The angle of the sun to the horizon. Olympiad tasks in geography: Sun height and latitude

φ = 90° - North Pole

Only at the Pole day and night last for six months. In a day spring equinox The sun makes a full circle on the horizon, then every day in a spiral rises higher, but not higher than 23 ° 27 (on the day summer solstice). After that, revolution after revolution, the Sun again descends to the horizon. Its light is repeatedly reflected from ice and hummocks. On the day of the autumnal equinox, the Sun once again bypasses the entire horizon, and its next turns very gradually go deeper and deeper below the horizon. Dawn lasts for weeks, even months, moving through all 360 °. The white night gradually darkens, and only near the day of the winter solstice does it become dark. This is the middle of the polar night. But the Sun does not fall under the horizon below 23°27. The polar night gradually brightens and the morning dawn lights up.

φ \u003d 80 ° - one of the latitudes of the Arctic

The motion of the Sun at latitude φ = 80° is typical for regions located north of the Arctic Circle, but south of the pole. After the day of the spring equinox, the days grow very quickly, and the nights shorten, the first period of white nights begins - from March 15 to April 15 (1 month). Then the Sun, instead of setting below the horizon, touches it at the north point and rises again, goes around the sky, moving all 360 °. The daily parallel is located at a slight angle to the horizon, the Sun culminates over the point of the south and descends to the north, but does not go beyond the horizon and does not even touch it, but passes above the point of the north and again makes another daily revolution in the sky. So the Sun rises in a spiral higher and higher until the day of the summer solstice, which marks the middle of the polar day. Then the turns of the daily motion of the Sun descend lower and lower. When the Sun touches the horizon at the north point, the polar day will end, which lasted 4.5 months (from April 16 to August 27), the second period of white nights will begin from August 27 to September 28. Then the duration of the nights increases rapidly, the days become shorter and shorter, because. the points of sunrise and sunset are rapidly shifting to the south, and the arc of the daily parallel over the horizon is shortening. On one of the days before the winter solstice, the Sun does not rise above the horizon at noon, the polar night begins. The sun, moving in a spiral, goes deeper and deeper below the horizon. The middle of the polar night is the day of the winter solstice. After it, the Sun again spirals towards the equator. In relation to the horizon, the turns of the spiral are inclined, therefore, when the Sun rises to the southern part of the horizon, it gets light, then it gets dark again, there is a struggle between light and darkness. With each turn, the daytime twilight becomes lighter and, finally, the Sun appears for a moment above the southern (!) horizon. This long-awaited beam marks the end of the polar night, which lasted 4.2 months from October 10 to February 23. Every day the Sun lingers longer and longer above the horizon, describing an ever larger arc. The greater the latitude, the longer the polar days and polar nights, and the shorter the period of daily change of days and nights between them. In these latitudes, long twilight, because The sun goes under the horizon at a slight angle. In the Arctic, the Sun can rise at any point on the eastern horizon from north to south, and set also at any point on the western horizon. Therefore, the navigator, who believes that the Sun always rises at the point of the east and sets at the point, runs the risk of making a heading error of 90 °.

φ = 66°33" - Arctic Circle

Latitude φ \u003d 66 ° 33 "- the maximum latitude that separates the regions in which the Sun rises and sets every day from the regions in which merged polar days and merged polar nights are observed. At this latitude in summer, the points of sunrise and sunset shift with "wide steps" from the points east and west 90 ° north, so that on the day of the summer solstice they meet at the point north. Therefore, the Sun, having descended to the northern horizon, immediately rises again, so that two days merge into a continuous polar day (June 21 and 22 ) Before and after the polar day, periods of white nights set in. The first - from April 20 to June 20 (67 white nights), the second - from June 23 to August 23 (62 white nights). On the day of the winter solstice, the points of sunrise and sunset meet at the south point There is no day between two nights Polar night lasts two days (December 22, 23) Between polar day and polar night the Sun rises and sets every day, but the duration of days and nights changes rapidly.

φ = 60° - latitude of St. Petersburg

The famous white nights are observed before and after the summer solstice, when "one dawn hurries to replace another", i.e. The sun descends shallowly below the horizon at night, so that its rays illuminate the atmosphere. But the inhabitants of St. Petersburg are silent about their "black days", when the Sun on the day of the winter solstice rises at noon only 6 ° 33" above the horizon. The white nights (navigational twilight) of St. Petersburg are especially good in combination with its architecture and the Neva. They begin around May 11 and last 83 days until August 1. The brightest time - the middle of the interval - is around June 21. During the year, the points of sunrise and sunset shift along the horizon by 106 ° But white nights are observed not only in St. Petersburg, and all along the parallel φ = 60° and northward up to φ = 90°, southward φ = 60° white nights become shorter and darker.Similar white nights are observed in the Southern Hemisphere, but at the opposite season.

φ = 54°19" - latitude of Ulyanovsk

This is the latitude of Ulyanovsk. The movement of the Sun in Ulyanovsk is typical for all middle latitudes. The radius of the sphere depicted in the figure is so large that, in comparison with it, the Earth looks like a point (it is symbolized by the observer). Geographic latitude φ is given by the height of the pole above the horizon, i.e. angle Pole (P) - Observer - North Point (C) in the horizon. On the day of the vernal equinox (21.03), the Sun rises exactly in the east, rises across the sky, shifting to the south. Above the south point - the highest position of the Sun on a given day - the upper culmination, i.e. noon, then it "downhill" descends and sets exactly in the west. The further movement of the Sun continues below the horizon, but the observer does not see this. At midnight, the Sun reaches a lower climax below the north point, then rises again to the eastern horizon. On the day of the equinox, half of the daily parallel of the Sun is above the horizon (day), half is below the horizon (night). On the next day, the Sun does not rise exactly at the point of the east, but at a point slightly shifted to the north, the daily parallel passes above the previous one, the height of the Sun at noon is greater than on the previous day, the setting point is also shifted to the north. Thus, the daily parallel of the Sun is no longer divided by the horizon in half: most of it is above the horizon, the smaller one is below the horizon. The summer half of the year is coming. The points of sunrise and sunset are increasingly shifting to the north, more and more of the parallel is above the horizon, the midday height of the Sun increases and on the day of the summer solstice (21.07 -22.07) in Ulyanovsk reaches 59 ° 08 ". At the same time, the points of sunrise and sunset are shifted relative to the points of the east and west to the north by 43.5 °.After the day of the summer solstice, the daily parallels of the Sun descend to the equator.On the day of the autumnal equinox (23.09), the Sun again rises and sets at the points of east and west, passes along the equator.In the future, the Sun gradually day by day descends under the equator, with the points of sunrise and sunset shifting to the south until the day of the winter solstice (23.12) also by 43.5 °. Most of parallels in winter time is below the horizon. The noon height of the Sun decreases to 12 ° 14 ". The further movement of the Sun along the ecliptic occurs along parallels, again approaching the equator, the points of sunrise and sunset return to the points of east and west, the days increase, spring comes again! It is interesting that in Ulyanovsk the points of sunrise are shifting along the eastern horizon by 87 °. The points of sunset respectively "walk" along the western horizon. The sun rises exactly in the east and sets exactly in the west only twice a year - on the equinoxes. The latter is true on the entire surface of the Earth, except for the poles.

φ = 0° - Earth's equator

The movement of the Sun over the horizon at different times of the year for an observer located at mid-latitudes (left) and at the Earth's equator (right).

At the equator, the Sun passes through the zenith twice a year, on the days of the spring and autumn equinoxes, i.e. There are two "summers" at the equator, when we have spring and autumn. Day at the equator is always equal to night (12 hours each). The points of sunrise and sunset shift slightly from the points of east and west, no more than 23 ° 27 "towards the south and by the same amount towards the north. There is practically no twilight, a hot bright day is abruptly replaced by a black night.

φ \u003d 23 ° 27 "- Northern Tropic

The sun rises steeply above the horizon, during the day it is very hot, then it drops steeply below the horizon. Twilight is short, nights are very dark. The most salient feature is that the Sun once a year, on the day of the summer solstice, reaches its zenith at noon.

φ = -54°19" - latitude corresponding to Ulyanovsk in the Southern Hemisphere

As in the entire southern hemisphere, the Sun rises on the eastern horizon and sets on the western. After sunrise, the Sun rises above the northern part of the horizon at noon, at midnight it goes under the southern horizon. Otherwise, the movement of the Sun is similar to its movement at the latitude of Ulyanovsk. The movement of the Sun in the southern hemisphere is similar to the movement of the Sun at the corresponding latitudes of the northern hemisphere. The only difference is that from the east, the Sun moves towards the northern horizon, and not the southern one, culminates over the north point at noon, and then also sets on the western horizon. The seasons in the northern and southern hemispheres are opposite.

φ \u003d 10 ° - one of the latitudes of the hot zone

The movement of the Sun at a given latitude is characteristic of all places located between the northern and southern tropics of the Earth. Here the Sun passes through the zenith twice a year: on April 16 and August 27, with an interval of 4.5 months. The days are very hot, the nights are dark, starry. Days and nights differ little in duration, there is practically no twilight, the Sun sets below the horizon, and it immediately becomes dark.

The sun is the main source of heat and the only star in our solar system, which, like a magnet, attracts all the planets, satellites, asteroids, comets and other "inhabitants" of space.

The distance from the Sun to the Earth is over 149 million kilometers. It is this distance of our planet from the Sun that is commonly called an astronomical unit.

Despite its significant distance, this star has a huge impact on our planet. Depending on the position of the Sun on Earth, day follows night, summer replaces winter, and magnetic storms and the most amazing auroras. And most importantly, without the participation of the Sun on Earth, the process of photosynthesis, the main source of oxygen, would be impossible.

The position of the sun at different times of the year

Our planet moves around the celestial source of light and heat in a closed orbit. This path can be schematically represented as an elongated ellipse. The Sun itself is not located in the center of the ellipse, but somewhat to the side.

The Earth moves in and out of the Sun, completing a full orbit in 365 days. Our planet is closest to the sun in January. At this time, the distance is reduced to 147 million km. The point in the earth's orbit closest to the sun is called perihelion.

The closer the Earth is to the Sun, the more the South Pole is illuminated, and summer begins in the countries of the southern hemisphere.

Closer to July, our planet is as far away from main star solar system. During this period, the distance is more than 152 million km. The farthest point in the Earth's orbit from the Sun is called aphelion. The farther the globe is from the Sun, the more light and heat the countries of the northern hemisphere receive. Then summer comes here, and, for example, in Australia and South America, winter dominates.

How the Sun illuminates the Earth at different times of the year

Illumination of the Earth by the Sun different time year directly depends on the remoteness of our planet in a given period of time and on which "sideways" the Earth is turned at that moment to the Sun.

The most important factor influencing the change of seasons is the earth's axis. Our planet, revolving around the Sun, has time to turn around its own imaginary axis at the same time. This axis is located at an angle of 23.5 degrees to the heavenly body and always turns out to be directed to the North Star. Full circle around earth's axis takes 24 hours. Axial rotation also provides a change of day and night.

By the way, if this deviation did not exist, then the seasons would not replace each other, but would remain constant. That is, somewhere a constant summer would reign, in other areas there would be a constant spring, a third of the earth would forever be watered with autumn rains.

Under the direct rays of the Sun on the days of the equinox is the earth's equator, while on the days of the solstice the sun at the zenith will be at latitudes of 23.5 degrees, gradually approaching zero latitude in the rest of the year, i.e. to the equator. The sun's rays falling vertically bring more light and heat, they do not dissipate in the atmosphere. Therefore, the inhabitants of countries located on the equator never know the cold.

poles the globe alternately exposed to the rays of the sun. Therefore, at the poles, day lasts half a year, and night lasts half a year. When the North Pole is illuminated, then spring comes in the northern hemisphere, replacing summer.

In the next six months, the picture changes. The South Pole is facing the Sun. Now summer is beginning in the southern hemisphere, and winter is setting in in the countries of the northern hemisphere.

Twice a year, our planet is in a position where the sun's rays equally illuminate its surface from the Far North to the South Pole. These days are called the equinoxes. Spring is celebrated on March 21, autumn - September 23.

Two more days of the year are called solstices. At this time, the Sun is either as high as possible above the horizon, or as low as possible.

In the northern hemisphere, December 21 or 22 is the longest night of the year, the winter solstice. And on June 20 or 21, on the contrary, the day is the longest, and the night is the shortest - this is the day of the summer solstice. In the southern hemisphere, the opposite is true. There in December long days and June has long nights.

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 big circle 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 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 position of the Sun in the sky during the year for observers located in different places on the surface of the earth.

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 on the ecliptic, will describe a circle parallel to the horizon, at a slightly 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 The sun reaches its highest height at 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. Polar day and polar night can last from 24 hours (at the northern and southern polar circles) to six months (at the north and south poles of the 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. In summer, the day is longer than the night, and in winter it is vice versa.

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 a consequence 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 during the year changes, and consequently, the conditions of their illumination and heating by the Sun change.

The unequal heating by the Sun of regions of the earth's surface with different geographic latitudes (or these same regions at different times of the year) can be easily ascertained by a 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 into 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:

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 noon 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 to establish the names and boundaries of the zodiac constellations, indicate those in which the main points of the ecliptic are located, and determine the average duration of 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 identical 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 stellar (sidereal) periods of revolution of some planet and the Earth around the Sun, and and are the semi-major axes of their orbits, then

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

Medium line speed the motion of the 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 plane of the ecliptic, these orbits are always located near the ecliptic, and in the first approximation, their heliocentric longitude can be considered, 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:

We will call configuration planets some fixed relative position of the planet, the Earth and the 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 retrograde 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 the unique astronomical phenomenon- the passage of the inner planet (Mercury or Venus) across the disk of the Sun.

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 it can be observed in the morning, before sunrise, in the eastern side of the 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 is always "bathed" in the sun's rays - 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, further relative motion planets on the celestial sphere will be backtracked. 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 confrontations on northern latitudes occur low on 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. If a day of the year is given on which the heliocentric ecliptic longitude of the Earth has a 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 ^, 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 opposite 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
in different days of the year

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 geographical latitude 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 of 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 geographical 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