Points and lines of the celestial sphere - how to find the almucantarate, where the celestial equator passes, which is the celestial meridian.

What is the Celestial Sphere

Celestial sphere– an abstract concept, an imaginary sphere of infinite radius, the center of which is the observer. In this case, the center of the celestial sphere is, as it were, at the level of the observer’s eyes (in other words, everything that you see above your head from horizon to horizon is this very sphere). However, for ease of perception, we can consider the center of the celestial sphere and the center of the Earth; there is no mistake in this. The positions of stars, planets, the Sun and the Moon are plotted on the sphere in the position in which they are visible in the sky at a certain moment in time from a given point of location of the observer.

In other words, although observing the position of the stars on the celestial sphere, we, being in different places on the planet, will constantly see a slightly different picture, knowing the principles of the “working” of the celestial sphere, by looking at the night sky we can easily find our way around using simple technology. Knowing the view overhead at point A, we will compare it with the view of the sky at point B, and by the deviations of familiar landmarks, we will be able to understand where exactly we are now.

People have already come up with this idea a long time ago whole line tools that make our task easier. If you navigate the “terrestrial” globe simply using latitude and longitude, then a whole series of similar elements - points and lines, are also provided for the “celestial” globe - the celestial sphere.

The celestial sphere and the position of the observer. If the observer moves, then the entire sphere visible to him will move.

Elements of the celestial sphere

The celestial sphere has a number of characteristic points, lines and circles; let us consider the main elements of the celestial sphere.

Observer vertical

Observer vertical- a straight line passing through the center of the celestial sphere and coinciding with the direction of the plumb line at the observer’s point. Zenith- the point of intersection of the observer’s vertical with the celestial sphere, located above the observer’s head. Nadir- the point of intersection of the observer’s vertical with the celestial sphere, opposite to the zenith.

True horizon- a large circle on the celestial sphere, the plane of which is perpendicular to the observer’s vertical. The true horizon divides the celestial sphere into two parts: above-horizon hemisphere, at which the zenith is located, and subhorizontal hemisphere, in which the nadir is located.

Axis mundi (Earth's axis)- a straight line around which the visible daily rotation of the celestial sphere occurs. The axis of the world is parallel to the axis of rotation of the Earth, and for an observer located at one of the poles of the Earth, it coincides with the axis of rotation of the Earth. The apparent daily rotation of the celestial sphere is a reflection of the actual daily rotation of the Earth around its axis. The celestial poles are the points of intersection of the axis of the world with the celestial sphere. The celestial pole located in the constellation area Ursa Minor, called North Pole world, and the opposite pole is called South Pole.

A great circle on the celestial sphere, the plane of which is perpendicular to the axis of the world. The plane of the celestial equator divides the celestial sphere into northern hemisphere, in which the North Pole is located, and southern hemisphere, where the South Pole is located.

Or the observer's meridian is a large circle on the celestial sphere, passing through the poles of the world, zenith and nadir. It coincides with the plane of the observer's earthly meridian and divides the celestial sphere into eastern And western hemisphere.

North and south points- the point of intersection of the celestial meridian with the true horizon. The point closest to the North Pole of the world is called the north point of the true horizon C, and the point closest to the South Pole of the world is called the south point S. The points of the east and west are the points of intersection of the celestial equator with the true horizon.

Noon Line- a straight line in the plane of the true horizon connecting the points of north and south. This line is called midday because at noon according to local true solar time, the shadow of a vertical pole coincides with this line, i.e., with the true meridian of a given point.

The intersection points of the celestial meridian with the celestial equator. The point closest to the southern point of the horizon is called south point of the celestial equator, and the point closest to northern point horizon, - north point of the celestial equator.

Vertical of the luminary

Vertical of the luminary, or height circle, - a large circle on the celestial sphere, passing through the zenith, nadir and luminary. The first vertical is the vertical passing through the points of east and west.

Declension circle, or , is a large circle on the celestial sphere, passing through the poles of the world and the luminary.

A small circle on the celestial sphere drawn through a luminary parallel to the plane of the celestial equator. Visible diurnal movement luminaries occur according to daily parallels.

Almucantarat luminaries

Almucantarat luminaries- a small circle on the celestial sphere drawn through the luminary parallel to the plane of the true horizon.

All the elements of the celestial sphere noted above are actively used to solve practical problems of orientation in space and determining the position of luminaries. Depending on the purpose and measurement conditions, two different systems are used spherical celestial coordinates .

In one system, the luminary is oriented relative to the true horizon and is called this system, and in the other, relative to the celestial equator and is called.

In each of these systems, the position of the star on the celestial sphere is determined by two angular quantities, just as the position of points on the surface of the Earth is determined using latitude and longitude.

§ 48. Celestial sphere. Basic points, lines and circles on the celestial sphere

A celestial sphere is a sphere of any radius with a center at an arbitrary point in space. Depending on the formulation of the problem, its center is taken to be the eye of the observer, the center of the instrument, the center of the Earth, etc.

Let us consider the main points and circles of the celestial sphere, the center of which is taken to be the eye of the observer (Fig. 72). Let's draw a plumb line through the center of the celestial sphere. The points of intersection of the plumb line with the sphere are called zenith Z and nadir n.

Rice. 72.

The plane passing through the center of the celestial sphere perpendicular to the plumb line is called the plane of the true horizon. This plane, intersecting with the celestial sphere, forms a great circle called the true horizon. The latter divides the celestial sphere into two parts: above the horizon and below the horizon.

The straight line passing through the center of the celestial sphere parallel to the earth's axis is called the mundi axis. The points of intersection of the axis of the world with the celestial sphere are called poles of the world. One of the poles, corresponding to the poles of the Earth, is called the north celestial pole and is designated Pn, the other is the south celestial pole Ps.

The QQ plane passing through the center of the celestial sphere perpendicular to the axis of the world is called plane of the celestial equator. This plane, intersecting with the celestial sphere, forms a great circle - celestial equator, which divides the celestial sphere into northern and southern parts.

The great circle of the celestial sphere passing through the celestial poles, zenith and nadir, is called observer's meridian PN nPsZ. The mundi axis divides the observer's meridian into the midday PN ZPs and midnight PN nPs parts.

The observer's meridian intersects with the true horizon at two points: the north point N and the south point S. The straight line connecting the points of north and south is called midday line.

If you look from the center of the sphere to point N, then on the right there will be a point of east O st, and on the left - a point of west W. Small circles of the celestial sphere aa", parallel to the plane of the true horizon, are called almucantarates; small bb" parallel to the plane of the celestial equator, - heavenly parallels.

The circles of the celestial sphere Zon passing through the zenith and nadir points are called verticals. The vertical line passing through the points of east and west is called the first vertical.

The circles of the celestial sphere of PNoPs passing through the poles of the world are called declination circles.

The observer's meridian is both a vertical and a circle of declination. It divides the celestial sphere into two parts - eastern and western.

The celestial pole located above the horizon (below the horizon) is called the elevated (lowered) celestial pole. The name of the elevated celestial pole is always the same as the name of the latitude of the place.

The axis of the world makes an angle with the plane of the true horizon equal to geographical latitude of the place.

The position of luminaries on the celestial sphere is determined using spherical coordinate systems. In nautical astronomy, horizontal and equatorial coordinate systems are used.

The stars are extremely distant from the Earth. Observing them even through a telescope, it is impossible to determine which of them is further and which is closer. When studying the starry sky, a mathematical model of the starry sky is used - the celestial sphere.

Celestial sphere called an imaginary sphere of arbitrary radius with a center at the observation point on which the celestial bodies are projected.

Angular distance between two points on the sphere is the angle between the radii drawn to these points. Note that the circle obtained by intersecting the celestial sphere with a plane passing through the center of the sphere is calledbig circle , and if the plane does not pass through the center -small circle .

A consequence of the Earth's rotation around its axis is the apparent rotation of the celestial sphere in the opposite direction. This is easy to verify. During the night, the stars describe arcs of concentric circles (with a common axis), the axis passing near the star Polaris (α Ursa Minor). Polar itself (m= 2; from the Greek field - I rotate) remains almost motionless. To study the movement of stars in more detail, it is necessary to become familiar with the basic elements of the celestial sphere.

The diameter of the celestial sphere around which its apparent rotation occurs is calledaxis mundi (PP′ see Fig.1).

The axis of the world intersects the celestial sphere at two points -poles of the world (from Greekstrip - axis ): northern (R - near it you can see the North Star) and the southern (R' - there are no bright stars near it). In 2000, the angular distance between the North Pole and North Star was only 42`. Polaris is called the compass star because it is a landmark that indicates the direction north.

Celestial equator called the great circle of the celestial sphere, perpendicular to the axis of the world.

The diameter of the celestial sphere along which the force of gravity acts and passing through the observation point is calledvertical , orplumb line ( ZZ). The points of intersection of a plumb line with the celestial sphere arezenith (from ArabicZemt Arrass - the top of the path ) Andnadir (from Arabic -foot direction ).

The great circle of the celestial sphere perpendicular to the vertical is calledmathematical , orreal, horizon .

The celestial equator divides the celestial sphere into the northern and southern hemispheres, and the horizon into the visible and invisible hemispheres. The visible hemisphere of the celestial sphere is also calledfirmament .

The great circle of the celestial sphere passing through the poles of the world - zenith and nadir - is calledcelestial meridian . The horizon intersects with the celestial meridian at points north (N ) and south (S ), and with the celestial equator - at points of the east (E ) and west (W ) . The diameter of the celestial sphere connecting the points north and south is callednoon line ( N S ).

The angular distance of the luminary from the horizon is calledthe height of the luminary h . For example, the altitude of a star at its zenith is 90°.

In Fig. 1 O - observation point,R - pole of the world,N - north point,T - the center of the Earth, andL - a point on the earth's equator. CornerOTL equals latitude? pointsABOUT , and the anglePONis the height of the celestial poleh p (or the North Star, which is almost the same thing). The axis of the world is parallel to the axis of rotation of the Earth, and the plane of the celestial equator is parallel to the plane of the earth.

So, the height of the celestial pole is equal to the geographic latitude of the area: h p =φ .

At different points on the Earth, the movement of stars across the celestial sphere looks different. For an observer at the pole of our planet, the celestial pole is at the zenith, the axis of the world coincides with the vertical. Stars move in circles parallel to the horizon. Some luminaries are always visible, others are never visible, here the stars do not rise or set and their height is always the same.

At the earth's equator, the celestial poles are located on the horizon, and the mundi axis coincides with the noon line. Stars move in circles perpendicular to the horizon plane. All luminaries rise and set, being in the sky for half of the day. If the Sun did not “interfere”, then in a day from the Earth’s equator one could see everything bright stars sky.

Observing the sky from mid-latitudes, you will notice that some stars rise and set, while others do not set at all. There are also stars that never appear above the horizon.

Stars located on the celestial equator above the horizon spend the same amount of time as those below it. The sun moves among the stars, describing a line calledeclitica. Twice a year (in spring - March 20-21 and in autumn - September 22-23) it is located on the celestial equator at the points of the spring and autumn equinoxes. At this time, day is equal to night.

Each star crosses the celestial meridian twice a day. The phenomenon of the passage of luminaries through the celestial meridian is calledculmination . INupper climax the height of the luminary is the highest, at the bottom - the smallest (see Fig. 6 ). The movement of the luminaries between neighboring culminations lasts half a day. At the pole, the height of the star in both culminations is the same (see Fig. 3). At the equator, only the upper culmination is visible, but all the luminaries are visible (see Fig. 4). In the middle latitudes of the Earth, both culminations are visible (if not for the Sun) for the circumpolar stars, for others (in particular, for the Sun) only the upper one, and for stars that do not descend - none (see Fig. 5). The moment of the upper culmination of the center of the Sun is called true noon, and at the lower - true north. At noon, the shadow of a vertical object falls along the noon line.

To construct star maps, it is necessary to introduce a celestial coordinate system. Several such systems are used in astronomy, each of which is convenient for solving various scientific and practical problems. In this case, special planes, circles and points of the celestial sphere are used. On it, the position of the star is uniquely determined by two angles. If (the plane in which and from which these angles are plotted is the plane of the celestial equator, then the coordinate system is calledequatorial . The coordinates in it are the declination and direct ascension of the luminaries.

Declination δ is the angular distance of the star from the celestial equator (see Fig. 7). Declination is within -90°< δ < 90° и принимается положительным в северном полушарии небесной сферы и отрицательным - в южной. Например, для точек на небесном экваторе δ = 0°, а для полюсов мира
,
.

Around the declination is called the great circle of the celestial sphere passing through the poles of the world and this luminary.

Straight lift (orright ascension ) α is the angular distance of the circle of declination of the luminary from the point of the vernal equinox. This coordinate is measured in the direction opposite direction rotation of the celestial sphere and are expressed in hourly units. Right ascension varies within 0 hours.< α < 24 час. Всему кругу небесного экватора соответствует 24 часа (или, что то же самое, 360 °). Тогда 1 ч = 15 °, а 4 мин = 1 °. Например, α γ = 0 hour., α Ω = 12 hours

One of the most famous and simplest celestial coordinate systems is horizontal. The main plane in it is the mathematical horizon, and the coordinates are the azimuthA luminaries and the height of the luminaries above the horizonh . The disadvantage of the horizontal system is that the coordinates of the luminary are constantly changing.

Time determines the order of change of phenomena. The need to measure and store time arose at the beginning of civilization. For this purpose, periodic processes occurring in nature were used. The movement of our planet produces the visible movement of the luminaries, in particular the Sun on the celestial sphere, which we observe. The oldest unit of time is the day, the duration of which is determined by the rotation of the Earth around its axis.

The time interval between two successive upper (or lower) culminations of the Sun's center is calledreal days (or real solar days) .

The duration of a complete revolution of the Sun along the ecliptic is a unit of time in astronomy.tropical year is the time interval between two successive passages of the center of the solar disk through the vernal equinox. The tropical year lasts approximately 365.2422 days. In everyday life they use the calendar year, which is almost equal to the tropical year.

It has been established that the Earth rotates unevenly around the Sun. Therefore, the length of the actual solar day changes periodically, although only slightly. In winter it is longer, in summer it is shorter. The longest real solar day is about 51 seconds longer than short. To eliminate this inconvenience in measuring time, usemean equatorial sun - an imaginary point that moves uniformly along the ecliptic and makes full turn according to it for the tropical year. The time interval between two successive culminations of the mean equatorial sun is calledaverage day (or average solar day). The average solar day begins at the moment of the lower culmination of the average equatorial sun. The mean equatorial sun is a fictitious point, not marked in any way in the sky. Therefore, it is impossible to observe its movement, and to determine its coordinates, the necessary calculations are made.

The measurement of time in a solar day depends on geographic longitude. For all points on a given meridian the time is the same, but it differs from the local time at other meridians. For example, if we have north according to local time (i.e. the day begins), then on the opposite meridian it is already noon according to their local time. In 1884, many countries introduced a zone time system. The Earth's surface was divided into 24 time zones. INeach of them lies the main meridian, the local time of which is T n considerwaist time of the entire belt. Distance between the main meridians of neighboringzones 15° or 1 hour. For convenience, time zone boundaries pass throughstate and administrative boundaries, and in the seas of sparsely populated areas along meridians that are distant from the main ones by 7.5 ° to the east and 7.5 ° to the west.

The Greenwich meridian (passes through the former Greenwich Observatory near London, because it has now been moved to another location) is the main one for the zero time zone. Further east, the zones are numbered from 1 to 23. Ukraine lies in the second time zone. Time T 0 zero time zone is calleduniversal time (or Western European). Fair ratio: T n = T 0 + n , Wheren - time zone number.

Standard time in some time zones has special names.European (or Central European) is the time of the first time zone,Eastern European - second.

To effectively use sunlight and save energy, some countries introduce summer time, which begins annually on the last Sunday in March at 2:00 by moving the clocks forward an hour. At 3 a.m. on the last Sunday in September, the clocks are moved back an hour, ending daylight saving time.

It is known that the basic unit of time in SI is the second. Previously, 1/86400 of a solar day was taken as one second. After discovering changes in the length of the solar day, the problem of finding a new time scale arose. In 1967, at the International Conference of Weights and Measures, the unit of time was adopted by the atomic second - a time equal to 9192631770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom. The atomic time scale is based on data from cesium atomic clocks that are available at some observatories and time laboratories. Atomic clocks are extremely accurate - they make an error of 1 s in a million years.

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CELESTIAL SPHERE. When we observe the sky, all astronomical objects appear to be located on a dome-shaped surface, in the center of which the observer is located. This imaginary dome forms the upper half of an imaginary sphere called the "celestial sphere." It plays a fundamental role in indicating the position of astronomical objects.

The Earth's rotation axis is tilted approximately 23.5° relative to the perpendicular to the plane of the Earth's orbit (to the ecliptic plane). The intersection of this plane with the celestial sphere gives a circle - the ecliptic, the apparent path of the Sun over a year. The orientation of the earth's axis in space remains almost unchanged. Therefore, every year in June, when the northern end of the axis is tilted towards the Sun, it rises high in the sky in the Northern Hemisphere, where the days become long and the nights short. Having moved to the opposite side of the orbit in December, the Earth turns out to be turned towards the Sun by the Southern Hemisphere, and in our north the days become short and the nights long. Cm. Also SEASONS .

However, under the influence of solar and lunar gravity, the orientation of the earth's axis gradually changes. The main movement of the axis caused by the influence of the Sun and Moon on the equatorial bulge of the Earth is called precession. As a result of precession, the earth's axis slowly rotates around a perpendicular to the orbital plane, describing a cone with a radius of 23.5° over 26 thousand years. For this reason, after a few centuries the pole will no longer be near the North Star. In addition, the Earth's axis undergoes small oscillations called nutation, which are associated with the ellipticity of the orbits of the Earth and the Moon, as well as with the fact that the plane of the Moon's orbit is slightly inclined to the plane of the Earth's orbit.

As we already know, the appearance of the celestial sphere changes during the night due to the rotation of the Earth around its axis. But even if you observe the sky at the same time throughout the year, its appearance will change due to the Earth's revolution around the Sun. For a complete 360° orbit, the Earth requires approx. 365 1/4 days – approximately one degree per day. By the way, a day, or more precisely a solar day, is the time during which the Earth rotates once around its axis in relation to the Sun. It consists of the time it takes for the Earth to rotate relative to the stars (“sidereal day”), plus a short time—about four minutes—required for the rotation to compensate for the Earth’s orbital movement by one degree per day. Thus, in a year approx. 365 1/4 solar days and approx. 366 1/4 stars.

When observed from a certain point on the Earth, stars located near the poles are either always above the horizon or never rise above it. All other stars rise and set, and each day the rising and setting of each star occurs 4 minutes earlier than the previous day. Some stars and constellations rise in the sky at night in winter - we call them “winter”, while others are “summer”.

Thus, the appearance of the celestial sphere is determined by three times: the time of day associated with the rotation of the Earth; the time of year associated with revolution around the Sun; an epoch associated with precession (although the latter effect is hardly noticeable “by eye” even in 100 years).

Coordinate systems.

There are various ways to indicate the position of objects on the celestial sphere. Each of them is suitable for a specific type of task.

Alt-azimuth system.

To indicate the position of an object in the sky in relation to the earthly objects surrounding the observer, an “alt-azimuth” or “horizontal” coordinate system is used. It indicates the angular distance of an object above the horizon, called “height,” as well as its “azimuth” - the angular distance along the horizon from a conventional point to a point lying directly below the object. In astronomy, azimuth is measured from the point south to the west, and in geodesy and navigation - from the point north to the east. Therefore, before using azimuth, you need to find out in which system it is indicated. The point in the sky directly above your head has a height of 90° and is called “zenith,” and the point diametrically opposite to it (under your feet) is called “nadir.” For many problems, the great circle of the celestial sphere, called the “celestial meridian”, is important; it passes through the zenith, nadir and poles of the world, and crosses the horizon at the points of north and south.

Equatorial system.

Due to the rotation of the Earth, stars constantly move relative to the horizon and cardinal points, and their coordinates in the horizontal system change. But for some astronomy problems, the coordinate system must be independent of the observer’s position and time of day. Such a system is called “equatorial”; its coordinates resemble geographic latitudes and longitudes. In it, the plane of the earth’s equator, extended to the intersection with the celestial sphere, defines the main circle - the “celestial equator”. The "declination" of a star resembles latitude and is measured by its angular distance north or south of the celestial equator. If the star is visible exactly at the zenith, then the latitude of the observation location is equal to the declination of the star. Geographic longitude corresponds to the “right ascension” of the star. It is measured east of the point of intersection of the ecliptic with the celestial equator, which the Sun passes in March, on the day of the beginning of spring in the Northern Hemisphere and autumn in the Southern. This point, important for astronomy, is called the “first point of Aries”, or the “vernal equinox point”, and is designated by the sign. Right ascension values ​​are usually given in hours and minutes, considering 24 hours to be equal to 360°.

The equatorial system is used when observing with telescopes. The telescope is installed so that it can rotate from east to west around an axis directed towards the celestial pole, thereby compensating for the rotation of the Earth.

Other systems.

For some purposes, other coordinate systems on the celestial sphere are also used. For example, when studying the movement of bodies in the solar system, they use a coordinate system whose main plane is the plane of the earth's orbit. The structure of the Galaxy is studied in a coordinate system, the main plane of which is the equatorial plane of the Galaxy, represented in the sky by a circle passing along the Milky Way.

Comparison of coordinate systems.

The most important details of the horizontal and equatorial systems are shown in the figures. In the table, these systems are compared with the geographic coordinate system.

Table: Comparison of coordinate systems

COMPARISON OF COORDINATE SYSTEMS
Characteristic	Alt-azimuth system	Equatorial system	Geographical system
Main circle	Horizon	Celestial equator	Equator
Poles	Zenith and nadir	North and south poles of the world	North and South Poles
Angular distance from the main circle	Height	Declension	Latitude
Angular distance along the base circle	Azimuth	Right ascension	Longitude
Reference point on the main circle	South point on the horizon (in geodesy – north point)	Vernal equinox point	Intersection with the Greenwich meridian

Transition from one system to another.

Often there is a need to calculate its equatorial coordinates from the alt-azimuthal coordinates of a star, and vice versa. To do this, it is necessary to know the moment of observation and the position of the observer on Earth. Mathematically, the problem is solved using a spherical triangle with vertices at the zenith, the north celestial pole and the star X; it is called the "astronomical triangle".

The angle with the vertex at the north celestial pole between the observer’s meridian and the direction to some point on the celestial sphere is called the “hour angle” of this point; it is measured west of the meridian. The hour angle of the vernal equinox, expressed in hours, minutes and seconds, is called “sidereal time” (Si. T. - sidereal time) at the observation point. And since the right ascension of a star is also the polar angle between the direction towards it and the point of the vernal equinox, sidereal time is equal to the right ascension of all points lying on the observer’s meridian.

Thus, the hour angle of any point on the celestial sphere is equal to the difference between sidereal time and its right ascension:

Let the observer's latitude be j. If the equatorial coordinates of the star are given a And d, then its horizontal coordinates A And can be calculated using the following formulas:

You can also solve the inverse problem: using the measured values A And h, knowing the time, calculate a And d. Declension d calculated directly from the last formula, then calculated from the penultimate one N, and from the first, if sidereal time is known, it is calculated a.

Representation of the celestial sphere.

For many centuries, scientists have been searching the best ways representations of the celestial sphere for its study or demonstration. Two types of models were proposed: two-dimensional and three-dimensional.

The celestial sphere can be depicted on a plane in the same way as the spherical Earth is depicted on maps. In both cases, it is necessary to select a geometric projection system. The first attempt to represent parts of the celestial sphere on a plane were rock paintings of star configurations in the caves of ancient people. Nowadays, there are various star maps, published in the form of hand-drawn or photographic star atlases covering the entire sky.

Ancient Chinese and Greek astronomers conceptualized the celestial sphere in a model known as the "armillary sphere." It consists of metal circles or rings connected together so as to show the most important circles of the celestial sphere. Nowadays, star globes are often used, on which the positions of the stars and the main circles of the celestial sphere are marked. Armillary spheres and globes have a common drawback: the positions of the stars and the markings of the circles are marked on their outer, convex side, which we view from the outside, while we look at the sky “from the inside,” and the stars seem to us to be placed on the concave side of the celestial sphere. This sometimes leads to confusion in the directions of movement of stars and constellation figures.

The most realistic representation of the celestial sphere is provided by a planetarium. The optical projection of stars onto a hemispherical screen from the inside allows you to very accurately reproduce the appearance of the sky and all kinds of movements of the luminaries on it.

The celestial sphere is an imaginary sphere of arbitrary radius, the center of which is located at the observation point (Fig. 1). A plane drawn through the center of the celestial sphere perpendicular to a line vertical with respect to the surface of the earth forms a large circle at the intersection with the celestial sphere, called the mathematical or true horizon.
The plumb line intersects with the celestial sphere at two diametrically opposite points - zenith Z and nadir Z'. The zenith is located exactly above the observer's head, the nadir is hidden by the earth's surface.
The daily rotation of the celestial sphere is a reflection of the rotation of the Earth and also occurs around the earth's axis, but in the opposite direction, that is, from east to west. The axis of rotation of the celestial sphere, coinciding with the axis of rotation of the Earth, is called the axis of the world.
The north celestial pole P is directed towards the North Star (0°51 from the North Star). The south celestial pole P' is located above the horizon of the southern hemisphere and is not visible from the northern hemisphere.

Fig.1. The intersection of the celestial equator and the celestial meridian with the true horizon

The great circle of the celestial sphere, the plane of which is perpendicular to the axis of the world, is called the celestial equator, which coincides with the plane of the earth's equator. The celestial equator divides the celestial sphere into two hemispheres - northern and southern. The celestial equator intersects with the true horizon at two points, which are called points of east E and west W. At the east point, the celestial equator rises above the true horizon, and at the west point it falls below it.
The great circle of the celestial sphere passing through the celestial pole (PP'), zenith and nadir (ZZ') is called the celestial meridian, which is reflected on the earth's surface in the form of the earth's (geographical) meridian. The celestial meridian divides the celestial sphere into eastern and western and intersects with the true horizon at two diametrically opposed points - the south point (S) and the north point (N).
A straight line passing through the points of south and north and being the line of intersection of the plane of the true horizon with the plane of the celestial meridian is called the noon line.
A large semicircle passing through the poles of the Earth and any point on its surface is called the meridian of this point. The meridian passing through Greenwich Observatory, the UK's main observatory, is called the prime or prime meridian. The prime meridian and the meridian, which is 180° away from the zero, divide the Earth's surface into two hemispheres - the eastern and western.
The great circle of the celestial sphere, the plane of which coincides with the plane of the earth's orbit around the Sun, is called the ecliptic plane. The line of intersection of the celestial sphere with the ecliptic plane is called the ecliptic line or simply the ecliptic (Fig. 3.2). Ecliptic is a Greek word and translated means eclipse. This circle was named so because eclipses of the Sun and Moon occur when both luminaries are close to the ecliptic plane. For an observer on earth, the visible annual movement of the Sun occurs along the ecliptic. A line perpendicular to the plane of the ecliptic and passing through the center of the celestial sphere forms the North (N) and South (S’) poles of the ecliptic at the points of intersection with it.
The line of intersection of the ecliptic plane with the plane of the celestial equator intersects the surface of the earth's sphere at two diametrically opposite points, called the points of the spring and autumn equinox. The point of the vernal equinox is usually designated (Aries), the point of the autumn equinox - (Libra). The sun appears at these points on March 21 and September 23, respectively. These days on Earth, day is equal to night. Points of the ecliptic, spaced 90° from the equinox points, are called solstices (July 22 – summer, December 23 – winter).
The plane of the celestial equator is inclined to the plane of the ecliptic at an angle of 23°27′. The inclination of the ecliptic to the equator does not remain constant. In 1896, when approving astronomical constants, it was decided to consider the inclination of the ecliptic to be equal to 23° 27′ 8.26.”
Due to the influence of the gravitational forces of the Sun and Moon on the Earth, it gradually changes from 22°59′ to 24°36′.

Rice. 2. The plane of the ecliptic and its intersection with the plane of the celestial equator
Celestial coordinate systems
To determine the location of a celestial body, one or another celestial coordinate system is used. Depending on which of the circles of the celestial sphere is chosen to construct the coordinate grid, these systems are called the ecliptic coordinate system or the equatorial system. To determine coordinates on the earth's surface, a geographic coordinate system is used. Let's consider all of the above systems.
Ecliptic coordinate system.

The ecliptic coordinate system is most often used by astrologers. This system is embedded in all ancient atlases starry sky. The ecliptic system is built on the plane of the ecliptic. The position of a celestial body in this system is determined by two spherical coordinates - ecliptic longitude (or simply longitude) and ecliptic latitude.
Ecliptic longitude L is measured from the plane passing through the poles of the ecliptic and the vernal equinox in the direction of the annual movement of the Sun, i.e. according to the course of the Zodiac signs (Fig. 3.3). Longitude is measured from 0° to 360°.
Ecliptic latitude B is the angular distance from the ecliptic towards the poles. The value of B is positive towards the north pole of the ecliptic, negative – towards the south. Measured from +90° to –90°.

Fig.3. Ecliptic celestial coordinate system.

Equatorial coordinate system.

The equatorial coordinate system is also sometimes used by astrologers. This system is built on the celestial equator, which coincides with the earth's equator (Fig. 4). The position of a celestial body in this system is determined by two coordinates - right ascension and declination.
Right ascension is measured from the vernal equinox 0° in the direction opposite to the daily rotation of the celestial sphere. It is measured either in the range from 0° to 360°, or in time units - from 0 hour. up to 24 hours Declension? is the angle between the celestial equator and the pole (similar to latitude in the ecliptic system) and is measured from –90° to +90°.

Fig.4. Equatorial celestial coordinate system

Geographic coordinate system.

Determined by geographic longitude and geographic latitude. In astrology it is used for the coordinates of the place of birth.
Geographic longitude? measured from the Greenwich meridian with the sign + to the east and – to the west from – 180° to + 180° (Fig. 3.5). Sometimes geographic longitude is measured in units of time from 0 to 24 hours, counting it east of Greenwich.
Geographic latitude? measured along the meridians in the direction of the geographic poles with the sign + to the north, with the sign – south of the equator. Geographic latitude takes a value from – 90° to + 90°.

Fig.5. Geographical coordinates

Precession
Ancient astronomers believed that the Earth's rotation axis was stationary relative to the stellar sphere, but Hiparchus (160 BC) discovered that the vernal equinox point slowly moves towards the annual movement of the Sun, i.e. against the course of the zodiac constellations. This phenomenon is called precession.
The displacement is 50'3.1" per year. The point of the vernal equinox completes a full circle in 25,729 years, i.e. 1° passes in approximately 72 years. The reference point on the celestial sphere is the north celestial pole. Due to precession, it slowly moves among the stars around the pole of the ecliptic along a circle of spherical radius 23°27′. Nowadays, it is getting closer and closer to the North Star.
Now the angular distance between the North Pole and the North Star is 57′. It will come to its closest distance (28′) in 2000, and after 12,000 years it will be close to the brightest star in the Northern Hemisphere, Vega.
Measuring time
The issue of measuring time has been resolved throughout the history of human development. It is difficult to imagine a more complex concept than time. The Greatest Philosopher ancient world Aristotle wrote four centuries BC that among the unknown in the nature around us, the most unknown is time, for no one knows what time is and how to control it.
The measurement of time is based on the rotation of the Earth around its axis and its revolution around the Sun. These processes are continuous and have fairly constant periods, which allows them to be used as natural units of time.
Due to the fact that the Earth's orbit is an ellipse, the Earth's movement along it occurs at an uneven speed, and, consequently, the speed of the apparent movement of the Sun along the ecliptic also occurs unevenly. All luminaries cross the celestial meridian twice in their apparent motion during the day. The intersection of the celestial meridian by the center of the luminary is called the culmination of the luminary (culmination is a Latin word and translated means “top”). There are upper and lower culminations of the luminary. The period of time between climaxes is called half a day. The moment of the upper culmination of the center of the Sun is called true noon, and the moment of the lower one is called true midnight. Both the upper and lower culminations can serve as the beginning or end of the period of time (days) we have chosen as a unit.
If we choose the center of the true Sun as the main point for determining the length of the day, i.e. the center of the solar disk that we see on the celestial sphere, we get a unit of time called a true solar day.
When choosing the so-called average equatorial Sun as the main point, i.e. of some fictitious point moving along the equator with a constant speed of movement of the Sun along the ecliptic, we obtain a unit of time called the average solar day.
If we choose the point of the vernal equinox as the main point when determining the length of the day, we obtain a unit of time called the sidereal day. The sidereal day is 3 minutes shorter than the solar day. 56.555 sec. The local sidereal day is the period of time from the moment of the upper culmination of the Aries point on the local meridian to a given point in time. In a certain area, each star always culminates at the same height above the horizon, because its angular distance from the celestial pole and from the celestial equator does not change. The Sun and Moon, on the other hand, change the height at which they culminate. The intervals between the culminations of the stars are four minutes shorter than the intervals between the culminations of the Sun. During the day (the time of one revolution of the celestial sphere), the sun manages to move relative to the stars to the east - in the direction opposite to the daily rotation of the sky, at a distance of about 1°, since the celestial sphere makes a full revolution (360°) in 24 hours (15° - in 1 hour, 1° in 4 minutes).
The Moon's climaxes are delayed by as much as 50 minutes every day, as the Moon makes approximately one rotation to meet the rotation of the sky per month.
In the starry sky, planets do not occupy a permanent place, just like the Moon and the Sun, therefore, on a star chart, as well as on cosmogram and horoscope maps, the position of the Sun, Moon and planets can be indicated only for a certain point in time.
Standard time. Standard time (Tp) of any point is called the local average solar time the main geographical meridian of the time zone in which this point is located. For the convenience of determining time, the Earth's surface is divided by 24 meridians - each of them is located exactly 15° in longitude from its neighbor. These meridians define 24 time zones. The boundaries of time zones are located 7.5° east and west from each of the corresponding meridians. The time of the same zone at each moment for all its points is considered the same. The Greenwich meridian is considered the zero meridian. A date line was also installed, i.e. a conventional line to the west of which the calendar date for all time zones of eastern longitude will be one day longer than for countries located in time zones of western longitude.
In Russia, standard time was introduced in 1919. Taking as a basis the international system of time zones and the administrative boundaries that existed at that time, time zones from II to XII inclusive were plotted on the map of the RSFSR (see Appendix 2, Table 12).
Local time. Time in any dimension, be it sidereal, true solar or mean solar time of some meridian, is called local sidereal, local true solar and local mean solar time. All points lying on the same meridian will have the same time at the same moment, which is called local time LT (Local Time). Local time is different on different meridians, because... The Earth, rotating around its axis, successively turns different parts of the surface towards the Sun. The sun does not rise and day breaks in all places on the globe at the same time. To the east of the Greenwich meridian, local time increases, and to the west it decreases. Local time is used by astrologers to find the so-called fields (houses) of the horoscope.
Universal time. The local mean solar time of the Greenwich meridian is called universal time or world time (UT, GMT). The local mean solar time of any point on the earth's surface is determined by the geographical longitude of this point, expressed in hourly units and measured from the Greenwich meridian. East of Greenwich time is considered positive, i.e. it is greater than in Greenwich, and to the west of Greenwich it is negative, i.e. Time in areas west of Greenwich is less than Greenwich.
Maternity time (td) – time entered throughout the territory Soviet Union June 21, 1930. Canceled March 31, 1991. Reintroduced in the CIS and Russia on March 19, 1992.
Daylight Saving Time (Tl) is a time introduced in the former Soviet Union on April 1, 1991.
Ephemeris time. The unevenness of the universal time scale led to the need to introduce a new scale determined by the orbital movements of bodies solar system and representing the scale of change of the independent variable differential equations Newtonian mechanics, which form the basis of the theory of motion of celestial bodies. An ephemeris second is equal to 1/31556925.9747 of the tropical year (cm.) of the beginning of our century (1900). The denominator of this fraction corresponds to the number of seconds in the tropical year 1900. The epoch of 1900 was chosen as the zero point of the ephemeris time scale. The beginning of this year corresponds to the moment when the Sun had a longitude of 279°42′.
Sidereal or sidereal year. This is the period of time during which the Sun, in its apparent annual motion around the Earth along the ecliptic, describes a full revolution (360°) and returns to its previous position relative to the stars.
Tropical year. This is the period of time between two successive passages of the Sun through the vernal equinox. Due to the precessional movement of the vernal equinox point towards the movement of the Sun, the tropical year is somewhat shorter than the sidereal year.
An anomalous year. This is the time interval between two successive passages of the Earth through perihelion.
Calendar year. The calendar year is used to count time. It contains an integer number of days. The length of the calendar year was chosen with a focus on the tropical year, since the correct periodic return of the seasons is associated precisely with the length of the tropical year. And since the tropical year does not contain an integer number of days, when constructing the calendar, it was necessary to resort to a system of inserting additional days that would compensate for the days accumulated due to the fractional part of the tropical year. In the Julian calendar, introduced by Julius Caesar in 46 BC. with the assistance of the Alexandrian astronomer Sosigenes, simple years contained 365 days, leap years - 366. Thus, the average length of the year in the Julian calendar was 0.0078 days longer than the length of the tropical year. Due to this, if, for example, the Sun in 325 passed through the vernal equinox on March 21, then in 1582, when Pope Gregory XIII adopted a calendar reform, the equinox fell on March 11. The calendar reform, carried out at the suggestion of the Italian physician and astronomer Luigi Lilio, provides for the skipping of some leap years. The years at the beginning of each century, in which the number of hundreds is not divisible by 4, were taken as such years, namely: 1700, 1800 and 1900. Thus, the average length of the Gregorian year became equal to 365.2425 average solar days. In a number of European countries, the transition to a new style was carried out on October 4, 1582, when the next day was considered October 15. In Russia, the new (Gregorian) style was introduced in 1918, when, according to the decree of the Council of People's Commissars, February 1, 1918 was prescribed to be counted as February 14.
In addition to the calendar system of counting days, a system of continuous counting of days from a certain starting date has become widespread in astronomy. Such a system was proposed in the 16th century by the Leiden professor Scaliger. It was named in honor of Scaliger's father Julius, and is therefore called the Julian period (not to be confused with the Julian calendar!). Greenwich noon on January 1, 4713 BC was taken as the starting point. By Julian calendar, so the Julian day begins at Greenwich noon. Each day according to this account of time has its own serial number. In ephemeris - astronomical tables - Julian days are counted from January 1, 1900. January 1, 1996 - 2,450,084th Julian day.

Planets of the solar system
There are nine major planets in the solar system. In order of distance from the Sun, these are Mercury, Venus, Earth (with the Moon), Mars, Jupiter, Saturn, Uranus, Neptune and Pluto (Fig. 6).

Fig.6. Orbits of the planets of the solar system

The planets revolve around the Sun in ellipses almost in the same plane. Small planets, so-called asteroids, the number of which approaches 2,000, orbit between Mars and Jupiter. The space between the planets is filled with rarefied gas and cosmic dust. It is penetrated by electromagnetic radiation, which is the carrier of magnetic, gravitational and other force fields.
The Sun is about 109 times the diameter of the Earth and 330 thousand times more massive than the Earth, and the mass of all the planets combined is only about 0.1 percent of the mass of the Sun. The sun, by the force of its gravity, controls the movement of the planets of the solar system. The closer a planet is to the Sun, the greater its linear and angular speed of revolution around the Sun. The period of revolution of the planet around the Sun in relation to the stars is called the sidereal or sidereal period (see Appendix 2, Tables 1,2). The period of rotation of the Earth relative to the stars is called the sidereal year.
Until the 16th century, there was the so-called geocentric system of the world of Claudius Ptolemy. In the 16th century, this system was revised by the Polish astronomer Nicolaus Copernicus, who placed the Sun at the center. Galileo, who built the first telescope, the prototype of the telescope, confirmed Copernicus' theory based on his observations.
At the beginning of the 17th century, Johannes Kepler, a mathematician and astrologer of the Austrian royal court, established three laws of motion of bodies in the solar system.
Kepler's first law. The planets move in ellipses, with the Sun at one focus.
Kepler's second law. The radius vector of the planet describes in equal time intervals equal areas, therefore, the closer a planet is to the Sun, the faster it moves, and, conversely, the further it is from the Sun, the slower its movement.
Kepler's third law. The squares of the planets' orbital times are related to each other as the cubes of their average distances from the Sun (the semimajor axes of their orbits). Thus, Kepler’s second law quantitatively determines the change in the speed of a planet’s motion along an ellipse, and Kepler’s third law connects the average distances of planets from the Sun with the periods of their stellar revolutions and allows the semimajor axes of all planetary orbits Express in units of the semimajor axis of the earth's orbit.
Based on observations of the movement of the Moon and Kepler's laws, Newton discovered the law of universal gravitation. He found that the type of orbit that a body describes depends on the speed of the celestial body. Thus, Kepler's laws, which make it possible to determine the orbit of a planet, are a consequence of a more general law of nature - the law of universal gravitation, which forms the basis of celestial mechanics. Kepler's laws are observed when the motion of two isolated bodies is considered taking into account their mutual attraction, but in the solar system not only the attraction of the Sun is active, but also the mutual attraction of all nine planets. In this regard, there is, although a fairly small, deviation from the movement that would occur if Kepler's laws were strictly followed. Such deviations are called disturbances. They have to be taken into account when calculating the apparent positions of the planets. Moreover, it was thanks to the disturbances that the planet Neptune was discovered; it was calculated, as they say, at the tip of a pen.
In the 40s of the 19th century, it was discovered that Uranus, discovered by W. Herschel at the end of the 18th century, barely noticeably deviates from the path it should follow, taking into account disturbances from all the already known planets. Astronomers Le Verrier (in France) and Adams (in England) suggested that Uranus is subject to the attraction of some unknown body. They calculated the orbit of the unknown planet, its mass, and even indicated the place in the sky where the unknown planet should be located at a given time. In 1846, this planet was found using a telescope in the location indicated by the German astronomer Halle. This is how Neptune was discovered.
Apparent motion of planets. From the point of view of an earthly observer, at certain intervals the planets change the direction of their movement, in contrast to the Sun and Moon, which move across the sky in the same direction. In this regard, a distinction is made between the direct movement of the planet (from west to east, like the Sun and the Moon), and retrograde or retrograde movement (from east to west). At the moment of transition from one type of movement to another, the planet appears to stop. Based on the above, the visible path of each planet against the background of stars is a complex line with zigzags and loops. The shapes and sizes of the described loops are different for different planets.
There is also a difference between the movements of the inner and outer planets. The inner planets include Mercury and Venus, whose orbits lie within the orbit of the Earth. The inner planets in their movement are closely connected with the Sun, Mercury moves away from the Sun no further than 28°, Venus - 48°. The configuration in which Mercury or Venus passes between the Sun and the Earth is called an inferior conjunction with the Sun; during a superior conjunction, the planet is behind the Sun, i.e. The sun is between the planet and the Earth. Outer planets are planets whose orbits lie outside the orbit of the Earth. The outer planets move against the background of stars as if independently of the Sun. They describe loops when they are in the opposite region of the sky from the Sun. The outer planets only have superior conjunctions. In cases where the Earth is between the Sun and the outer planet, the so-called opposition occurs.
The opposition of Mars at the time when the Earth and Mars are closest to each other is called the great opposition. Great confrontations are repeated after 15-17 years.
Characteristics of the planets of the solar system
Terrestrial planets. Mercury, Venus, Earth and Mars are called Earth planets. They differ in many respects from the giant planets: smaller in size and mass, higher density, etc.
Mercury is the planet closest to the Sun. It is 2.5 times closer to the Sun than the Earth. For an observer on Earth, Mercury moves away from the Sun by no more than 28°. Only near the extreme positions can the planet be seen in the rays of the evening or morning dawn. To the naked eye, Mercury is a bright point, but in a strong telescope it looks like a crescent or an incomplete circle. Mercury is surrounded by an atmosphere. Atmospheric pressure at the surface of the planet is approximately 1,000 times less than at the surface of the Earth. The surface of Mercury is dark brown and lunar-like, strewn with ring-shaped mountains and craters. Sidereal day, i.e. the period of rotation around the axis relative to the stars is equal to 58.6 of our days. A solar day on Mercury lasts two Mercury years, that is, about 176 Earth days. The length of day and night on Mercury results in sharp differences in temperature between the midday and midnight regions. The daytime hemisphere of Mercury heats up to 380°C and above.
Venus is the planet closest to Earth in the solar system. Venus is almost the same size as the globe. The surface of the planet is always hidden by clouds. The gaseous shell of Venus was discovered by M. V. Lomonosov in 1761. The atmosphere of Venus differs dramatically in chemical composition from the earth and completely unsuitable for breathing. It consists of approximately 97% carbon dioxide, nitrogen - 2%, oxygen - no more than 0.1%. A solar day is 117 Earth days. There is no change of seasons on it. At its surface the temperature is close to +450°C, and the pressure is about 100 atmospheres. The axis of rotation of Venus is almost exactly directed towards the pole of the orbit. The daily rotation of Venus occurs not in the forward direction, but in the opposite direction, i.e. in the direction opposite to the movement of the planet in its orbit around the Sun.
Mars is the fourth planet of the solar system, the last of the planets terrestrial group. Mars is almost half the size of Earth. The mass is approximately 10 times less than the mass of the Earth. The acceleration of gravity on its surface is 2.6 times less than on Earth. A solar day on Mars is 24 hours and 37.4 minutes, i.e. almost like on Earth. The duration of daylight and the midday altitude of the Sun above the horizon vary throughout the year in approximately the same way as on Earth, due to the almost identical inclination of the equatorial plane to the orbital plane for these planets (for Mars, about 25°). When Mars is at opposition, it is so bright that it can be distinguished from other luminaries by its red-orange color. Two polar caps are visible on the surface of Mars; when one grows, the other shrinks. It is dotted with ring mountains. The surface of the planet is shrouded in haze and covered with clouds. Powerful dust storms rage on Mars, sometimes lasting for months. The atmospheric pressure is 100 times less than that on Earth. The atmosphere itself is mainly composed of carbon dioxide. Daily temperature changes reach 80-100°C.
Giant planets. The giant planets include the four planets of the solar system: Jupiter, Saturn, Uranus and Neptune.
Jupiter is the largest planet in the solar system. It is twice as massive as all the other planets combined. But the mass of Jupiter is small compared to the Sun. It is 11 times larger than the Earth in diameter and more than 300 times larger in mass. Jupiter is removed from the Sun at a distance of 5.2 AU. The period of revolution around the Sun is about 12 years. The equatorial diameter of Jupiter is about 142 thousand km. The angular rate of daily rotation of this giant is 2.5 times greater than that of the Earth. The rotation period of Jupiter at the equator is 9 hours 50 minutes.
In its structure, chemical composition and physical conditions at the surface, Jupiter has nothing in common with the Earth and the terrestrial planets. It is unknown whether Jupiter's surface is solid or liquid. Through a telescope you can observe light and dark stripes of changing clouds. The outer layer of these clouds consists of particles of frozen ammonia. The temperature of the above-cloud layers is about –145°C. Above the clouds, Jupiter's atmosphere appears to consist of hydrogen and helium. The thickness of Jupiter's gas shell is extremely large, and the average density of Jupiter, on the contrary, is very small (from 1,260 to 1,400 kg/m3), which is only 24% of the average density of the Earth.
Jupiter has 14 moons, the thirteenth was discovered in 1974, and the fourteenth in 1979. They move in elliptical orbits around the planet. Of these, two moons stand out for their size: Callisto and Ganymede, the largest moon in the Solar System.
Saturn is the second largest planet. It is located twice as far from the Sun as Jupiter. Its equatorial diameter is 120 thousand km. Saturn's mass is half that of Jupiter. A small amount of methane gas has been found in Saturn's atmosphere, just like on Jupiter. The temperature on the visible side of Saturn is close to the freezing point of methane (-184°C), the solid particles of which most likely make up the cloud layer of this planet. The period of axial rotation is 10 hours. 14 min. Rotating rapidly, Saturn acquired a flattened shape. A flat system of rings encircles the planet around the equator, never touching its surface. The rings have three zones separated by narrow slits. The inner ring is very clear and the middle ring is the brightest. The rings of Saturn are a mass of small satellites of the giant planet located in the same plane. The plane of the rings has a constant inclination to the orbital plane, equal to approximately 27°. The thickness of Saturn's rings is about 3 km, and the diameter along the outer edge is 275 thousand km. The orbital period of Saturn around the Sun is 29.5 years.
Saturn has 15 satellites, the tenth was discovered in 1966, the last three - in 1980 by the American automatic spacecraft Voyager 1. The largest of them is Titan.
Uranus is the most eccentric planet in the solar system. It differs from other planets in that it rotates as if lying on its side: the plane of its equator is almost perpendicular to the plane of its orbit. The inclination of the rotation axis to the orbital plane is 8° greater than 90°, so the direction of rotation of the planet is reversed. The moons of Uranus also move in the opposite direction.
Uranus was discovered by the English scientist William Herschel in 1781. It is located twice as far from the Sun as Saturn. Hydrogen, helium and a small admixture of methane were found in the atmosphere of Uranus. The temperature at the subsolar point near the surface is 205-220°C. The period of revolution around the axis at the equator is 10 hours 49 minutes. Due to the unusual location of the axis of rotation of Uranus, the Sun there rises high above the horizon almost to the zenith, even at the poles. Polar day and polar night last 42 years at the poles.
Neptune - revealed himself by the force of his attraction. Its location was first calculated, after which the German astronomer Johann Halle discovered it in 1846. The average distance from the Sun is 30 AU. The orbital period is 164 years 280 days. Neptune is completely covered with clouds. It is assumed that Neptune's atmosphere contains hydrogen mixed with methane, and Neptune's surface is mainly water. Neptune has two satellites, the largest of which is Triton.
Pluto, the planet most distant from the Sun, the ninth in a row, was discovered in 1930 by Clyde Tombaugh at the Lowell Astrological Observatory (Arizona, USA).
Pluto looks like a point object of fifteenth magnitude, i.e. it is about 4 thousand times fainter than those stars that are at the limit of visibility naked eye. Pluto moves very slowly, at only 1.5° per year (4.7 km/s), in an orbit that has a large inclination (17°) to the ecliptic plane and is very elongated: at perihelion it approaches the Sun more short distance, than the orbit of Neptune, and at aphelion it moves 3 billion km further. At the average distance of Pluto from the Sun (5.9 billion km), our daylight star from this planet looks not like a disk, but like a shining point and gives illumination 1,560 times less than on Earth. And therefore it is not surprising that it is very difficult to study Pluto: we know almost nothing about it.
Pluto is 0.18 times the mass of the Earth and is half the diameter of the Earth. The period of revolution around the Sun is on average 247.7 years. The period of axial daily rotation is 6 days 9 hours.
The sun is the center of the solar system. His energy is enormous. Even that insignificant part that falls on the Earth is very large. The Earth receives tens of thousands of times more energy from the Sun than all the world's power plants would if they were operating at full capacity.
The distance from the Earth to the Sun is 107 times greater than its diameter, which in turn is 109 times larger than the Earth’s and is about 1,392 thousand km. The mass of the Sun is 333 thousand times greater than the mass of the Earth, and its volume is 1 million 304 thousand times. Inside the Sun, the matter is highly compressed by the pressure of the overlying layers and is ten times denser than lead, but the outer layers of the Sun are hundreds of times rarer than the air at the surface of the Earth. The gas pressure in the depths of the Sun is hundreds of billions of times greater than the air pressure at the surface of the Earth. All substances on the Sun are in a gaseous state. Almost all atoms completely lose their electrons and turn into “naked” atomic nuclei. Free electrons, breaking away from atoms, become an integral part of the gas. This gas is called plasma. Plasma particles move at enormous speeds - hundreds and thousands of kilometers per second. Nuclear reactions are constantly taking place in the Sun, which is a source of inexhaustible energy from the Sun.
The sun is made up of the same chemical elements, as the Earth, but there is incomparably more hydrogen on the Sun than on Earth. The sun has not used up even half of its hydrogen nuclear fuel reserves. It will shine for many billions of years until all the hydrogen in the depths of the Sun turns into helium.
The radio emission from the Sun that reaches us originates in the so-called corona of the Sun. The solar corona extends over a distance of several solar radii, it reaches the orbits of Mars and Earth. Thus, the Earth is immersed in the solar corona.
From time to time in solar atmosphere active regions appear, the number of which changes regularly, with a cycle on average of about 11 years.
The Moon is a satellite of the Earth, with a diameter 4 times smaller than the Earth. The Moon's orbit is an ellipse, with the Earth at one of its foci. The average distance between the centers of the Moon and the Earth is 384,400 km. The Moon's orbit is inclined 5°9′ to the Earth's orbit. The average angular velocity of the Moon is 13°, 176 per day. The inclination of the lunar equator to the ecliptic is 1°32.3′. The time the Moon rotates around its axis is equal to the time it takes to rotate around the Earth, as a result of which the Moon always faces the Earth with one side. The Moon's movement is uneven: in some parts of its visible path it moves faster, in others - slower. During its orbital movement, the distance of the Moon to the Earth varies from 356 to 406 thousand km. The uneven movement in orbit is associated with the influence of the Earth on the Moon, on the one hand, and the powerful gravitational force of the Sun, on the other. And if you consider that its movement is influenced by Venus, Mars, Jupiter and Saturn, then it is clear why the Moon continuously changes, within certain limits, the shape of the ellipse along which it revolves. Due to the fact that the Moon has an elliptical orbit, it either approaches the Earth or moves away from it. The point of the lunar orbit closest to Earth is called perigee, and the most distant point is called apogee.
The lunar orbit intersects the plane of the ecliptic at two diametrically opposite points, called the lunar nodes. The ascending (North) node crosses the plane of the ecliptic, moving from south to north, and the descending (South) node - from north to south. The lunar nodes continuously move along the ecliptic in the direction opposite to the course of the zodiacal constellations. The period of rotation of the lunar nodes along the ecliptic is 18 years and 7 months.
There are four periods of revolution of the Moon around the Earth:
a) sidereal or sidereal month - the period of revolution of the Moon around the Earth relative to the stars, it is 27.3217 days, i.e. 27 days 7 hours 43 minutes;
b) lunar, or synodic month - the period of revolution of the Moon around the Earth relative to the Sun, i.e. the interval between two new moons or full moons is on average 29.5306 days, i.e. 29 days 12 hours 44 minutes. Its duration is not constant due to the uneven movement of the Earth and the Moon and ranges from 29.25 to 29.83 days;
c) draconic month - the period of time between two successive passages of the Moon through the same node of its orbit, it is 27.21 average days;
d) anomalistic month - the time interval between two successive passages of the Moon through perigee; it is 27.55 average days.
As the Moon moves around the Earth, the conditions of illumination of the Moon by the Sun change, the so-called change of lunar phases occurs. The main phases of the Moon are new moon, first quarter, full moon and last quarter. The line on the disk of the Moon separating the illuminated part of the hemisphere facing us from the unlit one is called the terminator. Due to the excess of the synodic lunar month over the sidereal month, the Moon rises daily later by approximately 52 minutes, moonrises and moonsets occur at different hours of the day, and the same phases occur at various points lunar orbit in turn in all signs of the Zodiac.
Lunar and solar eclipses. Lunar and solar eclipses occur when the Sun and Moon are near the nodes. At the moment of an eclipse, the Sun, Moon and Earth are located almost on the same straight line.
A solar eclipse occurs when the Moon passes between the Earth and the Sun. At this time, the Moon faces the Earth with its unlit side, that is, a solar eclipse occurs only during the new moon (Fig. 3.7). The apparent sizes of the Moon and the Sun are almost the same, so the Moon can cover the Sun.

Fig.7. Solar eclipse diagram

The distances of the Sun and Moon from the Earth do not remain constant, since the orbits of the Earth and the Moon are not circles, but ellipses. Therefore, if at the moment of a solar eclipse the Moon is at its smallest distance from the Earth, then the Moon will completely cover the Sun. Such an eclipse is called total. The total phase of a solar eclipse lasts no more than 7 minutes 40 seconds.
If during an eclipse the Moon is at its greatest distance from the Earth, then it has a slightly smaller apparent size and does not completely cover the Sun; such an eclipse is called annular. The eclipse will be total or annular if the Sun and Moon are almost at a node at the new moon. If the Sun at the moment of the new moon is at some distance from the node, then the centers of the lunar and solar disks will not coincide and the Moon will partially cover the Sun, such an eclipse is called partial. There are at least two solar eclipses every year. The maximum possible number of eclipses during a year is five. Due to the fact that the shadow of the Moon during a solar eclipse does not fall on the entire Earth, a solar eclipse is observed in a certain area. This explains the rarity of this phenomenon.
A lunar eclipse occurs during a full moon, when the Earth is between the Moon and the Sun (Fig. 8). The diameter of the Earth is four times the diameter of the Moon, so the shadow from the Earth is 2.5 times the size of the Moon, i.e. The moon can be completely immersed in the earth's shadow. The longest duration of a total lunar eclipse is 1 hour 40 minutes.

Fig.8. Lunar eclipse diagram

Lunar eclipses are visible in the hemisphere where the Moon is currently above the horizon. One or two things happen throughout the year. lunar eclipses, some years there may be none at all, and sometimes there are three lunar eclipses per year. Depending on how far from the node of the lunar orbit the full moon occurs, the Moon will be more or less immersed in the Earth's shadow. There are also total and partial lunar eclipses.
Each specific eclipse repeats itself after 18 years, 11 days, 8 hours. This period is called Saros. During Saros, 70 eclipses occur: 43 solar, of which 15 are partial, 15 annular and 13 total; 28 lunar, of which 15 are partial and 13 are complete. After Saros, each eclipse repeats approximately 8 hours later than the previous one.