Before we study the Time, let us learn a few terminologies:
Transit: Instant at which a heavenly body is directly over a meridian is called transit.
- i) Axial Rotation: Earth rotates about its axis with respect to sun from West to East which causes Day and Night.
- ii) Orbital Rotation: Earth rotates about the Sun in an elliptical path, its axis being inclined at an angle of about 66.5º to the plane of rotation which causes seasons.
iii) Perihelion: The position when earth is closest to the Sun on its elliptical path (Jan 03).
- iv) Winter Solstice: Near the perihelion when Sun shines directly over its Southern most position (about 23 1/20S- Dec 22) and earth’s axis is away from the Sun.
- v) Aphelion: The position when earth is farthest from the Sun on its elliptical path (Jul 03).
- vi) Summer Solstice: Near aphelion when the Sun shines directly over its Northern most position (about 23 1/20 N) and earths axis is towards the Sun.
vii) Equinox: When Sun shines directly over the equatorial belt. It is called Autumnal equinox on Sept 23 and Spring equinox on Mar 21. Day and night are of equal duration.
DAY: Two successive transits of a heavenly body is called a day.
Sidereal Day: Two successive transits of a star over a meridian is called a Sidereal Day. Since a star is at infinite distance away, lights from it would appear to reach the earth in parallel rays on successive movement of earth on its orbital plane. The days are of uniform length covering 360º of rotation of earth on its axis. But this period is not related to light and dark periods, therefore not of much use in day to day life.
Apparent Solar Day: Two successive transits of true Sun or apparent Sun (meaning Sun as it appears every day). Earth’s Orbit is inclined to its plane of orbital rotation and its speed is variable depending upon its position in the orbit (Kepler’s Laws of Motion). This causes the Apparent Solar Day of variable length and therefore not of much use.
Mean Solar Day: To have a day of uniform length certain assumptions are made. An imaginary Astronomical Mean Sun (AMS) is assumed to orbit about the earth in the plane of equinoctial (equator) taking same time to complete one orbit as the true Sun (or apparent Sun).
– Mean solar day is defined as two successive transits of AMS. This day is divided into 24 hours, each hour being divided into 60 minutes and each minute into 60 seconds and so on.
– To avoid change of date during the mid-day, the time measurement is started when the AMS transits the anti-meridian of the place (or observer) so that it is about 1200 hrs Local Mean Time (LMT) during the mid-day.
– With this time, one full orbital rotation of earth is completed in 365 days, 5 hrs, 48 minutes and 45 seconds.
Civil Year: A year is taken to be of 365 days.
– To even things up, to every four years, one day is added to the year and it is called a Leap Year of 366 days and 3 days are dropped every four centuries.
GREGORIAN CALENDER: It is a calender which is based on civil year of 365 days with every fourth year (year divisible by 4) of 366 days, called a leap year, except the centuries whose century digit is not divisible by four is not a leap year eg 1700, 1800, 1900, 2100 etc are not leap years.
This is also called Gregorian Correction.
Time and Arc: 24 hours = 360º of longitude
1 hour = 15º of longitude
1 Minute = 15´ of longitude
1 Second = 15˝ of longitude
360º of longitude = 24 hrs of time
10º of longitude = 4 minutes of time
1´ of long = 4 seconds
1˝ of long = 1/15th seconds of time
Example: Convert i) 12h 32m 42s into arc
- ii) 1500 56`30“into time
Solution: 1h = 150 :. 12h = 15 x 12 = 180º
1m = 151 :. 32m = 15 x 32 = 480 = 6º
1s = 151 :. 42s = 15 x 42 = 630 = 10´30˝
12h = 32m 42s = 186º10´30˝
- ii) 150º 56´ 30˝
1º = 4m
∴ 150 x 1º = 150 x 4m = 600m = 10h
1´ = 4s
∴ 56 x 1´ = 56 x 4s = 2245 s = 3m 44s
1˝ = 1/15 s
∴ 30 x 1˝ = 30 x 1/15 s = 02s
150º 56´ 30˝ = 10h 3m 46s
Local Mean Time (LMT): Local Mean Time of a place is time which commences when the AMS transits the anti-meridian of the place. Watch is set to 0000 around mid-night at the time of first transit.
– LMT is different for different places
– Places East will have LMT earlier and places West will have LMT later than the place so compared.
– LMTA = LMTB + Ch long E
= LMTB – Ch long W
Greenwich Mean Time (GMT): Greenwich day and time commences when the AMS transits the anti-meridian of Greenwich.
– GMT is LMT of Greenwich, a village in UK
– Places of Easterly longitude have their LMT earlier than GMT
and of Westerly longitude have their LMT later than GMT.
LMTA = GMT + long E ] Longitude converted into time
= GMT – long W ] ”
– GMT is denoted by the letter Z.
Co-ordinated Universal Time (UTC): For all practical purposes UTC is same as GMT.
Example: LMT at Lucknow (2700N 8100E is 0930 on 5th April 1999. What is the :
a) LMT at Hongkong (2200N 1130E)
c) LMT at New York (4100N 7400W)
Solution: a) LMTHK = LMTLK + change East (:. HK is East of LK)
= 0930 + [(113-81)º converted into time]
= 0930 + (32º converted into time)
= 0930 + 02h 08m (:. 15º = 1 hr; 1º = 4 min)
= 1138 hrs.
b) LMTLK = UTC + long E (since GMT and UTC are almost the same)
:. UTC = LMTLK – long E
= 0930 – 81ºE (converted into time)
= 0930 – 05h 24m (:. 75º = 5 hrs; 1º = 4 min)
= 0406 UTC
c) LMTNY = LMTLK – Ch long W (NY is West of LK)
= 0930 – [(81+74) º Converted into time] on 5 Apr 99
= (0930 – 1020) on 5 Apr 99
= (0930 + 2400) – 1020 4 Apr 99
= 23h 10m on 4 Apr 99
STANDARD TIME: Every state nominates one meridian, LMT at which provides the standard time for the state. Generally the selected meridian is 15º or multiples therefore of longitude away from Greenwich Meridian eg. India has nominated the longitude 82º 30´E, LMT at which is taken as standard time for India called Indian Standard Time (IST). IST is 5h30m ahead of GMT and is denoted by letters EF.
Example: GMT = 0500 hrs
IST = 0500 + 82.5º converted to time
= 0500 + 0530 = 1030 EF
International Date Line (IDL): Places EAST of Greenwich (Easterly Longitude) have LMT ahead of GMT. A place 179ºE is 11 hrs 56 min ahead of GMT. Similarly places West of Greenwich have LMT less than GMT. A place 179ºW is 11 hrs 56 min behind GMT. The LMT at the anti-meridian of Greenwich ie. 180ºE/W is either 12 hrs ahead or 12 hrs behind GMT. A flight on easterly track, while crossing 180º E/W will experience an excess of 24 hrs in LMT and the reverse on Westerly Track. The anti- meridian of Greenwich is called International Date Line (IDL). It is a slightly curved line, adjusted to accommodate inhabited areas to avoid change of date on GMT during mid-day. The rule, therefore, is while crossing IDL:
i) On easterly track, subtract one day from LMT
ii) On westerly track, add one day to LMT
– While crossing IDL, the rule to change the date applies only to aircraft maintaining LMT or calculating arrival/departure on LMT. There is no change of date and time applied for crossing IDL, if GMT is used.
– On easterly track, the North Pole is to the left and on Westerly track it is to the right.
Example: An aircraft takes off from P (60N 165W) at LMT 0730 hrs on 5 Apr 99 for Q (60N 165E) at G/S of 300 K. What is the
a) LMT at Q when the a/c took off
b) Flying time from P to Q
c) LMT at Q at Landing
d) UTC Take off and landing
Solution: Aircraft is travelling on Westerly track and crossing the IDL. Therefore 1 day is to be added while calculating LMT at Q.
a) LMTQ = [LMTP – ch long] + 1 day
= (0730 – 0200) 5 Apr 99 + 1 day
= 0530 06 Apr 99
b) Distance between P and Q
Dep = Ch long Cos lat
= 300 x 60 x Cos 60 (ch long degree converted to minutes)
= 900 nm (DIST)
Time = 900/300 = 3hrs ( G/S = 300K )
c) LMTQ landing = 0530 06 Apr 99 + 0300 (Flying time)
= 0830 06 Apr 99
d) UTC Take-off
LMTP GMT-long W
:. GMT = LMTP + long W = 0730 + 165º converted to time
= 0730 + 1100 = 1830 Z on 05 Apr 99.
LMTQ = GMT + long E :. GMT = LMTQ – long E
= [0830-(165º converted to time)] 06 Apr 99 = (0830-1100) 06 Apr 99
= 2130 Z 05 Apr 99
Zone Time (ZT): The earth is divided into zones of 15º of longitude. Central Meridian of the Zones are separated from Greenwich Meridian by multiples of 15º. LMT of the central meridian of the Zone is used for Zone Time. Zone is covered by 7.5º of longitude on either side of the central meridian.
– Zones East of Greenwich are numbered 1 to 12 with positive (+) sign and West of Greenwich from 1 to 12 with negative (-) sign.
– Zone Time = GMT + Zone No (with algebraic sign)
Example: At 0730 hrs GMT what is the ZT at
- a) 85E b) 72W
Solution: a) (85/15) ie 5th zone + 10º or 6th zone – 5º
The later is closer to the central meridian which is 90ºE
:. Zone No is 6 and since longitude is East it is + 6
:. Zone Time = GMT + Zone No = 0730 + 0600 = 1330 hrs.
- b) (72/15)ie 4th zone + 12º or 5th zone – 3º
The later is closer to central meridian of 75ºW
:. Zone No is 5 and since longitude is West it is – 5
:. ZT = GMT + Zone No
0730 + (-0500) = 0230 hrs.