# CHAPTER 18 TIME TIME IN NAVIGATION

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1 CHAPTER 18 TIME TIME IN NAVIGATION Solar Time The Earth s rotation on its axis causes the Sun and other celestial bodies to appear to move across the sky from east to west each day. If a person located on the Earth s equator measured the time interval between two successive transits overhead of a very distant star, he would be measuring the period of the Earth s rotation. If he then made a similar measurement of the Sun, the resulting time would be about 4 minutes longer. This is due to the Earth s motion around the Sun, which continuously changes the apparent place of the Sun among the stars. Thus, during the course of a day the Sun appears to move a little to the east among the stars, so that the Earth must rotate on its axis through more than 360 in order to bring the Sun overhead again. See Figure If the Sun is on the observer s meridian when the Earth is at point A in its orbit around the Sun, it will not be on the observer s meridian after the Earth has rotated through 360 because the Earth will have moved along its orbit to point B. Before the Sun is again on the observer s meridian, the Earth must turn a little more on its axis. The Sun will be on the observer s meridian again when the Earth has moved to point C in its orbit. Thus, during the course of a day the Sun appears to move eastward with respect to the stars. The apparent positions of the stars are commonly reckoned with reference to an imaginary point called the vernal equinox, the intersection of the celestial equator and the ecliptic. The period of the Earth s rotation measured with respect to the vernal equinox is called a sidereal day. The period with respect to the Sun is called an apparent solar day. When measuring time by the Earth s rotation, using the actual position of the Sun, or the apparent Sun, results in apparent solar time. Use of the apparent Sun as a time reference results in time of non-constant rate for at least three reasons. First, revolution of the Earth in its orbit is not constant. Second, time is measured along the celestial equator and the path of the real Sun is not along the celestial equator. Rather, its path is along the ecliptic, which is tilted at an angle of 23 27' with respect to the celestial equator. Third, rotation of the Earth on its axis is not constant. Figure Apparent eastward movement of the Sun with respect to the stars. 275

2 276 TIME To obtain a constant rate of time, we replace the apparent Sun with a fictitious mean Sun. This mean Sun moves eastward along the celestial equator at a uniform speed equal to the average speed of the apparent Sun along the ecliptic. This mean Sun, therefore, provides a uniform measure of time which approximates the average apparent time. The speed of the mean Sun along the celestial equator is 15 per hour of mean solar time Equation of Time Mean solar time, ormean time as it is commonly called, is sometimes ahead of and sometimes behind apparent solar time. This difference, which never exceeds about 16.4 minutes, is called the equation of time. The navigator most often deals with the equation of time when determining the time of upper meridian passage of the Sun. The Sun transits the observer s upper meridian at local apparent noon. Were it not for the difference in rate between the mean and apparent Sun, the Sun would be on the observer s meridian when the mean Sun indicated 1200 local time. The apparent solar time of upper meridian passage, however, is offset from exactly 1200 mean solar time. This time difference, the equation of time at meridian transit, is listed on the right hand daily pages of the Nautical Almanac. The sign of the equation of time is negative if the time of Sun s meridian passage is earlier than 1200 and positive if later than Therefore: Apparent Time = Mean Time + (equation of time). Example 1: Determine the time of the Sun s meridian passage (Local Apparent Noon) on June 16, Solution: See Figure 2008 in Chapter 20, the Nautical Almanac s right hand daily page for June 16, The equation of time is listed in the bottom right hand corner of the page. There are two ways to solve the problem, depending on the accuracy required for the value of meridian passage. The time of the Sun at meridian passage is given to the nearest minute in the Mer. Pass. column. For June 16, 1994, this value is To determine the exact time of meridian passage, use the value given for the equation of time. This value is listed immediately to the left of the Mer. Pass. column on the daily pages. For June 16, 1994, the value is given as 00 m 37 s. Use the 12 h column because the problem asked for meridian passage at LAN. The value of meridian passage from the Mer. Pass. column indicates that meridian passage occurs after 1200; therefore, add the 37 second correction to 1200 to obtain the exact time of meridian passage. The exact time of meridian passage for June 16, 1994, is 12 h 00 m 37 s. The equation of time s maximum value approaches 16 m 22 s in November. If the Almanac lists the time of meridian passage as 1200, proceed as follows. Examine the equations of time listed in the Almanac to find the dividing line marking where the equation of time changes between positive and negative values. Examine the trend of the values near this dividing line to determine the correct sign for the equation of time. Example 2: See Figure Determine the time of the upper meridian passage of the Sun on April 16, Solution: From Figure 1801, upper meridian passage of the Sun on April 16, 1995, is given as The dividing line between the values for upper and lower meridian passage on April 16th indicates that the sign of the equation of time changes between lower meridian passage and upper meridian passage on this date; the question, therefore, becomes: does it become positive or negative? Note that on April 18, 1995, upper meridian passage is given as 1159, indicating that on April 18, 1995, the equation of time is positive. All values for the equation of time on the same side of the dividing line as April 18th are positive. Therefore, the equation of time for upper meridian passage of the Sun on April 16, 1995 is (+) 00 m 05 s. Upper meridian passage, therefore, takes place at 11 h 59 m 55 s. Day SUN MOON Eqn. of Time Mer. Mer. Pass. 00 h 12 h Pass. Upper Lower Age Phase m s m s h m h m h m d Figure The equation of time for April 16, 17, 18, To calculate latitude and longitude at LAN, the navigator seldom requires the time of meridian passage to accuracies greater than one minute. Therefore, use the time listed under the Mer. Pass. column to estimate LAN unless extraordinary accuracy is required Fundamental Systems of Time Atomic time is defined by the Systeme International (SI) second, with a duration of 9,192,631,770 cycles of radiation corresponding to the transition between two hyperfine levels of the ground state of cesium 133. International Atomic Time (TAI) is an international time scale based on the average of a number of atomic clocks. Universal time (UT) is counted from 0 hours at midnight, with a duration of one mean solar day, averaging out minor variations in the rotation of the Earth. UT0 is the rotational time of a particular place of observation, observed as the diurnal motion of stars or extraterrestrial radio sources. UT1 is computed by correcting UT0 for the effect of polar motion on the longitude of the observer, and varies because of irregularities in the Earth s rotation. Coordinated Universal Time, or UTC, used as a standard reference worldwide for certain purposes, is kept

3 TIME 277 within one second of TAI by the introduction of leap seconds. It differs from TAI by an integral number of seconds, but is always kept within 0.9 seconds of TAI. Dynamical time has replaced ephemeris time in theoretical usage, and is based on the orbital motions of the Earth, Moon, and planets. Terrestrial time (TT), also known as Terrestrial Dynamical Time (TDT), is defined as 86,400 seconds on the geoid. Sidereal time is the hour angle of the vernal equinox, and has a unit of duration related to the period of the Earth s rotation with respect to the stars. Delta T is the difference between UT1 and TDT. Dissemination of time is an inherent part of various electronic navigation systems. The U.S. Naval Observatory Master Clock is used to coordinate Loran signals, and GPS signals have a time reference encoded in the data message. GPS time is normally within 15 nanoseconds with SA off, about 70 nanoseconds with SA on. One nanosecond (one one-billionth of a second) of time is roughly equivalent to one foot on the Earth for the GPS system Time and Arc One day represents one complete rotation of the Earth. Each day is divided into 24 hours of 60 minutes; each minute has 60 seconds. Time of day is an indication of the phase of rotation of the Earth. That is, it indicates how much of a day has elapsed, or what part of a rotation has been completed. Thus, at zero hours the day begins. One hour later, the Earth has turned through 1/24 of a day, or 1/24 of 360, or = 15 Smaller intervals can also be stated in angular units; since 1 hour or 60 minutes is equivalent to 15 of arc, 1 minute of time is equivalent to = 0.25 = 15' of arc, and 1 second of time is equivalent to 15' 60 = 0.25' = 15" of arc. Summarizing in table form: 1 d =24 h = m =1 h =15 4 m =1 =60' 60 s =1 m = 15' 4 s = 1' = 60" 1 s = 15" = 0.25' Therefore any time interval can be expressed as an equivalent amount of rotation, and vice versa. Interconversion of these units can be made by the relationships indicated above. To convert time to arc: 1. Multiply the hours by 15 to obtain degrees of arc. 2. Divide the minutes of time by four to obtain degrees. 3. Multiply the remainder of step 2 by 15 to obtain minutes of arc. 4. Divide the seconds of time by four to obtain minutes of arc 5. Multiply the remainder by 15 to obtain seconds of arc. 6. Add the resulting degrees, minutes, and seconds. Example 1: Convert 14 h 21 m 39 s to arc. Solution: (1) 14 h 15 = ' 00" (2) 21 m 4 = ' 00" (remainder 1) (3) 1 15 = ' 00" (4) 39 s 4 = ' 00" (remainder 3) (5) 3 15 = ' 45" (6) 14 h 21 m 39 s = ' 45" To convert arc to time: 1. Divide the degrees by 15 to obtain hours. 2. Multiply the remainder from step 1 by four to obtain minutes of time. 3. Divide the minutes of arc by 15 to obtain minutes of time. 4. Multiply the remainder from step 3 by four to obtain seconds of time. 5. Divide the seconds of arc by 15 to obtain seconds of time. 6. Add the resulting hours, minutes, and seconds. Example 2: Convert ' 45" to time units. Solution: (1) = 14 h 00 m 00 s remainder 5 (2) 5 4 = 00 h 20 m 00 s (3) 24' 15 = 00 h 01 m 00 s remainder 9 (4) 9 4 = 00 h 00 m 36 s (5) 45" 15 = 00 h 00 m 03 s (6) ' 45" = 14 h 21 m 39 s Solutions can also be made using arc to time conversion tables in the almanacs. In the Nautical Almanac, the table given near the back of the volume is in two parts, permitting separate entries with degrees, minutes, and quarter minutes of arc. This table is arranged in this manner because the navigator converts arc to time more often than the reverse. Example 3: Convert '22" to time units, using the Nautical Almanac arc to time conversion table.

4 278 TIME Solution: Convert the 22" to the nearest quarter minute of arc for solution to the nearest second of time. Interpolate if more precise results are required m = 22 h 16 m 00 s m = 00 h 01 m 13 s ' 22" = 22 h 17 m 13 s Time and Longitude Suppose the Sun were directly over a certain point on the Earth at a given time. An hour later the Earth would have turned through 15, and the Sun would then be directly over a meridian 15 farther west. Thus, any difference of longitude between two points is a measure of the angle through which the Earth must rotate to separate them. Therefore, places east of an observer have later time, and those west have earlier time, and the difference is exactly equal to the difference in longitude, expressed in time units. The difference in time between two places is equal to the difference of longitude between their meridians, expressed in units of time instead of arc The Date Line Since time grows later toward the east and earlier toward the west of an observer, time at the lower branch of one s meridian is 12 hours earlier or later, depending upon the direction of reckoning. A traveler circling the Earth gains or loses an entire day depending on the direction of travel, and only for a single instant of time, at precisely Greenwich noon, is it the same date around the earth. To prevent the date from being in error and to provide a starting place for each new day, a date line is fixed by informal agreement. This line coincides with the 180th meridian over most of its length. In crossing this line, the date is altered by one day. If a person is traveling eastward from east longitude to west longitude, time is becoming later, and when the date line is crossed the date becomes 1 day earlier. At any instant the date immediately to the west of the date line (east longitude) is 1 day later than the date immediately to the east of the line. When solving celestial problems, we convert local time to Greenwich time and then convert this to local time on the opposite side of the date line Zone Time At sea, as well as ashore, watches and clocks are normally set to some form of zone time (ZT). At sea the nearest meridian exactly divisible by 15 is usually used as the time meridian or zone meridian. Thus, within a time zone extending 7.5 on each side of the time meridian the time is the same, and time in consecutive zones differs by exactly one hour. The time is changed as convenient, usually at a whole hour, when crossing the boundary between zones. Each time zone is identified by the number of times the longitude of its zone meridian is divisible by 15, positive in west longitude and negative in east longitude. This number and its sign, called the zone description (ZD), is the number of whole hours that are added to or subtracted from the zone time to obtain Greenwich Mean Time (GMT). The mean Sun is the celestial reference point for zone time. See Figure Converting ZT to GMT, a positive ZT is added and a negative one subtracted; converting GMT to ZT, a positive ZD is subtracted, and a negative one added. Example: The GMT is 15 h 27 m 09 s. Required: (1) ZT at long ' W. (2) ZT at long ' E. Solutions: (1) GMT 15 h 27 m 09 s ZD +10 h (rev.) ZT Chronometer Time 05 h 27 m 09 s (2) GMT 15 h 27 m 09 s ZD 03 h (rev.) ZT 18 h 27 m 09 s Chronometer time (C) is time indicated by a chronometer. Since a chronometer is set approximately to GMT and not reset until it is overhauled and cleaned about every 3 years, there is nearly always a chronometer error (CE), either fast (F) or slow (S). The change in chronometer error in 24 hours is called chronometer rate,or daily rate, and designated gaining or losing. With a consistent rate of 1 s per day for three years, the chronometer error would total approximately 18 m. Since chronometer error is subject to change, it should be determined from time to time, preferably daily at sea. Chronometer error is found by radio time signal, by comparison with another timepiece of known error, or by applying chronometer rate to previous readings of the same instrument. It is recorded to the nearest whole or half second. Chronometer rate is recorded to the nearest 0.1 second. Example: At GMT 1200 on May 12 the chronometer reads 12 h 04 m 21 s. At GMT 1600 on May 18 it reads 4 h 04 m 25 s. Required:. 1. Chronometer error at 1200 GMT May Chronometer error at 1600 GMT May Chronometer rate. 4. Chronometer error at GMT 0530, May 27.

5 Figure Time Zone Chart. TIME 279

10 284 TIME Figure 1816b. Broadcast format of station WWVH. The time ticks in the WWV and WWVH emissions are shown in Figure 1816a and Figure 1816b. The 1-second UTC markers are transmitted continuously by WWV and WWVH, except for omission of the 29th and 59th marker each minute. With the exception of the beginning tone at each minute (800 milliseconds) all 1-second markers are of 5 milliseconds duration. Each pulse is preceded by 10 milliseconds of silence and followed by 25 milliseconds of silence. Time voice announcements are given also at 1- minute intervals. All time announcements are UTC. Pub. No. 117, Radio Navigational Aids, should be referred to for further information on time signals Leap-Second Adjustments By international agreement, UTC is maintained within about 0.9 seconds of the celestial navigator s time scale, UT1. The introduction of leap seconds allows a clock to keep approximately in step with the Sun. Because of the variations in the rate of rotation of the Earth, however, the occurrences of the leap seconds are not predictable in detail. The Central Bureau of the International Earth Rotation Service (IERS) decides upon and announces the introduction of a leap second. The IERS announces the new leap second at least several weeks in advance. A positive or negative leap Figure 1817a. Dating of event in the vicinity of a positive leap second.

11 TIME 285 second is introduced the last second of a UTC month, but first preference is given to the end of December and June, and second preference is given to the end of March and September. A positive leap second begins at 23 h 59 m 60 s and ends at 00 h 00 m 00 s of the first day of the following month. In the case of a negative leap second, 23 h 59 m 58 s is followed one second later by 00 h 00 m 00 s of the first day of the following month. The dating of events in the vicinity of a leap second is effected in the manner indicated in Figure 1817a and Figure 1817b. Whenever leap second adjustments are to be made to UTC, mariners are advised by messages from NIMA. Figure 1817b. Dating of event in the vicinity of a negative leap second.

12 286 TIME

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