The height of the sun above the earth. Movement of the sun at different latitudes

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1. Determination of the height of the sun above the horizon at points located on the same parallel

Noon meridian (12 hours - Greenwich meridian time) * 15º - if the meridian is in the Eastern Hemisphere; (Greenwich meridian time is 12 hours) * 15º - if the meridian is in the Western Hemisphere. The closer the meridians proposed in the assignment are to the noon meridian, the higher the Sun will be in them; the further away, the lower.

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Determine which of the points indicated by letters on the map of Australia, on March 21, the sun will be highest above the horizon at 5 a.m. solar time Greenwich meridian. Write down the rationale for your answer.

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Determine which of the letters indicated on the map North America points The Sun will be lowest above the horizon at 18:00 Greenwich meridian time. Write down your reasoning.

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2. Determination of the height of the Sun above the horizon at various points that are not on the same parallel, and when there is an indication of the day of the winter (December 22) or summer (June 22) solstice

you need to remember that the Earth moves counterclockwise and the further east the point is, the earlier the Sun will rise above the horizon.; analyze the position of the points specified in the task relative to the polar circles and tropics. For example, if the question indicates the day - December 20, this means a day close to the day winter solstice, when the polar night is observed in the territory north of the Arctic Circle. This means that the further north the point is located, the later the Sun will rise above the horizon; the further south, the earlier.

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Determine at which of the points indicated by letters on the map of North America, on December 20, the Sun will rise above the horizon earlier than the Greenwich meridian. Write down your reasoning.

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3. Tasks to determine the length of day (night) in connection with changes in the angle of inclination of the earth’s axis to the orbital plane

you need to remember - the degree measure of the angle of inclination of the earth's axis to the plane of the earth's orbit determines the parallel on which the Arctic Circle will be located. Then the situation proposed in the task is analyzed. For example, if the territory is in conditions long duration days (in June in the northern hemisphere), then the closer the territory is to the Arctic Circle, the longer the day; the further away, the shorter.

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Determine which of the parallels: 20° N, 10° N, on the equator, 10° S, or 20° S. – the maximum day length will be observed on May 20

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On which of the parallels indicated by letters in the figure is December 22 duration daylight hours smallest?

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4. Determination of geographic latitude of an area

Determine the geographic coordinates of a point if it is known that on the days of the equinox the midday Sun stands there above the horizon at an altitude of 40º (the shadow of the object falls to the north), and the local time is 3 hours ahead of the Greenwich meridian. Record your calculations and reasoning

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Equinox days

(March 21 and September 23), when the rays of the Sun fall vertically on the equator 90º - angle of incidence sun rays= latitude of the area (north or south is determined by the shadow cast by objects).

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Solstice days

(June 22 and December 22) the rays of the Sun fall vertically (at an angle of 90º) on the tropics (23.5º N and 23.5º S). Therefore, to determine the latitude of the area in the illuminated hemisphere (for example, June 22 in the Northern Hemisphere), the formula is used: 90º- (angle of incidence of the sun's rays - 23.5º) = latitude of the area

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To determine the latitude of an area in the unlit hemisphere (for example, December 22 in the Northern Hemisphere), the formula is used: 90º - (angle of incidence of the sun's rays + 23.5º) = latitude of the area

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Determine the geographic coordinates of a point if it is known that on the days of the equinox the midday Sun stands there above the horizon at an altitude of 40º (the shadow of the object falls to the north), and the local time is 3 hours ahead of the Greenwich meridian. Write down your calculations and reasoning Answer. 50º N, 60º E 90º - 40º = 50º (N, because the shadow of objects falls to the north in the northern hemisphere) (12-9)x15 = 60º (E, because local time is ahead of Greenwich, which means the point located to the east)

If measure every day at what angle the Sun rises above the horizon at noon - this angle is called midday - then you can notice 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 midday height, and the longer the shadow, the less the midday height. On June 22, the midday height of the Sun is at its highest in the Northern Hemisphere. This is the longest day of the year in this half of the Earth. It's called day summer solstice. Several days in a row the midday height Sun changes extremely little (hence the expression “solstice”), and therefore And The length of the day also remains almost unchanged.

Six months later, December 22, is the winter solstice in the Northern Hemisphere. Then the midday altitude of the Sun is lowest and the day is shortest. Again, for several days in a row, the midday altitude of the Sun changes extremely slowly and the length of the day remains almost unchanged. The difference between the midday altitudes of the Sun on June 22 and December 22 is 47°. There are two days in the year when the midday altitude of the Sun is exactly 2301/2 lower than on the day of the summer solstice, and 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 is equal to night. That's why March 21 is called the vernal equinox, and September 23 is called the autumn equinox.

To understand why the midday altitude of the Sun changes throughout the year, let us perform the following experiment. Let's take a globe. The globe's axis of rotation is inclined to the plane of its stand at an angle of 6601/g, and the equator is inclined at an angle of 23C1/2. The magnitudes of these angles are not accidental: the earth's axis is inclined to the plane of its path around the Sun (orbit) also at 6601/2.

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

was to carry 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.

Let's try to find a position for the globe such that the boundary of light and shadow passes simultaneously through both poles. The globe has this position relative to the Sun 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 notice that in this position day should be equal to night, and, moreover, simultaneously in both hemispheres - the Northern and Southern.

Let's stick a pin perpendicular to the surface at a point on the equator so that its head looks directly at the lamp. Then we will not see the shadow of this pin; this means that for the inhabitants of the equator Sun at noon it is at its zenith, that is, it stands directly overhead.

Now let's move the globe around the table counterclockwise and go a quarter of our way around. 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. This is exactly the position the Earth is in when the longest day of the year in the Northern Hemisphere is the summer solstice.

At this time, the sun's rays fall on the northern half at a large angle. The midday Sun on this day is at its zenith in the northern tropics; In the Northern Hemisphere it is summer then, in the Southern Hemisphere it is winter. There at this time the rays fall on earth's surface more oblique.

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

It is not difficult to verify that on this day at the equator the Sun at noon is again at its zenith and falls vertically onto the earth's surface there. Consequently, for residents of the equator, the Sun is at its zenith twice a year: during the spring and autumn equinoxes. Now let's move the globe another quarter of a 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. In the northern half of the Earth it is winter, and in the southern half it is summer. This is the position the Earth occupies on the day of the winter solstice. At this time, in the southern tropics, the Sun is at its zenith, that is, its rays fall vertically. This is the longest day in the Southern Hemisphere and the shortest in the Northern Hemisphere.

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

Let's make another one interesting experience: we will not tilt the axis of the globe, but arrange it is perpendicular to the plane of the floor. If we go the same way With globe around the lamp, we will be convinced 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, always rise at noon 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 movement 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 six months, and at the equator, day is equal to night throughout the year. In mid-latitudes, for example in Moscow, the length of day and night throughout the year varies from 7 to 17.5 hours.

On In 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 occurs at its zenith twice a year. Space globe, located between the tropics, is called the hot zone due to its thermal characteristics. The equator runs through the middle of it.

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 for a whole day.

In these places in the Northern and Southern Hemispheres globe and on maps, imaginary lines are drawn, which are called polar circles.

The closer a place is located to the polar circles, the larger number days there continues a continuous day (or continuous night) and the Sun does not set or rise. And at the Earth’s poles themselves, 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 belts. There are long winters and short cold summers.

Between the polar circles and the tropics there are two temperate zones(north and south).

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

Olympiad tasks in geography require the student to be well prepared in the subject. The altitude of the Sun, declination and latitude of a place are related by simple relationships. To solve problems of determining geographic latitude, it 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 throughout the year.

On which parallel: 50 N; 40 N; in the southern tropics; at the equator; 10 S The sun will be lower above the horizon at noon on the summer solstice. Justify your answer.

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

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

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

2) The midday altitude 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

On which parallel: 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 parallel 66.5 N) to 182 days at the pole. The polar night is shorter at parallel 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.

This means the sun is higher in Rio de Janeiro.

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

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

the 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 this 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 distant from the northern tropic

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

Or 13 S.

Determine the geographic coordinates of the point on the globe at which the Sun will be at its zenith when the New Year is celebrated in London. Write down your thoughts.

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

23.5 - 2.6 = 21 S.

London is located on the prime meridian. At this moment, when London is celebrating New Year(0 o'clock) the sun is at its zenith above the opposite meridian i.e. 180. This means that the geographic coordinates of the desired point are

28 S. 180 E. d. or h. d.

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

1) Therefore, the Arctic Circle will have 80, the Northern Circle will retreat 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 your reasoning.

90 - 70 = 20 S

If the Earth stopped rotating around its own axis, then there would be no change of day and night on the planet. 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 effect 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 a height of 70.

1) 90 - (70 +(- 23.5) = 43.5 northern latitude.

23,5+- (90 - 70)

2) 43,5 - 23,5 = 20

23.5 - 20 = 3.5 northern latitude.

13.1 The values ​​of the height of the sun above the horizon are given in Table 13.1.

Table 13.1

Appendix b (informative) Methods for calculating climatic parameters

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

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

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 observations during the day.

The air temperature of the coldest day and the coldest five-day period was calculated as the value corresponding to the probability of 0.98 and 0.92 from the ranked series of air temperatures of the coldest day (five-day period) and the corresponding probability for the period from 1966 to 2010. The chronological data series was ranked in descending order of meteorological magnitude values. Each value was assigned a number, and its security was determined using the formula

where m is the serial number;

n is the number of members of the ranked series.

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

Air temperatures of different levels of probability were calculated based on observational data for eight periods for the whole year for the period 1966-2010. All air temperature values ​​were distributed into gradations of 2°C and the frequency of values ​​in each gradation was expressed through the frequency of occurrence of the total number of cases. The availability was calculated by summing the frequency. Security refers not to the middle, but to the boundaries of the gradations, if they are calculated according to distribution.

The air temperature with a probability of 0.94 corresponds to the air temperature of the coldest period. Uncertainty of air temperature exceeding the calculated value is equal to 528 hours/year.

For the warm period, the calculated probability temperature of 0.95 and 0.99 was adopted. In this case, the lack of air temperature exceeding the calculated values ​​is 440 and 88 hours/year, respectively.

Average maximum air temperature is calculated as the monthly average of daily maximum air temperatures.

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

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

Relative air humidity was calculated using series of average monthly values. Average monthly relative humidity during the day, calculated from observations during 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 layer of water 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 a meteorological day.

The frequency of wind directions is calculated as a percentage of the total number of observation cases, excluding calms.

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

Direct and diffuse solar radiation on surfaces of various orientations under cloudless skies was calculated using a method developed in the laboratory of construction climatology of the NIISF. In this case, actual observations of direct and diffuse radiation under cloudless skies 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 stations of the Russian Federation marked with "*" were calculated for the observation period 1966 - 2010.

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

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

Table B.1

The map of humidity zones was compiled by NIISF based on the values ​​of the complex indicator K, which is calculated according to the ratio of the monthly average for the 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, the annual amplitude of monthly averages ( 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 construction-climatic zone (NIISF) is based on the following indicators: absolute minimum air temperature, the temperature of the coldest day and the coldest five-day period with a probability of 0.98 and 0.92, the sum of average daily temperatures for heating season. According to the severity of the climate in the northern construction-climatic zone, areas are distinguished as severe, least severe and most severe (see Table B.2).

A map of the distribution of the annual average number of air temperature transitions through 0°C was developed by the State Geophysical Observatory based on the number of average daily air temperature transitions through 0°C, summed up for each year and averaged over the period 1961-1990.

Table B.2

a) For an observer at the north pole of the Earth ( j = + 90°) non-setting luminaries are those with d-- i?? 0, and non-ascending are those with d--< 0.

Table 1. Altitude of the midday Sun at different latitudes

The Sun has a positive declination from March 21 to September 23, and a negative declination from September 23 to March 21. Consequently, at the north pole of the Earth, the Sun is a non-setting luminary for approximately half the year, and a non-rising luminary for half the year. Around March 21, the Sun here appears above the horizon (rises) and, due to the daily rotation of the celestial sphere, describes curves close to a circle and almost parallel to the horizon, rising higher and higher every day. On the summer solstice (around June 22) the Sun reaches maximum height h max = + 23° 27 " . After this, the Sun begins to approach the horizon, its height gradually decreases, and after the autumn equinox (after September 23) it disappears under the horizon (sets). The day, which lasted six months, ends and the night begins, which also lasts six months. The sun, continuing to describe curves almost parallel to the horizon, but below it, sinks lower and lower. On the day of the winter solstice (around December 22) it will descend below the horizon to a height h min = - 23° 27 " , and then will again begin to approach the horizon, its height will increase, and before the spring equinox the Sun will again appear above the horizon. For the observer on south pole Earth ( j= - 90°) the daily movement of the Sun occurs in a similar way. Only here the Sun rises on September 23, and sets after March 21, and therefore when it is night at the North Pole of the Earth, it is day at the South Pole, and vice versa.

b) For an observer at the Arctic Circle ( j= + 66° 33 " ) non-setting luminaries are those with d--i + 23° 27 " , and non-ascending - with d < - 23° 27". Consequently, in the Arctic Circle the Sun does not set on the summer solstice (at midnight the center of the Sun only touches the horizon at the north point N) and does not rise on the day of the winter solstice (at noon the center of the solar disk will only touch the horizon at the point south S, and then drops below the horizon again). On the remaining days of the year, the Sun rises and sets at this latitude. Moreover, it reaches its maximum height at noon on the day of the summer solstice ( h max = + 46° 54"), and on the day of the winter solstice its midday height is minimal ( h min = 0°). In the southern polar circle ( j= - 66° 33") The sun does not set on the winter solstice and does not rise on the summer solstice.

The northern and southern polar circles are the theoretical boundaries of those geographical latitudes where polar days and nights(days and nights lasting more than 24 hours).

In places beyond the polar circles, the Sun remains a non-setting or non-rising luminary the longer, the closer the place is to the geographic poles. As you approach the poles, the length of the polar day and night increases.

c) For an observer in the northern tropic ( j--= + 23° 27") The sun is always a rising and setting luminary. On the summer solstice it reaches its maximum height at noon. h max = + 90°, i.e. passes through the zenith. On the remaining days of the year, the Sun culminates at noon south of the zenith. On the day of the winter solstice its minimum midday height is h min = + 43° 06".

In the southern tropics ( j = - 23° 27") The sun also always rises and sets. But at its maximum midday height above the horizon (+ 90°) it occurs on the day of the winter solstice, and at its minimum (+ 43° 06 " ) - on the day of the summer solstice. On the remaining days of the year, the Sun culminates here at noon north of the zenith.

In places lying between the tropics and the polar circles, the Sun rises and sets every day of the year. Half a year is the length of the day here longer duration nights, and for six months the night is longer than the day. The midday altitude of the Sun here is always less than 90° (except in the tropics) and more than 0° (except in the polar circles).

In places lying between the tropics, the Sun is at its zenith twice a year, on those days when its declination is equal to the geographical latitude of the place.

d) For an observer at the Earth's equator ( j--= 0) all luminaries, including the Sun, are rising and setting. At the same time, they are above the horizon for 12 hours, and below the horizon for 12 hours. Therefore, at the equator, the length of the day is always equal to the length of the night. Twice a year the Sun passes at its zenith at noon (March 21 and September 23).

From March 21 to September 23, the Sun at the equator culminates at noon north of the zenith, and from September 23 to March 21 - south of the zenith. The minimum noon altitude of the Sun here will be equal to h min = 90° - 23° 27 " = 66° 33 " (June 22 and December 22).