Sidereal time astronomy. sidereal time

The rotation time of the Earth around its axis can be measured by observing the daily rotation of the celestial sphere.

The duration of a complete rotation of the celestial sphere can be determined with a high degree of accuracy as the time interval between two consecutive climaxes of the same name (for example, upper ones) of a star or a certain point in the celestial sphere. The vernal equinox (T) is chosen as such a point.

Etc The time interval between two successive upper climaxes of the vernal equinox is called a sidereal day.

The moment of the upper culmination of point T is taken as the beginning of a sidereal day.

A sidereal day is divided into 24 sidereal hours, an hour into 60 minutes, and a minute into 60 seconds. It is easy to see that the position of the point T relative to the meridian, characterized by the arc of the celestial equator enclosed between the meridian and the point T and counted in the direction of the daily rotation of the celestial sphere (marked with a greenish arrow), determines the fraction of the day that has elapsed from the beginning of the given day to the moment under consideration. In other words, the specified arc of the equator is a measure of time at a given moment. Since this arc in degrees is equal to the spherical angle formed by the meridian and the great circle drawn through the pole and the point T (shown by the red arrow) and called hour angle, then we arrive at the following definition: sidereal time S is currently equal to the hour angle of the vernal equinox. Since the day is divided into 24 hours, and the circle contains 360 °, the following ratios will be obtained:

1 hour = 15°, 1 minute - 15", 1 second - 15".

Since the hour, minute and second represent the units of the hour angle, the designations of these units are placed, like the designations of the units of a degree measure, at the top right of the corresponding figure. Therefore, the record of the moment in time will look like this: S = 14h06m27s.

Sidereal time is used in astronomical observations. For worldly purposes, it is inconvenient, since our life is consistent with the Sun.

solar time

By analogy with sidereal days, the concept of true solar days is introduced, which is the time interval between two successive upper culminations of the center of the solar disk.

True solar time is the hour angle (/0) of the center of the Sun. Since the Sun, as a result of the annual movement along the ecliptic, moves in the direction opposite to the daily movement, approximately 1 ° per day, then the true solar day is longer than the sidereal day by an average of about 4 minutes.

Uneven flow of true solar time

True solar time is inconvenient in the sense that it is very difficult to build a clock running on this time, since the hour angle of the Sun varies unevenly. This occurs, firstly, as a result of the uneven motion of the Sun along the ecliptic and, secondly, due to the inclination of the ecliptic to the equator. The movements of the Sun along the ecliptic near perihelion and aphelion for equal periods of time will be unequal, and equal movements of the Sun along the ecliptic near the equinoxes and solstices will correspond to unequal changes in the hour angle (Fig. 38).

Mean ecliptic and mean equatorial sun

To eliminate the non-uniformity of true solar time, the concept of "average Sun" is introduced, meaning by this term some auxiliary moving point. The “mean ecliptic sun” is a point moving uniformly along the ecliptic and passing through perihelion and aphelion simultaneously with the center of the true solar disk. The replacement of the true Sun by the “mean ecliptic” eliminates the irregularity of solar time caused by the variability of the speed of the Sun along the ecliptic. To eliminate the influence of the inclination of the ecliptic to the equator, the concept of the "mean equatorial sun" is introduced, which is a point moving uniformly along the equator and passing through the points of the spring and autumn equinoxes simultaneously with the "mean ecliptic sun".

mean solar time

The imaginary "mean equatorial sun" participates in the daily rotation of the celestial sphere in the same way as the true Sun. The time interval between two successive equal climaxes of the "mean equatorial sun" is called the average day. The beginning of the middle day is taken as the moment of the pinnacle of the "mean equatorial sun". The hourly angle of the "mean equatorial sun" determines the average time at a given moment. The average day is divided into 24 average hours, an hour into 60 minutes and a minute into 60 seconds.

standard time

Each point on the surface of the Earth has its own local time, which differs (depending on longitude) from the time of another point by any number of hours, minutes and seconds. In practical life, using local time is very inconvenient, especially for transport and communications. This circumstance set the task of streamlining the counting of time throughout the Earth. At present, this problem is solved by the introduction of the standard time system.

The entire globe along the meridians every 15 ° is divided into 24 belts. middle "initial or zero"belt passes through the Greenwich meridian and in this entire belt the local time of the Greenwich meridian is adopted. In the next eastern belt, the local time of the middle meridian of this belt is adopted, which differs from the world time by an hour, etc. This time is denoted by Ta and is called the zone, and the belts are called sentries.

At any point on the Earth, standard time differs from local time by about half an hour (maximum). The introduction of standard time leads to the fact that in a number of settlements located in close proximity to each other, the time differs by an hour. However, this is redeemed by the fact that minutes and seconds are the same all over the globe when using standard time, and the time of various points differs from each other only by an integer number of hours.

The boundaries of time zones are drawn, in some cases, retreating from the meridians, along state, administrative or natural (rivers, mountain ranges) borders

Date change line

Local or standard time, counting east of the prime meridian (passing through Greenwich), will increase in proportion to longitude. If we consider local time, counting west of the zero meridian, then local time will decrease. In this regard, consider the following fact.

Let three observers, being at the same place of average latitude, begin simultaneously counting the days, marking them at sunrise, with the first one remaining in place, the second going on a round-the-world trip along the parallel to the east, and the third on a round-the-world trip along the parallel to the east. west. When all three observers gather again in one place, the observer who remains in place will say that between the meetings N days, and one who traveled east will say that (N + 1) days. This is due to the fact that the second observer, when moving to the east, will observe the culmination of the Sun each time somewhat earlier than a stationary observer.

An observer traveling westward will say that it has passed (N - 1) days, since, moving in the direction opposite to the rotation of the Earth, he will observe the culmination of the Sun each time with some delay compared to a stationary observer.

In order to harmonize the count of days, for stationary observers and travelers, by international agreement, date line ". It is all located on the surface of the ocean and runs approximately along the 180th meridian, counting from Greenwich. When crossing this line in a westerly direction, one day is discarded from the count of days (for example, the fourth number immediately follows the second number in the entries). When crossing the international date line in an easterly direction, an extra day is added when counting days (for example, when recording, a number is repeated twice).

Calculating the meridians from Greenwich is convenient, because in this case the date line falls on a longitude convenient for memorization (180 °), which will not be the case if the meridians are counted from some other observatory.

| time, sidereal, greenwich, offset, standard time

An average value based on measurements at a number of locations. mean solar time prime meridian. The meridian of the observatory in Greenwich (Great Britain) is conditionally taken as the initial meridian.

Coordinated Universal Time (UTC)

Replaces Greenwich Mean Time as the universally recognized international standard for clock time. It is the basis for civil time in many states and is used in the broadcasting of the universal time signal, which is used in aviation.

The local time

Time on the meridian of the observer. It can be true solar, average solar and stellar.

True solar time (Ti)

Hour angle (angular distance measured along the celestial equator to the west of the celestial meridian, expressed in hourly measure at the rate of 24 hours = 360o (1 hour = 15o, 1 min = 15"). Sun, increased by 12 hours (measured west of celestial meridian).

Converting time to angular value and vice versa

Mean Solar Time (MT)

Time measured by the hour angle of some imaginary point, called the mean sun, moving uniformly along the equator, the position of which coincides with the center of the true Sun at the moments of the autumn and spring equinoxes. It differs from solar time due to the ellipticity of the earth's orbit and its inclination to the equator. The difference between the mean solar and true solar times is equal to a correction called the equation of time (the current difference between true and mean solar time), not exceeding 16 minutes, calculated theoretically and given in astronomical calendars. Mean solar noon is 12 noon local time. The difference between the mean and true solar time or the difference between the right ascensions of the true and mean sun is called "equation of time".

sidereal time (S)

Local sidereal time at the moment is numerically equal to the hour angle of the vernal equinox, also called point of Aries. The time interval between two consecutive culminations of the same name of the vernal equinox on the same geographic meridian is called a sidereal day. A complete revolution of the vernal equinox, like any other point of the celestial sphere, occurs in 23 hours 56 minutes 04 seconds of mean solar time, since the Sun, moving along the ecliptic, lags behind the daily rotation of the celestial sphere. There are exactly one more sidereal days in a year than the average solar day. Sidereal days are divided into sidereal hours, minutes and seconds. The sidereal day is 3 min 56 sec shorter than the mean solar day, the sidereal hour is 9.86 s shorter than the generally accepted one. Sidereal time is used in aviation astronomy when determining the lines of position and course of an aircraft from the stars or the position of an aircraft (MS) using astronomical methods.

local civil time

Mean solar time, counted from the moment of the lower climax of the mean Sun.

Standard time (Tp)

Time equal to the local civil time of the middle meridian of the given time zone. It is established by international agreement in regions and countries so that the difference between local time and universal time throughout the planet is an integer number of hours. To do this, the entire surface of the Earth is divided approximately along the meridians into 24 time zones. The average meridians of time zones run along longitudes 15, 30, 45, ... degrees west of Greenwich along the points of the earth's surface, in which the mean solar time (MT), respectively, is 1, 2, 3, ... hours behind Greenwich. Usually, cities and the regions adjacent to them live according to the time of the nearest average meridian. The lines separating zones with different official times are called time zone boundaries. Usually they do not follow strictly along the meridians, but coincide with the administrative boundaries.

Time ratios

So, for each point on the Earth located at longitude X, you can specify the local true solar time Ti; local mean solar time MT; standard time Tp; seasonal winter time Tz; seasonal summer time Tl; local sidereal time S. Here are the formulas for those who need to convert one time to another (due to the standard time, the last two formulas are correct for Russia):

MT \u003d Ti + t,
MT = UTC + X,
Tp = UTC + n,
Тз = UTC + n + 1 h,
T = UTC + n + 2 h,
S = s + MT (approximately),

Where t is the equation of time; n - time zone number; s - sidereal time at Greenwich midnight (table of sidereal time is given in astronomical calendars).

Example: longitude of Moscow X is 2 hours 30 minutes. Mean solar noon is 12:00 local time (MT). According to world time, it corresponds to UT = 12 h - 2 h 30 min = 9 h 30 min, according to Moscow winter time - 12 h 30 min, according to Moscow summer time - 13 h 30 min.

Thus, if you are a resident of Moscow, then your time is 3 hours ahead of the world time in winter and 4 in summer. But all this, except for the true solar time, is conditional points that are not directly related to real astronomical events. Only the time of sunrise, sunset and the moment of true noon, set with the help of a sundial directly at the right moment at the right point on the Earth, have a real connection with cosmic processes. (although, to be completely accurate, the true sunrise occurs 5 minutes later than the observed one, and the true sunset occurs 5 minutes earlier due to the phenomenon of atmospheric refraction).

Time in FS2004

Timekeeping in FS2004 is based on GMT in full accordance with astronomy. Time zones change every 15 degrees of longitude. Accordingly, accounting for standard (winter, summer) time must be done independently by location and GMT time. For simulator time to standard time, additional utilities or scripts are used (see links). But it must be remembered that, in some cases, due to such utilities, the operation of some devices, traffic and other time-related applications will look different than without them.

Sidereal time is determined by 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 the sidereal day, the vernal equinox point is at its upper culmination 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. Consequently, sidereal time on a given meridian at any moment is numerically equal to the hour angle of the vernal equinox point, i.e. .

Considering sidereal time, it should be borne in mind that the vernal equinox point is at an infinitely large distance and therefore the movement of the Earth in orbit does not change its apparent position in 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 AAE for each hour of the corresponding date (see Appendix 5). 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 shows that the Sun only once a year culminates 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 climax 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 culmination 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.

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. .

From fig. 3.3, one more relationship 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 navigational stars are calculated according to sidereal time and right ascension, taken from the AAE. This calculation simplifies the compilation of the AAE and reduces its volume.

sidereal time

Sidereal time is the time elapsed from the top point of the vernal equinox or the point of Aries to any of its other positions, or, more simply, the hour angle of the vernal equinox. Used mainly by astronomers to determine where to point the telescope to see the desired object. Designated with the letter S.

When determining the point of the vernal equinox, one can take into account or not take into account nutation in different ways - a weak irregular movement of a rotating solid body that performs precession. Depending on this, sidereal time is: true, quasi-true and average.

At true sidereal time, the true point of the vernal equinox is considered, which has precessional and nutational motion, which shifts in the ecliptic plane at a speed of 50.25" per year due to the general precession in longitude and simultaneously fluctuates periodically due to nutation.

When determining the quasi-true, its short-period part is excluded from nutation.

And, finally, when determining the mean sidereal time, nutation is not taken into account at all.

Sidereal time differs at different longitudes of the Earth: when the longitude changes by 15 ° to the east, it increases by about 1 hour.

Depending on the place, they distinguish: local true sidereal time - the hour angle of the true point of the vernal equinox for a given place (for the local meridian); local mean sidereal time - the hour angle of the midpoint of the vernal equinox; Greenwich true sidereal time - the hour angle of the true point of the vernal equinox on the Greenwich meridian; Greenwich mean sidereal time - the hour angle of the midpoint of the vernal equinox on the Greenwich meridian.

The time interval between two successive upper climaxes of a star on the same geographic meridian, or in other words, the period of revolution of a celestial body relative to the stars around its axis, is called a sidereal day. Sometimes a definition is used in which a sidereal day is a period of time for a complete revolution of the Earth relative to the point of Aries.

To measure a sidereal day, you first need to measure the hour angle (t) of a star for which right ascension (α) is known. For the Aries point, the hour angle at the time of its upper climax is 0°. Since the beginning of the sidereal day coincides with the beginning of the calculation of the hour angles of the luminaries, then, consequently, sidereal time at a given moment is the hour angle of the vernal equinox, i.e. S = t.

Let's transfer the projection of the celestial sphere onto the plane of the celestial equator. Let point C represent the position of some star on the sphere at a given time; ♈ - the position of the vernal equinox (Aries point). It can be seen from the figure that sidereal time at a given moment is equal to the sum of the right ascension and the hour angle of the star at the same moment, i.e. S = t + α. This formula is also called the basic time formula.

At the moment of the upper culmination of the sun, its hourly angle t = 0°, and then s = α.

At the moment of the lower climax, its hour angle was t = 12h, and sidereal time was s = α + 12h.

Sidereal days are divided into smaller periods: sidereal hours, minutes and seconds.

A sidereal hour is equal to 1/24 sidereal day and is 0 hours 59 minutes. 50.1704387847 sec.

The duration of a sidereal minute is 0 hours 0 minutes. 59.8361739797451 sec. Sidereal second - 0.9972695663290856 sec.

In everyday life, it is inconvenient to use sidereal time, due to the beginning of sidereal days at different periods. The daily life of a person is connected with the apparent position of the Sun: its rising, the upper climax (during which the Sun rises to its maximum height above the horizon) and sunset. And every day the relative position of the Sun and the vernal equinox is constantly changing, i.e. The upper culmination of the Sun on different days of the year occurs at different moments of the sidereal day. Only once a year, on the day of the vernal equinox at noon, the position of the Sun and the vernal equinox coincide. 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 move eastward relative to the vernal equinox point by almost 1 ° towards its apparent movement. Those. 24 hours of sidereal time correspond to 23 hours 56 minutes. 4.091 sec. mean solar time. In a year, there are exactly one more sidereal days than the mean solar days.

So on March 21, the Sun is located at the point of Aries, while the sidereal day begins at noon. In a day, the Sun will move along the ecliptic by about 1 ° and will culminate 4 minutes after the point of Aries. Three months later - on June 22 - the climax of the point of Aries will occur at 6 o'clock in the morning. On September 23, the sidereal day will begin at midnight. On December 22, the sidereal day will begin at 18 pm.

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 the sidereal day, the vernal equinox point is at its upper culmination 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 point is at an infinitely large distance and therefore the movement of the Earth in orbit does not change its apparent position in 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.

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

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 according to 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 relationship 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.