I. The basic units of time are days, month and year. Days are related with rhythmical change of day and night that is caused by Earth rotation round its axis. It is the time of one complete revolution of the Earth round its axis relative some celestial body (reference point). As a reference point usually are taken the Sun or stars. Therefore in astronomy there are such concepts as solar and star days.

II. True and mean solar days. The moment of the lower culmination of the Sun¢s disk center is called the true midnight and the moment of the upper culmination is called the true noon (midday). The period between two successive returns of the Sun to its upper or lower culminations is called the true solar day. The solar day is considered to begin from the lower culmination of the Sun. However the duration of the true solar day varies in the course of an entire year as the apparent motion of the Sun occurs not along the equator but along the ecliptic (see § 39), besides it moves nonuniformly. For this reason in everyday life the mean solar day with constant duration of 24 h is used.

So the mean solar day is the period of time between two successive lower culminations of the Sun which uniformly moves along the celestial equator, making a complete revolution in a year.

III. Local, zone and universal time. The moment when the Sun transits the celestial meridian depends on the geographical longitude of the observer¢s location. The nearer is the observer to the east the earlier he notices this phenomenon. Thus the time corresponding to the transit of the Sun through a local meridian is called local solar time which is fair only for this local geographical longitude therefore it is more convenient to use in everyday life zone time.

The surface of the Earth is loosely divided by longitude into 24 time zones; each time zone 15° or 1^{h }wide. The mean solar time on the central meridian of each zone is taken as zone time.

The prime meridian, from which the longitudes on the Earth are numbered, passes through Greenwich (Great Britain). It is considered to be the zero meridian, and its time zone is taken as the zero time zone. The local mean solar time of the Greenwich meridian is taken as the universal time. The central meridian of the first time zone (n = 1) is located on 15 ° to the east of the Greenwich meridian. The central meridians of other time zones are determined similarly. The borders of time zones are along the state and administrative borders or along the natural boundaries (the rivers, mountains). The territory of the Republic of Kazakhstan lies on the 4th and 5th time zones.

If the universal time (T_{0}) and serial number of the zone (n) are known then it is possible to find easily the zone time (T_{n}) of any place:

T_{n} = T_{0} + n

Astana and Almaty are in one time zone (5-th) which leads the universal time by 6 h:

T_{5} = T_{0} +( n+1) = T_{0} +(5+1) =T_{0} + 6 h

In the spring of 1930 by the government decree a daylight saving time was introduced in the USSR: hands of all clocks were put forward for an hour relative the zone time. Besides, in many countries annually the summer time is introduced by putting clocks forward for an hour.

The local mean solar time T_{l} on the geographical longitude of l to the East from Greenwich is determined by adding the value of longitude in hours to the universal time T_{0}:

T_{l} = T_{0} + l

IV. Sidereal time. We will choose any star and note its position in the sky. On the same place it will appear in a day, more exactly in 23 h 56 min. The days measured relative the stars are called sidereal. More exactly, the sidereal day is a period of time between two successive upper culminations of the point of vernal equinox. But the solar day is equal to 24 h and how to explain an extra 4 min? The point is that due to movement of the Earth on its orbit the terrestrial observer sees the Sun displaced against stars on 1° in a day in the direction opposite to rotation of the celestial sphere.

These 4 minutes are necessary to the earth «to overtake» the Sun. So, the Earth rotates round its axis once every 23 hours 56 minutes with respect to the stars and once in about 24 hours - mean solar days – with respect the Sun center. The man lives and works by a sundial. On the other hand, astronomers for observation need the sidereal time

The sidereal time (S) is the time which past since the upper culmination of the point of vernal equinox.

There is a simple relationship between a local sidereal time and a right ascension of stars. If the star is located at its upper culmination then S =a.

Therefore, the sidereal time of a particular locality is equal to the right ascension of the star at its upper culmination.

The local sidereal time (S) on the geographical longitude (l) is determined by the sum of the sidereal times on the Greenwich meridian (S_{0}) and on this longitude:

S = S_{0} + l

Thus, using this formula we can find the geographical longitude of the observer¢s location provided the local sidereal time is known.

Self-testing questions

1. What is the difference between true and mean solar days?

2. What time is taken as the universal time?

3. How many time zones and of what numbers pass through the territory of the Republic of Kazakhstan?

4. Are the local times in two capitals of Kazakhstan identical? What is necessary to know for calculating the difference of local times of these cities?

5. Are the zone times in Astana and Almaty identical?

6. Are the durations of solar and star days equal? What is the difference between them?

Exercise 33

1. Knowing that the cities Almaty and Astana are in the 5th time zone, calculate the geographical longitude of the local time of Almaty or Astana.

2. The most eastern frontier of the Republic of Kazakhstan passes on the longitude of l = 87°20' and the most western frontier passes on the longitude of l = 46^{o} 30'. What is the difference of a local mean and zone times in these two geographical points?

3. Determine the local time in the cities Astana and Almaty, which longitudes are l_{1} = 71^{o} 25' and l_{2} = 76^{o} 55' respectively, if the daylight saving time of Astana is 18 hours 38 minutes.