Lat_by_polaris.doc

POLARIS

Consider a Celestial Body, Declination N90°

                                                                                                                                                                                                                                                                                                                                                                                                                                    Celestial                                                                                                                                                          Body                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            Rational                                                                                                                                                            Horizon                                                                                                                                                                                                                                                                                                             Zenith                                                                                                                                                                                                                                                                          Obs'd                                                                                                                                                 P                                 Alt                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               True                                                                                                                                                                        Alt                                                                                                                                   Earth                                                                                                                                                                                                                                Latitude                                                                                                                                                                                      Equator                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   

As can be seen: True Altitude = Latitude.

Because the Pole Star declination is not exactly N90° corrections must be applied to the True Altitude to obtain the Latitude through which the Position Line cuts the D.R. Longitude.

The corrections are based on LHA ¡, Latitude and month of observation.

The bearing of Polaris is based on LHA ¡ and observer's Latitude.

The position line runs at 90° to the bearing of the body.
PROCEDURE

1. Correct the Sextant Altitude to bring it to True Altitude. (I.E., Dip & Total Corr’n)

2. Obtain LHA ¡.

3. Using LHA ¡ obtain correction aO, interpolating as necessary.

4. Staying in the same column, entering with Latitude, obtain correction a1, interpolating as necessary.

5. Staying in the same column, entering with month, obtain correction a2.

Latitude = True Altitude + a0 + a1 + a2 - 1°

Direction of Polaris is obtained form the final table, staying in the same column as LHA ¡ and entering with Latitude.

a0 , a1 and a2 are corrections to allow for the fact that Polaris is not at exactly Dec'n N90°.

So as to always make the corrections positive, for ease of calculation,              

              a constant of               58.8' has been added to a0

              “       “       “              0.6'   "      "        "     "   a1

              “       “       “              0.6'   "      "        "     "   a2

                                 Total  =              60.0'                                                        \ 1° must be subtracted.

The tables are based on an average SHA and Declination of Polaris for the year, consequently the tables must be updated annually. The update will also allow for "Precession and Nutation".

EXAMPLE

From the following observation of Polaris find the direction of the Position Line and the Latitude at which it cuts the D.R. Longitude.

Approx Ship Time = 0500 hrs, 31st August 1995.

D.R Latitude                   39° 27'N

        Longitude  118° 17'E

Sextant Altitude of Polaris 40° 24.4'.  Index Error 2.7' On The Arc.  Height of Eye 14.0m.

Chronometer showed 9:03:58.                Chronometer Error 0m 59s Fast.