Stellar Navigation Calculations

Calculation of the Hour Angle and Declination — Example Using Sirius

Determine the hour angle and declination at 01:20 UTC on January 1.

Step 1
Locate E＊ in the Nautical Almanac.
For fixed stars, only the value at 00:00 is provided, as the variation is negligible.

Step 2
Since the rate of change of E＊ is identical for all fixed stars, obtain the correction for the desired time from the P.P. distribution table in the Appendix and apply it to the value of E＊.

Step 3
Add the observation time (UTC) to the corrected value of E＊ to obtain the hour angle.

Step 4
The resulting hour angle is expressed in hours.
To convert it into degrees, multiply by 15.

Step 5
The declination of a fixed star can be taken directly from the Nautical Almanac, as it does not vary significantly on a daily basis.
No further correction is required.

Calculation of the Meridian Passage Time — Example Using Sirius

Determine the meridian passage time on January 1 at 140°E

Step 1
Subtract the given value from 24:00.
This is because the meridian passage time of a celestial body does not necessarily occur near 12:00, unlike that of the Sun.

Step 2
Obtain the value of E＊ corresponding to the approximate U.T. from the Nautical Almanac.

Step 3
The obtained value represents the Local Mean Time (LMT).
To convert it to Greenwich Mean Time (GMT), apply the longitude correction.
Longitude Time (L.T.) is obtained by dividing the longitude by 15.
East longitude is treated as negative, and west longitude as positive.

Step 4
For each celestial body, the approximate meridian passage time (LMT) for the day may also be obtained directly from the daily data in the Nautical Almanac.

Correction of the Observed Altitude — Example Using Sirius

Step 1
The procedure is essentially the same as that used for the Sun.

Step 2
Apply the sextant index error (I.E.) to the observed sextant altitude.
This corrected value is used as the basis for all subsequent corrections.

Step 3
Using the correction tables for planets and stars, obtain the required correction values in the same manner as for the Sun
(Example: height of eye = 7 m, altitude = 54°)

Step 4
The fourth correction is not required for fixed stars, as their distance is extremely large and the parallax is negligible.

Step 5
The fifth correction accounts for the difference between air temperature and sea surface temperature.
Determine the temperature difference and obtain the corresponding correction value from the table.