3. Celestial sphere. Basic planes, lines and points of the celestial sphere.
Under celestial sphere it is customary to understand a sphere of arbitrary radius, the center of which is at the observation point, and all the celestial bodies or luminaries surrounding us are projected onto the surface of this sphere
The rotation of the celestial sphere for an observer located on the surface of the Earth reproduces diurnal movement shining in the sky
ZOZ" – a plumb (vertical) line,
S.W.N.E.– true (mathematical) horizon,
aMa" - almucantarat,
ZMZ" – height circle (vertical circle), or vertical
P 
OP" – axis of rotation of the celestial sphere (axis of the world),
P– the north pole of the world,
P" - south pole of the world,
Ð PON= j (latitude of the observation site),
QWQ" E- celestial equator,
bMb" – daily parallel,
PMP" – declination circle,
PZQSP" Z" Q" N- celestial meridian,
NOS– midday line
4. Celestial coordinate systems (horizontal, first and second equatorial, ecliptic).
Since the radius of the celestial sphere is arbitrary, the position of the luminary on the celestial sphere is uniquely determined by two angular coordinates if the main plane and the origin are given.
The following celestial coordinate systems are used in spherical astronomy:
Horizontal, 1st equatorial, 2nd equatorial, Ecliptic
Horizontal coordinate system
The main plane is the plane of the mathematical horizon
1
)Ð mOM
= h
(height)
0 £ h£90 0
–90 0 £ h £ 0
or Р ZOM = z (zenith distance)
0 £ z£180 0
z + h = 90 0
2) Р SOm = A(azimuth)
0 £ A£360 0
1st equatorial coordinate system
The main plane is the plane of the celestial equator
1) Р mOM= d (declension)
0 £ d £90 0
–90 0 £ d £ 0
or Р P.O.M. = p (pole distance)
0 £ p£180 0
p+ d = 90 0
2) Р QOm = t (hour angle)
0 £ t£360 0
or 0 h £ t£24h
All horizontal coordinates ( h, z, A) and hour angle t the first equatorial SC continuously change during the daily rotation of the celestial sphere.
Declension d does not change.
Must be entered instead t such an equatorial coordinate that would be measured from a fixed point on the celestial sphere.
2nd equatorial coordinate system
ABOUT 
main plane – the plane of the celestial equator
1) Р mOM= d (declension)
0 £ d £90 0
–90 0 £ d £ 0
or Р P.O.M. = p (pole distance)
0
£
p£180 0
p+ d = 90 0
2) Ð ¡ Om= a (right ascension)
or 0 h £ a £ 24 h
Horizontal CS is used to determine the direction to the star relative to terrestrial objects.
The 1st equatorial CS is used primarily when determining the exact time.
2
The -th equatorial SC is generally accepted in astrometry.
Ecliptic SC
The main plane is the ecliptic plane E¡E"d
The plane of the ecliptic is inclined to the plane of the celestial meridian at an angle ε = 23 0 26"
PP" – ecliptic axis
E – summer solstice point
E" – winter solstice point
1) m = λ (ecliptic longitude)
2) mM= b (ecliptic latitude)
5. Daily rotation of the celestial sphere at different latitudes and associated phenomena. Daily movement of the Sun. Change of seasons and heat zones.
Measurements of the height of the Sun at noon (i.e. at the time of its upper culmination) at the same geographical latitude showed that the declination of the Sun d throughout the year varies from +23 0 36 "to –23 0 36", two passing through zero times.
The direct ascension of the Sun a throughout the year also constantly changes from 0 to 360 0 or from 0 to 24 h.
Considering the continuous change in both coordinates of the Sun, we can establish that it moves among the stars from west to east along a large circle of the celestial sphere, which is called ecliptic.
March 20-21, the Sun is at point ¡, its declination δ = 0 and right ascension a = 0. On this day (vernal equinox) the Sun rises exactly at the point E and comes to a point W. The maximum height of the center of the Sun above the horizon at noon of this day (upper culmination): h= 90 0 – φ + δ = 90 0 – φ
Then the Sun will move along the ecliptic closer to point E, i.e. δ > 0 and a > 0.
On June 21-22, the Sun is at point E, its maximum declination is δ = 23 0 26", and its right ascension is a = 6 h. At noon of this day (summer solstice) the Sun rises to its maximum height above the horizon: h= 90 0 – φ + 23 0 26"
Thus, in mid-latitudes the Sun is NEVER at its zenith
Latitude of Minsk φ = 53 0 55"
Then the Sun will move along the ecliptic closer to point d, i.e. δ will begin to decrease
Around September 23, the Sun will come to point d, its declination δ = 0, right ascension a = 12 h. This day (the beginning of astronomical autumn) is called the autumnal equinox.
On December 22-23, the Sun will be at point E", its declination is minimal δ = – 23 0 26", and right ascension a = 18 h.
Maximum height above horizon: h= 90 0 – φ – 23 0 26"
The change in the equatorial coordinates of the Sun occurs unevenly throughout the year.
Declination changes most quickly when the Sun moves near the equinoxes, and slowest near the solstices.
Right ascension, on the contrary, changes more slowly near the equinoxes and faster near the solstices.
The apparent motion of the Sun along the ecliptic is associated with the actual motion of the Earth in its orbit around the Sun, as well as with the fact that the Earth's axis of rotation is not perpendicular to the plane of its orbit, but makes an angle ε = 23 0 26".
If ε = 0, then at any latitude on any day of the year, day would be equal to night (without taking into account refraction and the size of the Sun).
Polar days, lasting from 24 hours to six months and corresponding nights, are observed in the polar circles, the latitudes of which are determined by the conditions:
φ = ±(90 0 – ε) = ± 66 0 34"
The position of the axis of the world and, consequently, the plane of the celestial equator, as well as points ¡ and d, is not constant, but changes periodically.
Due to the precession of the earth's axis, the axis of the world describes a cone around the ecliptic axis with an opening angle of ~23.5 0 in 26,000 years.
Due to the disturbing action of the planets, the curves described by the poles of the world do not close, but are contracted into a spiral.
T 
.To. Both the plane of the celestial equator and the plane of the ecliptic slowly change their position in space, then their points of intersection (¡ and d) slowly move to the west.
Speed of movement (total annual precession in the ecliptic) per year: l = 360 0 /26 000 = 50,26"".
Total annual precession at the equator: m = l cos ε = 46.11"".
At the beginning of our era, the vernal equinox point was in the constellation Aries, from which it received its designation (¡), and the autumn equinox point was in the constellation Libra (d). Since then, point ¡ has moved to the constellation Pisces, and point d to the constellation Virgo, but their designations remain the same.
| " |
The celestial sphere is an imaginary sphere of arbitrary radius, used in astronomy to describe the relative positions of luminaries in the sky. For simplicity of calculations, its radius is taken equal to unity; The center of the celestial sphere, depending on the problem being solved, is combined with the observer’s pupil, with the center of the Earth, Moon, Sun, or even with an arbitrary point in space.
The idea of the celestial sphere arose in ancient times. It was based on the visual impression of the existence of a crystal dome of the sky, on which the stars seemed to be fixed. The celestial sphere in the imagination of ancient peoples was the most important element Universe. With the development of astronomy, this view of the celestial sphere disappeared. However, the geometry of the celestial sphere, laid down in ancient times, as a result of development and improvement, received modern look, in which for the convenience of various calculations it is used in astrometry.
Let us consider the celestial sphere as it appears to the Observer at mid-latitudes from the surface of the Earth (Fig. 1).
Two straight lines, the position of which can be established experimentally using physical and astronomical instruments, play important role when defining concepts related to the celestial sphere. The first of them is a plumb line; This is a straight line that coincides at a given point with the direction of gravity. This line, drawn through the center of the celestial sphere, intersects it at two diametrically opposite points: the upper one is called the zenith, the lower one is called the nadir. The plane passing through the center of the celestial sphere perpendicular to the plumb line is called the plane of the mathematical (or true) horizon. The line of intersection of this plane with the celestial sphere is called the horizon.
The second straight line is the axis of the world - a straight line passing through the center of the celestial sphere parallel to the axis of rotation of the Earth; There is a visible daily rotation of the entire sky around the axis of the world. The points of intersection of the axis of the world with the celestial sphere are called the North and South poles of the world. The most noticeable of the stars near the North Pole is the North Star. Bright stars There is no world near the South Pole.
The plane passing through the center of the celestial sphere perpendicular to the axis of the world is called the plane of the celestial equator. The line of intersection of this plane with the celestial sphere is called the celestial equator.
Let us recall that the circle that is obtained when the celestial sphere is intersected by a plane passing through its center is called a great circle in mathematics, and if the plane does not pass through the center, then a small circle is obtained. The horizon and celestial equator represent great circles of the celestial sphere and divide it into two equal hemispheres. The horizon divides the celestial sphere into visible and invisible hemispheres. The celestial equator divides it into the Northern and Southern Hemispheres, respectively.
During the daily rotation of the sky, the luminaries rotate around the axis of the world, describing small circles on the celestial sphere, called daily parallels; luminaries, 90° distant from the poles of the world, move along the great circle of the celestial sphere - the celestial equator.
Having defined the plumb line and the axis of the world, it is not difficult to define all other planes and circles of the celestial sphere.
The plane passing through the center of the celestial sphere, in which both the plumb line and the axis of the world lie simultaneously, is called the plane of the celestial meridian. The great circle from the intersection of this plane with the celestial sphere is called the celestial meridian. That one of the points of intersection of the celestial meridian with the horizon, which is closer to the North Pole of the world, is called the north point; diametrically opposite - the point of the south. The straight line passing through these points is the noon line.
Points on the horizon that are 90° from the north and south points are called east and west points. These four points are called the main points of the horizon.
Planes passing through a plumb line intersect the celestial sphere in great circles and are called verticals. The celestial meridian is one of the verticals. The vertical perpendicular to the meridian and passing through the points of east and west is called the first vertical.
By definition, the three main planes - the mathematical horizon, the celestial meridian and the first vertical - are mutually perpendicular. The plane of the celestial equator is perpendicular only to the plane of the celestial meridian, forming a dihedral angle with the plane of the horizon. At the geographic poles of the Earth, the plane of the celestial equator coincides with the plane of the horizon, and at the equator of the Earth it becomes perpendicular to it. In the first case, at the geographic poles of the Earth, the axis of the world coincides with a plumb line and any of the verticals can be taken as the celestial meridian, depending on the conditions of the task at hand. In the second case, at the equator, the axis of the world lies in the plane of the horizon and coincides with the noon line; The North Pole of the world coincides with the point of north, and the South Pole of the world coincides with the point of south (see figure).
When using the celestial sphere, the center of which coincides with the center of the Earth or some other point in space, a number of features also arise, but the principle of introducing basic concepts - horizon, celestial meridian, first vertical, celestial equator, etc. - remains the same.
The main planes and circles of the celestial sphere are used when introducing horizontal, equatorial and ecliptic celestial coordinates, as well as when describing the features of the apparent daily rotation of luminaries.
The great circle formed when the celestial sphere is intersected by a plane passing through its center and parallel to the plane of the earth's orbit is called the ecliptic. The visible annual movement of the Sun occurs along the ecliptic. The point of intersection of the ecliptic with the celestial equator, at which the Sun passes from the Southern Hemisphere of the celestial sphere to the Northern, is called the point of the vernal equinox. The opposite point of the celestial sphere is called the autumnal equinox. A straight line passing through the center of the celestial sphere perpendicular to the ecliptic plane intersects the sphere at two poles of the ecliptic: the North Pole in the Northern Hemisphere and the South Pole in the Southern Hemisphere.
All celestial bodies are at unusually large and very different distances from us. But to us they seem equally distant and seem to be located on some sphere. When deciding practical problems in aviation astronomy, it is important to know not the distance to the stars, but their position on the celestial sphere at the moment of observation.
The celestial sphere is an imaginary sphere of infinite radius, the center of which is the observer. When examining the celestial sphere, its center is aligned with the observer's eye. The dimensions of the Earth are neglected, so the center of the celestial sphere is often combined with the center of the Earth. The luminaries are applied to the sphere in the position in which they are visible in the sky at some point in time from a given point of location of the observer.
The celestial sphere has a number of characteristic points, lines and circles. In Fig. 1.1, a circle of arbitrary radius depicts the celestial sphere, in the center of which, designated by point O, the observer is located. Let's consider the main elements of the celestial sphere.
The observer's vertical is 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 Z is the point of intersection of the observer's vertical with the celestial sphere, located above the observer's head. Nadir Z" is the point of intersection of the observer's vertical with the celestial sphere, opposite to the zenith.
The true horizon N E S W is a great 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: the above-horizon hemisphere, in which the zenith is located, and the subhorizon hemisphere, in which the nadir is located.
The world axis PP" is a straight line around which the visible daily rotation of the celestial sphere occurs.
Rice. 1.1. Basic points, lines and circles on the celestial sphere
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 region of the Ursa Minor constellation is called the North celestial pole P, and the opposite pole is called the South Pole.
The celestial equator is a large 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 the northern hemisphere, in which the North Celestial Pole is located, and the southern hemisphere, in which the South Celestial Pole is located.
The celestial meridian, or meridian of the observer, 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 the eastern and western hemispheres.
The points of north and south are the points 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.
The noon line is 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 southern and northern points of the celestial equator are the points of intersection of the celestial meridian with the celestial equator. The point closest to the southern point of the horizon is called the south point of the celestial equator, and the point closest to the northern point of the horizon is called the north point
The vertical of a luminary, or the circle of altitude, is 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.
The circle of declination, or the hour circle of a luminary, RMR, is a large circle on the celestial sphere, passing through the poles of myoa and the luminary.
The daily parallel of a luminary is a small circle on the celestial sphere drawn through the luminary parallel to the plane of the celestial equator. The apparent daily movement of the luminaries occurs along daily parallels.
Almucantarat of the luminary AMAG is a small circle on the celestial sphere drawn through the luminary parallel to the plane of the true horizon.
The considered elements of the celestial sphere are widely used in aviation astronomy.
Celestial sphere is an imaginary sphere of arbitrary radius with a center at an arbitrary point, on the surface of which the positions of the luminaries are plotted as they are visible in the sky at some point in time from a given point.
The celestial sphere rotates. It is not difficult to verify this simply by observing the change in the position of the celestial bodies relative to the observer or the horizon. If you point the camera at the Ursa Minor star and open the lens for several hours, the images of the stars on the photographic plate will describe arcs, the central angles of which are the same (Fig. 17). Material from the site
Due to the rotation of the celestial sphere, each luminary moves in a small circle, the plane of which is parallel to the plane of the equator - daily parallel. As can be seen from Figure 18, the daily parallel may intersect the mathematical horizon, but may not intersect it. The intersection of the horizon by a luminary is called sunrise, if it passes into the upper part of the celestial sphere, and by setting when the luminary passes into the lower part of the celestial sphere. In the event that the daily parallel along which the luminary moves does not cross the horizon, the luminary is called non-ascending or non-visitors depending on where it is located: always in the upper or always in the lower part of the celestial sphere.
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. Line, perpendicular to the plane the ecliptic and passing through the center of the celestial sphere, forms the North (N) and South (P’) 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 for constructing 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 of the 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 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 the local mean solar time of 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 in the independent variable of the differential equations of Newtonian mechanics, which form the basis of the theory of the 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. according to the Julian calendar, so the Julian day begins at Greenwich noon. Each day according to this time account 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, Table 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 a planet describes equal areas in equal periods of time, 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 semi-major axes of all planetary orbits to be expressed in units of the semi-major 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 robotic 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 approximately 4 thousand times fainter than those stars that are at the limit of visibility with the 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 highly elongated: at perihelion it approaches the Sun at a shorter 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 consists 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, active regions appear in the solar atmosphere, 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 about 52 minutes, the Moon rises and sets at different hours of the day, and the same phases occur at different points of the 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.