Having established the star"s general east and west direction, its north and south position can be found from its declination.
_4. Time of Meridian Pa.s.sage of a Star_
It is often invaluable to know first, when a certain star will be on your meridian or second, what star will be on your meridian at a certain specified time. Here is the formula for each case, which put in your Note Book:
1. To find when a certain star will cross your meridian, take from the Nautical Almanac, the R.A. of the Mean Sun for Greenwich Mean Noon of the proper astronomical day. Apply to it the correction for longitude in time (West +, East -) as per Table at bottom of page 2, Nautical Almanac, and the result will be the R.A. of the Mean Sun at local mean noon, i.e., the distance in sidereal time the mean sun is from the First Point of Aries when it is on your meridian. Subtract this from the star"s R.A., i.e., the distance in sidereal time the star is from the First Point of Aries (adding 24 hours to the star"s R.A., if necessary to make the subtraction possible). The result will be the distance in sidereal time the star is from your meridian i.e., the time interval from local mean noon expressed in units of sidereal time. Convert this sidereal time interval into a mean time interval by always subtracting the reduction for the proper number of hours, minutes and seconds as given in Table 8, Bowditch. The result will be the local mean time of the star"s meridian pa.s.sage.
Example:
April 22nd, 1919, A.M. at ship. In Lo. 75 E. What is the local mean time of the Star Etamin"s meridian pa.s.sage?
R.A.M.S. Gr. 21d--0h 1h--54m--02s Red. for 75 E (--5h) --49.3 ________________
R.A.M.S. local mean noon 1h--53m--12.7s
Star"s R.A. 17h--54m--44s -- 1 --53 --12.7 ___________________
Sidereal interval from L.M. Noon 16h--01m--31.3s Red. for Sid. Int. (Table 8) -- 2 --37.3 ___________________ L.M.T. 21 d 15h--58m--54s
Hence, star will cross meridian at 3h--58m--54s A.M. April 22nd.
2. To find at any hour desired what star will cross your meridian, take the R.A. of the Mean Sun for Greenwich Mean Noon of the proper astronomical day. Apply to it the correction for longitude in time (West +, East -) as per table at bottom of page 2, Nautical Almanac, and the result will be the R.A. of the Mean Sun at local mean noon; i.e., the distance in sidereal time the mean sun is from the First Point of Aries when it is on your meridian. Suppose you wish to find the star at 10 P.M. Add 10 sidereal hours to the sun"s R.A. just found. The result will be the R.A. of your meridian at approximately 10 P.M.
Select in the table on p. 94 the R.A. of the star nearest in time to your R.A. just secured. Subtract the R.A. of the Mean Sun at local mean noon from the star"s R.A. just found on p. 94 of the N.A. and the result will be the exact distance in sidereal time the star you have just identified is from your meridian, i.e., the time interval from local mean noon expressed in units of sidereal time. Convert this sidereal time interval into a mean time interval by always subtracting for the proper number of hours, minutes and seconds as per Table 8, Bowditch.
You will then have secured the name of the star desired and the exact local mean time of the star"s meridian pa.s.sage.
Example No. 2: At sea Dec. 14, 1919. Desired to get a star on my meridian at 11 P.M. Lo. by D.R. 74 W.
(.).R.A.G.M.N. 17h--28m--26s Corr. 74 W. (4th - 56m W + ) + 0 --48.6 ___________________ (.).R.A. your M. 17h--29m--14.6s + 11 ___________________
R.A.M. 28h--29m--14.6s
-- 24 ___________________ 4h--29m--14.6s
R.A. of Star Aldebaran 4h--31m--18.5s Star R.A. 28h--31m--18.5 (.).R.A. your M. 17 -- 29--14.6 ---------------- Sid. Int. from L.M. Noon 11h--02m--03.9s Red for Sid. Int. (Table 8) -- 1 --48 ---------------- L.M.T. 11h--00m--15.9s
Aldebaran, then, is the star and the exact L.M.T. of its meridian pa.s.sage will be 11h 00m 15.9s
Note: If the R.A.M. is more than 24 hours, deduct 24 hours. You will know whether the star is North or South of you by its declination. If you are in North lat.i.tude, the star will be south of you if its declination is South or if its declination is North and less than your lat.i.tude. If its declination and your lat.i.tude are both North and its declination is greater, the star will be north of you. The same principle applies if you are in South lat.i.tude.
a.s.sign any of the following to be worked in the cla.s.s room or at night:
1. At sea, November 1st, 1919. In Lat.i.tude 40 N., Longitude 74 W.
WT 8h 30m P.M. Observed unknown star about 80 east of my meridian and 25 south of me. What was the star?
2. At sea, December 1st, 1919. CT 10h 45m 01s. CC 20m 16s slow.
In D.R. Lat.i.tude 30 N., Longitude 60 30" W. Observed unknown star about 60 west of meridian and about 22 S. What was the star?
3. March 15th, 1919. In D.R. Lat.i.tude 10 42" N, Longitude 150 14" 28" W. CT 5h 14m 28s. CC--2m 10s. Observed unknown star almost on my meridian and about 28 north of me. What was the star?
4. Aug. 3, 1919, P.M. at ship. In D.R. Lat.i.tude 37 37" N. Longitude 38 37" W. At what local mean time will the Star Antares be on the meridian?
5. What star will transit at about 4:10 A.M. on Aug. 3rd, 1919? In D.R. position Lat.i.tude 38 10" N, Longitude 34 38" W.
6. At what local mean time will the Star Arcturus transit on July 17th, 1919, in Lat.i.tude 45 35" N., Longitude 28 06" W.?
WEDNESDAY LECTURE
LAt.i.tUDE BY MERIDIAN ALt.i.tUDE OF A STAR--LAt.i.tUDE BY POLARIS (POLE OR NORTH STAR)
To find your lat.i.tude by taking an alt.i.tude of a star when it is on your meridian, is one of the quickest and easiest of calculations in all Navigation. The formula is exactly the same as for lat.i.tude by meridian alt.i.tude of the sun. In using a star, however, you do not have to consult your Nautical Almanac to get the G.M.T. and from that the declination. All you have to do is to turn to page 95 of the Nautical Almanac, on which is given the declination for every month of the year, of any star you desire. The rest of the computation is, as said before, the same as for lat.i.tude by the sun and follows the formula Lat. = Dec.
Z.D. (90 - true alt.i.tude). As when working lat.i.tude by the sun, you subtract the Z.D. and Dec. when of opposite name and add them when of the same name. Put in your Note-Book:
Formula: Lat. = Dec. Z.D. (90 - true alt.i.tude).
At sea, Dec. 24th, 1919. Meridian alt.i.tude Star Aldebaran 52 36" S. HE 20 ft. Required lat.i.tude of ship.
Obs. Alt. 52 36" S Corr. - 5 08 ---------- True Alt. 52 30" 52" S - 90 00 00 ---------- Z.D. 37 29" 08" N Dec. 16 21 00 N ---------- Lat. 53 50" 08" N
Note to Instructor:
Have cla.s.s work examples such as the following before taking up Lat.i.tude by Pole Star:
1. At sea, May 5th, 1919. Meridian alt.i.tude Star Capella, 70 29" S. HE 32 ft. Required lat.i.tude of ship.
2. At sea, August 14th, 1919. Meridian alt.i.tude Star Vega, 60 15" 45"
N. HE 28 ft. Required lat.i.tude of ship.
Etc.
_Lat.i.tude by Polaris_ (_Pole or North Star_)
You remember we examined the formula in the N.A. for Lat. by the pole star when we were discussing sidereal time some weeks ago. We will now take up a practical case of securing your lat.i.tude by this method.
Before doing so, however, it may be of benefit to understand how we can get our lat.i.tude by the pole star. In the first place, imagine that the Pole Star is directly over the N pole of the earth and is fixed. If that were so, and imagine for a minute that it is so, then it would be exactly 90 from the Pole Star to the celestial equator. Now, no matter where you stand, it is 90 from your zenith to your true horizon. Hence if you stood at the equator, your zenith would be in the celestial equator and your true horizon would exactly cut the Pole Star. Now, supposing you went 10 N of the equator. Then your northerly horizon would drop by 10 and the Pole Star would have an alt.i.tude of 10. In other words, when you were in 10 N lat.i.tude, the pole star would measure 10 high by s.e.xtant. And so on up to 90, where the Pole Star would be directly over you and you would be at the North Pole. Now all this is based upon the Pole Star being in the celestial sphere exactly over the North Pole of the earth. It is not, however. Owing to the revolution of the earth, the star appears to move in an orbit of a maximum of 1 08". Just what part of that 1 08" is to be applied to the true alt.i.tude of the star for any time of the sidereal day, has been figured out in the table on page 107 of the Nautical Almanac. What you have to get first is the L.S.T. Find from the table the correction corresponding to the L.S.T. and apply this correction with the proper sign to the true alt.i.tude of Polaris. The result is the lat.i.tude in. Put in your Note-Book:
To get lat.i.tude by pole star, first get L.S.T. This can be secured by using any one of the three formulas given you in Week III--Thursday"s Lecture on Sidereal Time and Right Ascension. Then proceed as per formula in N.A.
Note to Instructor: