TIME & ANGLE MEASUREMENT

<   SUMMARY OF INTRODUCTION

6 APPARENT TIME AND MEAN TIME

21. THE DEFINITION OF TIME.

It was shown in § 1-4 that the determination of the position of a celestial body in the celestial sphere by the equinoctial system is closely connected with time. This is because the rotation of the Earth on its axis once in every 24 hours causes an apparent motion of the celestial sphere so that even the so called fixed bodies are continually changing their celestial position. Defining a celestial position precisely, therefore, can only be done in relation to a specific instant of time. To do this, a navigator must not only know the definition of time, but also the various ways in which time is measured, the instruments used for time-keeping and how these are rated

Time in the Astronomical sense denotes something enduring while events take place. Events are contained in time as objects are contained in space. Time is, therefore, a measurable duration (Length or period of time). Time not only exists be fore and after an event, but (as in the question “What is the Time?) Also measures the event as it happens. - specifies a particular instant in its own measurable duration.

The common units of time are related to Astronomical patterns. The uniform rotation of the Earth about its own axis is one such pattern, one complete revolution defining a day. The apparent motion of the Sun around the ecliptic is another pattern, a year being defined as the time taken for the Sun to complete this apparent revolution.

The year and the day are the principal divisions of time; they depend on Astronomical phenomena and the human race must accept them as they are. The lengths of shorter divisions of time - the hour,the minute, and the second – are chosen to suit man’s convenience and are quite arbitrary subdivisions of the day. Similarly, the week and the month are more or less arbitrary subdivisions of the year. Thus, it can be seen that particular instants of time can be related to the rhythmic repetitions of recognisable Astronomical patterns, and if these repetitions are annotated or numbered, then it becomes relatively easy to identify an instant of time. Duration of time can be expressed as a function of these same repetitions.

As explained in § 1-5, the uniform rotation of the Earth results in the apparent and equally uniform rotation of the celestial sphere, so that celestial bodies are continually crossing and returning to an observer’s meridian. When a celestial object crosses the observer’s celestial meridian it is said to culminate. A simple definition of the basic unit of time might be: A day is the interval of time between successive risings, culmination’s or settings of a celestial body, but it is comparatively difficult to time the rising or setting of a celestial body, yet comparatively easy to time its culmination. This is done in an observatory using a transit instrument, which in a telescope of special design set precisely in the plane of the meridian. Thus, a more satisfactory definition of a day is, A day is an interval which elapsed between two successive transits of a celestial body across the same meridian.

All celestial bodies are thus timekeepers, but for reasons, which will be shown in these Chapters, some are more convenient than others. The Sun is not a perfect timekeeper because it’s apparent - speed along the ecliptic is not constant. The Sun, however, gives light and heat to the Earth and so governs life on Earth. The human race is therefore compelled to accept the Sun as the Celestial body by which the day is decided in ordinary human affairs. Depending on which celestial object is used establish the unit of time, decides the type of time. If the celestial body selected is a star, the interval known as a sidereal day, to distinguish it from the solar day, which is derived from the apparent diurnal movement of the Sun. The unit derived from the apparent movement of the Moon is known as the lunar day.

 

23. SOLAR TIME

The interval of time which elapses between two successive transits of the Sun across a stationary observer’s lower celestial meridian is a unit of time called a solar day.

It should be noted that the points from which solar and sidereal time are  measured are diametrically opposed to one another, the solar day commencing at lower transit and the sidereal day at upper transit. A clock registering correct solar time will indicate 00h.00m.00s at the instant when the Sun is at lower transit. When it is at upper transit (crossing the observer’s upper celestial meridian) half a solar day will have elapsed since the Solar day commenced, and a clock registering solar time will  indicate 12h.00m.00s because the day is subdivided into 24 hours. It is for this  reason that the time of the Sun’s upper Mer. Pass. is called mid-day, and solar time differs from sidereal time by twelve hours.

Fig. 6-1 serves to illustrate that a solar day is longer than a sidereal day. The period of the Earth’s revolution around the Sun is about 365 days so that, as the Earth moves in her orbit, the Sun appears to move eastwards across the celestial sphere at the rate of (360° - 365°) approximately 1° per day. Imagine the Sun and any fixed star to be on the upper meridian of the observer 0 in fig. 6-1. The next time the star is on the upper meridian of the same observer is when he has been carried with the Earth to position 2. The observer is now at position 01. In travelling from 0 to 01 the observer has been carried around the Earth’s axis through an angle of exactly 360° and one sidereal day has elapsed. But before the Sun is again on the observer’s upper meridian, the Earth has to swing through a further angle of about 1° in order to carry the observer to position 02 A solar day is, therefore, a longer period of time than a sidereal day.

Not only is the solar day longer than the sidereal day, but also the solar day is not an interval of fixed length because the Earth does not move along its orbit around the Sun at a constant speed. Its speed is greatest when it is nearest the Sun (in Jan) and least when it is farthest away (in Jul); therefore, a solar day is longer in Jan than it is in Jul. The distance the Earth travels along its orbit in any fixed interval is, therefore, variable. To an observer on Earth, this irregular motion is revealed by corresponding variations in the apparent speed of the Sun along the ecliptic, and further variations are introduced when the Sun’s motion is projected onto the celestial equator, where hour angles are measured. The hour angle of the True Sun does not, therefore, increase at a uniform rate, and it does not give a practical unit of measurement, which must be uniform.

It is not convenient to use sidereal time in everyday life because the Sun governs to a great extent, the factors, which are required for an orderly existence. Nor is it convenient to use solar time because of the inconstant length of the solar day.

To overcome the variations in the length of the solar day due to the combination of the effects of the varying speed of the Earth’s orbital motion and the obliquity of the ecliptic, and yet use the Sun as the basis of time measuring, an imaginary point known as the Mean Sun is employed. The Mean Sun is a point that moves along the celestial equator at a uniform rate. The Mean Sun moves at the average speed of the True Sun, but instead of in the ecliptic, which is the path of the True Sun, the Mean Sun is imagined to move in the plane of the Earth’s rotation, which is along the celestial equator.

A definition of the Mean Sun would, therefore, be an imaginary body which is assumed to move in the celestial equator at a uniform speed around the Earth, and to complete one revolution in the time taken by the True Sun to complete one revolution in the ecliptic.

The unit of time derived from the imaginary diurnal motion of the Mean Sun is known as the mean solar day. The day by the True Sun is usually called the apparent solar day because it is derived from the apparent diurnal motion of the True Sun.

 

24. TIME AT A GIVEN INSTANT

Having described the principal units of time, it is now necessary to understand the meaning of the term time at a given instant. Time at any instant is a measure of the angle swept out by a semi-great circle whose axes are at the celestial poles and which swings with diurnal motion around the celestial sphere making one rotation in a day.

For indicating sidereal time the semi-great circle referred to is that on which the F.P. of Aries is located

(P ♈︎ in fig. 6-2) For indicating Apparent Solar Time it is that on which the True Sun in located

(P ♈︎ in fig. 6-2) and

for indicating Mean Solar Time it is that on which the Mean Sun is located (PM in fig. 6-2).

The semi-great circles referred to above may be imagined to sweep out time and for this reason, they are called hour circles, though, as explained in § 1-5 of this 'Ocean Navigation', they are simply celestial  meridians. Local time at any instant may be defined generally as the angle at the celestial pole  (or arc of the celestial equator) contained between the observer’s meridian (the upper celestial meridian for sidereal time and the lower for solar time) and the hour circle of the celestial body or point used for indicating time, measured westwards from the observer’s celestial meridian.

The angle at the celestial pole can also be represented as an arc of the celestial equator. The upper celestial meridian is the datum for sidereal time and the lower for solar time. Since this angle when measured from  the observer’s upper celestial meridian is the L.H.A. as defined in § 1-5, it, therefore, follows that: -

The Local Sidereal Time (LST) at any instant is equivalent to the L.H.A. of the F.P. of Aries, i.e. LST = L.H.A. ♈︎ (arc O♈︎ in fig. 6-2)

The Local Apparent Solar Time (LAT) at any instant is equivalent to the L.H.A. of the True Sun. ± 12 hrs i.e. - LAT = L.H.A.T.S. ± 12 hrs (arc O♈︎XT - 12 hrs)

The Local Mean Solar Time (L.M.T.) at any instant is equivalent to the L.H.A. of the Mean Sun ± 12 hrs, i.e. - L.M.T. = L.H.A.M.S. ± 12 hrs (arc O♈︎XM - 12 hrs)

 

25. THE CONNECTION BETWEEN UNITS OF ARC AND UNITS OF TIME.

Units of arc are expressed in degrees, minutes and seconds and units of time are expressed in hours, minutes and seconds, and, as has been shown above, time can be expressed in both types of unit, it is obvious there must be a connection between the two.

Because the hour circles which sweep out the time as described above complete one revolution of 360° in 24 hours, and an hour is divided into 60 minutes which are in turn divided into 60 seconds, then it can be said: -

15°      =      1 hour           1°       =      4 minutes

15'      =      1 minute      1'        =      4" seconds

A Table for converting the arc into time or time into arc is included in the N.A. and this will be found on Page 20 of the AN pamphlet of extracts. If this is not available, the conversion can be done mentally by remembering the above scale of equivalents or by one of the following methods: -

To convert Arc into Time:    multiply by 4 and divide by 60

If, for example, the angle is 123° 43 the conversion is done as follows:

 

To convert Time into Arc:

multiply the hours by 15 and divide the minutes and seconds by 4.

If, for example, the time is 08h. 14m. 52s., the conversion to arc is as follows: -

 

26. CIVIL AND ASTRONOMICAL TIMES

As the name suggests, the civil day is the day, which suffices for human affairs. It begins at midnight when the Mean Sun makes its lower transit (that is when the L.H.A.M.S is 12h.) and it ends at the next midnight. It is divided into 24 mean solar hours, which are counted in two series of 12 hours, the firstdenoted a.m. (ante meridian), and the second p.m. (post meridian). The first therefore extends from midnight to noon, a period during which the L.H.A.M.S lies between 12h and 24h, and the second from noon to midnight, when the L.H.A.M.S lies between Oh and 12h. It should be borne in mind that the units of time in everyday use are mean solar units.

For tabulation purposes, it is clearly more convenient to write 0735 and 1935 or  07h.35m and 19h.35m as in the N.A. instead of 7.35 a.m. and 7.35 p.m. A day reckoned in one series of hours from 0 to 24 is therefore  used for all Astronomical and navigational purposes and is referred to as the Astronomical day.

Local Mean Time (LMT) is the mean time kept at any place when the L.H.A. of the Mean Sun is measured from the meridian of that place, and, as has been defined above, L.M.T. at any instant is the L.H.A. of the Mean Sun at that instant, measured westwards from the meridian of the place, plus or minus twelve hours (L.M.T. = L.H.A.M.S. ± 12 hours).

Greenwich Mean Time (GMT) is the local mean time on the meridian of Greenwich hence the definition G.M.T. at any instant is the Greenwich hour angle of the Mean Sun at that instant, plus or minus twelve hours (G.M.T.. - G.H.A.M.S. ±12 hours).

Fig. 6-3(a) and (b) show the Celestial equator as viewed from a point directly above the celestial pole. PA is the upper celestial meridian of Greenwich and PB is its lower celestial meridian (equivalent to the 180° meridian on Earth). PM is the celestial meridian of the Mean Sun.

In Fig. 6-3 (a) the G.H.A.M.S arc AM or angle APM) is about 3h.but as G.M.T. (like L.M.T.) is measured from the lower celestial meridian (PB). G.M.T. is thus G.H.A.M.S. + 12h, or 3h + 12h = 15h, and we would say that the time at this instant was 1500 G.M.T.

In Fig. 6-3 (b) the G.H.A.M.S S. (arc ABM) is about 21½h, but again as G.M.T. is measured from PB, G.M.T., in this case, is G.H.A.M.S. - 12h or 21½ - 12h = 9½h, and we would say the time at this instant was 0930 G.M.T.

 

27. G.M.T. AND UNIVERSAL TIME (UT)

Since the introduction of time measurement on the atomic scale, irregularities have been found in the Earth’s rotational speed. When G.M.T. is corrected for this factor it is known as Universal Time (UT).

The basis of all entries in the N.A. is really UT although this is likely to be referred to as G.M.T. for many years to come. The difference is very small and the error arising from the use of chronometer G.M.T. will not exceed 0.9 of a second, corresponding to 0.2 of Longitude In order to maintain this difference, step adjustments of exactly one second are made to radio time signals as required (normally at midnight on 30th Jun and 31st December). There is no requirement to attain a precision of less than one second, but when step adjustment is to be made to time signals (as advised in Notices to Mariners). Care must be taken that the chronometer rate is correctly established.

 

28. YEARS AND THE CALENDAR

The period of revolution of the Earth around the Sun provides a natural unit of time called a year. The time taken for the Earth to make one revolution relative to any fixed celestial point is called a sidereal year and is 365 days 06h.09m.09s of Mean Solar Time. However, the time taken for the Mean Sun to move from the F.P. of Aries back to the same point is slightly shorter than a sidereal year, being 365 days 05h.48m.46s of Mean Solar Time, and this is called a tropical year. The systematic arrangement of units of time constitutes a calendar. The incommensurable nature of the natural units of time namely the day, the month and the year, made the problem of fitting them together in an orderly way one of great difficulty to the early Astronomers.

The Romans employed a calendar in which the period of the Moon’s revolution around the Earth played the principal part, but whereas this was reasonably consistent with the months it did not coincide with the seasons and the year.

A later attempt was known as the Julian calendar named in honour of Julius Caesar and contrived by the Alexandrine Astronomer Sosigenes. The year, by this calendar, was 365 days 6 hours exactly.

The 365 days were divided into twelve months each containing an integral but not necessarily the same, number of days. The extra six hours in the year were allowed to accumulate for four years making an extra day, which was intercalated to form a year containing 366 days instead of 365 days as in the common or ordinary year. The intercalated day was called the bi-sextus, and a year, which contained it a leap year.

The year of greatest significance in calendar making is the tropical year, this regulating, as it does the seasons. By taking the year as 365 days 6 hours an error amount to about 11 minutes a year throws out the calendar according to the recurring seasons. The Julian calendar was used in Britain until 1752, by which date the accumulated error amounted to 11 days.

In 1752, the Gregorian calendar was introduced in Britain, named after Pope Gregory X111 who prescribed it in the year 1582.

This calendar took into account the error in the Julian calendar which amounts to very nearly 72 hours or three days in 400 years and three bisestile or leap years are dropped every 400 years, these being the opening years of centuries except those in which the first two numbers of the year is . divisible by 4. Thus, the year 2000 will be a leap year whereas the year 1900 was not. Ordinary leap years are those whose entire numbers are divisible by 4. The Gregorian calendar is the present system used over most of the Earth and is not likely to be changed for some considerable time since it is only in error to the extent of about 2 days in 6,000 years.

© 2017 . Sidaerum. All Rights Reserved