# EXERCISE 36 – INTERCEPT STAR (Numerical Solution)

1. ###### On 19th Jan 2008, at about 1900 at ship in DR 00˚ 02’N 170˚ 50’E, the sextant altitude of the star BETELGUESE was 43˚ 11.1’ at 07h 33m 44s by GPS clock. If IE was 1.3’ off the arc & HE was 18m, find the direction of the LOP and the intercept.

d       h    m   s
GMT                             19    07  33  44
LIT (E)                          (+)    11  23  20
LMT                             19    18  57  04

###### GMT     19 Jan 07h  33m  44s

GHA Ȣ(19d 07h)             223˚  03.7’                                           Dec         N  07˚  24.6’
Incr. (33m 44s)             008˚  27.4’                                             Lat            00˚  02’ N
GHA Ȣ                                 231˚  31.1’
SHA *                         (+) 271˚  05.4’
GHA *                              142˚  36.5’
Long (E)                 (+) 170˚  50.0’
LHA  *                             313˚  26.5’

P  = (360˚ – LHA)
= (46˚ 33.5’)

We know that :
Cos CZD = ( Cos P × Cos Dec × Cos Lat) + ( Sin Lat × Sin Dec )
Cos CZD = ( Cos 46˚ 33.5’ × Cos 07˚  24.6’ × Cos 00˚  02’ ) + ( Sin 00˚  02’ × Sin 07˚  24.6’ )
CZD = 47˚  00.2’

Sext Alt                            43˚ 11.1’
IE (OFF)                         (+) 01.3’
Observed Alt                43˚ 12.4’
Dip (HE 18m)               (-) 07.5’
App Alt                         43˚ 04.9’
T Corrn.                          (-)01.0’
T Alt                              43˚ 03.9’
TZD                               46˚ 56.1’

TZD             =   46˚ 56.1’
CZD             =   47˚ 00.2’
Intercept    =   04.1’ TOWARDS

Azimuth = N 79.9˚ E

T Az = 079.9˚ (T)

LOP = 169.9˚ – 349.9˚