How to find the height of the sun above the horizon. The movement of the sun at different latitudes

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

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

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

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

If the angle of the sun's rays on the ground is right, this indicates that

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

How does the sun change its height above the horizon?

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

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

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

Autumn and spring equinoxes

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

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

Summer and winter solstices

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

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

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

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

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

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

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

In the South it's the other way around. Interesting natural phenomena are associated with this day. Beyond the Arctic Circle comes the polar day, the sun does not set below the horizon at the North Pole for 6 months. Mysterious white nights begin in St. Petersburg in June. They last from about mid-June for two to three weeks.

All these 4 astrological dates can vary by 1-2 days, since the solar year does not always coincide with the calendar year. Also offsets occur in leap years.

The height of the sun above the horizon and climatic conditions

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

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

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

Measuring the height of the sun above the horizon

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Let's make one more interesting experience: we will not tilt the axis of the globe, but arrange it is perpendicular to the floor plane. If we take the same path With globe around the lamp, we will make sure that in this case there will be all year round the equinox lasts. In our latitudes there would be eternal spring and autumn days and there would be no abrupt 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, rising at noon always to the same for this place height and would set due west at 6 pm local time.

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

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

On the 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 is at its zenith twice a year. The space of the globe, enclosed between the tropics, due to its thermal features, was called the hot zone. In the middle of it is the equator.

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

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

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

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

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

§ 52. Apparent annual motion of the Sun and its explanation

1. The place of sunrise and sunset, and consequently, its azimuth change from day to day. Starting from March 21 (when the Sun rises in the east point and sets in the west point) to September 23, the sunrise is observed in the northeast quarter, and the sunset is observed in the northwest quarter. At the beginning of this time, the points of sunrise and sunset move to the north, and then in the opposite direction. On September 23, just like on March 21, the Sun rises in the east and sets in the west. Starting from September 23 to March 21, a similar phenomenon will be repeated in the southeast and southwest quarters. The movement of the points of sunrise and sunset has a one-year period.

Stars always rise and set at the same points on the horizon.

2. The meridional height of the Sun changes every day. For example, in Odessa (av = 46°.5 N) on June 22 it will be the largest and equal to 67°, then it will begin to decrease and on December 22 it will reach the smallest value 20°. After December 22, the meridional height of the Sun will begin to increase. This phenomenon is also an annual period. The meridional height of stars is always constant. 3. The length of time between the climaxes of any star and the Sun is constantly changing, while the length of time between two culminations of the same stars remains constant. So, at midnight we see those constellations culminating, which in given time located on the opposite side of the sphere from the Sun. Then some constellations give way to others, and during the year at midnight all the constellations culminate in turn.

4. The length of the day (or night) is not constant throughout the year. This is especially noticeable if we compare the duration of summer and winter days at high latitudes, for example in Leningrad. This happens because the time the Sun is above the horizon during the year is different. The stars above the horizon are always the same amount of time.

Thus, the Sun, in addition to the daily movement performed together with the stars, also has a visible movement along the sphere with an annual period. This movement is called visible the annual motion of the Sun across the celestial sphere.

We will get the most visual representation of this movement of the Sun if we daily determine its equatorial coordinates - right ascension a and declination b. Then, using the found coordinate values, we plot points on the auxiliary celestial sphere and connect them with a smooth curve. As a result, we get a large circle on the sphere, which will indicate the path of the apparent annual movement of the Sun. The circle on the celestial sphere along which the Sun moves is called the ecliptic. The plane of the ecliptic is inclined to the plane of the equator at a constant angle g \u003d \u003d 23 ° 27 ", which is called the angle of inclination ecliptic to equator(Fig. 82).

Rice. 82.

The opposite point at which the Sun moves from the northern hemisphere to the southern and changes the name of its declination from b N to b S is called point of the autumnal equinox. It is designated by the sign of the constellation Libra O, in which it was once located. The autumnal equinox is currently in the constellation Virgo.

The point L is called summer point, and point L" - point winter solstices.

Let's follow the apparent movement of the Sun along the ecliptic during the year.

The sun arrives at the vernal equinox on March 21st. Right ascension a and solar declination b are zero. On everything the globe The sun rises at point O st and sets at point W, and day equals night. Since March 21, the Sun moves along the ecliptic towards the point of the summer solstice. The right ascension and declination of the Sun are constantly increasing. Astronomical spring is coming in the northern hemisphere, and autumn is coming in the southern hemisphere.

On June 22, after about 3 months, the Sun comes to the summer solstice point L. Right ascension of the Sun a \u003d 90 °, a declination b \u003d 23 ° 27 "N. Astronomical summer begins in the northern hemisphere (the most long days and short nights), and in the south - winter (the longest nights and short days) . With further movement of the Sun, its northern declination begins to decrease, and right ascension continues to increase.

Approximately three months later, on September 23, the Sun comes to the point of the autumnal equinox Q. Right ascension of the Sun a=180°, declination b=0°. Since b \u003d 0 ° (like March 21), then for all points on the earth's surface the Sun rises at point O st and sets at point W. Day will be equal to night. The name of the declination of the Sun changes from northern 8n to southern - bS. Astronomical autumn comes in the northern hemisphere, and spring in the southern hemisphere. With further movement of the Sun along the ecliptic to the point of the winter solstice U, declination 6 and right ascension aO increase.

On December 22, the Sun comes to the point of the winter solstice L ". Right ascension a \u003d 270 ° and declination b \u003d 23 ° 27" S. In the northern hemisphere, astronomical winter sets in, and in the southern hemisphere, summer.

After December 22, the Sun moves to point T. The name of its declination remains south, but decreases, and right ascension increases. Approximately 3 months later, on March 21, the Sun, having made a full revolution along the ecliptic, returns to the point of Aries.

Changes in the right ascension and declination of the Sun during the year do not remain constant. For approximate calculations, the daily change in the right ascension of the Sun is taken equal to 1 °. The change in declination per day is taken equal to 0°.4 for one month before the equinox and one month after, and the change of 0°.1 for one month before the solstices and one month after the solstices; the rest of the time, the change in the declination of the Sun is taken equal to 0 °.3.

The peculiarity of the change in the right ascension of the Sun plays an important role in choosing the basic units for measuring time.

The vernal equinox moves along the ecliptic towards the annual movement of the Sun. Its annual movement is 50", 27 or rounded 50", 3 (for 1950). Consequently, the Sun does not reach its original place relative to the fixed stars by 50 "3. For the Sun to pass the indicated path, 20 m m 24 s will be needed. For this reason, spring

It comes before the Sun finishes and its apparent annual movement is a full circle of 360 ° relative to the fixed stars. The shift in the moment of the onset of spring was discovered by Hipparchus in the 2nd century BC. BC e. from the observations of the stars he made on the island of Rhodes. He called this phenomenon the precession of the equinoxes, or precession.

The phenomenon of the movement of the vernal equinox necessitated the introduction of the concepts of tropical and sidereal years. A tropical year is a period of time during which the Sun makes a complete revolution in the celestial sphere relative to the vernal equinox point T. "The duration of a tropical year is 365.2422 days. The tropical year is consistent with natural phenomena and accurately contains the full cycle of the seasons of the year: spring, summer, autumn and winter.

A sidereal year is a period of time during which the Sun makes a complete revolution in the celestial sphere relative to the stars. The duration of a sidereal year is 365.2561 days. sidereal year longer than tropical.

In its apparent annual movement across the celestial sphere, the Sun passes among various stars located along the ecliptic. Even in ancient times, these stars were divided into 12 constellations, most of which were given the names of animals. The strip of sky along the ecliptic formed by these constellations was called the Zodiac (circle of animals), and the constellations were called zodiac.

According to the seasons of the year, the Sun passes through the following constellations:

On June 22, when the Sun describes the extreme daily parallel in the northern celestial hemisphere, it is in the constellation Gemini. In the distant past, the Sun was in the constellation Cancer. On December 22, the Sun is in the constellation of Sagittarius, and in the past it was in the constellation of Capricorn. Therefore, the extreme northern celestial parallel was called the Tropic of Cancer, and the southern - the Tropic of Capricorn. The corresponding terrestrial parallels with latitudes cp = bemax = 23 ° 27 "in the northern hemisphere were called the Tropic of Cancer, or the northern tropic, and in the southern - the Tropic of Capricorn, or the southern tropic.

In the joint motion of the Sun, which occurs along the ecliptic with the simultaneous rotation of the celestial sphere, there are a number of features: the length of the daily parallel above the horizon and below the horizon changes (and, consequently, the length of day and night), the meridional heights of the Sun, the points of sunrise and sunset, etc. All these phenomena depend on the relationship between the geographic latitude of a place and the declination of the Sun. Therefore, for an observer located at different latitudes, they will be different.

Consider these phenomena in some latitudes:

1. The observer is at the equator, cp = 0°. The axis of the world lies in the plane of the true horizon. The celestial equator coincides with the first vertical. The daily parallels of the Sun are parallel to the first vertical, so the Sun in its daily movement never crosses the first vertical. The sun rises and sets daily. Day is always equal to night. The sun is at its zenith twice a year - March 21 and September 23.

Rice. 83.

5. The observer is at the pole φ=90°N or S. The axis of the world coincides with the plumb line and, therefore, the equator with the plane of the true horizon. The position of the observer's meridian will be uncertain, so parts of the world are missing. During the day, the Sun moves parallel to the horizon.

On the days of the equinoxes, polar sunrises or sunsets occur. At the solstices, the height of the sun reaches highest values. The altitude of the Sun is always equal to its declination. Polar day and polar night last for 6 months.

Thus, due to various astronomical phenomena caused by the joint daily and annual motion of the Sun at different latitudes (passing through the zenith, phenomena of the polar day and night) and the climatic features caused by these phenomena, the earth's surface is divided into tropical, temperate and polar zones.

tropical belt the part of the earth's surface is called (between latitudes φ \u003d 23 ° 27 "N and 23 ° 27" S), in which the Sun rises and sets every day and is at its zenith twice a year. The tropical zone occupies 40% of the entire earth's surface.

temperate zone called the part of the earth's surface in which the sun rises and sets every day, but never at its zenith. There are two temperate zones. In the northern hemisphere between latitudes φ = 23°27"N and φ = 66°33"N, and in the southern hemisphere between latitudes φ=23°27"S and φ = 66°33"S. Temperate zones occupy 50% of the earth's surface.

polar belt called the part of the earth's surface in which polar days and nights are observed. There are two polar belts. The northern polar belt extends from latitude φ \u003d 66 ° 33 "N to north pole, and the south one - from φ \u003d 66 ° 33 "S to the south pole. They occupy 10% of the earth's surface.

Nicolaus Copernicus (1473-1543) was the first to give a correct explanation of the apparent annual motion of the Sun in the celestial sphere. He showed that the annual movement of the Sun in the celestial sphere is not its actual movement, but only the visible one, reflecting the annual movement of the Earth around the Sun. The Copernican world system was called heliocentric. According to this system in the center solar system the Sun is located around which the planets, including our Earth, move.

The Earth simultaneously participates in two movements: it rotates around its axis and moves in an ellipse around the Sun. The rotation of the Earth around its axis causes a change of day and night. Its movement around the Sun causes the change of seasons. From the joint rotation of the Earth around its axis and movement around the Sun, the apparent movement of the Sun in the celestial sphere occurs.

To explain the apparent annual motion of the Sun in the celestial sphere, we use Fig. 84. In the center is the Sun S, around which the Earth moves counterclockwise. The earth's axis maintains an unchanged position in space and makes an angle equal to 66 ° 33 with the ecliptic plane. Therefore, the equatorial plane is inclined to the ecliptic plane at an angle e = 23 ° 27 ". Next comes the celestial sphere with the ecliptic and the signs of the constellations of the Zodiac inscribed on it in their current location.

The Earth comes into position I on March 21st. Seen from Earth, the Sun is projected onto the celestial sphere at point T, currently in the constellation Pisces. Declination of the Sun be=0°. An observer located at the Earth's equator sees the Sun at noon at its zenith. All terrestrial parallels are illuminated by half, therefore, at all points on the earth's surface, day is equal to night. Astronomical spring begins in the northern hemisphere, and autumn begins in the southern hemisphere.

Rice. 84.

into position III Earth comes September 23rd. The declination of the Sun is bo=0° and it is projected to the point of Libra, which is now in the constellation Virgo. An observer at the equator sees the sun at noon at its zenith. All terrestrial parallels are half illuminated by the Sun, therefore, in all points of the Earth, day is equal to night. Astronomical autumn begins in the northern hemisphere, and spring begins in the southern hemisphere.

December 22 Earth comes to position IV The sun is projected into the constellation Sagittarius. Sun declination 6=23°,5S. Illuminated in the southern hemisphere most of diurnal parallels than in the northern, so in the southern hemisphere the day is longer than the night, and in the northern - vice versa. The rays of the sun fall almost vertically into the southern hemisphere, and at an angle into the northern hemisphere. Therefore, astronomical summer comes in the southern hemisphere, and winter in the northern hemisphere. The sun illuminates the southern polar belt and does not illuminate the northern one. The polar day is observed in the southern polar belt, and the night is observed in the northern one.

Appropriate explanations can be given for other intermediate positions of the Earth.

Forward
Table of contents
Back

Since the latitude of the area does not change, it follows from changes in the height of the Sun that its declination changes. The latitude of the area is approximate for a given locality can be determined by geographical map(for Rostov 47 ° 13 "), then by measuring the height h it can be found that in summer the maximum distance from the celestial equator is + 23.5 °, and in winter time equals -23.5°. It can also be established that the Sun is at the celestial equator on March 21 and September 23 (the days of the equinoxes), on these days the declination of the Sun is 0 °.

For example, you need to determine the maximum and minimum height rise of the Sun above the horizon for the city of Kyiv. Latitude of Kyiv: 50° 24"

H = 90° - 50.2° + 23.5° = 63.3° (during the summer solstice);

H = 90° - 50.2° - 23.5° = 16.3° (during the winter solstice).

During the spring and autumn equinoxes, the midday height of the Sun is equal to the addition of the geographic latitude of the place up to 90 °, and during the winter and summer solstices it is less or more than the equinoctial by an angle equal to the inclination of the ecliptic to the equator.

On the days of the equinoxes, the height of the midday Sun (φ0) above the horizon for different latitudes (φ1) is determined by the formula:
φ0 = 90° - φ1
Donetsk coordinates: 48°00′32″ s. sh. 37°48′15″ in. d.
In Donetsk on March 21 and September 23 at noon the Sun is at the height:
φ0 = 90° - 48°= 42°
In summer, when the Sun is above the tropic of each hemisphere, its height at noon increases by 23° 27", i.e.
φ0 = 90° - φ1 + 23° 27"
φ0 = 90°- 48° +23° 27"= 65° 27"
In Donetsk on June 21, the height of the Sun is 65 ° 27 "

In winter, when the Sun moves to the opposite hemisphere, its height decreases accordingly and reaches a minimum on the days of the solstice, when it should be reduced by 23 ° 27 ", i.e.
φ0 = 90° - φ1- 23° 27"
φ0 = 90°- 48° - 23° 27"= 18° 33"

Problem 31

Z - zenith point * - Polaris

The angle at which the North Star is visible to the horizon area
the angle between the zenith and the North Star.
On the days of the equinoxes, the height of the midday Sun above the horizon for different latitudes is determined by the formula:

So, for example, in Kyiv on March 21 and September 23 at noon the Sun is at a height:

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

Thus, for the city of Kyiv on June 21, the height of the Sun is 61°27". .

So, for Kyiv on December 22, the Sun is at a height

Problem 33
From the ship on February 20, the height of the Sun above the horizon was measured. It was 50°. The sun was in the south. Which geographical latitude is the ship located if on this day the Sun was at its zenith at a latitude of 1105 "S?

Answer:
The ship was at 28°55"N.

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

Answer:

The distance between Kyiv and St. Petersburg is 8°, and in kilometers -890.4 km.

Problem 34
In the Northern Hemisphere, where there are tourists, the Sun at noon is above the horizon at an angle of 53030 ". On the same day, the noon Sun is at zenith at 12 ° 20" N. latitude. At what degree of latitude are the tourists?

Answer:
Tourists are located at 48 ° 50 "N. w.

- The height of the Polar is ALWAYS equal to the latitude of the place of observation (this is for the northern hemisphere) = and at any time of the day!

©2015-2019 site
All rights belong to their authors. This site does not claim authorship, but provides free use.
Page creation date: 2017-10-25

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 changes throughout the year, and consequently, the conditions for their illumination and heating by the Sun change.

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

(6.3)

Substituting 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

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

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

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

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

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

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

Due to the small inclination of the orbits of large planets to the 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
on different days of the year