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Just as a traveler going coasttocoast across the US will cross several time zones, the mariner sailing across the Atlantic or Pacific Ocean will also cross time zones. During this passage the ship will keep Zone Time while the navigator will use GMT if using celestial work. When giving an ETA for destination the navigator will also need to convert the GMT of arrival to the local time of the destination. The conversion from one reference time to another is fairly easy once you have an understanding of these different times. That and knowledge of their relationship to one another is a necessary requirement for learning celestial navigation.
Basically, time is measured in terms of the rotation of the earth and the resulting apparent motions of the celestial bodies. Before getting into the actual discussion of the various kinds of time, the term 'transit' must be defined. Transit occurs at the exact instance when a celestial body crosses the observer's meridian. At this time a great circle can be visualized going from one of the celestial poles, through the body and the observer's zenith to the other celestial pole, and then continuing around the celestial sphere to the starting pole.
Local Apparent Time (LAT) The sun as seen in the sky is called the true sun and is also referred to as the apparent sun. Apparent time is based upon the movement of the sun as it crosses the sky. A sundial would accurately indicate apparent solar time. The upper transit of the sun occurs at noon apparent time as it crosses the observer's meridian and lower transit of the sun is at midnight apparent time. However, the use of apparent time is impractical because the apparent length of the day is not uniform and varies throughout the year. The navigator has little use for apparent time, except for finding the time of local apparent noon (LAN), when the apparent sun crosses the observer's meridian. The height of the sun at LAN can be easily used to determine one's latitude.
Mean Solar Time A mean day is an artificial unit of constant length, based on the average of all apparent solar days over a period of years. Mean time is measured with reference to a fictitious body, the mean sun, so designed that its hour circle moves westward at a constant rate along the celestial equator. The speed of the mean sun along the celestial equator is 15 degrees per hour of mean solar time. At any moment, the accumulated difference between LAT and local mean time is indicated by the equation of time (Eq.T). The coordinates of celestial bodies are tabulated in the Nautical Almanac with respect to mean solar time.
"GMT is the time used by navigators for navigation and most celestial computations." 
Greenwich Mean Time (GMT) GMT is the time used by navigators for navigation and most celestial computations. It is measured from the lower branch of the Greenwich meridian (180 degree meridian) westward to the upper branch of the hour circle of the mean Sun. Each day the mean sun transits the Greenwich meridian at 1200 GMT and the lower branch of the Greenwich meridian at 2400 (0000) GMT. Perhaps you have heard the terms Universal Time (UT) and Coordinated Universal Time (UTC) used in reference to GMT. There are some differences, but for practical purposes, you can consider them the same. UTC is the time used by the GPS satellites and by the National Observatory in their time broadcasts and is the time used by navigators, even if they do call it GMT.
Local Mean Time (LMT) Just as GMT is mean solar time measured with reference to the Greenwich meridian, so Local Mean Time (LMT) is mean solar time measured with reference to the local meridian of the observer. LMT is measured from the lower branch of the observer's meridian westward to the upper branch of the mean Sun. The mean Sun transits the lower branch of the observer's meridian at 0000 (2400) LMT and the upper branch at 1200 LMT. If an observer were at the Greenwich meridian, GMT would also be the same as LMT. The navigator uses LMT to compute local sunrise, sunset, twilight, moonrise and moonset. This LMT must then be converted to Zone Time (ZT) for use at sea. This is done by applying a correct equal to the difference in longitude between the central zone meridian and the observer's meridian. If the observer is west of the central meridian the correction is added and subtracted if east of it. If GMT is desired, it is calculated from the ZT.
Zone Time (ZT) At sea and ashore, watches and clocks are normally set to some form of Zone Time (ZT). At sea, the nearest meridian exactly divisible by 15 degrees is used as the zone meridian. For example, starting at 0 degrees, the zone meridians are 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, and 180 in both an east and west direction from Greenwich. Each zone extends 7.5 degrees of longitude either side of this central zone meridian and the zone time is the same everywhere within this zone. At this central meridian only, both ZT and LMT are identical.
Standard Time Zones The world has been divided into 24 zones, each one being 15 degrees of longitude in width. Each zone uses the LMT of its central meridian throughout the zone. Since Greenwich is the central meridian for one of these zones, and each zone is 15 degrees wide or one 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 which must be added or subtracted to zone time to obtain GMT. These numbers are positive in west longitude and negative in east longitude. The number and its sign is called the Zone Description (ZD).
Typically, when traveling west from Greenwich around the world and setting one's watch back an hour for each time zone, a navigator would have set the watch back a total of 24 hours upon arriving back at Greenwich and the date would be one day behind that of Greenwich. Conversely, traveling eastward, the watch would have been advanced a total of 24 hours, thereby gaining a day in comparison with Greenwich. To keep the records straight, it is necessary to add a day somewhere if going around the world to the west. and to subtract a day if going around to the east. The 180 degree meridian was selected as the International Date Line (IDL) where a day is gained or lost. The Greenwich (zero) meridian is the opposite meridian and is the starting point for longitude. The IDL follows the 180 degree meridian except where it makes broad detours to avoid eastern Siberia, the western Aleutian Islands, and several groups of islands in the South Pacific. This can easily be seen on any globe of the world. Many places in the world use a local time that is different from the standard time zone for various commercial or political reasons, so you should check the Nautical Almanac for this information before converting arrival time in GMT to local.
Time and Longitude In the two previous articles, I discussed at length the discovery of this relationship; now I need to get into this as it pertains to time conversions. We have defined the mean Sun as traveling at a constant rate, so consequently, the mean Sun will travel an arc of 360 degrees in 24 hours, or 15 degrees in one hour. The relationships between time and arc that you should memorize are:
Time  Arc 
24 hours  360 degrees 
1 hour  15 degrees 
4 minutes  1 degree 
1 minute  15 minutes 
4 seconds  1 minute 
Local time is the time at one particular meridian. Since the sun cannot transit two meridians at the same time, no two meridians have exactly the same local time. The difference in time between two meridians is the length of time for the sun's passage from one meridian to the other. This time is also proportional to the angular distance between the two meridians. If two meridians are 30 degrees apart, their time differs by two hours, the time being later at the easternmost of the two meridians, since the sun crossed there first.
The date changes at midnight. If you have ever stayed up to ring in the New Year, you know that the date always changes at midnight, but only for your time zone. The local date changes at midnight when the mean sun transits the lower branch of the local meridian. Consider this date change in another way. On the lower branch of the mean sun, it is always midnight local mean time. As the lower branch moves westward, it pushes the old date before it and drags the new date after it. As the lower branch approaches the 180 degree meridian, the area of the world using the old date decreases and the area using the new date increases. When the lower branch reaches the IDL, that is, when the mean sun transits the Greenwich meridian, the old date is out and the new date, for that instant of time, prevails worldwide. Then as the lower branch passes the 180 degree meridian, a newer date begins east of the lower branch. The new date is pushed westward and the date change process starts all over again. The Zone Date changes at midnight Zone Time (ZT), or when the lower branch transits the central meridian of the zone.
The reckoning of time is based upon the motion of the sun relative to a given meridian, where the time is 2400 (0000) at lower transit and 1200 at upper transit. For Greenwich Mean Time, the reference meridian is that of Greenwich; for Local Mean Time, the reference meridian is that of a given place, and for zone time, the reference meridian is the standard meridian of a given zone.
The difference between two times is equal to the difference of longitude of their referenced meridians, expressed in units of time. GMT differs from LMT by the longitude of the place; GMT differs from ZT by the longitude of the standard meridian of the zone; LMT differs from ZT by the difference of longitude between the standard meridian of the zone and the meridian of the place. In applying a time difference, a place which is east of another place has a later time than that place, and a place which is west of another place has an earlier time than that place.
The zone description (ZD) is used to make the calculations between different reference times. For example, when converting from ZT to GMT a positive ZD is added while a negative ZD is subtracted. In converting GMT to ZT, a positive ZD is subtracted and a negative one is added. When performing these calculations the date should be watched carefully. If a sum exceeds 24 hours, subtract 24 from it and add one day to the date. When the ZD value is greater than the time and needs to be subtracted, you should add 24 hours to the time and subtract one day from the date. Bowditch has a complete chapter devoted to time and many examples of calculations from one reference time to another. If you require additional explanations, I suggest that you read Bowditch or get some help from a navigator who is experienced in celestial navigation.
From the above discussion, I think you'll agree that for a navigator, the meaning of time is quite different from the average person's take on it.
Suggested Reading:
Time and the Evolution of Longitude by Jim Sexton
Understanding Time for Navigation by Jim Sexton
Running Fixes by Jim Sexton
Buying Guide: Binoculars
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