Hour angle of the vernal equinox. Star time. Universal, standard and standard time
On observations of the daily rotation of the celestial vault and the annual motion of the Sun, i.e. on the rotation of the Earth around its axis and on the revolution of the Earth around the Sun, the measurement of time is based.
The rotation of the Earth around its axis occurs almost uniformly, with a period equal to the period of rotation of the firmament, which can be determined quite accurately from observations. Therefore, according to the angle of rotation of the Earth from a certain initial position, one can judge the elapsed time. The initial position of the Earth is taken as the moment of passage of the plane of the earth's meridian of the place of observation through a chosen point in the sky, or, which is the same thing, the moment of the upper (or lower) climax of this point on the given meridian.
The length of the basic unit of time, called a day, depends on a chosen point in the sky. In astronomy, such points are taken: a) the vernal equinox b) the center of the visible disk of the Sun (the true Sun); c) "mean sun" - a fictitious point, whose position in the sky can be calculated theoretically for any moment in time.
The three different units of time defined by these points are called respectively sidereal, true solar and mean solar days, and the time they measure, - sidereal, true solar and mean solar time.
tropical year called the time interval between two successive passages of the center of the true Sun through the vernal equinox.
3.2. Starry day. sidereal time
The time interval between two successive culminations of the same name of the vernal equinox on the same geographic meridian is called a sidereal day.
The moment of the upper climax of the vernal equinox is taken as the beginning of a sidereal day on a given meridian.
The angle by which the Earth will turn from the moment of the upper climax of the vernal equinox to some other moment is equal to the hour angle of the vernal equinox at that moment. Therefore, sidereal time s on a given meridian at any moment is numerically equal to the hour angle of the vernal equinox point t, expressed in hours, i.e.
s = t 
.
(1.14)
The vernal equinox is not marked in the sky. It is impossible to directly measure its hour angle or notice the moment of its passage through the meridian. Therefore, in practice, to establish the beginning of a sidereal day or sidereal time at some point, it is necessary to measure the hour angle t of any luminary M, the right ascension of which 
known (Fig. 12).
Then, since t = Qm 
=
m, and the hour angle of the vernal equinox t 
= Q 
and, by definition, is equal to sidereal time s,
s = t 
=
+t, (1.15)
those. sidereal time at any moment is equal to the right ascension of any luminary plus its hour angle.
At the moment of the upper climax, its hour angle t = 0 shone, and then
s= 
.
(1.16)
At the moment of the lower climax, its hour angle t = 12h shone, and sidereal time
s= 
+12h. (1.17)
Measuring time by sidereal days and their fractions is the simplest and therefore very beneficial in solving many astronomical problems. But in Everyday life using sidereal time is extremely inconvenient. The daily routine of a person's life is connected with the apparent position of the Sun above the horizon, with its rising, culmination and setting, and not with the position of the fictitious point of the vernal equinox. And since mutual arrangement The sun and the point of the vernal equinox continuously change during the year, for example, the upper culmination of the Sun (noon) on different days of the year occurs at different moments of the sidereal day. Indeed, only once a year, when the Sun passes through the vernal equinox, i.e. when its right ascension 
= 0h, it will culminate along with the vernal equinox at noon, at 0h sidereal time. After one sidereal day, the vernal equinox point will again be at the upper culmination, and the Sun will come to the meridian only after about 4 minutes, since in one sidereal day it will shift to the east by almost 1 ° relative to the vernal equinox point, and its right ascension will be narrower. equals 
=0h4m. In another sidereal day, the right ascension of the Sun will again increase by 4m, i.e. noon will come at about 0h8m sidereal time, and so on. Thus, the sidereal time of the Sun's climax is continuously growing, and noon occurs at different moments of the sidereal day. The inconvenience is quite obvious.
A sidereal day is the period of time between two consecutive upper climaxes of the point of Aries on the same meridian.
Sidereal time S is the time interval from the moment of the upper climax of the point of Aries on a given meridian to this moment.
But the angle of rotation of the point ¡ from the midday part of the meridian of the observer (Fig. 3.15.) Is the hour angle of Aries *, therefore, the sidereal time elapsed from the upper climax of the point of Aries is numerically equal to the news hour angle of this point, i.e. ¡ .
If t¡ or S is counted from the local meridian, then we get the local
sidereal time S m = t m ¡ , if from Greenwich, we get Greenwich sidereal time S gr = t gr ¡ .
Large periods of time are not expressed in sidereal days, so sidereal time has no date, and if S or t¡ exceeds 24 hours (360 °), then this period is discarded, for example, S = 375 ° 20¢, 0 = 15 ° 20¢ ,0.
Basic formula for time. On fig. 3.15 shows the image of the sphere on the plane of the equator, constructed as we would see the sphere from the side P N . The earth in the center, together with the meridian P N E and the plumb line ZO, are considered fixed, and the sphere is considered to be rotating from E to W; the midnight part of the meridian of the observer (P N Q) is depicted by a wavy line. The hour angle of the point ¡ is represented by ÈE¡, the local hour angle of the star C is represented by ÈED, and the right ascension is represented by È¡D. It can be seen from the figure that
those. sidereal time at any moment is equal to the star's hourly angle plus its right ascension.
Equality (*), called the basic formula of time, is valid for any luminary and point of the sphere, for example:
From the formula (*) you can determine the hour angle of the star
To the right side of the equation (*) you can add 360° (24 hours) as needed. With this in mind, the formula takes the form
where t * = 360° - a * - star addition, counted from ¡ to the meridian
luminaries to W.
The formula (*) is used to calculate the hour angles of the stars, with t * and S selected from the Yearbook. Formulas allow you to solve a number of problems for measuring time. For example, for particular positions of the luminary: in the upper culmination t = 0 and S = a; at the bottom t = 180° and S = 180° + a. For the upper climax ¡ we get: S = 0 and t = t * .
Sidereal time is convenient for observing objects of the starry sky and for solving astronomical problems, but is not suitable for use in everyday life. This is due to the fact that the beginning of the sidereal day falls on different time day and night, i.e. sunny days.
A true solar day is the time interval between two successive culminations of the same name of the center of the visible disk of the Sun on the same meridian.
True midnight is taken as the beginning of the true day, i.e. lower culmination of the Sun.
True solar time is the time interval from the moment of the lower culmination of the center of the visible disk of the Sun to this moment, expressed in parts of a solar day. The difference in the length of a solar day is 12¢.8, or 51 s.2; in winter, the true day is longer, and at the end of summer it is shorter. Obviously, the variable unit is inconvenient. In life and technology, a constant unit is required, for which the average solar day can be taken.
The unit of time in astronomy is day- the period of time during which the Earth makes a complete rotation around its axis relative to some point in the sky. Depending on this point of reference, there are sidereal day- the time interval between two consecutive culminations of the same name of the vernal equinox, and true solar day- the time interval between two successive climaxes of the same name of the center of the Sun. The solar day is about 4 minutes longer than the stellar one, since the Sun moves among the stars in the direction of the Earth's rotation, and in order to catch up with it, the Earth needs to make a little more than one revolution relative to the stars. Used to measure long time intervals tropical year- the time interval between two successive passages of the center of the Sun through the vernal equinox.
Both sidereal and true solar days can be used to measure time. If sidereal days are used, the time being measured is called sidereal time, and if the true solar day - then true solar time. However, this does not mean that we are measuring some two independent times. In fact, these are like two different rulers for measuring time. So, the distance between cities can be expressed both in kilometers and in miles. The situation with the measurement of time is the same.
The moment of the upper climax of the vernal equinox is taken as the beginning of a sidereal day on a given geographic meridian. sidereal time- the time elapsed from the moment of the upper culmination of the vernal equinox to any other of its positions, expressed in fractions of a sidereal day (sidereal hours, minutes and seconds). So sidereal time s equal in magnitude to the hour angle of the vernal equinox, or the sum of the hour angle of any luminary O and its right ascension (see Fig. 17):
From this, in particular, it follows that at the moment of the upper culmination of any star O sidereal time is exactly equal to its right ascension.
9.2. True solar time
The moment of the lower culmination of the center of the Sun is taken as the beginning of a true solar day. True solar time is the time elapsed from the moment of the lower culmination of the center of the Sun to any other position, expressed in fractions of a true solar day (true solar hours, minutes and seconds). So, true solar time is equal to the hour angle of the center of the Sun plus 12 hours:
Unfortunately, the length of a true solar day varies throughout the year, because:
1) The Sun does not move along the celestial equator, but along the ecliptic inclined to it, i.e. the change in the right ascension of the Sun in one day near the solstices is greater than near the equinoxes. Therefore, slightly different time intervals pass between the lower culminations of the Sun near the solstices and equinoxes.
2) The Sun also moves unevenly along the ecliptic due to the ellipticity of the Earth's orbit.
For these reasons, for example, the true solar day on December 22 is about 50 seconds longer than on September 23. It is clear that the use of true solar time is inconvenient, and therefore the mean solar time was introduced.
9.3. mean solar time
Two fictitious points were introduced - mean ecliptic sun and mean equatorial sun. The mean ecliptic Sun moves uniformly along the ecliptic and coincides with the true one at the moment the Earth passes perihelion. The average equatorial Sun moves uniformly along the equator with the average speed of the true Sun and simultaneously with the average ecliptic Sun passes the vernal equinox.
Mean solar day- the time interval between two successive lower climaxes of the mean equatorial Sun on the same geographic meridian. The beginning of a solar day is taken as the lower climax of the mean equatorial Sun, and the mean solar time T M equals
where t M is the hourly angle of the mean equatorial Sun.
It is clear that the mean solar time cannot be directly measured from astronomical observations, it can only be calculated. The relationship between true solar time and mean solar time is expressed through equation of time:
 |
| Rice. 18. Changing the equation of time during the year |
9.4. ephemeris time
Observations have shown that the average day is not a constant value. The reason is the uneven rotation of the Earth around its axis. There is a secular slowdown of the Earth's rotation due to tidal friction, seasonal changes associated with the redistribution of air and water masses on the Earth's surface. Irregular, abrupt changes in the Earth's speed have also been detected, the cause of which is unknown. The magnitude of these irregularities is thousandths of a second.
Therefore, a uniform ephemeris time was introduced, which is determined by the movement of the Moon and planets. In 1956, the International Committee for Weights and Measures adopted ephemeris time as the basis ephemeris second, as 1/31 556 925.9747 part of the tropical year at 12 o'clock ephemeris time on January 0, 1900.
At present, instead of the ephemeris time, the so-called terrestrial dynamic time is used, which approximately corresponds to the ephemeris.
9.5. atomic time
The development of science has led to a situation where technical means can provide time measurement with greater accuracy than from astronomical observations. In 1964, the International Committee for Weights and Measures adopted the cesium atomic clock as the standard of time.
Atomic time is based on atomic second, as a period of time during which 9 192 631 771 oscillations of an electromagnetic wave occur, which are emitted by a cesium atom during the transition from one fixed energy level to another.
The atomic second is slightly less than the ephemeris, and in a year the difference between the atomic and ephemeris times reaches 0.9 sec. Therefore, almost every year, atomic clocks are set back 1 second. Radio time signals correspond to atomic time. These signals are transmitted in the form of six second pulses, with the beginning of the last signal marking the end of the hour. Several radio stations around the world continuously transmit accurate time signals around the clock.
9.6. Time counting systems
The local time is the time measured on a given geographic meridian.
The difference of any local times on two meridians at the same physical moment is equal to the difference in longitudes of these meridians:
UTC- local mean solar time of the Greenwich (=0) meridian. If the longitude of a place on Earth is expressed in hours and considered positive east of Greenwich, then the following relation takes place:
Standard time. In 1884, a belt system for calculating mean time was introduced. Time is kept only on 24 main geographic meridians located from each other in longitude exactly 15 o starting from the prime meridian. The boundaries of the belts are separated, as a rule, from the main meridian. Belt numbers N from 0 to 23. The local mean solar time of the main meridian of any time zone is called the standard time T n, according to which time is kept in the entire territory lying in a given time zone. Standard time is related to universal time through the time zone number:
Decree time. In 1930, by decree of the government of the USSR, the clock hands were moved 1 hour ahead of standard time:
This time is called the daylight savings time.
Summer time. In 1981, in the USSR, following the example of most countries of the world, it was also introduced summer time, 1 hour ahead of maternity. Summer time is introduced from the last Sunday of March to the last Sunday of October:
Thus, the time, which we call Moscow, in winter is the maternity time of the second time zone and is ahead of the universal time UT by 3 hours. In summer, the difference from Greenwich Mean Time is 4 hours.
It is most convenient to move from sidereal to mean time through a tropical year. Its duration in sidereal days is exactly one day longer than the duration in average solar days. This is due to the fact that in a year the Sun makes a full revolution on celestial sphere in the same direction as the earth rotates. Therefore, in a year, the Earth makes one revolution less relative to the Sun than relative to the stars.
A tropical year is equal to 365.2422 mean solar days and 366.2422 sidereal days. Therefore, the connection between the mean solar time and sidereal time is carried out through the equation: 365.2422 average days = 366.2422 superdays. Or
All other units of time correlate with each other through the same coefficients, i.e. 1 Wed hour = 1.002738 hours, etc., i.e.
and
For the convenience of calculating sidereal time at a particular moment, determined by mean solar time, the Astronomical Yearbook gives the value of sidereal time at Greenwich Mean Midnight S 0 . For an average solar day, the value S 0 increases by 3 m 56 s.555, because sidereal days are shorter than the average by this value.
Knowing S 0 , sidereal time can be calculated s 0 at midnight on the given meridian. Since on this meridian midnight will come earlier than in Greenwich, then the value s 0 will be slightly less than S 0:
Example. It is necessary to find sidereal time in Kazan at the moment 3 h mean solar time. To do this, you need to find sidereal time at local mean midnight s 0 , and add to it a period of time in the average 3 h, translated into sidereal time interval:
9.8. Calendar
A calendar is a system for counting long periods of time.
Nature has provided us with 3 natural periodic processes: the change of day and night, the change of lunar phases, the change of seasons. At different times, different peoples based the calendar on different processes, so there were solar, lunar, lunar-solar calendars. The solar calendars are based on the duration of the tropical year, the lunar calendars are based on the lunar month, and the lunisolar calendars combine both periods.
We live according to the solar calendar. For practical reasons, the calendar must meet the following conditions:
1) The calendar year must contain an integer number of days.
2) The length of the calendar year should be as close as possible to the length of the tropical year.
9.8.1. Julian calendar
As we already know, a tropical year contains 365.2422 solar days or 365 d 5 h 48 m 46 s 365 d 6 h. Based on this fact, the Alexandrian astronomer Sosigenes developed, and the Roman emperor Julius Caesar in 46 BC introduced a calendar, now called Julian. Its essence is as follows. The length of a simple calendar year is set to 365 d. At the same time, a difference of almost 1 day accumulates over 4 years, so every fourth year contains 366 d and is called a leap year. It is customary to consider leap years those years whose numbers are divisible by 4 without a remainder (for example, 2004).
The Julian year is 0 longer than the tropical year d.0078 and for 128 years the discrepancy begins to be 1 day. The Julian calendar was used for about 16 centuries, and during this time a difference of 10 days accumulated. This led to confusion in determining the dates of church holidays.
For example, according to the rules of the Christian church, the Easter holiday should occur on the first Sunday after the first full moon after the vernal equinox. In 325, the vernal equinox fell on March 21, and in 1582 on March 11, which led to difficulties in determining the date of Easter.
9.8.2. Gregorian calendar
The reform of the Julian calendar became a necessity and in 1582 was carried out by Pope Gregory XIII, so the new calendar is called Gregorian. The draft of the new calendar was developed by the Italian mathematician and physician Lilio and is aimed at bringing the average length of the calendar year closer to the length of the tropical year. The essence of the reform is as follows.
1) The accumulated discrepancy of 10 days of the Julian calendar with the account of tropical years was eliminated (after October 4, it was decided to consider October 15).
2) In the Julian calendar for 400 years, the discrepancy with real time is almost exactly 3 days. Therefore, in the Gregorian calendar, it is customary not to consider leap years those years of centuries in which numbers are not divisible by 400 without a remainder. For example, 2000 was a leap year, but 1900 was not.
As a result, the average length of a calendar year in the Gregorian calendar over 400 years is 365 d.2425, difference only 0 d.0003, which will give a discrepancy of 1 day only after 3300 years.
In Russia, the Gregorian calendar was introduced only in 1918 (after February 1, it was decided to immediately consider February 14), and Orthodox Church still uses Julian.
The Gregorian calendar is also called the new style, and the Julian is called the old style.
The beginning of the calendar year (January 1), the beginning of the counting of years (from the birth of Christ), the division of the year into 12 months and a week of 7 days is a convention adopted by agreement, a tradition.
9.9. Date line
When counting calendar days, it is necessary to agree on which meridian a new day begins. By international agreement, such a meridian is a meridian that is 180 from Greenwich o . Date line, in the ocean passes along this meridian, and goes around the islands. So the date line runs everywhere along the ocean.
To the west of the date change line, also called the demarcation line, the number of the month is always one more than to the east of it (for example, to the west, in Chukotka, on September 15, and to the east, in Alaska, on September 14), therefore, when crossing the demarcation line must take this into account. When crossing this line from west to east, one must decrease the number of the month by one, and add it from east to west. On seagoing ships, this change is made at the nearest midnight after crossing the international date line. Ships sailing east (from China to California) count the same date twice (after September 15, September 15 comes again), and ships sailing west (from California to China) skip one date (after September 14, they immediately count 16 September). It's obvious that New Year and the new month also begin on the date line.
9.10. Julian days
In astronomy, the problem often arises of determining the number of days that have passed between two distant dates (observations of comets, variable stars, outbreaks of new and supernovae).
For the convenience of solving this problem in the 16th century A.D. Scaliger introduced the concept Julian period 7980 years long, proposed to consider January 1, 4713 BC as its beginning. and keep a continuous count of days called Julian days JD starting from this date. The Julian day begins at Greenwich Mean Noon. Julian dates for the days of the current year are given in astronomical calendars and the Astronomical Yearbook. For example, 0000 hours on January 1, 2000 in Greenwich is JD 2451544.5. Often the first two digits of the Julian date are omitted.
The period and days are named Julian by Scaliger in honor of his father Julius, and are not related to Julius Caesar.
Tasks
35. (269) The Ursa Minor Star () was observed at the lower climax, and the sidereal clock at that time showed 3 h 39 m 33 s. What is the clock correction?
Decision: Clock correction is the difference between the correct time and the clock reading. 
. At the time of the lower culmination, in accordance with the formula (), sidereal time is 3 h 20 m 49 s, hence the clock correction 
.
36. (228) In Orel, according to the clock going according to Kiev sidereal time, at 4 h 48 m the upper culmination of the Capella () was observed. What is the difference between the longitudes of these two cities?
Decision: The difference between the longitudes of two points is equal to the difference between any two local times, in this case stellar. In Orel, sidereal time is equal to the right ascension of the star at the time of the upper culmination, so the difference in longitudes is .
37. (233) The lunar eclipse on April 2, 1950 began at 19 h 03 m according to universal time. When did it start in Alma-Ata (, V time zone) according to standard, maternity and local solar time?
sidereal time i, s - hour angle of the vernal equinox. sidereal time i is used by astronomers to determine where to point the telescope in order to see the desired object.
Define sidereal time taken at the vernal equinox. The time interval between two successive upper climaxes of the vernal equinox on the same meridian is called a sidereal day. The beginning of a sidereal day on a given meridian is taken as the moment of the upper culmination of the vernal equinox (Fig. 3.1). Sidereal time is measured by the hour angle of the vernal equinox. At the beginning of a sidereal day, the vernal equinox point is at its upper climax and therefore its hourly angle is 0. Since the Earth continuously rotates around its axis, the hourly angle will increase over time and its value can be used to judge the elapsed time. Thus sidereal time S is the western hour angle of the vernal equinox. Therefore, sidereal time on a given meridian at any moment is numerically equal to the hour angle of the vernal equinox.
Considering sidereal time, it should be borne in mind that the vernal equinox is at an infinitely large distance and therefore the movement of the Earth in orbit does not change its apparent position on the celestial sphere. The period of rotation of the Earth relative to the vernal equinox remains unchanged. Therefore, sidereal days have a constant duration. Sidereal time is widely used in aviation astronomy. For the Greenwich meridian, it is given in MAE for each hour of the corresponding date. It is inconvenient to use sidereal time, since it is not connected with the Sun, in relation to which the daily routine of people's lives is built.
The mutual position of the Sun and the vernal equinox is constantly changing throughout the year. Moving along the ecliptic, the Sun shifts by almost 1 ° per day relative to the vernal equinox (Fig. 3.2). As a result, the sidereal day is shorter than the solar day by 3 min 56 s and their beginning during the year falls at different times of the day and night. From fig. 3.2 it can be seen that the Sun culminates only once a year together with the vernal equinox at noon at zero hours of sidereal time. This happens when the Sun passes through the vernal equinox, i.e. when its right ascension is 0.
Rice. 3.1. sidereal time
Rice. 3.3. The relationship between sidereal time, hour angle and right ascension of the luminaries 
Rice. 3.2. Relationship between sidereal and solar days
After one sidereal day, the vernal equinox point will again be at the upper culmination, and the culmination of the Sun will come only after about 4 minutes, since in one sidereal day it will shift to the east relative to the vernal equinox point by about 1 °. After another sidereal day, the climax of the Sun will come already approximately 8 minutes after the beginning of the sidereal day.
Thus, the time of the climax of the Sun is continuously increasing. In a month, the sidereal time of the climax will increase by about 2 hours, and in a year - by 24 hours. Consequently, zero hours of sidereal time falls at different times of the solar day, which makes it difficult to use sidereal time in everyday life.
Relationship between sidereal time, hour angle and right ascension of a star.
It is impossible to measure the hour angle of the vernal equinox point or to notice the moment of its passage through the observer's meridian, since it is imaginary and is not visible on the celestial sphere. Therefore, it is impossible to directly determine sidereal time from the vernal equinox. Therefore, in practice, the determination of the beginning of a sidereal day and sidereal time at any moment is carried out using any star, the right ascension of which is known (Fig. 3.3.). By knowing the right ascension of a star and measuring its hour angle, sidereal time can be determined. From fig. 3.3 it can be seen that there is an obvious relationship between sidereal time, hour angle and right ascension of the star, which can be written in terms of the coordinates of the star in the form
From this dependence it follows that sidereal time at any moment is equal to the sum of the hour angle of the star and its right ascension. Usually in astronomical observatories, sidereal hours are checked by the culminating star. Since at this moment the hour angle of the star is equal to zero, then sidereal time will correspond to the right ascension of this star, i.e. S=a.
From fig. 3.3, one more dependence can be derived, which is widely used in the practice of aviation astronomy to determine the hourly angles of stars: t = S-a. Based on this formula, the hourly angles of navigation stars are calculated from sidereal time and right ascension, taken from the MAE. This calculation simplifies the compilation of the MAE and reduces its volume.
Let us assume that the rotation of the sphere is measured by the point of Aries. In this case, we obtain star units and time counting systems.
sidereal day the time interval between two successive culminations of the same name of the Aries point on the same meridian is called. The moment of the upper culmination of the point of Aries is taken as the beginning of a sidereal day. A sidereal day is divided (in stellar units) into 24 hours, an hour into 60 minutes, and a minute into 60 seconds.
sidereal time S called the period of time (in stellar units) elapsed from the moment of the upper culmination of the point of Aries to this moment. Let's depict a sphere on the plane of the equator (Fig. 43): the Earth and the meridian associated with it are shown inside EQ and the zenith of the place G. When the sphere rotates, the Earth and the meridian EQ remain motionless. By definition of sidereal time, it is equal to the time of rotation of the point of Aries from E up to γ. i.e. arc Ev, but this arc measures the hour angle of Aries point t v , therefore, sidereal time is numerically equal to the hourly angle of the point of Aries, i.e. S = t γ . On this basis, sidereal time can be expressed in hour or degree units, for example, S \u003d 8 H 44 M 16 C or t v = 131 about 04.0 "; it is usually expressed in degree units. Sidereal time does not have a date, since time intervals of more than a day are not expressed in it. Sidereal time on a given meridian is reproduced on a star chronometer. This time is convenient for observing stars and processing stellar observations.
The Aries point moves around the sphere due to precession and nutation. If we take into account the precession of the Aries point - by 46, 1" per year towards the diurnal movement, it turns out that the sidereal day is shorter than the full revolution of the sphere by 0.0084 e. This is a uniform mean sidereal time and is used in nautical astronomy. If we also take into account nutation, we get an uneven (true)
sidereal time.
Basic time formula. Let be P N D(see Fig. 43) - the meridian of the star C, then γD - its right ascension a, a ˇED- hour angle t. From fig. 43 shows that the sum of the arcs ED and γ D equal to the arc Ev, i.e. t v== S, or S= t + a.(69)
sidereal time in this moment equal to the sum of the hourly angle of the luminary and its right ascension. This formula is valid for any luminary (for one moment), i.e.
S= t +α* = t +α סּ = t- α = ....
For the moment of the upper climax t= 0 and S = α . Hence, knowing α* , you can determine sidereal time or clock correction, and vice versa - determine a * from S.
hour angle formula. Solving formula (69) with respect to t, we get t = S - a.(70) Adding 360° (24 h) to both parts, we get t+ 360° = S + 360o - a.
But the value of 360° - a * is the stellar complement τ*, and the period of 360° is discarded from the hour angle, so for the stars we have: t* = S - τ* (71)
This formula calculates the hour angles of the stars; it is also used in machine algorithms for the hour angles of the stars (see § 31).
Sidereal time is inconvenient for everyday life, since the beginning of a sidereal day falls at different times of the solar day. So, 21/111 the Sun (position 1 in Fig. 44, showing the Sun at the moment of climax γ) is located at the point y, while the sidereal day will begin at noon. In a day, the Sun will move along the ecliptic by about 1° = 4 m and will culminate 4 m after the point of Aries. Three months later - 22/VI Sun
move to position 3 - the culmination of the point of Aries will occur in the morning, six months later 4 the sidereal day will begin at midnight, three months later - 22/XII - in the evening and after a tropical year - again at noon. And rice. 44, moreover, it follows that a tropical year equal to 365.2422 mean days contains exactly 1 more sidereal day, i.e. 366.2422 sidereal days.
For everyday life, it is more convenient to count the time by the Sun..
True sunny days called the time interval between two successive climaxes of the same name of the Sun on the same meridian. The lower culmination of the Sun is usually taken as the beginning of a solar day, so the true solar time (T &) called the period of time elapsed from the lower culmination of the Sun to the present moment.
However, the value of the true day varies throughout the year. From fig. 44 shows that the solar day is longer than the sidereal day by Da 0 . When studying the coordinates of the Sun in § 14, it was noted that due to the uneven motion of the Sun and the inclination of the ecliptic e, the value of Aa 0 changes unevenly during the year: around 22/XP we have the largest Da © = 66.6 "per day, and around 18/IX - the smallest Dss 0 = 53.8 "per day. Therefore, in winter the day is longer, and in summer - in autumn it is shorter. The difference in the duration of the solar day on these dates will be 12.8 "-4 \u003d 51.2 °. On average, Da 0 \u003d 59.14". The variability of the length of the true day makes it inconvenient as a unit of measurement, and true solar time is now used only as the hour angle of the Sun.
№5. Local, Greenwich, standard time.
