EXERCISE 36 – INTERCEPT STAR (Numerical Solution)

1. On 30^thApril 2008, PM at ship in DR 34˚ 18’S 040˚ 20’W, the sextant altitude of the star SIRIUS was 57˚ 51.9’ at 08h 53m 03s chron time. If CE was 01m 40s FAST, IE was 1.2’ on the arc & HE was 21m, find the direction of the LOP and the intercept.

GMT     30 April 20h  51m  23s

GHA Ȣ(30d 20h)             147˚  06.9’                                   Dec         S  16˚  43.7’
Incr. (51m 23s)               012˚  52.9’                                    Lat            34˚  18’ S
GHA Ȣ                            172˚  00.7’
SHA *                       (+) 258˚  37.3’
GHA *                            070˚  38.0’
Long (W)                 (-) 040˚  20.0’
LHA  *                         030˚  18.0’

P  = LHA
= 030˚  18.0’

 

We know that :
Cos CZD = ( Cos P × Cos Dec × Cos Lat) + ( Sin Lat × Sin Dec )
Cos CZD = ( Cos 030˚  18.0’ × Cos 16˚  43.7’ × Cos 34˚  18’ ) + ( Sin 34˚  18’ × Sin 16˚  43.7’ )
CZD = 32˚  18.0’

Sext Alt                             57˚ 51.9’
IE (ON)                                (-) 01.2’
Observed Alt                    57˚ 50.7’
Dip (HE 21m)                     (-) 08.1’
App Alt                          57˚ 42.6’
T Corrn.                             (-)00.6’
T Alt                                57˚ 42.0’
TZD                               32˚ 18.0’

TZD             =   32˚ 18.0’
CZD             =   32˚ 18.0’
Intercept    =   NIL

Azimuth = N 64.7˚ W

T Az          = 295.3˚ (T)

LOP = 025.3˚ – 205.3˚