Chapt-18.pdf

CHAPTER 18

TIME

TIME IN NAVIGATION

1800. Solar Time

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 ref-

erence results in time of non-constant rate for at least three

reasons. First, revolution of the Earth in its orbit is not con-

stant. Second, time is measured along the celestial equator

and the path of the real Sun is not along the celestial equa-

tor. Rather, its path is along the ecliptic, which is tilted at an

angle of 23

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 1800 . 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

27' with respect to the celestial equator. Third,

rotation of the Earth on its axis is not constant.

Figure 1800. Apparent eastward movement of the Sun with respect to the stars.

275

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

276

TIME

To obtain a constant rate of time, we replace the appar-

ent 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

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.

per

Example 2: See Figure 1801 . Determine the time of the

upper meridian passage of the Sun on April 16, 1995.

Solution: From Figure 1801 , upper meridian passage

of the Sun on April 16, 1995, is given as 1200. 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 .

hour of mean solar time.

1801. Equation of Time

Mean solar time ,or mean 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 1200. Therefore: Apparent Time = Mean Time

+ (equation of time).

SUN

MOON

Day

Eqn. of Time

Mer.

Mer. Pass.

00 h

12 h

Pass.

Upper Lower Age Phase

m d

00 02 00 05 12 00 00 26 12 55 16

00 13 00 20 12 00 01 25 13 54 17

00 27 00 33 11 59 02 25 14 55 18

Figure 1801. The equation of time for April 16, 17, 18, 1995.

Example 1: Determine the time of the Sun’s meridian

passage (Local Apparent Noon) on June 16, 1994.

Solution: See Figure 2008 in Chapter 20, the Nautical

Almanac’s right hand daily page for June 16, 1994. 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 1201.

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 .

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.

1802. 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

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

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.

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

= 210

00' 00"

(2) 21 m

= 005

00' 00" (remainder 1)

(3) 1

= 000

15' 00"

(4) 39 s

= 000

09' 00" (remainder 3)

(5) 3

= 000

00' 45"

(6) 14 h 21 m 39 s

= 215

24' 45"

1803. Time and Arc

To convert arc to time:

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 360

°¸

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.

Smaller intervals can also be stated in angular units;

since 1 hour or 60 minutes is equivalent to 15

of arc, 1

Example 2: Convert 215

24' 45" to time units.

minute of time is equivalent to 15

60 = 0.25

= 15' of arc,

and 1 second of time is equivalent to 15'

60 = 0.25' = 15"

Solution:

of arc.

(1) 215

°¸

= 14 h 00 m 00 s

remainder 5

Summarizing in table form:

(2) 5

= 00 h 20 m 00 s

(3) 24'

= 00 h 01 m 00 s

remainder 9

1 d

=24 h

=360

(4) 9

= 00 h 00 m 36 s

(5) 45"

= 00 h 00 m 03 s

60 m

=1 h

=15

4 m

=60'

(6) 215

24' 45" = 14 h 21 m 39 s

60 s

=1 m

= 15'

4 s

= 1'

= 60"

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.

1 s

= 15"

= 0.25'

Therefore any time interval can be expressed as an

equivalent amount of rotation, and vice versa. Intercon-

version of these units can be made by the relationships

indicated above.

18'22" to time units, using the

Nautical Almanac arc to time conversion table.

To convert time to arc:

24 = 15

°¸

Example 3: Convert 334

278

TIME

Solution:

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

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.

, 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 1806.

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.

334

00.00 m

= h 16 m 00 s

000

18.25 m

= 00 h 01 m 13 s

334

18' 22"

= 22 h 17 m 13 s

1804. 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

Example: The GMT is 15 h 27 m 09 s .

, and the Sun would then be directly

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.

Required: (1) ZT at long. 156

24.4' W.

(2) ZT at long. 039

04.8' E.

Solutions:

(1)

GMT

15 h 27 m 09 s

+10 h (rev.)

05 h 27 m 09 s

1805. The Date Line

(2)

GMT

15 h 27 m 09 s

–03 h (rev.)

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.

18 h 27 m 09 s

1807. Chronometer Time

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.

1806. Zone Time

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 .

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

Required: . 1. Chronometer error at 1200 GMT May 12.

2. Chronometer error at 1600 GMT May 18.

3. Chronometer rate.

4. Chronometer error at GMT 0530, May 27.

on each side of the time meridian the

time is the same, and time in consecutive zones differs by

over a meridian 15

Figure 1806. Time Zone Chart.

Plik z chomika:

Inne pliki z tego folderu:

Inne foldery tego chomika: