Lectures in Navigation Part 9

--12 ------------------------ L.M.T. 9d--16h--40m--16s

Now we come to a very important application of time. You will remember that in one of the former lectures we stated that to find our lat.i.tude, we had to find how far North or South of the equator we were, and to find our longitude, we had to find how far East or West of the meridian at Greenwich we were. Never mind about lat.i.tude for the present. We can find our longitude exactly if we know our Greenwich time and our time at ship. For instance, in the accompanying diagram:

[Ill.u.s.tration]

Suppose PG is the meridian at Greenwich, then anything to the west of PG is West longitude and anything to the East of PG is East longitude. Now suppose GPS is the H.A. of G. or G.A.T.--i.e., the distance in time G.

is from the sun. And L P S is the H.A. of the ship or L.A.T.--i.e., the distance in time the ship is from the sun. Then the difference between G P S and L P S is G P L, measured by the arc L G, and that is the difference that the ship, represented by its meridian PL, is from the Greenwich meridian PG. In other words, that is the ship's longitude for, as mentioned before, longitude is the distance East or West of Greenwich that any point is, measured on the arc of the celestial equator. The longitude is West, for you can see LPG or the arc LG is west of the meridian PG.

Likewise if P E is the meridian of your ship, the Longitude in time is the S.H.A. or L.A.T., E P S (the distance your ship is from the sun) less the G.H.A. or G.A.T., G P S (the distance Greenwich is from the sun) which is the angle G P E measured by the arc G E. And this Longitude is East for you can see G P E, measured by G E, is east of the Greenwich meridian, P G.

In both these cases, however, the longitude is expressed in time, i.e., so many hours, minutes and seconds from the Greenwich meridian and we wish to express this distance in degrees, minutes and seconds of arc.

The earth describes a circle of 360 every 24 hours. Then if you are 1 hour from Greenwich, you are 1/24 of 360 or 15 from Greenwich and if you are 12 hours from Greenwich, you are 1/2 of 360 or 180 from Greenwich. By keeping this in mind, you should be able to transpose time into degrees, minutes and seconds of arc for any fraction of time. It is, however, all worked out in Table 7 of Bowditch which turn to. (Note to Instructor: Explain this table carefully). Put in your Note-Book:

89 24' 26" = (89) 5h--56m (24') 1m--36s (26") 1--44/60s -------------------- 5h--57m--37s 44/60s = 38s

4h--42m--26s 4h--40m = 70 2m--24s = 36'

2s = 30"

----------- 70 36' 30"

Also put in your Note-Book this diagram and these formulas: (For diagram use ill.u.s.tration on p. 40.)

L.M.T. + West Lo. = G.M.T. L.A.T. + West Lo. = G.A.T.

L.M.T. - East Lo. = G.M.T. L.A.T. - East Lo. = G.A.T.

G.M.T. - West Lo. = L.M.T. G.A.T. - West Lo. = L.A.T.

G.M.T. + East Lo. = L.M.T. G.A.T. + East Lo. = L.A.T.

If G.M.T. or G.A.T. is greater than L.M.T. or L.A.T. respectively, Lo.

is West.

If G.M.T. or G.A.T. is less than L.M.T. or L.A.T. respectively, Lo. is East.

Example:

In longitude 81 15' W, L.M.T. is April 15d--10h--17m--30s A.M. What is G.M.T.?

L.M.T. 15d--10h--17m--30s A.M.

--12 ------------------ L.M.T. 14d--22h--17m--30s 5 --25 W + ------------------ G.M.T. 15d-- 3h--42m--30s --------

G.M.T. April 15d-- 3h--42m--30s L.M.T. April 15d--10h--17m--30s A.M.

In what Lo. is ship?

G.M.T. 15d 3h--42m--30s L.M.T. 14d 22h--17m--30s ------------------ Lo. in T 5h--25m--00s W

Lo. = 81 15'W

a.s.sign also for Night Work reading the following articles in Bowditch: 276-278-279-226-228-286-287-288-290-291-294 (omitting everything on page 114.)

THURSDAY LECTURE

SIDEREAL TIME--RIGHT ASCENSION

Our last lecture was devoted to a discussion of sun time. Today we are going to talk about star time, or, using the more common words, sidereal time.

Now, just one word of review. You remember that we have learned that astronomical time is reckoned from noon of one day to noon of the next and hence the astronomical day corresponds to the 24 hours of a ship's run. The hours are counted from 0 to 24, so that 10 o'clock in the morning of October 25th is astronomically October 24th, 22 hours or 22 o'clock of October 24th.

Now Right Ascension is different from both astronomical and civil time.

Right Ascension is practically celestial longitude. For instance, the position of a place on the earth is fixed by its lat.i.tude and longitude; the position of a heavenly body is fixed by its declination and right ascension. But Right Ascension is not measured in degrees and minutes nor is it measured East and West. It is reckoned in hours and minutes all the way around the sky, eastward from a certain point, through the approximate 24 hours. The point from which this celestial longitude begins is not at Greenwich, but the point where the celestial equator intersects the ecliptic in the spring of the year, i.e., the point where the sun, coming North in the Spring, crosses the celestial equator. This point is called the First Point of Aries. You will frequently hear me speak of a star having, for instance, a Right Ascension of 5h 16m 32s. I mean by that, that starting at the celestial meridian, i.e., the meridian pa.s.sing through the First Point of Aries, it will take a spot on the earth 5h 16m 32s to travel until it reaches the meridian of the star in question.

Roughly speaking then, just as Greenwich Apparent Time means the distance East or West the Greenwich meridian is from the sun and Local Apparent Time means the distance East or West your ship is from the sun, so R.A.M.G. means the distance in time the Meridian of Greenwich is from the First Point of Aries, measured eastward in a circle. And this distance is the same as Greenwich Sidereal Time, i.e., Sidereal Time at Greenwich or the distance in time the meridian of Greenwich is from the First Point of Aries.

Now, what is the star time that corresponds to local time? It is called the Right Ascension of the Meridian, which means the R. A. of the meridian which intersects your zenith. Just as L.A.T. is the distance in time your meridian is from the sun, so Local Sidereal Time is the R. A.

of your meridian, i.e., the distance in time your meridian is from the First Point of Aries. Put in your Note-Book:

G.S.T. and R.A.M.G. are one and the same thing.

L.S.T. and R.A.M. are one and the same thing.

G.M.T. + (.).R.A. + (+).C.P. = G.S.T. (R.A.M.G.) If the result is more than 24 hours, subtract 24 hours.

G.S.T. - (.).R.A. - (+).C.P. = G.M.T.

G.S.T. - W.Lo. = L.S.T.

+ E.Lo.

L.S.T. + W.Lo. = G.S.T.

- E.Lo.

I can explain all these formulas very easily by the following ill.u.s.tration which put in your Note-Book: (Note to Instructor: If possible have copies of this ill.u.s.tration mimeographed and distributed to each student.)

[Ill.u.s.tration: FIRST POINT OF ARIES.]

There is one term I have used which does not appear in the ill.u.s.tration.

It is the Earth's Central Progress ((+).C.P.). The astronomical day based on the sun, is 24 hours long, as said before. The sidereal day, however, is only 23h 56m 04s long. This is due to the fact that whereas the earth is moving in its ecliptic track around the sun while revolving on its own axis, the First Point of Aries is a fixed point and hence never moves. The correction, then, for the difference in the length of time between a sidereal day and a mean solar day is called the Earth's Central Progress and, of course, has to be figured for all amounts of time after mean noon at Greenwich, since the Sun's Right Ascension tables in the Nautical Almanac are based on time at mean noon at Greenwich.

Now you have a formula for practically all kinds of conversion except for converting L.M.T. into L.S.T. You could do it by the formula

L.M.T. + W.Lo. = G.M.T. + (.).R.A. + (+).C.P. = G.S.T. - W.Lo. = L.S.T.

- E.Lo. + E.Lo.

But that involves too many operations.

A shorter way, though not so simple perhaps, is as follows: L.M.T. + Reduction page 2 N.A. for time after local mean noon + (.).R.A. of Greenwich mean noon Reduction page 2 N.A. for Lo. in T. (W+, E-) = L.S.T.

Note to Instructor:

Explain this formula by turning to page 107 N.A. and work it out by the formula L.M.T. + Lo. in T (W) = G.M.T. + (.).R.A. + (+).C.P. = G.S.T. - Lo. in T (W) = L.S.T. Example:

L.M.T. 10h--40m--30s Lo. in T 4 --56 W + ------------- G.M.T. 15 --36 --30 (.).R.A. 5 --11 --10 (+).C.P. -- 2 --34 ------------- G.S.T. 20 --50 --14 Lo. W - 4 --56 ------------- L.S.T. 15h--54m--14s