If a measure every day at what angle the Sun rises above the horizon at noon - this angle is called noon - then you can see that it is not the same in different days and much more in summer than in winter. This can be judged without any goniometric instrument, simply by the length of the shadow cast by the pole at noon: the shorter the shadow, the greater the noon height, and the longer the shadow, the smaller the noon height. On June 22, in the Northern Hemisphere, the noon height of the Sun is at its highest. It is the longest day of the year in this half of the Earth. It is called the summer solstice. Several days in a row midday height sun changes extremely little (hence the expression "solstice"), and therefore and the length of the day also hardly changes.

Six months later, December 22, - the day winter solstice in the Northern Hemisphere. Then the midday height of the Sun is the smallest and the day is the shortest. Again, for several days in a row, the noon height of the Sun changes extremely slowly and the length of the day hardly changes. The difference between the midday heights of the Sun on June 22 and December 22 is 47°. There are two days in a year when the noon height of the Sun is exactly 2301/2 lower than on the day of the summer solstice, and by the same amount higher than on the day of the winter solstice. This happens on March 21 (beginning of spring) and September 23 (beginning of autumn). On these days, the length of day and night is the same: day equals night. That's why March 21 is called the vernal equinox, and September 23 is the day autumn equinox.

To understand why there is a change in the midday height of the Sun during the year, we will make the following experiment. Let's take a globe. The axis of rotation of the globe is inclined to the plane of its stand at an angle of 6601/r, and the equator at an angle of 23C1/2. The values ​​of these angles are not accidental: the Earth's axis is inclined to the plane of its path around the Sun (orbit) also by 6601/2.

Let's put a bright lamp on the table. She will be portray Sun. Let's move away with the globe some distance from the lamp so that we can

was to wear a globe around a lamp; the middle of the globe should remain at the level of the Lamp, and the globe stand should be parallel to the floor.

The entire side of the globe facing the lamp is illuminated.

We will try to find such a position of the globe that the border of light and shadow passes simultaneously through both poles. This position relative to the Sun the globe has on the day of the vernal equinox or on the day of the autumn equinox. Rotating the globe around its axis, it is easy to see that in this position the day should be equal to the night, and, moreover, simultaneously in both hemispheres - Northern and Southern.

We stick a pin perpendicular to the surface at such a point on the equator that it looks directly at the lamp with its head. Then we will not see the shadow from this pin; this means that for the inhabitants of the equator Sun at noon it is at its zenith, that is, it stands directly above its head.

Now let's move with the globe around the table counterclockwise and go through a quarter of our circular path. At the same time, we must remember that during the annual movement of the Earth around the Sun, the direction of its axis remains unchanged all the time, that is, the axis of the globe must move parallel to itself without changing its inclination.

With the new position of the globe, we see that North Pole illuminated by a lamp (representing the Sun) and the South Pole is in darkness. It is in this position that the Earth is when in the Northern Hemisphere the longest day of the year is the day of the summer solstice.

At this time, the rays of the Sun fall on the northern half at a large angle. The noon Sun on this day is at its zenith on the northern tropic; in the Northern Hemisphere then - summer, in the Southern Hemisphere - winter. There, at this time, the rays fall on the earth's surface more obliquely.

Let's move on with the globe another quarter of the circle further. Now our globe has taken a position directly opposite to the spring one. Again we notice that the boundary of day and night passes through both poles, and again day on the whole Earth is equal to night, that is, it lasts 12 hours. It happens on the autumn equinox.

It is easy to make sure that on this day at the equator the Sun at noon is again at its zenith and falls vertically on the earth's surface there. Therefore, for the inhabitants of the equator, the Sun is at its zenith twice a year: during the spring and autumn equinoxes. Let's go now with the globe another quarter of the circle further. The earth (globe) will be on the other side of the lamp (sun). The picture will change dramatically: the North Pole is now in darkness, and the South Pole is illuminated by the Sun. The Southern Hemisphere is heated by the Sun more than the Northern Hemisphere. The northern half of the Earth is winter, and the southern half is summer. This is the position the Earth takes on the day of the winter solstice. At this time, on the southern tropic, the Sun is at its zenith, that is, its rays fall vertically. This is the longest day in southern hemisphere and the shortest in the North.

Having bypassed another quarter of the circle, we return again to the starting position.

Let's make another interesting experiment: we will not tilt the axis of the globe, but arrange it is perpendicular to the floor plane. If we take the same path With globe around the lamp, we will make sure that in this case there will be all year round the equinox lasts. In our latitudes, there would be eternal spring-autumn days and there would be no sharp transitions from warm to cold months. Everywhere (except, of course, the poles themselves), the Sun would rise exactly in the east at 6 o'clock in the morning local time, rise at noon always to the same height for a given place, and set exactly in the west at 6 o'clock in the evening local time.

Thus, due to the motion of the Earth around the Sun and the constant inclination of the earth's axis to the plane of its orbit, change of seasons.

This also explains the fact that at the North and South Poles day and night last for half a year, and at the equator throughout the year day is equal to night. In middle latitudes, for example in Moscow, the length of day and night varies from 7 to 17.5 hours during the year.

On the northern and southern tropics located at latitude 2301/2 north and south of the equator, the Sun is at its zenith only once a year. In all places located between the tropics, the midday Sun is at its zenith twice a year. Space the globe, concluded between the tropics, due to its thermal features, was called the hot zone. In the middle of it is the equator.

At a distance of 23°'/2 from the pole, i.e. at latitude 6601/2, once a year in winter for a whole day the Sun does not appear above the horizon, and in summer, on the contrary, once a year not for a whole day.

In these places in the northern and southern hemispheres of the globe and on maps, imaginary lines are drawn, which are called the polar circles.

The closer one or another place is located from the polar circles to the poles, the more days there continues continuous day (or continuous night) and the Sun does not set or rise. And at the very poles of the Earth, the Sun shines continuously for six months. At the same time, here the sun's rays fall on the earth's surface very obliquely. The sun never rises high above the horizon. That's why around the poles, in the space surrounded by the polar circles, it is especially cold. There are two such belts - northern and southern; they are called cold zones. There are long winters and short cold summers.

Between the polar circles and the tropics there are two temperate zones (northern and southern).

The closer to the tropics, the winter shorter and warmer, and the closer to the polar circles, the longer and more severe it is.

13.1 The height of the sun above the horizon is given in Table 13.1.

Table 13.1

Geographic latitude in °C. sh.

Annex b (informative) Methods for calculating climatic parameters

The basis for the development of climatic parameters was the Scientific and Applied Handbook on the Climate of the USSR, vol. 1 - 34, parts 1 - 6 (Gidrometeoizdat, 1987 - 1998) and observational data at meteorological stations.

Average values ​​of climatic parameters (average monthly air temperature and humidity, average monthly precipitation) are the sum of average monthly values ​​of the members of a series (years) of observations divided by their total number.

The extreme values ​​of climatic parameters (absolute minimum and absolute maximum air temperature, daily maximum precipitation) characterize the limits within which the values ​​of climatic parameters are contained. These characteristics were selected from extreme daily observations.

The air temperature of the coldest day and the coldest five-day period is calculated as a value corresponding to the probability of 0.98 and 0.92 from the ranged series of air temperature of the coldest day (five-day period) and the corresponding provision for the period from 1966 to 2010. The chronological data series was ranked in descending order of meteorological quantities. Each value was assigned a number, and its availability was determined by the formula

where m is a serial number;

n is the number of members of the ranked series.

The values ​​of the air temperature of the coldest day (five days) of a given probability were determined by interpolation according to the integral curve of the temperature distribution of the coldest day (five days), built on a probabilistic retina. A double exponential distribution retina was used.

The air temperature of various security levels was calculated based on observational data for eight periods for the whole year for the period 1966-2010. All air temperature values ​​were distributed over gradations at intervals of 2°C, and the frequency of values ​​in each gradation was expressed through the frequency of total number cases. Provision was calculated by summing the frequency. Security refers not to the middle, but to the boundaries of gradations, if they are considered by distribution.

The air temperature with a security of 0.94 corresponds to the air temperature of the coldest period. The air temperature uncertainty exceeding the calculated value is equal to 528 h/year.

For the warm period, the calculated temperature with a probability of 0.95 and 0.99 was adopted. In this case, the unavailability of air temperature, which exceeds the calculated values, is 440 and 88 h/year, respectively.

The average maximum air temperature is calculated as a monthly average of the daily maximum air temperature values.

The average daily air temperature amplitude was calculated regardless of the cloudiness as the difference between the average maximum and average minimum air temperatures.

duration and average temperature air periods with an average daily temperature of air equal to or less than 0°С, 8°С and 10°С characterize a period with stable values ​​of these temperatures, individual days with an average daily air temperature equal to or less than 0°С, 8°С and 10°С are not taken into account .

Relative air humidity is calculated from series of average monthly values. Average monthly relative humidity during the day is calculated from observations in the daytime (mainly at 15:00).

The amount of precipitation is calculated for the cold (November - March) and warm (April - October) periods (without correction for wind underestimation) as the sum of average monthly values; characterizes the height of the water layer formed on a horizontal surface from rain, drizzle, heavy dew and fog, melted snow, hail and snow pellets in the absence of runoff, seepage and evaporation.

The daily maximum precipitation is selected from daily observations and characterizes the largest amount of precipitation that fell during the meteorological day.

The repeatability of wind directions is calculated as a percentage of the total number of observations without taking into account calms.

The maximum of the average wind speeds for points for January and the minimum of the average wind speeds for points for July are calculated as the highest of the average wind speeds for points for January, the frequency of which is 16% or more, and as the lowest of the average wind speeds for points for July , the repeatability of which is 16% or more.

Direct and diffuse solar radiation on the surface of various orientations in a cloudless sky was calculated according to the method developed in the laboratory of building climatology of the NIISF. In this case, actual observations of direct and diffuse radiation with a cloudless sky were used, taking into account the daily variation of the sun's height above the horizon and the actual distribution of atmospheric transparency.

Climatic parameters for the stations of the Russian Federation marked with "*" were calculated for the observation period 1966 - 2010.

* When developing territorial building codes (TSN), the clarification of climatic parameters should be carried out taking into account meteorological observations for the period after 1980.

Climatic zoning was developed on the basis of a complex combination of the average monthly air temperature in January and July, the average wind speed for three winter months, and the average monthly relative air humidity in July (see Table B.1).

Table B.1

climatic regions	Climatic subregions	Average monthly air temperature in January, °C	Average wind speed over three winter months, m/s	Average monthly air temperature in July, °С	Average monthly relative air humidity in July, %
		From -32 and below		+4 to +19
		From -28 and below
		-14 to -28		+12 to +21
		-14 to -28
		-14 to -32		+10 to +20
		-4 to -14		+8 to +12
				+12 to +21
		-4 to -14		+12 to +21
		-5 to -14		+12 to +21
		-14 to -20		+21 to +25
				+21 to +25
		-5 to -14		+21 to +25
		-10 to +2		From +28 and above
				+22 to +28	50 or more at 15:00
				+25 to +28
				+25 to +28
Note - The climatic subregion ID is characterized by the duration of the cold period of the year (with an average daily air temperature below 0 ° C) of 190 days a year or more.

The map of humidity zones was compiled by NIISF based on the values ​​of the complex indicator K, which is calculated by the ratio of the monthly average for a frost-free period of precipitation on a horizontal surface, relative air humidity at 15:00 of the warmest month, the average annual total solar radiation on a horizontal surface, and the annual amplitude of average monthly ( January and July) air temperatures.

In accordance with the complex indicator K, the territory is divided into zones according to the degree of humidity: dry (K less than 5), normal (K = 5 - 9) and wet (K more than 9).

The zoning of the northern building-climatic zone (NIISF) is based on the following indicators: the absolute minimum air temperature, the temperature of the coldest day and the coldest five-day period with a security of 0.98 and 0.92, the sum of average daily temperatures for the heating period. According to the severity of the climate on the territory of the northern building-climatic zone, the areas are severe, the least severe and the most severe (see Table B.2).

The distribution map of the annual average number of air temperature transitions through 0°С was developed by the GGO on the basis of the number of transitions through 0°С of the average daily air temperature, summed up for each year and averaged over the period 1961-1990.

Table B.2

	Air temperature, °С					The sum of average daily temperatures for the period with an average daily air temperature of 8°С
	absolute minimum	the coldest days of security		the coldest five-day period of security
Least severe conditions
Harsh conditions
The most severe conditions
Note - The first line is the maximum values, the second line is the minimum values.

Olympiad tasks in geography require the student to be well prepared in the subject. The height of the Sun, the declination and the latitude of the place are connected by simple ratios. To solve problems of determining the geographic latitude requires knowledge of the dependence of the angle of incidence of the sun's rays on the latitude of the area. The latitude at which the area is located determines the change in the height of the sun above the horizon during the year.

Which of the parallels: 50 N; 40 N; on the southern tropic; at the equator; 10 S The sun will be lower on the horizon at noon on the summer solstice. Justify your answer.

1) On June 22, the sun is at its zenith above 23.5 N.L. and the sun will be lower over the parallel farthest from the northern tropic.

2) It will be the southern tropic, because distance will be 47.

On which of the parallels: 30 N; 10 N; equator; 10 S, 30 S the sun will be at noon above above the horizon on the winter solstice. Justify your answer.

2) The midday height of the sun at any parallel depends on the distance from the parallel where the sun is at its zenith that day, i.e. 23.5 S

A) 30 S - 23.5 S = 6.5 S

B) 10 - 23.5 = 13.5

Which of the parallels: 68 N; 72 N; 71 S; 83 S - is the polar night shorter? Justify your answer.

The duration of the polar night increases from 1 day (at the 66.5 N latitude) to 182 days at the pole. The polar night is shorter at the parallel of 68 N,

In which city: Delhi or Rio de Janeiro is the sun higher above the horizon at noon of the spring equinox?

2) Closer to the equator of Rio de Janeiro, because its latitude is 23 S, and Delhi is 28.

So the sun is higher in Rio de Janeiro.

Determine the geographical latitude of the point, if it is known that on the days of the equinox the midday sun stands there above the horizon at a height of 63 (the shadow from objects falls to the south.) Write down the solution.

The formula for determining the height of the sun H

where Y is the difference in latitude between the parallel where the sun is at its zenith on a given day and

desired parallel.

90 - (63 - 0) = 27 S

Determine the height of the Sun above the horizon on the day of the summer solstice at noon in St. Petersburg. Where else on that day will the Sun be at the same height above the horizon?

1) 90 - (60 - 23,5) = 53,5

2) The midday height of the Sun above the horizon is the same on parallels located at the same distance from the parallel where the Sun is at its zenith. St. Petersburg is 60 - 23.5 = 36.5 away from the northern tropic

At this distance from the northern tropic there is a parallel 23.5 - 36.5 \u003d -13

Or 13 S

Determine geographical coordinates the point on the globe where the Sun will be at its zenith when New Year's Eve is celebrated in London. Write down the course of your thoughts.

From December 22 to March 21, 3 months or 90 days pass. During this time, the Sun moves 23.5. The Sun moves 7.8 in a month. For one day 0.26.

23.5 - 2.6 = 21 S

London is on the prime meridian. At this moment, when London is celebrating New Year(0 hours) the sun is at its zenith above the opposite meridian i.e. 180. So, the geographical coordinates of the desired point are

28 S 180 E e. or h. d.

How will the length of the day on December 22 in St. Petersburg change if the angle of inclination of the axis of rotation relative to the plane of the orbit increases to 80. Write down the course of your thoughts.

1) Therefore, the polar circle will have 80, the northern circle will recede from the existing one by 80 - 66.5 = 13.5

Determine the geographic latitude of a point in Australia if it is known that on September 21 at noon local solar time, the height of the Sun above the horizon is 70 . Write down the reasoning.

90 - 70 = 20 S

If the Earth would cease to rotate around its own axis, then the planet would not have a change of day and night. Name three more changes in the nature of the Earth in the absence of axial rotation.

a) the shape of the Earth would change, since there would be no polar compression

b) there would be no Coriolis force - the deflecting action of the Earth's rotation. The trade winds would have a meridional direction.

c) there would be no ebb and flow

Determine at what parallels on the day of the summer solstice the Sun is above the horizon at an altitude of 70.

1) 90 - (70 + (- 23.5) = 43.5 s.l.

23,5+- (90 - 70)

2) 43,5 - 23,5 = 20

23.5 - 20 = 3.5 N

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Life on our planet depends on the amount of sunlight and heat. It is terrible 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 enters the earth's surface is directly proportional to the angle of incidence of the rays. The sun's rays can fall on the Earth at an angle from 0 to 90 degrees. The angle at which the rays hit the earth is different, because our planet has the shape of a ball. The larger it is, the lighter and warmer it is.

Thus, if the beam comes at an angle of 0 degrees, it only slides along the surface of the earth without heating it. This angle of incidence occurs at the North 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 the sun's rays on the ground is right, this indicates that

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

How does the sun change its height above the horizon?

The height of the sun above the horizon is not a constant value. 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, the day follows the night, and the seasons 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 beyond the Arctic Circle receives less and less heat and light; here there are such concepts as night, which last about six months.

Autumn and spring equinoxes

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

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

Summer and winter solstices

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

Above a latitude of 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 the 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 year with the longest nights in the Northern Hemisphere. Men in Central Russia wake up to work in the dark and return at night too. This is a difficult month for many, as the lack of sunlight takes a toll on the physical and moral condition of the people. For this reason, depression can even develop.

In Moscow in 2016, the sunrise on December 1 will be at 08.33. In this case, the length of the day will be 7 hours 29 minutes. beyond the horizon will be very early, at 16.03. The night will be 16 hours 31 minutes. Thus, it turns out that the longitude of the night is 2 times greater than the longitude 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 already from December 24, the day will go to profit slowly but surely.

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

June 22 is the summer solstice. Everything happens exactly the opposite. For the whole year, it is on this date that the longest day in duration and the shortest night. This is for the Northern Hemisphere.

In the South it's the other way around. This day is associated with interesting natural phenomena. Beyond the Arctic Circle comes the polar day, 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 solar year does not always coincide with the calendar year. Also offsets occur in 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 changed over a specific area earth's surface, change climatic conditions and seasons.

For example, on Far North the rays of the sun fall at a very small angle and only glide along the surface of the earth without heating it at all. Under the condition of this factor, the climate here is extremely severe, there is permafrost, cold winters with freezing winds and snows.

The higher the sun above the horizon, the warmer the climate. For example, at the equator it is unusually hot, 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 here. The device for measuring the height of the sun above the horizon is elementary simple. It is a horizontal surface with a pole in the middle 1 meter long. On a sunny day at noon, the pole casts the shortest shadow. With the help of this shortest shadow, calculations and measurements are carried out. It is necessary 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 value of the angle will be the angle of the sun above the horizon. This device is called a gnomon.

The gnomon is an ancient astrological instrument. There are other devices for measuring the height of the sun above the horizon, such as the sextant, quadrant, astrolabe.

Apparent annual motion of the Sun

Due to the annual revolution of the Earth around the Sun in the direction from west to east, it seems to us that the Sun moves among the stars from west to east along a great circle of the celestial sphere, which is called ecliptic, with a period of 1 year . The plane of the ecliptic (the plane of the earth's orbit) is inclined to the plane of the celestial (as well as the earth's) equator at an angle. This corner is called ecliptic inclination.

The position of the ecliptic on the celestial sphere, that is, the equatorial coordinates and points of the ecliptic and its inclination to the celestial equator are determined from daily observations of the Sun. By measuring the zenith distance (or height) of the Sun at the time of its upper climax at the same geographical latitude,

,	(6.1)
,	(6.2)

it can be established that the declination of the Sun during the year varies from to . In this case, the right ascension of the Sun during the year varies from to, or from to.

Let us consider in more detail the change in the coordinates of the Sun.

At the point spring equinox^ which the Sun passes annually on March 21, the right ascension and declination of the Sun wound to zero. Then every day the right ascension and declination of the Sun increase.

At the point summer solstice a, in which the Sun enters on June 22, its right ascension is 6 h, and the declination reaches its maximum value + . After that, the declination of the Sun decreases, while right ascension still increases.

When the Sun on September 23 comes to a point autumn equinox d, its right ascension becomes , and its declination becomes zero again.

Further, right ascension, continuing to increase, at the point winter solstice g, where the Sun hits on December 22, becomes equal to , and the declination reaches its minimum value - . After that, the declination increases, and after three months the Sun comes back to the vernal equinox.

Consider the change in the location of the Sun in the sky during the year for observers located in different places on the Earth's surface.

north pole of the earth, on the day of the vernal equinox (21.03) the Sun makes a circle on the horizon. (Recall that at the North Pole of the earth there are no phenomena of sunrise and sunset, that is, any luminary moves parallel to the horizon without crossing it). This marks the beginning of the polar day at the North Pole. The next day, the Sun, having slightly risen along the ecliptic, will describe a circle parallel to the horizon for a little higher altitude. Every day it will rise higher and higher. Max Height The sun will reach on the day of the summer solstice (22.06) -. After that, a slow decrease in height will begin. On the day of the autumn equinox (23.09), the Sun will again be at the celestial equator, which coincides with the horizon at the North Pole. Having made a farewell circle along the horizon on this day, the Sun descends under the horizon (under the celestial equator) for half a year. The half-year-long polar day is over. The polar night begins.

For an observer located on Arctic Circle greatest height The sun reaches noon on the day of the summer solstice -. The midnight altitude of the Sun on this day is 0°, meaning the Sun does not set on that day. Such a phenomenon is called polar day.

On the day of the winter solstice, its midday height is minimal - that is, the Sun does not rise. It is called polar night. The latitude of the Arctic Circle is the smallest in the northern hemisphere of the Earth, where the phenomena of polar day and night are observed.

For an observer located on northern tropic The sun rises and sets every day. The Sun reaches its maximum midday height above the horizon on the day of the summer solstice - on this day it passes the zenith point (). The Tropic of the North is the northernmost parallel where the Sun is at its zenith. The minimum noon height, , occurs on the winter solstice.

For an observer located on equator, absolutely all the luminaries come and rise. At the same time, any luminary, including the Sun, spends exactly 12 hours above the horizon and 12 hours below the horizon. This means that the length of the day is always equal to the length of the night - 12 hours each. Twice a year - on the days of the equinoxes - the midday height of the Sun becomes 90 °, that is, it passes through the zenith point.

For an observer located on latitude of Sterlitamak, that is, in the temperate zone, the Sun is never at its zenith. It reaches its highest height at noon on June 22, on the day of the summer solstice, -. On the day of the winter solstice, December 22, its height is minimal -.

So, let's formulate the following astronomical signs of thermal zones:

1. In cold zones (from the polar circles to the poles of the Earth), the Sun can be both a non-setting and a non-rising luminary. The polar day and polar night can last from 24 hours (in the northern and southern polar circles) to six months (in the northern and south poles Earth).

2. In temperate zones(from the northern and southern tropics to the northern and southern polar circles) The sun rises and sets every day, but never at its zenith. summer day longer than the night and vice versa in winter.

3. In the hot zone (from the northern tropic to the southern tropic) the Sun is always rising and setting. At the zenith, the Sun occurs from once - in the northern and southern tropics, up to twice - at other latitudes of the belt.

The regular change of seasons on Earth is the result of three reasons: the annual revolution of the Earth around the Sun, the inclination of the earth's axis to the plane of the earth's orbit (the ecliptic plane) and the preservation of the earth's axis of its direction in space over long periods of time. Due to the combined action of these three causes, the apparent annual movement of the Sun along the ecliptic inclined to the celestial equator occurs, and therefore the position of the daily path of the Sun above the horizon various places Earth's surface changes throughout the year, and consequently, the conditions for their illumination and heating by the Sun change.

Unequal heating by the Sun of areas of the earth's surface with different geographical latitudes (or these same areas in different time years) can be easily determined by simple calculation. Let us denote by the amount of heat transferred to a unit area of ​​the earth's surface by vertically falling sun rays (the Sun at its zenith). Then, at a different zenith distance of the Sun, the same unit area will receive the amount of heat

(6.3)

Substituting in this formula the values ​​of the Sun at true noon on different days of the year and dividing the resulting equalities by each other, we can find the ratio of the amount of heat received from the Sun at noon on these days of the year.

Tasks:

1. Calculate the inclination of the ecliptic and determine the equatorial and ecliptic coordinates of its main points from the measured zenith distance. Sun at its highest climax on the solstices:

№	22nd of June	December 22
1)	29〫48ʹ yu	76〫42ʹ yu
№	22nd of June	December 22
2)	19〫23ʹ yu	66〫17ʹ yu
3)	34〫57ʹ yu	81〫51ʹ yu
4)	32〫21ʹ yu	79〫15ʹ yu
5)	14〫18ʹ yu	61〫12ʹ yu
6)	28〫12ʹ yu	75〫06ʹ yu
7)	17〫51ʹ yu	64〫45ʹ yu
8)	26〫44ʹ yu	73〫38ʹ yu

2. Determine the inclination of the apparent annual path of the Sun to the celestial equator on the planets Mars, Jupiter and Uranus.

3. Determine the inclination of the ecliptic about 3000 years ago, if according to observations at that time in some place of the northern hemisphere of the Earth, the midday height of the Sun on the day of the summer solstice was +63〫48ʹ, and on the day of the winter solstice +16〫00ʹ south of the zenith.

4. According to the maps of the star atlas of Academician A.A. Mikhailov set titles and boundaries zodiac constellations, indicate those of them in which the main points of the ecliptic are located, and determine average duration the movement of the Sun against the background of each zodiac constellation.

5. Using a mobile map of the starry sky, determine the azimuths of points and times of sunrise and sunset, as well as the approximate duration of day and night at the geographic latitude of Sterlitamak on the days of equinoxes and solstices.

6. Calculate for the days of equinoxes and solstices the noon and midnight heights of the Sun in: 1) Moscow; 2) Tver; 3) Kazan; 4) Omsk; 5) Novosibirsk; 6) Smolensk; 7) Krasnoyarsk; 8) Volgograd.

7. Calculate the ratios of the amounts of heat received at noon from the Sun on the days of the solstices by the same sites at two points on the earth's surface located at latitude: 1) +60〫30ʹ and in Maikop; 2) +70〫00ʹ and in Grozny; 3) +66〫30ʹ and in Makhachkala; 4) +69〫30ʹ and in Vladivostok; 5) +67〫30ʹ and in Makhachkala; 6) +67〫00ʹ and in Yuzhno-Kurilsk; 7) +68〫00ʹ and in Yuzhno-Sakhalinsk; 8) +69〫00ʹ and in Rostov-on-Don.

Kepler's laws and planetary configurations

Under the influence of gravitational attraction to the Sun, the planets revolve around it in slightly elongated elliptical orbits. The sun is at one of the foci of the planet's elliptical orbit. This movement obeys Kepler's laws.

The value of the semi-major axis of the elliptical orbit of the planet is also the average distance from the planet to the Sun. Due to slight eccentricities and small orbital inclinations major planets, it is possible, when solving many problems, to approximately assume these orbits are circular with a radius and lying practically in the same plane - in the plane of the ecliptic (the plane of the earth's orbit).

According to Kepler's third law, if and are, respectively, the sidereal (sidereal) periods of revolution of a certain planet and the Earth around the Sun, and and are the semi-major axes of their orbits, then

.

(7.1)

Here, the periods of revolution of the planet and the Earth can be expressed in any units, but the dimensions and must be the same. A similar statement is also true for the major semiaxes and .

If we take 1 tropical year as a unit of time ( - the period of revolution of the Earth around the Sun), and 1 astronomical unit () as a unit of distance, then Kepler's third law (7.1) can be rewritten as

where is the sidereal period of the planet's revolution around the Sun, expressed in mean solar days.

Obviously, for the Earth, the average angular velocity is determined by the formula

If we take as the unit of measurement of the angular velocities of the planet and the Earth , and the rotation periods are measured in tropical years, then formula (7.5) can be written as

The average linear velocity of a planet in orbit can be calculated by the formula

The average value of the Earth's orbital velocity is known and is . Dividing (7.8) by (7.9) and using Kepler's third law (7.2), we find the dependence on

The "-" sign corresponds internal or lower planets (Mercury, Venus), and "+" - external or upper (Mars, Jupiter, Saturn, Uranus, Neptune). In this formula, and are expressed in years. If necessary, the found values ​​and can always be expressed in days.

The relative position of the planets is easily established by their heliocentric ecliptic spherical coordinates, the values ​​of which for various days of the year are published in astronomical yearbooks, in a table called "heliocentric longitudes of the planets."

The center of this coordinate system (Fig. 7.1) is the center of the Sun, and the main circle is the ecliptic, the poles of which are 90º apart from it.

Great circles drawn through the poles of the ecliptic are called circles of ecliptic latitude, according to them is counted from the ecliptic heliocentric ecliptic latitude, which is considered positive in the northern ecliptic hemisphere and negative in the southern ecliptic hemisphere of the celestial sphere. Heliocentric ecliptic longitude is measured along the ecliptic from the vernal equinox point ¡ counterclockwise to the base of the latitude circle of the star and has values ​​​​ranging from 0º to 360º.

Due to the small inclination of the orbits of large planets to the ecliptic plane, these orbits are always located near the ecliptic, and in the first approximation, one can consider their heliocentric longitude, determining the position of the planet relative to the Sun with only its heliocentric ecliptic longitude.

Rice. 7.1. Ecliptic celestial coordinate system

Consider the orbits of the Earth and some inner planet (Figure 7.2) using heliocentric ecliptic coordinate system. In it, the main circle is the ecliptic, and the zero point is the vernal equinox ^. The ecliptic heliocentric longitude of the planet is counted from the direction "Sun - vernal equinox ^" to the direction "Sun - planet" counterclockwise. For simplicity, we will consider the planes of the orbits of the Earth and the planet to coincide, and the orbits themselves to be circular. The planet's position in orbit is then given by its ecliptic heliocentric longitude.

If the center of the ecliptic coordinate system is aligned with the center of the Earth, then this will be geocentric ecliptic coordinate system. Then the angle between the directions "the center of the Earth - the vernal equinox ^" and "the center of the Earth - the planet" is called ecliptic geocentric longitude planets. The heliocentric ecliptic longitude of the Earth and the geocentric ecliptic longitude of the Sun, as can be seen from Fig. 7.2 are related by:

.

(7.12)

We will call configuration planets some fixed mutual arrangement planets, earth and sun.

Consider separately the configurations of internal and outer planets.

Rice. 7.2. Helio- and geocentric systems
ecliptic coordinates

There are four configurations of the inner planets: bottom connection(n.s.), top connection(v.s.), greatest western elongation(n.z.e.) and greatest eastern elongation(n.v.e.).

In inferior conjunction (NS), the inner planet is on the straight line connecting the Sun and the Earth, between the Sun and the Earth (Fig. 7.3). For an earthly observer at this moment, the inner planet "connects" with the Sun, that is, it is visible against the background of the Sun. In this case, the ecliptic geocentric longitudes of the Sun and the inner planet are equal, that is: .

Near the lower conjunction, the planet moves in the sky in backward motion near the Sun, it is above the horizon during the day, and near the Sun, and it is impossible to observe it by looking at anything on its surface. It is very rare to see a unique astronomical phenomenon - the passage of an inner planet (Mercury or Venus) across the solar disk.

Rice. 7.3. Inner planet configurations

Since the angular velocity of the inner planet is greater than the angular velocity of the Earth, after some time the planet will shift to a position where the directions "planet-Sun" and "planet-Earth" differ by (Fig. 7.3). For an earthly observer, the planet is at the same time removed from the solar disk at the maximum angle, or they say that the planet at this moment is at its greatest elongation (distance from the Sun). There are two largest elongations of the inner planet - western(n.z.e.) and eastern(n.v.e.). In the greatest western elongation () and the planet sets beyond the horizon and rises earlier than the Sun. This means that you can observe it in the morning, before sunrise, at east side sky. It is called morning visibility planets.

After passing the greatest western elongation, the disk of the planet begins to approach the disk of the Sun in the celestial sphere until the planet disappears behind the disk of the Sun. This configuration, when the Earth, the Sun and the planet lie on one straight line, and the planet is behind the Sun, is called top connection(v.s.) planets. It is impossible to conduct observations of the inner planet at this moment.

After the upper conjunction, the angular distance between the planet and the Sun begins to grow, reaching its maximum value at the greatest eastern elongation (E.E.). At the same time, the heliocentric ecliptic longitude of the planet is greater than that of the Sun (and the geocentric longitude, on the contrary, is less, that is, ). The planet in this configuration rises and sets later than the Sun, which makes it possible to observe it in the evening after sunset ( evening visibility).

Due to the ellipticity of the orbits of the planets and the Earth, the angle between the directions to the Sun and to the planet at the greatest elongation is not constant, but varies within certain limits, for Mercury - from to, for Venus - from to.

The greatest elongations are the most convenient moments for observing the inner planets. But since even in these configurations Mercury and Venus do not move far from the Sun in the celestial sphere, they cannot be observed throughout the night. The duration of evening (and morning) visibility for Venus does not exceed 4 hours, and for Mercury - no more than 1.5 hours. We can say that Mercury always "baths" in sunshine- it has to be observed either immediately before sunrise, or immediately after sunset, in a bright sky. The apparent brilliance (magnitude) of Mercury varies with time in the range from to . The apparent magnitude of Venus varies from to . Venus is the brightest object in the sky after the Sun and Moon.

The outer planets also distinguish four configurations (Fig. 7.4): compound(With.), confrontation(P.), eastern and western quadrature(z.kv. and v.kv.).

Rice. 7.4. Outer planet configurations

In the conjunction configuration, the outer planet is located on the line joining the Sun and the Earth, behind the Sun. At this point, you can't watch it.

Since the angular velocity of the outer planet is less than that of the Earth, the further relative motion of the planet on the celestial sphere will be backward. At the same time, it will gradually shift to the west of the Sun. When the outer planet's angular distance from the Sun reaches , it will fall into the "western quadrature" configuration. In this case, the planet will be visible in the eastern side of the sky for the entire second half of the night until sunrise.

In the "opposition" configuration, sometimes also called "opposition", the planet is separated in the sky from the Sun by , then

A planet located in the eastern quadrature can be observed from evening to midnight.

The most favorable conditions for observing the outer planets are during the epoch of their opposition. At this time, the planet is available for observations throughout the night. At the same time, it is as close as possible to the Earth and has the largest angular diameter and maximum brightness. For observers, it is important that all the upper planets reach their greatest height above the horizon during winter oppositions, when they move across the sky in the same constellations where the Sun is in summer. Summer oppositions at northern latitudes occur low above the horizon, which can make observations very difficult.

When calculating the date of a particular configuration of the planet, its location relative to the Sun is depicted on a drawing, the plane of which is taken as the plane of the ecliptic. The direction to the vernal equinox ^ is chosen arbitrarily. Given the day of the year on which the Earth's heliocentric ecliptic longitude has certain value, then the location of the Earth should first be noted on the drawing.

The approximate value of the heliocentric ecliptic longitude of the Earth is very easy to find from the date of observation. It is easy to see (Fig. 7.5) that, for example, on March 21, looking from the Earth towards the Sun, we look at the vernal equinox point ^, that is, the direction "Sun - vernal equinox" differs from the direction "Sun - Earth" by , which means that the Earth's heliocentric ecliptic longitude is . Looking at the Sun on the day of the autumn equinox (September 23), we see it in the direction of the point of the autumn equinox (in the drawing it is diametrically opposed to the point ^). In this case, the ecliptic longitude of the Earth is . From fig. 7.5 it can be seen that on the day of the winter solstice (December 22) the ecliptic longitude of the Earth is , and on the day of the summer solstice (June 22) - .

Rice. 7.5. Ecliptic heliocentric longitudes of the Earth
on different days of the year