true noon. But to check the clock,
to determine the exact time there is no need to mark them
precisely the moment of the culmination of the Sun. It is more convenient and accurate to mark mo-
ments of the climax of the stars, since the difference in the moments of climax
any star and sun is known exactly for any time.
Therefore, to determine the exact time using special
optical instruments mark the moments of stellar culminations and test
They indicate the correct operation of the clocks that “keep” time. Defining
the time obtained in this way would be absolutely accurate if
the observed rotation of the sky occurred with a strictly constant
angular speed. However, it turned out that the rotation speed
The Earth around its axis, and therefore the apparent rotation of the celestial

spheres, experiences very minor changes. Poe-
Therefore, to “save” exact time, special
al atomic clocks, the course of which is controlled by oscillatory
processes in atoms that occur at a constant frequency.
The clocks of individual observatories are checked against atomic signals.
time. Comparison of time determined by atomic clocks and
By visible movement stars, allows you to study the uneven
ity of the Earth's rotation.

Determination of exact time, its storage and transmission
dio to the entire population constitute the task of the precision service
time, which exists in many countries.

Precise time signals are received via radio by naval navigators.
go and air fleet, many scientific and industrial organizations
nizations that need to know the exact time. Know exactly
time is needed, in particular, to determine geographical debts
goth different items earth's surface.

In a given area, each star always culminates at the same height above the horizon, because its angular distance from the celestial pole and from the celestial equator remains unchanged. The Sun and Moon change the height at which they culminate. From this we can conclude that their position relative to the stars (declination) changes. We know that the Earth moves around the Sun, and the Moon around the Earth. Let's see how the position of both luminaries in the sky changes as a result.

If you use an accurate clock to notice the time intervals between the upper culminations of the stars and the Sun, then you can be convinced that the intervals between the culminations of the stars are four minutes shorter than the intervals between solar climaxes. This is explained by the fact that during one revolution around its axis (day), the Earth travels approximately 1/365 of its path around the Sun. It seems to us that the Sun is moving against the background of stars to the east - in the direction opposite to the daily rotation of the sky. This shift is about 1°. To turn this angle, celestial sphere another 4 minutes are needed, by which the culmination of the Sun is “delayed”. Thus, as a result of the movement of the Earth in its orbit, the Sun describes a large circle in the sky relative to the stars per year, called ecliptic(Fig. 17).

Since the Moon makes one revolution in line with the rotation of the sky in a month and therefore passes not 1°, but approximately 13° per day, its climaxes are delayed every day not by 4 minutes, but by 50 minutes.

When determining the height of the Sun at noon, we noticed that twice a year it occurs on the celestial equator, at the so-called equinox points. This happens in days spring And autumn equinox(around March 21 and around September 23). The horizon plane divides the celestial equator in half (Fig. 18). Therefore, on the days of the equinoxes, the paths of the Sun above and below the horizon are equal, therefore, the lengths of day and night are equal.

What is the declination of the Sun on the equinoxes?

Moving along the ecliptic, the Sun moves farthest away from the celestial equator on June 22 north pole world (at 23°27"). At noon for northern hemisphere On Earth, it is highest above the horizon (this amount is higher than the celestial equator, see Fig. 17 and 18). The longest day, it's called summer solstice.

The great circle of the ecliptic intersects the great circle of the celestial quator at an angle of 23°27". The Sun is the same amount below the quator in winter solstice day, December 22 (see Fig. 17 and 18). Thus, on this day the height of the Sun at the upper culmination decreases by 46°54" compared to June 22, and the day is the shortest. (From the course physical geography you know that differences in lighting conditions and heating of the Earth by the Sun determine its climatic zones and the change of seasons.)

The deification of the Sun in ancient times gave rise to myths describing periodically repeating events of the “birth”, “resurrection” of the “Sun God” throughout the year: the dying of nature in winter, its rebirth in spring, etc. Christian holidays bear traces of the cult of the Sun.

The path of the Sun runs through 12 constellations called zodiac(from the Greek word zoon - animal), and their totality is called the zodiac belt. It includes the following constellations: Fish, Aries,Taurus, Twins, Cancer, Lion, Virgo, Scales, Scorpion, Sagittarius, Capricorn,Aquarius. The Sun travels through each zodiac constellation for about a month. The vernal equinox point (one of the two intersections of the ecliptic with the celestial equator) is located in the constellation Pisces.

It is clear that at midnight the zodiacal constellation opposite to the one in which the Sun is located passes the upper culmination. For example, in March the Sun passes through the constellation Pisces, and at midnight it culminates in the constellation Virgo.

So, we are convinced that the apparent motion of the Moon, which revolves around the Earth, and the Sun, around which the Earth revolves, is detected and described in the same way. And based on these observations alone, it is impossible to decide whether the Sun moves around the Earth or the Earth moves around it.

Planets move against the background of the starry sky in a more complex way. They move in one direction or the other, sometimes slowly making loops (Fig. 19). This is due to the combination of their true motion with the motion of the Earth. In the starry sky, planets (translated from ancient Greek as “wandering”) do not occupy permanent place, just like the Moon and the Sun. Therefore, on a star chart the position of the Sun, Moon and planets can be indicated only for a certain moment.

Example of problem solution

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

Pay attention to how the difference in the midday heights of the Sun on the days of the solstices (for each city) is related to the difference in its declination on these dates.

Compare the difference in the height of the Sun on the same day in these two cities with the difference in their geographical latitudes. Draw a conclusion.

How, knowing on the day of the summer solstice the height of the Sun at noon in one of the cities, can one calculate its height in another city?

Exercise 4

1. At what latitude does the Sun culminate at its zenith on the day of the summer solstice?

2. On what days of the year does the Sun reach its zenith for an observer located at the earth’s equator?

3. Determine the geographic latitude of the point at which, on the day of the winter solstice, the culmination of the Sun occurs at the point of the south.

Task 3

1. Find the 12 zodiac constellations on the star map. Using a moving star chart, determine which of them will be visible above the horizon on the evening of observation.

2. Using the “School Astronomical Calendar”, find the coordinates of the planets at a given time and determine from the map in which constellation they are located. Find them in the evening sky.

Target: to develop the ability to navigate by the sun, determine the midday line, the height of the midday sun above the horizon.
Equipment: gnomon (flat pole 1-1.5 m long), vertical protractor-eclimeter or protractor with a plumb line, thin strip or piece of twine 2 m long.

Methodical recommendations
Throughout the year, the height of the sun above the horizon changes: on June 22 - on the day of the summer solstice - it occupies the highest position, on December 22 - on the day of the winter solstice - it is the lowest, and on the days of the equinox - March 21 and September 23 - the intermediate ones. In the Northern and Southern Hemispheres, the change in the height of the midday sun has the opposite direction.

Work progress

Task 1. Definition of the noon line.
On a flat area towards noon, install the gnomon vertically. Fix the end of the shadow falling from it with the first peg and a radius (point 1) equal to the length of the shadow and draw a circle with another peg. Watch carefully how the shadow shortens. After a certain time, the shadow will begin to lengthen and touch the circle a second time, but at a different point (point 2) (see Fig. 1).

Rice. 1. Determination of the noon line
In the second, drive a peg into this point. Stretch the twine from the first peg to the second peg. Find the middle of this segment. Drive in the third peg. Connect this peg with twine to the base of the gnomon. This will be the noon line, which shows the direction north and coincides with the local meridian. Check the compass direction.

Task 2. Determining the height of the sun above the horizon.
Install the rail so that one end rests against the base of the third peg, and the other rests on the upper end of the gnomon, forming an angle with the horizontal surface. Determine its value using an eclimeter or vertical goniometer. This will determine the height of the sun above the horizon at noon.

Task 3. Answer the questions.

1. How does the height of the sun above the horizon change during the day?
and year?

2. Determine the time of solar noon using your watch. Does noon (12 o'clock) coincide with solar time? Explain why.

Orientation in space

Target: teach techniques for orienting in space local characteristics and a compass.
Equipment: compass, measuring tape or 15-meter tape measure, mechanical wristwatch, school rangefinder, tablet.

Methodical recommendations
Orientation in space is the determination on the ground of one’s location or standing point relative to the sides of the horizon, surrounding terrain objects, as well as directions and distances of movement.

Orientation in space includes:
1) correlation of the real area with the plan and map;
2) determination on the ground of the sides of the horizon and one’s position in relation to terrain objects: locality, river, railway etc.;
3) determination of distances on the ground and their graphic expression on paper.
4) selection of the required direction of movement.

Work progress
Task 1. Determining the direction of the sides of the horizon using a compass.
The most accurate way of general orientation on the ground is orientation using a compass. In order to determine the direction of the horizon using a compass, you must do the following:
1. Remove all metal objects at a distance of 1-2 m from the compass;

2. Place the compass in a horizontal plane on your palm or tablet;

3. By rotating the compass in a horizontal plane, ensure that the northern end of the magnetic needle of the compass aligns with the letter C. In this position, the compass is oriented and now you can use it to determine the sides of the horizon.

Task 2. Orientation by the sun using a watch.
With the help of a mechanical wristwatch you can determine the direction of the north-south line in at the moment time. To do this you need to do the following:

1. place the watch in a horizontal plane and point the hour hand towards the sun;

2. mentally construct the angle between the small hour hand
and the number 11 on the watch dial. The bisector of this angle will be the local meridian.

Azimuth movement

Target: teach techniques for orienting in space and determining the direction of movement in azimuth.
Equipment: compass, measuring tape or 10-15 meter tape measure, mechanical wrist watch, school rangefinder, tablet.

Methodical recommendations
Using a compass, you can determine the sides of the horizon and the direction of movement in azimuth. Azimuth is the angle between the direction north and the direction towards a given object, which is measured clockwise.
For example, knowing that the azimuth from point A to point B is 45º (A = 45º), you, having oriented the compass, determine the azimuth and go in the right direction.
When moving, it is either given or determined. To determine the azimuth of movement from one point (standing point) to another, a map is needed.

To navigate the terrain, it is important to be able to determine not only the direction, but also the distance. Measure distance using various methods: counts of steps and movement time, visual, instrumental. Visual (by eye) assessment of distances is the observation of terrain objects and their visibility depending on the distance from the observer (see Table 1). This method allows you to determine the distance approximately; this requires constant training.

Table 1

Visual determination of distances

Distance	Observable objects
10 km	Pipes from large factories
5 km	General outlines of houses (without doors and windows)
4 km	The outlines of windows and doors are barely visible
2 km	Tall lonely trees; a person is a barely visible dot
1 500 m	Large cars on the road, a person is still visible as a dot
1 200 m	Individual trees average size
1,000 m	Telegraph poles; Individual logs are visible in the buildings
700 m	The figure of a man without details of clothing is already emerging
400 m	The movements of a person’s hands are noticeable, the color of clothing, the bindings on window frames vary
200 m	Head outline
150 m	Hands, eye line, clothing details
70 m	Eyes in the form of dots

Work progress

Task 1. Determination of azimuth 90º, 145º, 225º using a compass.
Walk a short distance in these directions. To
do not stray from the chosen direction of movement, write down noticeable objects in the area, these will be landmarks of the direction in which you should move.

Task 2. Determining the distance to selected terrain objects.
For precise definition distances in professional activity use tape measures, measuring tapes, theodolites, direction finders
and other tools. In everyday life, non-instrumental methods are used.
1. Select an object in an open area and visually determine the distance to it using Table 1.
2. To more accurately determine the distance by eye, you can use a technique that is based on a simple mathematical calculation. Let's take the ruler in our hand and point it at a distant object whose height you know, say 10 m. By moving the ruler in the fingers, we will achieve a position where a segment of the ruler, say 10 cm, completely covers this object. Determine the distance from the eye to the ruler. It is approximately 70 cm. Now you know three quantities, but
the distance to the object is not known. Let's create a formula in which the length of the ruler relates to the height of the object X in the same way as the length of an outstretched arm relates to the distance to the object. Let's solve the proportion:
10 m: X = 10 cm: 70 cm,
10 m: X = 0.1 m: 0.7 m,
X = 70 m.

This method is convenient to use when determining the distance to inaccessible objects located, for example, on the other side of the river.

Task 3. Measuring distance in steps.
You need to know your stride length. Set aside a 50 m long section on a flat piece of terrain. Walk this distance several times
and determine the arithmetic average number of steps.
For example, 71 + 74 + 72 = 217 steps. Total quantity divide the steps by 3 (217: 3 = 72). The average number of steps is 72. Divide 50 m by 72 steps and you get average length your step is approximately 55 cm.

You can measure the distance to any accessible object in steps. For example, if you took 690 steps, i.e. 55 cm × 690 = 37 m.
Record in your diary and compare the results of determining distances in different ways. Determine the degree of accuracy of each method.

Life on our planet depends on the quantity sunlight and warmth. It’s scary to imagine even for a moment what would have happened if there had not been such a star in the sky as the Sun. Every blade of grass, every leaf, every flower needs warmth and light, like people in the air.

The angle of incidence of the sun's rays is equal to the height of the sun above the horizon

The amount of sunlight and heat that reaches the earth's surface is directly proportional to the angle of incidence of the rays. The sun's rays can strike the Earth at an angle of 0 to 90 degrees. The angle of impact of the rays on the earth is different, because our planet is spherical. The larger it is, the lighter and warmer it is.

Thus, if the beam comes at an angle of 0 degrees, it only glides along the surface of the earth without heating it. This angle of incidence occurs in the Northern and South Poles, beyond the Arctic Circle. At right angles, the sun's rays fall on the equator and on the surface between the South and

If the angle of impact sun rays straight to the ground, this means that

Thus, the rays on the surface of the earth and the height of the sun above the horizon are equal. They depend on geographic latitude. The closer to zero latitude, the closer the angle of incidence of the rays is to 90 degrees, the higher the sun is above the horizon, the warmer and brighter it is.

How the sun changes its height above the horizon

The height of the sun above the horizon is not constant. On the contrary, it is always changing. The reason for this lies in the continuous movement of the planet Earth around the star Sun, as well as the rotation of the planet Earth around its own axis. As a result, day follows night, and seasons follow each other.

The territory between the tropics receives the most heat and light; here day and night are almost equal in duration, and the sun is at its zenith 2 times a year.

The surface above the Arctic Circle receives less heat and light; here there are such concepts as night, which last about six months.

Days of autumn and spring equinox

There are 4 main astrological dates, which are determined by the height of the sun above the horizon. September 23 and March 21 are the days of the autumn and spring equinox. This means that the height of the sun above the horizon in September and March on these days is 90 degrees.

Southern and are equally illuminated by the sun, and the length of the night is equal to the length of the day. When astrological autumn begins in the Northern Hemisphere, then in the Southern Hemisphere, on the contrary, it is spring. The same can be said about winter and summer. If in Southern Hemisphere winter, then in Northern - summer.

Days of summer and winter solstice

June 22 and December 22 are summer days and December 22 has the shortest day and longest night in the Northern Hemisphere, and the winter sun is at its lowest altitude above the horizon for the entire year.

Above latitude 66.5 degrees, the sun is below the horizon and does not rise. This phenomenon, when the winter sun does not rise to the horizon, is called polar night. The most short night happens at a latitude of 67 degrees and lasts only 2 days, and the longest happens at the poles and lasts 6 months!

December is the month of the entire year when the nights are longest in the Northern Hemisphere. People in Central Russia They wake up for work in the dark and return in the dark. This is a difficult month for many, as the lack of sunlight affects people's physical and mental well-being. For this reason, depression may even develop.

In Moscow in 2016, sunrise on December 1st will be at 08.33. In this case, the length of the day will be 7 hours 29 minutes. It will be very early, at 16.03. The night will be 16 hours 31 minutes. Thus, it turns out that the length of the night is 2 times greater than the length of the day!

This year the winter solstice is December 21st. The shortest day will last exactly 7 hours. Then the same situation will last for 2 days. And starting from December 24, the day will start to make a profit, slowly but surely.

On average, one minute of daylight will be added per day. At the end of the month, sunrise in December will be exactly 9 o'clock, which is 27 minutes later than December 1st

June 22 is the summer solstice. Everything happens exactly the opposite. For the entire year, this date is the longest day in duration and the shortest night. This applies to the Northern Hemisphere.

In Yuzhny it’s the other way around. There are interesting things associated with this day natural phenomena. A polar day begins above the Arctic Circle; the sun does not set below the horizon at the North Pole for 6 months. Mysterious white nights begin in St. Petersburg in June. They last from about mid-June for two to three weeks.

All these 4 astrological dates can change by 1-2 days, since the solar year does not always coincide with calendar year. Shifts also occur during leap years.

The height of the sun above the horizon and climatic conditions

The sun is one of the most important climate-forming factors. Depending on how the height of the sun above the horizon over a specific area of ​​the earth’s surface changed, the climatic conditions and seasons.

For example, in the Far North, the sun's rays fall at a very small angle and only glide along the surface of the earth, without heating it at all. Due to this factor, the climate here is extremely harsh, there is permafrost, cold winters with freezing winds and snow.

The higher the sun's height above the horizon, the warmer the climate. For example, at the equator it is unusually hot and tropical. Seasonal fluctuations are also practically not felt in the equator region; in these areas there is eternal summer.

Measuring the height of the sun above the horizon

As they say, everything ingenious is simple. So it is here. The device for measuring the height of the sun above the horizon is simply simple. It is a horizontal surface with a pole in the middle 1 meter long. On a sunny day at noon, the pole casts its shortest shadow. With the help of this shortest shadow, calculations and measurements are carried out. You need to measure the angle between the end of the shadow and the segment connecting the end of the pole to the end of the shadow. This angle value will be the angle of the sun above the horizon. This device is called a gnomon.

Gnomon is an ancient astrological tool. There are other instruments for measuring the height of the sun above the horizon, such as the sextant, quadrant, and astrolabe.

At true noon, use a protractor to measure the height of the Sun hc. When using a gnomon, the height of the Sun is determined by the formula

tgh c = AB – penumbra length; BC – height of the gnomon

Explanations: redraw the drawing, indicate the angle corresponding to the specified height, use a tree (building) as a segment BC known height, measure segment AC along the shadow in steps. Formulate the solution in the form of a table, where you enter the values ​​​​of the quantities and make calculations.

Calculate the latitude of the area using the formula

φ = 90 0 – h s – δ s

where δ с is the declination of the Sun on the date of observation (determined by the astronomical calendar or by the position of the Sun on the ecliptic of the star chart), h с taken from the previous task.

Explanations: formulate it as a task using given.

Draw conclusions (compare the obtained data φ with the data geographical map and justify the possibility of determining the geographic latitude of an area using this method; explain the reason for the change in the height of the Sun)

Observing sunspots

Draw a drawing of the surface of the Sun's photosphere with groups of spots.

Determine the activity of the Sun using the formula

where W is the relative Wolf number; g – number of groups of spots; f – number of individual spots

Explanations: the solution should be presented in the form of a table with the entered values ​​of quantities and calculations.

Draw conclusions about the activity of the Sun at the present time. Analyze the activity of the Sun in previous years, now and give a forecast of activity for the next 1 - 2 years, build a graph of the Wolf number versus time, starting from 2000 to 2020

Explanations: redraw the schedule, mark the indicated period.

Determination of the noon line by the movement of the sunspot

The method is as follows. In one of the windows facing south, a screen with a small hole (about 1 cm in diameter) is installed at a suitable height. Starting observation 1.5 - 2 hours before noon, mark the position of the sunspot from this hole on the floor within 3-4 hours. The result will be line AB (Fig. 53). Holding the thread at hole 0, its other end describes an arc (dashed line) that will intersect line AB at points C and D. From these points, two notches of equal radius are made and points E and F are obtained. Line EF will be the noon line. Make a drawing, fixing the position of the sun spot on the floor every 15 minutes.

It should be noted that the curve that it describes during the day sunspot, varies depending on the declination of the Sun. On the days of the equinoxes it is a straight line, with positive declinations of the Sun (from March 21 to September 23) the curves are hyperbolas, convex from the base, and with negative declinations (from September 23 to March 21) - convex to the base.

Explanations: Redraw the drawing, add the necessary constructions described in the method and label the resulting noon line

Draw conclusions, justifying the considered method of finding the noon line. What other methods can you use to determine the noon line? practical significance has the location of the noon line.