EXERCISE 32 — LONG BY CHRONOMETER SUN (Numerical Solution)

  1. On 19th Jan 2008, PM at ship in DR 40˚ 16’S 175˚ 31’E, the sextant altitude of the sun’s LL was 43˚ 27.4’ when the GPS clock showed 03h 48m 00s. If IE was 1.5’ on the arc & HE was 22m, find the direction of the LOP and the longitude where it cuts the DR latitude.

                                d     h       m       s
GMT                       19   03     48    00
LIT (E)                    (+)    11     58   04
LMT                       19     15    46   04

      GMT     19 Jan 03h  48m  00s

GHA (19d 03h)            222˚  23.0’                                           Dec          S  20˚  28.9’
Incr. (48m 00s)          012˚  00.0’                                           d(-0.5)                 00.4’
GHA                             234˚  23.0’                                           Dec          S  20˚  28.5’
Lat                              40˚  16’ S

Sext Alt                               43˚ 27.4’
IE (on)                              (-)       01.5’
Observed Alt                      43˚ 25.9’
Dip (HE 22m)                 (-)        08.3’
App Alt                               43˚ 17.6’
T Corrn. LL                     (+)       15.2’
T Alt                                   43˚ 32.8’

dia32q2

NOTE:

In the following formula, if the LAT and DEC are of same name then sign is (-), If of contrary names then sign is (+).

e32q1p1

P = 49˚ 38.8’

Since, sight is after mer. Pass. ,so LHA = P

NOTE:

  • Before meridian passage (Mer. Pass.) , LHA wil be between 180 and 360. After meridian passage, LHA will be between 000 and 180.So, to calculate LHA,
  • If it given that the sight is taken AM at ship or meridian of east, then P = LHA.
  • If it is given that the sight is taken at PM at ship, then P = 360 – LHA
  • When P>90, the minus sign obtained for the value of A is to be ignored and is taken care by changing the name of A.

LHA          = 049˚ 38.8’
GHA         = 234˚ 23.0’
Long. W   = 184˚ 44.2’

Obs. Long. = 175˚ 15.8’ E

We know that:

e32q1p2

Azimuth = N 80.3˚ W
T Az= 279.7˚ (T)
LOP = 009.7˚ – 189.7˚

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