Formula half the height of the sun. Geography Tasks: Sun Height and Latitude

What kind of transport you can quickly make a "round-the-world" journey

(with return to the point of departure):

aircraft by equator (average speed of 800 km / h),

on the sea vessel at 60 ° sh. (average speed 40 km / h) or

on dog sleds 80 ° sh. (Average speed of 30 km / h).

Answer:

By plane - 50 hours, 360 * 111.3 \u003d 40068 km 40068: 800 \u003d 50 hours.

on the sea vessel - 502 hours, 360 * 55,8 \u003d 20088 km 20088: 40 \u003d 502 hours

skiing - 233 h., 360 * 19,4 \u003d 6984 km 8984: 30 \u003d 233 hours

How long will each of these travels continue (without taking into account stops)?

№1 on which of the parallels: 50 s.sh.; 40 s.sh.; on the southern tropics; at the equator; 10 Yu.Sh. The sun at noon will be lower above the horizon on the day of the summer solstice. Justify your answer.

Decision:

1) June 22 Sun in Zenith over 23.5 S.Sh. And the sun will be lower above the parallel most remote from the northern tropical.

2) it will be the southern tropic, because Estimation will be 47.

№2 on which parallel: 30 s.sh.; 10 s.sh.; Equator; 10 Yu.Sh., 30 Yu.Sh. the sun at noon will be above Above the horizon on the day of the winter solstice. Justify your answer.

Decision:

1) 30 Yu.Sh.

2) the midday height of the sun on any parallel depends on the remoteness from the parallel, where the sun on this day in the zenith, i.e. 23.5 Yu.Sh.

A) 30 Yu.Sh.- 23.5 Yu.Sh. \u003d 6.5 Yu.Sh

B) 10 - 23.5 \u003d 13.5

№3 on which of the parallels: 68 s.sh.; 72 s.sh.; 71 Yu.Sh; 83 Yu.Sh - Polar night shorter? Justify your answer.

Decision:

The duration of the polar night increases from 1 day (on parallels 66.5 s.sh.) to 182 days per pole. The polar night is shorter on parallels 68 S.Sh., because. She further from the pole.

№4 In which city: Delhi or Rio de Janeiro Sun is above the horizon at noon of spring equinox?

Decision:

2) closer to the Equator of the city of Rio de Janeiro. His latitude 23 Yu.Sh., and Delhi 28.

So the sun is higher in Rio de Janeiro.

№5 Determine the geographical latitude of the point, if it is known that in the days of the equinox, the midday sun stands there above the horizon at an altitude of 63 (the shadow of the items falls to the south.) Solution stroke.

Decision:

Sun height definition formula

90 - Y \u003d H

where y is the difference of latitudes between the parallel, where the sun is in Zenith in a given day and

the desired parallel.

90- (63 - 0) \u003d 27 Yu.Sh.

№6 Determine the height of the sun over the horizon on the day of the summer solstice at noon in St. Petersburg. Where else on this day the sun will be at the same height above the horizon?

1) 90 – (60 – 23,5) = 53,5

2) The midday sun height over the horizon is the same on the parallels located at the same distance from the parallel, where the sun is in the zenith. St. Petersburg removed from the northern tropic to 60 - 23.5 \u003d 36.5

At such a distance from the Northern Tropics there is a parallel 23.5 - 36.5 \u003d -13 or 13 Yu.Sh.

№7 Determine the geographical coordinates of the point of the globe, in which the sun will be in Zenith when the new year is celebrated in London. Write down your thoughts.

Solution: from December 22 until March 21 passes 3 months or 90 days. During this time, the sun moves to 23.5. For the month, the sun moves by 7.8. In one day 0.26.

23.5 - 2.6 \u003d 21 Yu.Sh.

London is at zero meridian. At this moment, when in London is celebrated New Year (0 hours) The sun is in Zenith over the opposite meridian. 180. So, the geographical coordinates of the desired point constitute 28U.s..180 V. d. or h. d.

№8. How the length of the day is changing December 22 in St. Petersburg, if the angle of inclination of the axis of rotation relative to the orbit plane will increase to 80. Record the course of your thoughts.

Solution 1) Consequently, the polar circle will have 80, the north circle will retreat from the existing 80 - 66.5 \u003d 13.5 2) the length of the day on December 22 in St. Petersburg will increase.

№9 Determine the geographical latitude of the point on the territory of Australia, if it is known that on September 21 at noon local sunny time, the height of the sun over the horizon is 70. The course of reasoning is recorded.

Solution: 90 - 70 \u003d 20U.Sh.

№10 If the Earth would stop rotating around their 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.

Solution: a) the form of the Earth would have changed, because there would be no polar compression

b) Coriolis's strength would not be a defecting effect of the Earth's rotation. The trade winds would have a meridional direction. c) there would be no tides and sings

№11 Determine which parallels on the day of summer solstice the sun is above the horizon at an altitude of 70.

Decision

1) 90 - (70 + (- 23.5) \u003d 43.5 S.Sh.

23,5+- (90 – 70)

2) 43,5 – 23,5 = 20

23,5 - 20 \u003d 3.5 s.sh

Task 3.

Z - point of Zenith * - Polar Star

the angle under which the polar star is seen to the skyline
the angle between the zenith point and the polar star.
In the days of equinox, the height of the midday sun over the horizon for different languid definitions by the formula:

In the summer, when the sun is above the tropical of each hemisphere, its height at noon increases by 23 ° 27, i.e.

Thus, for the city of Kiev on June 21, the height of the sun is equal to 61 ° 27. "In winter, when the sun moves to the opposite hemisphere, the height of it respectively decreases and reaches a minimum on the days of solstice when it should be reduced by 23 ° 27", i.e. .

Task 32.
St. Petersburg and Kiev are located almost at one meridian. On June 22, at noon, the Sun in St. Petersburg rises above the horizon at 53 ° 30, and in Kiev at that moment - by 61.5 °. What is the distance between cities in degrees and kilometers?

Answer:
Distance between Kiev and St. Petersburg - 8 °, and kilometers -890.4 km.

Task 33.
From the ship on February 20, the height of the sun was measured over the horizon. It was 50 °. The sun was in the south. What kind of geographic latitude is the ship, if on this day the sun, stood in the zenith par with a latitude of 1105 "Yu.Sh.?

Answer:
The ship was 28 ° 55 "S.Sh.

Task 34.
In the northern hemisphere, where tourists are located, the sun at noon stands above the horizon at an angle of 53030. "On the same day, the midday sun is in Zenith at 12 ° 20" S.Sh. What degree latitude are tourists?

Answer:
Tourists are located at 48 ° 50 "s. Sh.

Questions for the Blitz tournament "I believe - I do not believe"

Under the constellation understand the sky area within certain boundaries. All the sky is divided into 88 constellations that can be found by the arrangement of stars characteristic.
Some calls for constellations are associated with Greek mythology, for example Andromeda, Perseus, Pegasus, some - with objects that resemble the figures formed by bright stars of constellations: Arrow, Triangle, Scales, etc .. There are constellations called animal names, such as lion, cancer, Scorpio.
Constellations in the sky are found, mentally connecting their brightest stars with straight lines into some shape. In every constellation, bright stars have long been denoted by Greek letters, most often the most vivid star of the constellation - the letter, then letters, etc. in the order of the alphabet as brightness decreases; eg, polar Star There are constellations Small Majer.
Stars have different brightness and color: white, yellow, reddish. Than red Star, it is colder. Our sun refers to yellow stars.
Bright stars Ancient Arabs gave their own names. White stars: Vega in the constellation Lyra, Altair In the constellation Eagle, (visible in the summer and autumn), Sirius - the brightest star of the sky (visible in winter); Red stars: Bethelgeuse In the constellation Orion and Aldebaran. In the constellation Taurus (visible in winter), Antares in the constellation of Scorpio (visible in summer); Yellow Capella In the constellation of the erection (visible in winter).
Accurate measurements show that stars have both fractional and negative stellar values, for example: for Aldebaran Star quantity m. \u003d 1,06, for vega m. \u003d 0.14, for Sirius m. \u003d -1,58, for the sun m. = - 26,80.
The phenomena of the daily movement of the stars are studied using the mathematical construction - the heavenly sphere, i.e. the imaginary sphere of an arbitrary radius, the center of which is at the observation point.
The axis of the visible rotation of the heavenly sphere connecting both poles of the world (P and P ") and passing through the observer, called axis of the world. The axis of the world for any observer will always be parallel to the axis of rotation of the Earth.
To make a star map depicting constellations on the plane, you need to know the coordinates of the stars. In the equatorial system, the same coordinate is the distance of the shone from the heavenly equator called declining. It changes within ± 90 ° and is considered positive to the north of the equator and negative to the south. Declination is similar to geographic latitude. The second coordinate is similar to the geographical longitude and is called direct ascent.
The direct climb of the luminaries is measured by the angle between the planes of large circles, one passes through the poles of the world and this shine, and the other - through the poles of the world and the spring equinox, lying on the equator. So they called this point because the sun is in it (in the heavenly sphere) in the spring of March 20-21, when the day is equal to the night.

Determination of geographic latitude

The phenomena of passage shone through heavenly meridian is called climax. In the upper climax, the height of the shine is maximal, in the lower climax - minimal. The time interval between the climax is equal to half the day.
Geographical latitude can be determined by measuring the height of any luminaries with a known decline in the upper climax. It should be borne in mind that if the luminous at the time of the climax is south of the equator, then his declination is negative.

An example of solving the problem

A task. Sirius was in the upper climax at an altitude of 10 °. What is the latitude of observation location?

Ecliptic. Visible movement of the sun and the moon

The sun and the moon change the height on which they culture. From here we can conclude that their position relative to the stars (declination) changes. It is known that the Earth moves around the Sun, and the moon around the earth.
Determining the height of the sun at noon, noticed that twice a year it happens in the heavenly equator, in the so-called equamertic points. It happens on days spring and autumn equinoxy (about March 21 and around September 23). The horizon plane divides the heavenly equator in half. Therefore, in the days of the equinoxies of the Sun path above and under the horizon are equal, therefore, equal to the duration of the day and night. Moving along the ecliptic, the sun on June 22 moves farther from the heavenly equator towards the North Pole of the world (23 ° 27 "). At noon, for the Northern Hemisphere of the Earth, it is above all over the horizon (on this magnitude above the heavenly equator). The longest day, It is called day summer Solstice.
The sun's path runs through 12 constellations called zodiacal (from the Greek word zon - an animal), and their totality is called the zodiac belt. It includes the following constellations: Fish, Aries, Taurus, Gemini, Cancer, Leo, Virgo, Scales, Scorpio, Sagittarius, Capricorn, Aquarius. Each zodiac constellation the sun takes about a month. Point of spring equinox (one of the two intersections of ecliptic with heavenly equator) is in the constellation of fish.

An example of solving the problem

A task. Determine the midwood height of the sun in Arkhangelsk and in Ashgabat in the days of summer and winter Solstice

Moon movement. Solar and lunar eclipses

Not being self-losing, the moon is visible only in the part where the sun rays fall, or rays, reflected land. This explains the Phases of the Moon. Every month the moon, moving in orbit, passes between the Earth and the Sun and addressed to us dark PartyAt this time there is a new moon. After 1 - 2 days after that, a narrow bright sickle of a young moon appears on the western sky. The rest of the moon disk occurs at this time weakly lit by the earth, turned to the moon with its daily hemisphere. After 7 days, the moon moves away from the sun on 90 °, the first quarter comes, when exactly half the moon disk and the "Terminator" disc is lit, that is, the line of section of the light and dark side becomes the line - the diameter of the lunar disk. In the following days, the Terminator becomes convex, the view of the moon is approaching a light circle and after 14 - 15 days the full moon occurs. On the 22nd day is observed last quarter. The angular distance of the moon from the cut decreases, it becomes a sickle again and after 29.5 days the new moon comes again. The gap between two consecutive novices is called a synodic month having a middle duration of 29.5 days. The synodic month is more syderician. If the new moon occurs near one of the nodes of the lunar orbit, the solar eclipse occurs, and the full moon near the node is accompanied by a lunar eclipse.

Lunny I. solar eclipses

Due to a small change in the distance of the Earth from the Moon and the Sun, the visible angular diameter of the moon is a little more, then a little less solar, it is equal to him. In the first case, the total eclipse of the sun lasts up to 7 minutes. 40 C, in the third - only one instant, and in the second case, the moon does not close the sun at all, is observed ring-shaped eclipse. Then around the dark disk of the moon is visible shining bezel of the solar disk.
Based on the exact knowledge of the laws of the Movement of the Earth and the Moon calculated for hundreds of years ahead of the moments of eclipses and where and how they will be visible. The cards are drawn up on which the full eclipse strip is shown, the line (isophase), where the eclipse will be seen in the same phase, and the lines relative to which for each area you can count the moments of the beginning, end and middle of the eclipse.
Solar eclipses in the year for the earth can be from two to five, in last case certainly private. On average, in the same place, a complete solar eclipse can be seen extremely rarely - only one day during 200-300 years.
If the moon is between the Sun and the Earth to the new moon, then solar eclipses occur. With full eclipse, the moon completely covers a sun disc. A few minutes for a few minutes, twilight and the naked eye comes to the unarmed eye, the weakly luminous crown of the Sun and the brightest stars are becoming visible.

Full solar eclipse

Current time and definition of geographic longitude

To measure short time intervals in astronomy, the main unit is average duration of sunny day, i.e. the average period of time between two tops (or lower) climax of the center of the Sun. This is due to the fact that the Earth turns around the sun in a circle, but by ellipse and the speed of its movement changes slightly.
The moment of the upper climax of the center of the Sun is called true half a day. But to test the clock, to determine the exact time, there is no need to note on them exactly the moment of the climax of the sun. It is more convenient and more accurate to celebrate the moments of the climax of stars, since the difference in the moments of the climax of any star and the sun is definitely known for any time.
Determining the exact time, its storage, and the transfer of radio to the whole population is the task current time serviceswhich exists in many countries.
For the account of large periods of time, people since ancient pores used the duration of either the lunar month, or a sunny year, i.e. the duration of the sun turnover by ecliptic. Year defines frequency seasonal changes. Sunny year lasts 365 sunny day 5 hours 48 minutes 46 seconds.
When drawing up a calendar, it is necessary to take into account that the duration of the calendar year should be as close as possible to the duration of the sun turnover by ecliptic, and that the calendar year should contain an integer number of sunny day, as it is inconvenient to start a year at different times of the day.

Life on our planet depends on the quantity sunlight And heat. It is terrible to imagine even on a moment, which would be if there was no such star in the sky like the sun. Each blade, every leaf, each flower needs warm and light as people in the air.

Sun rays angle equal to the height of the sun over the horizon

The amount of sunlight and heat that enters the ground surface is directly proportional to the alarm of the drop of rays. The sun rays can fall on the ground at an angle from 0 to 90 degrees. The angle of rays on the ground is different, because our planet has a shape of a ball. What he is more, the lighter and warmer.

Thus, if the ray goes at an angle of 0 degrees, it only slides along the surface of the earth, without heating it. Such angle of falling happens in the northern and southern poles, behind the polar circle. At a right angle, the sun rays fall on the equator and on the surface between the southern and

If the angle of sunlight on the ground is straight, it says that

Thus, the rays on the surface of the Earth and the height of the sun over the horizon are equal to each other. They depend on geographic latitude. The closer to zero latitude, the angle of falling rays is closer to 90 degrees, the higher the sun over the horizon, the warmer and lighter.

How the sun changes its height above the horizon

The height of the sun over the horizon is not a permanent value. On the contrary, it always changes. 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 replaces the night, and the seasons of each other.

The territory between the tropics receives more than all heat and light, here the day and night are almost equal to each other by duration, and the sun is in Zenith 2 times a year.

The surface of the polar circle receives all less heat and light, there are such concepts, like the night that last about six months.

Days of Autumn and Spring Equinox

4 major astrological dates are highlighted, which determines the height of the sun over the horizon. September 23 and March 21 - the Days of Autumn and Spring Equinox. This means that the height of the Sun over the horizon in September and March these days are 90 degrees.

Southern 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 South, on the contrary, spring. The same can be said about Winter and summer. If in the Southern Hemisphere Winter, then in the North - Summer.

Summer Days and Winter Solstice

June 22 and December 22 - the days of the summer and on December 22, there is the shortest day and the longest night in the northern hemisphere, and the winter sun is on the lowest height over the horizon for the entire year.

Above the latitude of 66.5 degrees The sun is under the horizon and does not go. This phenomenon when the winter sun does not go on the horizon, is called polar night. The shortest night happens on the latitude of 67 degrees and lasts only 2 days, and the longest happens on the poles and lasts 6 months!

December is from the whole month to those months when in the northern hemisphere the longest nights. People in Central Russia wake up to work in the dark and return too in the dark. This is a difficult month for many, since the lack of sunlight affects the physical and moral state of people. For this reason, depression may even develop.

In Moscow in 2016, the sunrise in December 1 will be at 08.33. At the same time, the longitude of the day will be 7 hours 29 minutes. Behind 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 more than the longitude of the day!

This year the Day of the Winter Solstice is December 21. The shortest day will last exactly 7 hours. Then 2 days will last the same situation. And from December 24, the day will go to profit slowly, but right.

On average, per day will be added for one minute of light time. At the end of the month, the sunrise in December will be exactly 9 hours, which is 27 minutes later than December 1st

June 22 - Day Summer Solstice. Everything happens exactly the opposite. For the whole year it is at this date the longest day for duration and the shortest night. This is relating to the northern hemisphere.

In South, the other way around. Interesting days are connected with this day. natural phenomena. A polar day comes for the polar circle, the sun does not go beyond the horizon on the North Pole of 6 months. In June, mysterious white nights begin in June. They last from mid-June for two or three weeks.

All of these 4 astrological dates may vary for 1-2 days, as the sunny year does not always coincide with the calendar year. Also bias occur in leap years.

Sun height over the horizon and climatic conditions

The sun is one of the most important climate-forming factors. Depending on how the height of the sun has changed over the horizon over a specific part of the earth's surface, climatic conditions and seasons change.

For example, in the extreme north, the rays of the sun fall at a very small angle and only slide along the surface of the Earth, without heating it at all. Under the condition of this factor, the climate is extremely severe here, there are permafrost, cold winters with candy winds and snow.

Than more height Sun over the horizon, the warmer climate. For example, at the equator it is unusually hot, tropical. Seasonal oscillations also in the area of \u200b\u200bthe equator are practically not felt, in these areas the eternal summer.

Sun height measurement over the horizon

As they say, everything is ingenious - simple. So here. The device for measuring the height of the sun over the horizon is elementary simple. It is a horizontal surface with a sixth in the middle of 1 meter long. On a sunny day at noon, the pole sweeps the shortest shadow. With this shortest shade and the calculation and measurement are carried out. You need to measure the angle between the end of the shadow and the segment connecting the end of the pole with the end of the shade. This magnitude of the angle will be an angle of finding the sun over the horizon. This device is called a gnomon.

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

a) for an observer in the North Pole of the Earth ( j. = + 90 °) Siplies are those whose d--і ?? 0, and non-existence those whose d.--< 0.

Table.1. Height of the midday sun in different latitudes

A positive declination by the Sun is from March 21 to September 23, and negative - from September 23 to March 21. Consequently, in the North Pole of the Earth, the Sun is approximately six months old, and half a year - an unbalanced luminaire. Around March 21, the Sun here appears above the horizon (dates) and due to the daily rotation of the heavenly sphere describes curves close to the circle and almost parallel horizons, rising every day above and higher. On the day of summer solstice (around June 22) the sun reaches the maximum height h. Mach \u003d + 23 ° 27 " . After that, the sun begins to approach the horizon, height it gradually decreases and after the day of the autumn equinox (after September 23) it is hidden under the horizon (enters). A day that lasted half a year ends and the night starts, which lasts also half a year. The sun, continuing to describe the curves, almost parallel to the horizon, but under it, is lowered and lower, on the day of the winter solstice (around December 22) it will fall under the horizon to height h. MIN \u003d - 23 ° 27 " And then again starts to approach the horizon, the height of it will increase, and before the spring of the spring equinox, the sun will appear over the horizon again. For an observer in the South Pole of the Earth ( j. \u003d - 90 °) The daily movement of the sun occurs in a similar way. Only here the Sun dates back on September 23, and it comes after March 21, and therefore when the night on the North Pole is the night, on the south - day, and vice versa.

b) for an observer on the Northern Polar Circle ( j. \u003d + 66 ° 33 " ) are suitable with shining with d.--І + 23 ° 27 " and non-existence - with d. < - 23° 27". Consequently, on the Northern Polar Circle the Sun does not enter the day of the summer solstice (at midnight the center of the sun only touches the horizon at the point of the North N.) And does not go on the day of the winter solstice (at noon, the sun disk center only touches the horizon at the south point S, And then drop out again under the horizon). On the other days of the year the sun on this latitude rises and comes. At the same time, the maximum height at noon it reaches on the day of the summer solstice ( h. max \u003d + 46 ° 54 "), and on the day of the winter solstice, his midday height is minimal ( h. min \u003d 0 °). On the southern polar circle ( j. \u003d - 66 ° 33 ") The sun does not enter the day of the winter solstice and does not go on the day of the summer solstice.

Northern and South Polar Circles are theoretical borders of those geographic latitudes where possible polar days and nights (days and nights for more than 24 hours).

In places underlying the polar circles, the sun is in a good or unwarked luminaries, the longer, the closer place to the geographical poles. As the duration of polar days and nights approaches the poles.

c) for an observer on the northern tropics ( j.- \u003d + 23 ° 27 ") The sun is always ascending and setting luminaire. On the day of summer solstice, it reaches a maximum height at noon. h. Max \u003d + 90 °, i.e. passes through Zenit. On other days of the year, the sun at noon cultures south of Zenith. On the Day of the Winter Solstice His minimum midday height h. MIN \u003d + 43 ° 06 ".

On southern tropics ( j. = - 23 ° 27 ") The sun also always goes back and comes. But at the maximum half-hearted height over the horizon (+ 90 °) it happens on the day of the winter solstice, and on the minimum (+ 43 ° 06 " ) - on the day of summer solstice. On the other days of the year, the sun at noon cultures here north of Zenith.

In places lying between tropics and polar circles, the sun rises and comes every day. Six months here the duration of the day is more duration of the night, and half a year - the night is longer than the day. The midday height of the Sun is always less than 90 ° (except for tropics) and more than 0 ° (except polar circles).

In places lying between the tropics, the sun is in Zenith twice a year, in those days when his declination is equal to the geographical latitude of the place.

d) for an observer at the Earth Equator ( j.- \u003d 0) All the shines, including the sun, are rising and incoming. At the same time, 12 hours they are above the horizon, and 12 hours - under the horizon. Consequently, at the equator, the duration of the day is always equal to the duration of the night. Twice a year the sun at noon takes place in Zenith (March 21 and September 23).

From March 21 to September 23, the Sun at the Equator cultures at noon north of Zenith, and from September 23 to March 21 - south of Zenith. The minimum midday sun height here will be equal h. MIN \u003d 90 ° - 23 ° 27 " \u003d 66 ° 33 " (June 22 and December 22).