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How the diurnal paths of the stars are located. Astronomical experiments

Celestial sphere

For many centuries, the "earthly firmament" was considered a model of inviolability and immobility. It is not surprising that this error lasted so long, because all our senses speak of the immobility of the Earth and the rotation of the "firmament" around it with the stars, the Sun and the Moon. But even now in astronomy, as a memory of those ancient times, the concept of the celestial sphere is used - an imaginary infinitely large sphere, in the center of which there is an observer and on the surface of which the movements of the celestial bodies are displayed.

Of course, the most noticeable is the diurnal rotation of the sky - in the morning the Sun rises, passes across the sky and falls below the horizon, the stars that are visible in the east in the evening rise high in the south by midnight and then descend to the west, the Sun rises again ... the sky revolves around an invisible axis located near the Pole Star.

The movement of stars around the Pole of the World. Photo by A. Mironov

But the daily rotation of the sky depends very much on our position on the globe - if we find ourselves in the southern hemisphere, it will be very unusual for us that the Sun moves across the sky in the opposite direction - from right to left. Let's take a closer look at how the apparent rotation of the firmament changes in different parts of the Earth.

To begin with, you should remember that the height of the Pole of the World (the point around which the sky rotates) above the horizon is always equal to the geographical latitude of the place of observation. This means that at the North Pole the Polar Star will be at its zenith, and all the luminaries in their daily rotation will move from left to right parallel to the horizon, never rising or setting. Being at the pole, we could see the stars of only one hemisphere, but on any night.

On the contrary, for an observer at the equator there are no non-rising stars (as well as non-setting ones) - all the stars in the sky are available for observation, they rise vertically in the eastern part of the horizon and set in the western part of the sky exactly 12 hours later.

In mid-latitudes, some of the stars in the vicinity of the pole never sink under the horizon, but the same region of the sky around the opposite pole is never accessible for observation, while the rest of the stars, located in stripes on both sides of the celestial equator, rise and set during the day.

The movement of the luminaries in the middle latitudes of the southern hemisphere will look approximately the same, with the only difference that the South Pole of the World will be visible above the horizon, around which the stars rotate clockwise, and the familiar equatorial constellations, turned upside down, rise above all in the northern part of the sky and move from right to left.

Sun movement and day

Speaking about the movement of stars, we were not interested in the distance to them and the movement of the Earth around the Sun - the distances to the stars are huge and the changes in their positions due to the annual movement of the Earth are very small and can only be measured with very accurate instruments. The sun is quite another matter. The Earth's orbital motion results in visible motion of the Sun among the stars. The path that the Sun travels in the sky throughout the year is called the ecliptic. Since the Earth's axis is tilted by 23.5 °, then when the Earth revolves around the Sun, it turns out to be either the northern or the southern hemisphere - this explains the change of seasons on our planet.

When the northern hemisphere is turned to the Sun, summer begins there, the Sun in its visible path along the ecliptic is in its northern part and in our northern hemisphere it rises higher above the horizon. At the North Pole for six months the Sun becomes a non-setting star - there is a polar day. A little further south, the polar day lasts less and at the latitude of the polar circle (66.5 ° - the polar circle is 23.5 ° from the pole) the Sun does not set for only a few days in the middle of summer, near the summer solstice (June 22). In winter, the Sun does not rise at the pole for almost six months (a little less due to refraction), to the south, the polar night becomes shorter and outside the Arctic circle, the Sun rises above the horizon even in the middle of winter.

In middle and equatorial latitudes, the Sun always rises and sets, the length of the day strongly depends not only on the time of the year, but also on latitude - the closer to the equator, the less the duration of the day differs in winter and summer, and the closer the duration of the day and night is to 12 o'clock. But only at the equator the length of day and night is always constant. The duration of twilight also depends on latitude - in equatorial latitudes the Sun sets perpendicular to the horizon and twilight is shortest, and at the latitude of St. Petersburg in the middle of summer they continue from sunset to sunrise - these are the famous white nights.

Latitude depends on how high the Sun can rise above the horizon - on the day of the solstice, this height will be 90 ° -φ + 23.5 °.

By the way, there is a very widespread misconception that at the equator the Sun is always at its zenith at noon - this is not the case, at any point on the Earth lying between the lines of the tropics (from 23.5 ° S to 23.5 ° N). ) exactly through the zenith the Sun passes only twice a year, at the equator - on the days of the equinoxes, and on the lines of the tropics - only once a year, on the summer solstice in the northern tropics and on the winter solstice - in the southern ones.

The movement of the Earth around the Sun leads to another important phenomenon - the duration of a solar day (the time interval between two noons) does not coincide with stellar days (the time interval between the passage of a star through the meridian). The fact is that the Earth needs additional time to turn through the angle that it passes in a day in its orbit. Moreover, the duration of a solar day is not constant (see the article Equation of Time). It is easy to make a rough estimate - in a day the earth passes 1/365 of its orbit or slightly less than 1 °, and if the Earth rotates around its axis (360 °) in about 24 hours, then it will rotate 1 ° in about 4 minutes. Indeed, a sidereal day is 23 hours 56 minutes 4 seconds.

moon

Since ancient times, our satellite has served people for counting time, and this is not accidental - the change in the phases of the moon is easy to observe and the length of the month is not difficult to determine, moreover, the month has become a very convenient intermediate unit for measuring time between days and years. By the way, everyone's familiar seven-day week is also associated with the Moon - 7 days is about a quarter of a month (and the phases of the Moon are also measured in quarters). Most of the ancient calendars were lunar and lunisolar.

Of course, the first thing that catches your eye when observing the Moon is a change in its appearance within a month from a thin crescent, which can be seen immediately after sunset, 2-3 days after the new moon, to the phase of the first quarter (in the northern hemisphere, the right half of the disk is illuminated Moon), then to the full moon, the last quarter (the left half of the disk is illuminated) and, finally, to the new moon, when the Moon approaches the Sun and disappears in its rays. The phase change is explained by the change in the position of the Moon relative to the Sun when it revolves around the Earth, the full cycle of phase change - the revolution relative to the Sun or a synodic month lasts about 29.5 days. The orbital period relative to the stars (sidereal month) is slightly less and amounts to 27.3 days. As you can see, the year contains a non-integer number of months, so lunisolar calendars use special rules for alternating 12-month and 13-month years, because of this they are rather complicated and are now supplanted in most countries by the Gregorian calendar, which has nothing to do with the Moon - only months (though longer than lunar ones) and weeks remained in memory of his predecessors ...

There is another one in the movement of the moon interesting feature- the period of its rotation around its axis coincides with the period of revolution around the Earth, therefore our satellite is always turned towards the Earth by one hemisphere. But it cannot be said that we can see only half of the Moon's surface - due to the uneven orbital motion of the Moon and the inclination of its orbit to the Earth's equator, the Moon rotates slightly both in latitude and longitude relative to the terrestrial observer (this phenomenon is called libration) and we can to see the edge zones of the disk - in total, about 60% of the lunar surface is accessible to observations.

Jean Effel, "Creation of the World"
-It's not easy to start the universe!

Meet with starry sky it is necessary on a cloudless night, when the light of the moon does not interfere with observing faint stars. A beautiful picture of the night sky with twinkling stars scattered over it. Their number seems endless. But it only seems so until you take a closer look and learn to find familiar groups of stars in the sky, unchanged in their relative position. These groups, called constellations, were identified by people thousands of years ago. A constellation is understood to mean the entire region of the sky within certain established boundaries. The entire sky is divided into 88 constellations, which can be found by their characteristic arrangement of stars.

Many constellations have retained their name since ancient times. Some names are associated with Greek mythology, for example Andromeda, Perseus, Pegasus, some with objects that resemble figures formed by the bright stars of the constellations (Arrow, Triangle, Libra, etc.). There are constellations named after animals (for example, Leo, Cancer, Scorpio).

Constellations in the sky are found by mentally connecting their brightest stars with straight lines into a certain figure, as shown on star maps (see Fig. 4, 8, 10, as well as the star map in the appendix). In each constellation, bright stars have long been designated by Greek letters, most often the brightest star of the constellation - by the letter a, then by letters, etc. in alphabetical order in decreasing brightness; for example, the North Star is and the constellation Ursa Minor

Figures 4 and 8 show the location of the main stars of the Big Dipper and the figure of this constellation, as it was depicted on old star maps (you are familiar with the method of finding the North Star from the course of geography).

Rice. 8. Figure of the constellation Ursa Major (from an old star map), its modern borders are indicated by a dotted line.

With the naked eye, on a moonless night, you can see about 3,000 stars above the horizon. At present, astronomers have determined the exact location of several million stars, measured the energy flows coming from them and compiled catalogs of these stars.

2. The brightness and color of the stars.

During the day, the sky appears blue because the inhomogeneities of the air environment scatter the blue rays of sunlight the most.

Outside of the earth's atmosphere, the sky is always black, and stars and the sun can be observed on it at the same time.

Stars have different brightness and color: white, yellow, reddish. The redder the star, the colder it is. Our Sun is one of the yellow stars. The ancient Arabs gave their own names to the bright stars.

White stars: Vega in the constellation Lyra, Altair in the constellation Eagle (visible in summer and autumn). Sirius is the brightest star in the sky (visible in winter); red stars: Betelgeuse in the constellation Orion and Aldebaran in the constellation Taurus (visible in winter), Antares in the constellation Scorpio (visible in summer); yellow Capella in the constellation Auriga (visible in winter).

The brightest stars in ancient times were called stars of the 1st magnitude, and the faintest, visible at the limit of sight to the naked eye, stars of the 6th magnitude. This old terminology has survived to this day. The term "magnitude" has nothing to do with the true sizes of stars; it characterizes the luminous flux coming to Earth from a star. It is accepted that with a difference of one magnitude, the brightness of the stars differs by about 2.5 times. A difference of 5 magnitudes corresponds to a difference in brightness of exactly 100 times. So, stars of the 1st magnitude are 100 times brighter than stars of the 6th magnitude.

Modern observation methods make it possible to detect stars up to about 25th magnitude. Measurements have shown that stars can have fractional or negative stellar magnitudes, for example: for Aldebaran, stellar magnitude for Vega for Sirius for the Sun

3. Visible diurnal movement of stars. Celestial sphere.

Due to the axial rotation of the Earth, stars appear to us moving across the sky. Upon close observation, you can see that the North Star almost does not change its position relative to the horizon.

Rice. 9. Photo of the near-polar region of the sky, taken by a fixed camera with an exposure of about an hour.

Rice. 10. Constellations in the vicinity of the Pole Star.

All the same, other stars describe full circles during the day with a center near Polar. This can be easily verified by doing the following experiment. The camera, set at "infinity", will be directed to the Polar Star and securely fixed in this position. Open the shutter with the lens fully open for half an hour or an hour. Having developed the image photographed in this way, we will see concentric arcs on it - traces of the paths of the stars (Fig. 9). The common center of these arcs is a point that remains stationary during the diurnal movement of stars, conventionally called the north pole of the world. The North Star is very close to it (Fig. 10). The point diametrically opposite to it is called the south pole of the world. In the northern hemisphere, it is below the horizon.

It is convenient to study the phenomena of the diurnal movement of stars using a mathematical construction - the celestial sphere, that is, an imaginary sphere of arbitrary radius, the center of which is at the point of observation. The visible positions of all the luminaries are projected onto the surface of this sphere, and a number of points and lines are plotted for the convenience of measurements (Fig. 11). So, the plumb line passing through the observer crosses the sky above the head - at the zenith point. The diametrically opposite point is called nadir. The plane perpendicular to the plumb line is the horizon plane - this plane touches the surface of the globe at the point where the observer is located (point C in Fig. 12). It divides the surface of the celestial sphere into two hemispheres: visible, all points of which are above the horizon, and invisible, whose points lie below the horizon.

The axis of the apparent rotation of the celestial sphere, connecting both poles of the world (P and P) and passing through the observer is called

Rice. 11. The main points and lines of the celestial sphere.

Rice. 12. The relationship between lines and planes on the celestial sphere and on the globe.

the axis of the world (Fig. 11). The axis of the world for any observer will always be parallel to the axis of rotation of the Earth (Fig. 12). On the horizon under the North Pole of the world lies the north point N (Fig. 11 and 12), the diametrically opposite point S is the point of the south. The NS line is called the midday line (Fig. 11), since a shadow from a vertically placed rod falls along it on the horizontal plane at noon. (You studied how to draw the midday line on the ground and how to navigate along the horizon along it and along the Polar Star in grade V in the course of physical geography.) The points of east E and west W lie on the horizon line. They are spaced from points north N and south S by

Rice. 13. Daily paths of the stars relative to the horizon for an observer who is: a - at the Earth's pole; b - in middle geographic latitudes; c - at the equator.

90 °. Through the point the poles of the world, the zenith and point S, the plane of the celestial meridian passes (Fig. 11), which coincides for the observer C with the plane of his geographic meridian (Fig. 12). Finally, the plane passing through the observer (point C) perpendicular to the axis of the world, forms the plane of the celestial equator, parallel to the plane of the earth's equator (Fig. 11). The celestial equator divides the surface of the celestial sphere into two hemispheres: the north with a peak at the north pole of the world and the south with a peak at the south pole of the world.

4. Determination of geographic latitude.

Refer to Figure 12.

The angle (the height of the pole of the world above the horizon) is equal to the angle (latitude of the place), as angles with mutually perpendicular sides Equality of these angles gives the simplest way determining the geographic latitude of the area, the angular distance of the pole of the world from the horizon is equal to the geographic latitude of the area. To determine the latitude of the area, it is enough to measure the height of the pole of the world above the horizon.

5. Daily movement of stars at different latitudes.

Now we know that with a change in the geographical latitude of the observation site, the orientation of the axis of rotation of the celestial sphere relative to the horizon changes. Consider what will be the apparent motions of celestial bodies in the North Pole region, at the equator and at the middle latitudes of the Earth.

At the Earth's pole, the pole of the world is at its zenith, and the stars move in circles parallel to the horizon (Fig. 13, a). Here the stars do not set and do not rise, their height above the horizon is unchanged.

At mid-latitudes, there are both rising and setting stars, and those that never descend under the horizon (Fig. 13, b). For example, the circumpolar constellations (Fig. 10) never set at the geographic latitudes of the USSR. Constellations farther from the north pole of the world appear briefly above the horizon. And the constellations lying even further to the south are non-ascending (Fig. 14).

Rice. 14. Visible diurnal paths of the stars relative to the horizon in the northern side of the sky.

Rice. 15. Upper and lower culminations of the luminaries.

during the day (Fig. 13, c). For an observer at the equator, all stars rise and set perpendicular to the plane of the horizon. Each star here spends exactly half of its path above the horizon.

For an observer at the Earth's equator, the north pole of the world coincides with the north point, and the south pole of the world - with the south point (Fig. 13, c). The axis of the world for him is located in the plane of the horizon.

6. Climaxes.

The pole of the world with the apparent rotation of the sky, reflecting the rotation of the Earth around the axis, occupies a constant position above the horizon at a given latitude (Fig. 12). During the day, the stars describe circles above the horizon around the axis of the world, parallel to the equator. Moreover, each star crosses the celestial meridian twice a day (Fig. 15).

The phenomena of the passage of luminaries through the celestial meridian are called culminations. In the upper culmination the height of the luminary is maximum, in the lower culmination it is minimum. The time interval between culminations is half a day.

At a star M that does not set at a given latitude (Fig. 15), both culminations are visible (above the horizon), at stars that rise and set, the lower culmination occurs under the horizon, below the north point. At a star located far south of the celestial equator, both culminations may be invisible.

The moment of the upper climax of the center of the Sun is called true noon, and the moment of the lower climax is called true midnight. At true noon, the shadow of the vertical rod falls along the midday line.

no arcs - traces of the paths of the stars. The common center of these arcs is a point that remains stationary during the diurnal movement of stars, conventionally called the north pole of the world. The North Star is very close to him. The point diametrically opposite to it is called the south pole of the world. In the northern hemisphere, it is below the horizon.

It is convenient to study the phenomena of the diurnal motion of stars using a mathematical construction - the celestial sphere, i.e. an imaginary sphere of arbitrary radius centered at the observation point. The visible positions of all the luminaries are projected onto the surface of this sphere, and for the convenience of measurements, a series of points and lines are built. Thus, the plumb line ZCZ΄ passing through the observer crosses the sky overhead at the zenith point Z. The diametrically opposite point Z΄ is called the nadir. The plane (NESW) perpendicular to the plumb line ZZ΄ is the horizon plane - this plane touches the surface of the globe at the point where the observer is located. It divides the surface of the celestial sphere into two hemispheres: visible, all points of which are above the horizon, and invisible, whose points lie below the horizon.

The axis of the apparent rotation of the celestial sphere, connecting both poles of the world (P and P ") and passing through the observer (C), is called the axis of the world. The axis of the world for any observer will always be parallel to the axis of rotation of the Earth. On the horizon under the north pole of the world lies the north point N , the diametrically opposite point S is the point of the south. The NS line is called the midday line, since a shadow from a vertically placed rod falls along it on a horizontal plane at noon. (How to draw a midday line on the ground and how to navigate along it and along the Polar Star horizon, you studied in grade V in the course of physical geography.) The points of east E of west W lie on the horizon line. They are 90 ° from points north N and south S. A plane passes through point N, the poles of the world, zenith Z and point S celestial meridian, coinciding for the observer C with the plane of his geographic meridian. Finally, the plane (AWQE) passing through the observer (point C) perpendicular to the axis of the world, forms a plane b the celestial equator, parallel to the plane of the earth's equator. The celestial equator divides the surface of the celestial sphere into two hemispheres: the north with a peak at the north pole of the world and the south with a peak at the south pole of the world.

Daily movement of stars at different latitudes

At the Earth's pole, the pole of the world is at its zenith, and the stars move in circles parallel to the horizon. Here the stars do not set and do not rise, their height above the horizon is unchanged.

At mid-latitudes, there are both rising and setting stars, and those that never descend under the horizon (Fig. 13, b). For example, the circumpolar constellations never set at the geographic latitudes of the USSR. Constellations located farther from the North Pole of the world, the daily paths of the luminaries give up for a short while above the horizon. And the constellations further south are not ascending.

But the further the observer moves to the south, the more southern constellations he can see. At the earth's equator, one could see the constellations of the entire starry sky in a day, if the Sun did not interfere during the day. For an observer at the equator, all stars rise and set perpendicular to the horizon. Each star here spends exactly half of its path above the horizon. For an observer at the equator of the Earth, the north pole of the world coincides with the north point, and the south pole of the world coincides with the south point. The axis of the world for him is located in the plane of the horizon.

Climax

The pole of the world, with the apparent rotation of the sky, reflecting the rotation of the Earth around its axis, occupies a constant position above the horizon at a given latitude. During the day, the stars describe circles above the horizon around the axis of the world, parallel to the equator. Moreover, each star crosses the celestial meridian twice a day.

The phenomena of the passage of luminaries through the celestial meridian are called culminations. In the upper culmination the height of the luminary is maximum, in the lower culmination it is minimum. The time interval between culminations is half a day.

For the star M, which does not set at a given latitude, both culminations are visible (above the horizon), for stars that rise and set, M1 and M2, the lower culmination occurs under the horizon, below the north point. At the luminary M3, located far south of the celestial equator, both climaxes may be invisible. The moment of the upper climax of the center of the Sun is called true noon, and the moment of the lower climax is called true midnight. At true noon, the shadow of the vertical rod falls along the midday line.

4. Ecliptic and "wandering" luminaries-planets

In a given locality, each star always culminates at the same height above the horizon, because its angular distance from the pole of the world and from the celestial equator does not change. The sun and moon change the altitude at which they culminate.

If we observe the time intervals between the upper culminations of the stars and the Sun by the precise hours, then we can be convinced that the intervals between the culminations of the stars are four minutes shorter than the intervals between the culminations of the Sun. This means that during one revolution of the celestial sphere, the Sun has time to move relative to the stars to the east - in the direction opposite to the daily rotation of the sky. This shift is about 1 °, since the celestial sphere makes a full revolution - 360 ° in 24 hours. In 1 hour, equal to 60 minutes, it rotates by 15 °, and in 4 minutes - by 1 °. Over the course of a year, the Sun makes a large circle against the background of the starry sky.

The climax of the Moon is lagging every day not by 4 minutes, but by 50 minutes, since the Moon makes one revolution towards the rotation of the sky in a month.

The planets move in a slower and more complex manner. They move against the background of the starry sky in one direction or the other, sometimes slowly writing out loops. This is due to the combination of their true motion with the movements of the Earth. In the starry sky, the planets (translated from the ancient Greek as "wandering") do not occupy a permanent place, just like the Moon and the Sun. If you draw up a map of the starry sky, then you can indicate the position of the Sun, Moon and planets on it only for a certain moment.

The apparent annual motion of the Sun occurs along a large circle of the celestial sphere, called the ecliptic.

Moving along the ecliptic, the Sun crosses the celestial equator twice at the so-called equinox points. It happens around March 21 and around September 23, on the days of the equinox. These days the Sun is at the celestial equator, and it is always divided by the horizon plane in half. Therefore the paths

Daily path of the Sun. Every day, rising from the horizon in the eastern side of the sky, the Sun passes across the sky and again hides in the west. For residents of the Northern Hemisphere, this movement occurs from left to right, for southerners - from right to left. At noon, the Sun reaches its greatest height, or, as astronomers say, climaxes. Noon is the upper culmination, and there is also the lower one - at midnight. In our mid-latitudes, the sun's lower culmination is not visible, as it occurs below the horizon. But beyond the Arctic Circle, where the Sun sometimes does not set in summer, one can observe both the upper and lower culminations. At the geographic pole, the diurnal path of the Sun is practically parallel to the horizon. Appearing on the day of the vernal equinox, the Sun rises higher and higher for a quarter of a year, making circles above the horizon. On the day of the summer solstice, it reaches its maximum height (23.5?).

The next quarter of the year, before the autumnal equinox, the Sun descends. This is a polar day. Then the polar night sets in for six months. In mid-latitudes, throughout the year, the apparent diurnal path of the Sun either decreases or increases. It turns out to be the smallest on the day of the winter solstice, and the largest on the day of the summer solstice. On the days of the equinox, the Sun is at the celestial equator. At the same time, it rises at the point of the east and sets at the point of the west. In the period from the vernal equinox to the summer solstice, the place of sunrise shifts slightly from the point of sunrise to the left, to the north. And the place of entry moves away from the west point to the right, although also to the north. On the day of the summer solstice, the Sun appears in the northeast, and at noon it culminates at its highest altitude in a year. The sun sets in the northwest. Then the places of sunrise and sunset are shifted back to the south. On the winter solstice, the Sun rises in the southeast, crosses the celestial meridian at its minimum height, and sets in the southwest. It should be borne in mind that due to refraction (that is, the refraction of light rays in the earth's atmosphere), the apparent height of the star is always greater than the true one. Therefore, the sunrise occurs earlier, and the sunset - later than it would be in the absence of the atmosphere. So, the diurnal path of the Sun is a small circle of the celestial sphere, parallel to the celestial equator. At the same time, during the year, the Sun moves relative to the celestial equator to the north, then to the south. The day and night parts of his journey are not the same. They are equal only on the days of the equinoxes, when the Sun is at the celestial equator.

Yearly path of the Sun The expression "the path of the Sun among the stars" will seem strange to some. After all, the stars are not visible during the day. Therefore, it is not easy to notice that the Sun is slow, by about 1? per day, moves among the stars from right to left. But you can trace how the appearance of the starry sky changes throughout the year. All this is a consequence of the revolution of the Earth around the Sun. The path of the apparent annual movement of the Sun against the background of stars is called the ecliptic (from the Greek "eclipse" - "eclipse"), and the period of revolution along the ecliptic is called a sidereal year. It is equal to 265 days 6 hours 9 minutes 10 seconds, or 365, 2564 average solar days. The ecliptic and the celestial equator intersect at an angle of 23? 26 "at the vernal and autumnal equinox points. At the first of these points, the Sun usually occurs on March 21, when it passes from the southern hemisphere of the sky to the northern one. In the second, on September 23, at the transition of their northern hemisphere At the ecliptic farthest to the north, the Sun occurs on June 22 (summer solstice), and to the south on December 22 (winter solstice). In a leap year, these dates are shifted by one day. Of the four points of the ecliptic, the vernal equinox is the main point. It is from it that one of the celestial coordinates, right ascension, is counted. It also serves to count the sidereal time and the tropical year - the time interval between two successive passages of the Sun's center through the vernal equinox. The tropical year determines the change of seasons on our planet. the equinox moves slowly among the stars due to the precession of the earth's axis, the duration of the tropical about a year less than the duration of a stellar one. It is 365.2422 solar average days. About 2 thousand years ago, when Hipparchus compiled his stellar catalog (the first one that has come down to us in its entirety), the vernal equinox was in the constellation Aries. By our time, it has moved almost 30?, To the constellation Pisces, and the point of the autumnal equinox - from the constellation Libra to the constellation Virgo.

But according to tradition, the points of equinox are designated by the same signs of the former "equinox" constellations - Aries and Libra. The same happened with the solstice points: summer in the constellation Taurus is marked with the sign of Cancer, and winter in the constellation Sagittarius is marked with the sign of Capricorn. And finally, the last thing that is associated with the apparent annual motion of the Sun. Half of the ecliptic from the vernal equinox to the autumn (from March 21 to September 23), the Sun passes in 186 days. The second half, from the autumnal and spring equinox, - in 179 days (180 in a leap year). But the halves of the ecliptic are equal: 180? Each. Consequently, the Sun moves unevenly along the ecliptic. This unevenness is explained by a change in the speed of the Earth in an elliptical orbit around the Sun. The uneven motion of the Sun along the ecliptic leads to different lengths of the seasons. For residents of the northern hemisphere, for example, spring and summer are six days longer than autumn and winter. The Earth on June 2-4 is located 5 million kilometers from the Sun longer than January 2-3, and moves in its orbit more slowly in accordance with Kepler's second law. In summer, the Earth receives less heat from the Sun, but summer in the Northern Hemisphere is longer than winter. Therefore, the Northern Hemisphere is warmer than the Southern Hemisphere.

Verification work No. 2 (self control)

Determination of geographical latitude

on astronomical observations

Option 1

1. At what altitude occurs in Leningrad, the geographical latitude of which is 60 °, the upper culmination of the star Altair?

2. The luminary rises at the point east. Where will it be in 12 hours?

Option 2

1. What is the declination of a star if it culminates in Moscow, whose latitude is 56 °, at an altitude of 63 °?

2. How are the diurnal paths of the stars relative to the celestial equator?

Option 3

1. What is the latitude of the place of observation, if the star Regulus was observed in the upper culmination at an altitude of 57 °?

2. Where on Earth are no stars in the southern hemisphere of the sky visible?

Option 4

1. At what altitude does the upper climax of the Spica star occur in a city whose latitude is 50 °?

2. How are the diurnal paths of the stars relative to the horizon for an observer at the Earth's pole?

Option 5

1. What is the declination of a star if its upper culmination in Yerevan, whose latitude is 40 °, occurs at an altitude of 37 °?

2. What circle of the celestial sphere do all the stars cross twice a day, if observations are carried out in middle latitudes. "

Option b

1. What is the latitude of the place of observation, if the star Betelgeuse was observed in the upper culmination at an altitude of 48 °?

2. How is the axis of the world relative to the earth's axis? relative to the plane of the horizon?

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1. How many times is a star of magnitude 3.4 fainter than Sirius, which has an apparent magnitude of -1.6?

2. What is the absolute stellar magnitude of Sirius, if the distance to it is 2.7 ps?

3. What is the luminosity of Begi? Take the absolute stellar magnitude of the Sun to be 4.8.

1. How many times is a star with an apparent magnitude of 3, brighter than a star second magnitude?

2. Calculate the absolute magnitude of Begi if the distance to it is 8.1 ps?

3. What is the luminosity of Sirius? Take the absolute stellar magnitude of the Sun to be 4.8.

Grade

II Building Solar system

(celestial mechanics)

Verification work No. 3 (self control)

Kepler's Laws Option 1

1. What) is the major half of the orbital axis of Uranus, if the stellar period of this planet's revolution around the Sun is 84 years?

2. How does the value of the speed of the planet change when it moves from aphelion to perihelion?

Option 2

1. The semi-major axis of Saturn's orbit is 9.5 AU. e. What is the stellar period of its revolution around the Sun?

2. At what point of the elliptical orbit is the kinetic energy of an artificial earth satellite (AES) maximum and at what point - minimum?

Option 3

1. The semi-major axis of the orbit of Jupiter 5 a. e. What is the stellar period of its revolution around the Sun?

2. At what point of the elliptical orbit is the potential energy of an artificial Earth satellite (AES) minimal and at what point is it maximal?

Option 4

1.The stellar period of Jupiter's revolution around the Sun is 12 years. What is the average distance of Jupiter to the Sun?

2. At what point of the planet's orbit is its kinetic energy maximal, at what point is it minimal?

Option 5

1. The semi-major axis of the Mars orbit is 1.5 AU. e. What) is the stellar period of its revolution around the Sun?

2. How does the value of the speed of the planet's movement change when it moves from perihelion to aphelion?

Option 6

1. The semi-major axis of the orbit of Venus is 0.7 AU. e. What) is the stellar period of its revolution around the Sun?

2. How is the apparent motion of the planets?

Creative task:

Determine your age on the planet

__________________________________________________________

Verification work No. 6 (self control)

"Determination of distances to stars"

1. The distance to the star Betelgeuse is 652 s.years. What is its parallax?

2. Parallax of Procyon 0.28 ". How long does the light travel from this star to the Earth?

3. The parallax of a star is 0.5 "Determine how many times this star is further from us than the Sun.

4. Altair's parallax is 0.20 ". The distance to Vega is 29 light years. Which of these stars is farther from us and how many times?

2) Name the color of the following stars by their spectral

3) What stars belong to the following luminosity classes of stars

Grade

Verification work No. 4 (self control)

Configurations and visibility conditions of planets

Option 1

(1) Over what time interval are the moments of the maximum distance of Venus from the Earth repeated if its sidereal period is 225 days?

2. What planets can be observed in opposition? Which ones can't?

Option 2

1. Over what period of time are the oppositions of Mars repeated if the stellar period of its revolution around the Sun is 1.9 years?

2. What planets cannot be in the lower conjunction?

Option 3

1. What is the stellar period of Venus's revolution around the Sun if its upper conjunctions with the Sun are repeated in 1.6 years?

2. In what configuration and why is it most convenient to observe Mars?

Option 4

1. What is the stellar period of Jupiter's revolution if its synodic period is 400 days?

2. What planets can be in the upper conjunction?

Option 5

1. Determine the synodic orbital period of Mercury, knowing that its stellar orbital period around the Sun is 0.24 years.

2. In which of the configurations can there be both inner and outer planets?

Option 6

1. What will be the stellar period of the outer planet's revolution around the Sun, if its oppositions repeat in 1.5 years?

2.What planets can be seen near the moon during a full moon?

Conclusion:




	Grade

How the diurnal paths of the stars are located. Astronomical experiments

Celestial sphere

Sun movement and day

moon

2. The brightness and color of the stars.

3. Visible diurnal movement of stars. Celestial sphere.

4. Determination of geographic latitude.

5. Daily movement of stars at different latitudes.

6. Climaxes.

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