FOR THE TIME AT SHIP AND LONGITUDE BY AN ALTITUDE OF , FIXED STAR, A PLANET, OR THE MOON REMARKS.—When the hour angle of a heavenly body, or the time at ship, is to be determined by an altitude of a fixed star, or planet, or by the moon, the observation is the same as for the sun, already described on pages 419-420: the remarks there given also apply to the best position of the object, as well as to the taking of the mean of the times by chronometer or watch, and the mean of the altitudes. The same method is also to be adopted in finding the error of the chronometer on approximate and mean time at ship. For the true Altitude.—The observed altitude must also be corrected as already indicated on p. 258 for a fixed star ; on p. 257 for a planet; and on p. 256 for the moon. For the Mean Sun's Right Ascension, take out (from Nautical Almanac, p. II.) the sidereal time for the given date, and accelerate it for the Greenwich mean time : it is required for whichever object you observe (see also p. 247). The other elements to be taken from the Nautical Almanac, and corrected for the Greenwich date, are as follow : For a Fixed Star, the declination and right ascension are taken from the Nautical Almanac under the heading “ Apparent Places of Stars," for a given day, no correction of these elements being required. For a Planet.—Turn to the Nautical Almanac under the heading of the given planet (Venus, Mars, Jupiter, or Saturn), and Greenwich mean time, where the declination and right ascension are given for every day, Greenwich mean noon ; being hence a difference for 24 hours, you must correct it accordingly for the Greenwich date, mean time. The planet's horizontal parallax is found under the heading of the given planet, “ at Transit at Greenwich.” Under the same heading, “at Transit at Greenwich," you will also find the “Var. of R.A. in 1 hour of Long.” and the “ Var. in Decl, in 1 hour of Long."; these you can conveniently use for the correction of the given planet's right ascension and declination, in the same manner as you use the “ Var. in 1 hour” in correcting the sun's declination. For the Moon.-The declination and right ascension come from Nautical Almanac, pp. V. to XII., and have the “Var. in rom."attached, through which each can be corrected for the Greenwich date, mean time (see p. 241). The moon's semi-diameter and horizontal parallax are given in Nautical Almanac, p. III., and require correction for Greenwich date, mean time; and also the first augmented for altitude (Table D.), and the second reduced for latitude (Table E.) in Norie's Tables. To compute the Object's Hour Angle, or Meridian Distance in Time. -With the true altitude, the latitude and the corrected declination, you find object's hour angle as in the case of the sun (see p. 420). You require the Westerly Meridian Distance.-If the object is west of the meridian the hour angle taken from the Haversine Table will be the westerly meridian distance, but if the object is east of the meridian subtract the hour angle from 24h. for the westerly meridian distance. For the Mean Time at Ship:—To the object's westerly meridian distance add the object's corrected right ascension ; the sum will be the right ascension of the meridian, or sidereal time of observation, from which subtract the mean sun's right ascension, borrowing 24h. if necessary; the remainder will be the mean time at ship, before which write down the day. For the Longitude.—The difference (as before) between the mean time at ship and mean time at Greenwich (see p. 421, paragraph 9) will be the longitude in time, which convert into arc. Another Method of finding the Longitude.—To the Greenwich mean time add the mean sun's right ascension ; the sum is the sidereal time at Greenwich. The difference between the sidereal time at ship or right ascension of the meridian and the sidereal time at Greenwich, is the longitude in time, which convert into arc. Example 4.- January 5th, a.m. at ship, in lat. by D.R. 18° 17' N., and long. by D.R. 55° 20' W.; the following altitudes of the star Procyon (a Canis Minoris) were taken when it was west of the meridian; the height of the eye 19 feet. The chronometer was iom. 205. slow of Greenwich mean time, and the mean of times by ship's watch was 4h. 49m. 50s. a.m. 5th January. Required the longitude by chronometer. 28 50 30 10 M. 4 16 I.IIS. 2 H. M. S. Time by chron. Obs. alts. Procyon. H. M. S. 8 27 30 24° 44' 20" Sid. T. (N.A. p. II.) 18 56 10.9 29 30 Accel, for zoh. 39m. Ios. 3 23.6 14 IO Mean sun's R.A. 18 59 34:5 3) 86 30 3) 88 00 Mean 8 28 50 Mean 24 29 20 Equat. of T. 5th Jan. 5 43.7 X 3}h. 37 Chron. slow + 10 20 Ref. Corr. equat. 5 40 Star's decl. (N.A.) 5° 30' 22" N. 90 Star's R. A. (N.A.) 7 33 32.8 Star's pol. dist. 84 29 38 (See Altitude cos. S. sin. (s — a) a + I + P Fig. 4). Hav. P where s= | Latitude cos. l. sin. Þ 2 р Polar dist. and substituting the reciprocals of cos. I and sin. p, we get Hav. P = sec. I. co-sec. p. cos. s. sin. (s — a) Log. hav. P log. sec. I + log. co-sec. p + log. cos. S + log. sin. (s — c) — 30 T. alt. 24° 22' 58" Sec. 0.022497 P.D. 84 29 38 Co-sec. 0.002008 9 36 63 34 48 Cos. 9.648309 (s – a) 39 II 50 Sin. 9.800711 H. M. S. Hav. 9:473525 7 33 33 Sid T. at ship II 58 Mean sun's R A. 18 59 35 M.T at ship 4d. 16 58 25 M.T. Gr. 20 39 IO Long. in time 3 40 45 55° 11' 15" W. 18 17 Sum 127 S Example 4. By Direct Method. In the spherical triangle Z P X, Fig. 4, given side 2 = zenith distance side co-latitude, and side p polar distance to find _P, the hour angle. V sin. s. sin. (s 2) 2 + 1 + P where s = sin. l'. sin. Log.cos. = } {Log.co-sec. + log. co-sec. p + log. sin. s + log. sin. (s— 2) — 2C) Alt. 24° 22' 58" 2 65° 37' 2" Zenith dist. (2) 65 37 Ľ 71 43 10.022497 P 84 29 28 P 2 2 2 L. CO-sec. L. co-sec. 10.002061 o W. S. 5 16 2 3 28.1 + 4 42 42 9 28 Example 5.—April 22nd, p.m. at ship, lat. by D.R. 42° 9' N.; long. by D.R. II° 45' West, when a chronometer which was 5m. 16s. fast for à Greenwich mean time showed gh. 8m. 46s., the observed altitude of the star Arcturus (a Bootis) east of the meridian, was 36° 53' 30', the error of the instrument being 3' 0" to add, and the height of the eye 23 feet. Required the longitude of the ship. D. H. M. S. Ship T. by watch, Apr. 22 8 15 10 Since ship time and long. make Green, time Long. 47 gh.; the gh. by chron. are gh. Approx. ast. T. at Gr. 9 2 10 H. M. H. M. S. Time by chron. Apr. 22d. 9 8 46 Sid. T. (N.A.) (p. II.) 2 I 58.8 Chron. fast Accel. for gh. 3m. 30s. I 29:3 Mean sun's R.A. H. M М. S. Star's R.A. (N.A.) 14 10 39.8 Star's decl. (N.A.) 19° 45' 14' N. Dip P.D 70 14 46 36 51 48 Lat. 9 Co-lat. 47 51 (Formula same as last problem.] N 47 51 oo Co-sec. 0·129953 Co-sec. 0.026340 P I'l W 2) Z ха ТА P P Cos. 9.942439 2 IN NN 25 2 P 3 50 • H.A. 20 9 IO 40 Sid. T. ship 10 19 50 S Fig 5 Explanation of Fig. s same as Fig. 1, 9 3 30 47 8 MG Pole. Р R.A.M. O B Meridian through Arcturus QPB Easterly H.A. of X, the object. Whenever the R. A. M. is less than the R A of the object the H. A. is Easterly. Fig. 5a. 50 E. 10 W. R.A. 14 oo W AMQ AM QB Example 6.-September 13th, at about 7h. 3om. p.m. at ship; lat. by D.R. 39° 43'S., long. by D.R. 158o E., when a chronometer which was rom. 48s. (by error and rate) slow on Greenwich mean time showed 8h. 49m. IIS., the altitude of the planet Venus (centre) was 25° 4' west of the meridian; height of eye 22 feet. Required the true longitude. The R.A. and Dec. of Venus are corrected for nearest Gr. noon. Mean sun's R.A. II 29 13:30 M.T.G. 20 59 59 Corr. R.A. 14 13 56 Venus' corr. decl. 15 56 16 S. 90 . Sid. T. at Gr. 8 29 12:3 S.P.D. 74 3 44 Formula Alt. cos. s. sin. (s -- a) a +1+pl Lat. Hav. P wheres = cos. l. sin. P - Polar dist. 2 P N Sec. 10:113953 Co-sec 10.017024 |