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Celestial Navigation Summary By: Mahdi Bordbar
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BY: Mahdi Bordbar – IRISL Training Institute
Correction of Altitudes – All celestial bodies except Moon
Sextant Altitude (Sex Alt)
(±)𝑰𝑬 ON: - OFF: +
Observed Altitude (Obs Alt)
(-) DIP (Related to Height of Eye)
Apparent Altitude (App Alt)
Total Correction (Tot. Corrn) Lower Limb (LL): + Upper Limb (UL): -
True Altitude (T.Alt)
Note:
1. UL or LL is only applicable for the Sun and the Moon because they appear as large discs to the observer.
2. For STARS & PLANETS, total correction is given in a separate table from the Sun and is always to be subtracted.
3. In the case of Venus and Mars, one more correction called 'Additional correction' is to be applied.
BY: Mahdi Bordbar – IRISL Training Institute
Correction of Altitudes –Moon
The apparent altitude is obtained as explained Total correction for the Moon is given in the inside part of the back cover of the Nautical Almanac.
Sextant Altitude (Sex Alt)
(±)𝑰𝑬 ON: - OFF: +
Observed Altitude (Obs Alt)
(-) DIP (Related to Height of Eye)
Apparent Altitude (App Alt)
Main Correction (Main Corr)
HP Correction (HP Corrn)
True Altitude (T.Alt)
1. HP stands for Horizontal Parallax of the Moon. It is obtained from that day's page of the Almanac, alongside the declination.
2. Both main and HP corrections are always positive. 3. For UL, 30° has to be subtracted from the total to get true altitude.
Back angle observations (180° − 𝐴𝑝𝑝 𝐴𝑙𝑡)
Sometimes, the horizon under the celestial body may not be clearly visible owing to the presence of land, haze, mist, rain, etc. In such cases, it may be possible to observe the altitude of the body in the opposite direction i.e., if the azimuth (bearing of the celestial body) is 080°, the altitude is taken while facing 260°. Since the observer would then have his back to the celestial body, such a measurement is called a 'Back angle' observation. For SUN Total correction cannot be used here. The individual corrections Dip, Refraction, Semi- diameter and Parallax have to be applied separately. Slogan for easy remembrance: Don't Rob Spare Parts Semi Diameter: Lower Limb (LL): - Upper Limb (UL): + not as usual
BY: Mahdi Bordbar – IRISL Training Institute
Calculation of Azimuth by scientific calculator
A = Tan LAT
Tan P
B =Tan Dec
Sin P
𝑇𝑎𝑛 𝐴𝑧 = 1
𝐶. 𝐶𝑜𝑠 𝐿𝐴𝑇
LHA < 180° → 𝑃 = 𝐿𝐻𝐴 LHA > 180° → 𝑃 = 360° − 𝐿𝐻𝐴
Factor A Named Opposite to Lat Except when: 90° < 𝐿𝐻𝐴 < 270° Factor B Named Same as Declination. Factor 𝑪 = 𝐴 ± 𝐵
AZ
Naming of Azimuth:
Prefix (N or S): Name of Factor C
Suffix (E or W): IF 000° < 𝐿𝐻𝐴 < 180° ↔ 𝑊 , 180° < 𝐿𝐻𝐴 < 360° ↔ 𝐸
Amplitude (Sun)
sin Amp = Sin Dec × Sec Lat
AMP
N
or
S
E
or
W
E
or
W
N
or
S
Rising
Setting Same as Declination
BY: Mahdi Bordbar – IRISL Training Institute
Longitude by chronometer – SUN
Hav LHA = Sec L × Sec D [Hav ZD - Hav (𝐿~𝐷)]
90° − True Altitude T. Alt = True Zenuth Distance (TZD OR ZD)
1. To obtain (𝐿 ~𝐷), same names subtract, opposite names add.
Solution by scientific calculator:
Cos P =Sin T. Alt ∓ Sin Lat. Sin Dec
Cos Lat . Cos Dec
2. If Lat and dec are same name (-), contrary names (+).Hence in the formula, (-) has been put above the (+)
3. Before Meridian Passage ↔ 180° < 𝐿𝐻𝐴 < 360° 4. After Meridian Passage ↔ 000° < 𝐿𝐻𝐴 < 180° 5. Direction on Position Line : (AZ-90°) – (AZ+90°)
Intercept – SUN
𝐻𝑎𝑣 𝐶𝑍𝐷 = 𝐻𝑎𝑣 𝐿𝐻𝐴 × 𝐶𝑜𝑠 𝐿 × 𝐶𝑜𝑠 𝐷 + 𝐻𝑎𝑣 (𝐿~𝐷)
Solution by scientific calculator:
Cos CZD = (Cos P × Cos Lat × Cos Dec) ± (Sin Lat × Sin Dec)
1. If Lat and dec are same name (+), contrary names (-).Hence in the formula, (+) has been
put above the (-) 2. Intercept= 𝐶𝑍𝐷 − 𝑇𝑍𝐷 3. 𝐶𝑍𝐷 > 𝑇𝑍𝐷 → Intercept Toward 4. 𝐶𝑍𝐷 < 𝑇𝑍𝐷 → Intercept Away
BY: Mahdi Bordbar – IRISL Training Institute
Ex-meridian – SUN:
Note: Near the meridian means that working is to be by the ex-meridian method. There are 3 different ways to obtain MZD:
1. By Nautical Tables 2. By Haversine Formula:
Hav MZD = Hav TZD - (Hav LHA × Cos L × Cos D).
3. Solution by scientific calculator:
𝐶𝑜𝑠 𝑀𝑍𝐷 = 𝐶𝑜𝑠 𝑇𝑍𝐷 + 1 − 𝐶𝑜𝑠 𝑃 × 𝐶𝑜𝑠 𝐷𝑅 𝐿𝑎𝑡 × 𝐶𝑜𝑠 𝐷𝑒𝑐
Latitude by Meridian Altitude:
𝐿𝐻𝐴 = 𝐺𝐻𝐴 + 𝐸 𝐿𝑜𝑛𝑔 𝑂𝑟 − 𝑊 𝐿𝑜𝑛𝑔
𝐺𝐻𝐴 = 𝑆𝐻𝐴 + 𝐺𝐻𝐴 𝛾 Hence:
𝐿𝐻𝐴 = 𝑆𝐻𝐴 + 𝐺𝐻𝐴 𝛾 + 𝐸 𝐿𝑜𝑛𝑔 𝑂𝑟 − 𝑊 𝐿𝑜𝑛𝑔
Meridian Altitude Means : 𝐿𝐻𝐴 = 360° 𝑜𝑟 000°