Relationship of Time and Longitude

The mean sun travels at a constant rate, covering 360° of arc in 24 hours. The mean sun transits the same meridian twice in 24 hours. The following relationships exists between time and arc:

Time/Arc
24 hours/360°
1 hour/15°
4 minutes/1°
1 minute/15′

Local time is the time at one particular meridian. Since the sun cannot transit two meridians simultaneously, no two meridians have exactly the same local time. The difference in time between two meridians is the time of the sun’s passage from one meridian to the other. This time is proportional to the angular distance between the two meridians. One hour is equivalent to 15°.

If two meridians are 30° apart, their time differs by 2 hours. The easternmost meridian has a later local time, because the sun has crossed its lower branch first; thus, the day is older there. These statements hold true whether referring to the apparent sun or the mean sun. Figure 1-14 demonstrates that the sun crossed the lower branch of the meridian of observer 1 at 60° east longitude 4 hours before it crossed the lower branch of the Greenwich meridian (60 ÷ 15) and 6 hours before it crossed the lower branch of the meridian of observer 2 at 30° west longitude (90 ÷ 15). Therefore, the local time at 60° east longitude is later by the respective amounts.

Figure 1-14. Local time differences at different longitudes.

Standard Time Zone

The world is divided into 24 zones, each zone being 15° of longitude wide. Each zone uses the LMT of its central meridian. (A few areas of the world are further divided and use half-hour increments from GMT. Some notable examples include India, Bangladesh, Newfoundland, and parts of Australia and Thailand.) Since the Greenwich meridian is the central meridian for one of the zones, and each zone is 15° or 1 hour wide, the time in each zone differs from GMT by an integral number of hours. The zones are designated by numbers from 0 to 12 and –12, each indicating the number of hours that must be added or subtracted to local zone time (LZT) to obtain GMT. Since the time is earlier in the zones west of Greenwich, the numbers of these zones are plus; in those zones east of Greenwich, the numbers are minus. [Figure 1-15]

Figure 1-15. Standard time zones.

Ground forces frequently refer to the zones by letters of the alphabet, and air forces use one of these letters (Z) for GMT. The zone boundaries have been modified to conform with geographical boundaries for greater convenience. For example, in case a zone boundary passed through a city, it would be impractical to use the time of one zone in one part of the city and the time of the adjacent zone in the other part. In some countries, which overlap two or three zones, one time is used throughout.

Date Changes at Midnight

If travelling west from Greenwich around the world and setting a watch back an hour for each time zone, the watch would have been set back a total of 24 hours on arriving back at Greenwich, and the date would be 1 day behind. Conversely, traveling eastward, the watch would have been advanced a total of 24 hours, gaining a day.

To keep straight, a day must be added somewhere if going around the world to the west and a day must be lost if going around to the east. The 180° meridian is the international dateline where a day is gained or lost. The date line follows the meridian except where it detours to avoid eastern Siberia, the western Aleutian Islands, and several groups of islands in the South Pacific.

The local civil date changes at 2400 or midnight. Thus, the date changes as the mean sun transits the lower branch of the meridian. Consider the situation in another way. The hour circle of the mean sun is divided in half at the poles. On the half away from the sun (the lower branch), it is always midnight LMT. As the lower branch moves westward, it pushes the old date before it and drags the new date after it. [Figure 1-16] As the lower branch approaches the 180° meridian, the area of the old date decreases and the area of the new date increases. When the lower branch reaches the date line; that is, when the mean sun transits the Greenwich meridian, the old date is crowded out and the new date for that instant prevails in the world. Then, as the lower branch passes the date line, a newer date begins east of the lower branch and the process starts all over again. The zone date changes at midnight zone time (ZT) or when the lower branch of the mean sun transits the central meridian of the zone.

Figure 1-16. Zone date changes. [click image to enlarge]

Time Conversion

Sometimes it is necessary to convert LMT time to GMT, or GMT to LMT. The Air Almanac contains a table for conversion of arc to time at a rate of 15° of arc per hour of time. [Figure 1-17] This conversion is only good for LMT to GMT, or GMT to LMT. ZT is influenced by daylight savings time and geographical boundaries. For example, to convert GMT to LMT at 126° –36′ W:

126° 00 = 8 h 24 min 00s
36′ = 02 min 24s
126° 36′ = 8 h 26 min 24s

To derive LMT from GMT, subtract the time in the Western Hemisphere and add it in the Eastern Hemisphere. Do the opposite to convert LMT to GMT.

Figure 1-17. Air almanac conversion of arc to time. [click image to enlarge]

Sidereal Time

Solar time is measured with reference to the true sun or the mean sun. Time may also be measured relative to a fixed point in space. Time measured with reference to the first point of Aries, which is considered stationary although it moves slightly, is sidereal or star time. The first point of Aries is defined as where the sun crosses the equator northbound on the first day of spring.

The sidereal day begins when the first point of Aries transits the upper branch of the observer’s meridian. Local sidereal time (LST) is the number of hours that the first point of Aries has moved westward from the observers meridian. Expressed in degrees, it equals the local hour angle (LHA) of Aries. [Figure 1-18] LST at Greenwich is Greenwich sidereal time (GST), which is equivalent to the GHA of Aries. GST, or GHA of Aries, specifies the position of the stars with relation to the earth. Thus, a given star is in the same position relative to the earth at the same sidereal time each day.

Figure 1-18. Greenwich sidereal time.

Number of Days in a Year

The earth revolves around the sun in a year. The number of days in the year equals the number of rotations of the earth during one revolution. The earth rotates eastward about 366.24 times during its yearly eastward revolution. The total effect of one revolution and 366.24 rotations is that the sun appears to revolve around the earth 365.24 times per year. Therefore, there are 365.24 solar days per year. Since the sidereal day is measured with reference to a fixed point, the length of the sidereal day is the period of the earth’s rotation. Therefore, the number of sidereal days in the year is equal to the number of rotations per year, 366.24.

Navigator’s Use of Time

Navigators use three different kinds of time: GMT, LMT, and ZT. All three are based upon the motions of the fictitious mean sun. The mean sun revolves about the earth at the average rate of the apparent sun, completing one revolution in 24 hours. Time is based upon the motion of the sun relative to a given meridian. The time is 2400/0000 at lower transit and 1200 at upper transit. In GMT, the reference meridian is that of Greenwich; in LMT, the reference meridian is that of a given place; in ZT, the reference meridian is the standard meridian of a given zone.

The difference between two times equals the difference of longitude of their reference meridians expressed in time. GMT differs from ZT by the longitude of the zone’s standard meridian; LMT differs from ZT by the difference of longitude between the zone’s standard meridian and the meridian of the place. In interconverting ZT and GMT, the navigator uses the zone description. The zone difference is the time difference between its standard meridian and GMT, and it has a sign to indicate the correction to ZT to obtain GMT. The sign is plus (+) for west longitude and minus (–) for east longitude.

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