Sunday, May 11, 2008

Determining the GHA and Declination of a Planet

The use of the Nautical Almanac to find the GHA and declination of a navigational planet differs somewhat from the procedure for a star, because both the GHA and declination for the navigational planets are tabulated in the Almanac for each whole hour of GMT. These tabulations are necessitated by the fact that the planets, being relatively close to earth in the solar system, seem to move across the unchanging patterns of the stars from one hour to the next.

Suppose that the planet Venus was observed at watch time 04-03-36 and its observed altitude was determined to be 16° 38.6'. The DR position at the time of the sight was L 34° 17.0'S, Long. 163° 09.1'E.

The Nautical Almanac is first entered to compute the GHA of Venus for the time of the observation. The tabulated value of the GHA of Venus for the whole hour of GMT immediately preceding the observation is recorded on your form. In addition, the "v" value at the bottom of the column containing the Venus tabulations is noted and recorded on the form alongside the tabulated GHA. This "v" value represents the average irregularity in the rate of increase of the GHA of Venus from one hour to the next over the three-day period covered by the daily page, as a result of the motion of the planet in its orbit.

Because the rate of increase of the GHA is not constant, a v correction derived from this v value must be applied to the tabulated GHA of the planet, in addition to the GHA increment. The v correction, like the GHA increment, is taken from the appropriate "Increments and Corrections" table in the back of the Almanac.

I should mentioned that all bodies in the solar system are characterized by this irregular rate of increase of GHA. A "v" correction is applied to the GHA increments of all the navigational planets and the moon; the "v" correction for the sun is so small that it is ignored when using the Nautical Almanac. The "v" corrections for Mars, Jupiter, Saturn, and the moon are always positive, at certain times of the year, the Venus "v" correction can be negative.

Returning to the example at hand, a GHA increment for 4 minutes 12 seconds is found from the 4-minute "Increments and Corrections" table and entered on the sight form. To find the "v" correction, the columns in the appropriate table with the headings "v" or "d" correction are used (the d correction is explained below.

The left side of each column contains "v" or "d" values, and the right side, the corresponding "v" or "d" correction. In this case, a "v" correction of +0.1' corresponding to a "v" value of + 1.1 is obtained. The tabulated GHA, GHA increment, and "v" correction are all summed to yield the GHA of Venus of 117° 51.6'.

To find the declination of Venus for the time of the observation the tabulated declination for the whole hour of GMT preceding the sight is first extracted and entered on the form as the tabulated declination (Tab. Dec.). Just as the GHA of a body in the solar system is continually changing from one hour to the next, the declination of these bodies is also changing. In contrast to the irregular rate of change of GHA, however, the rate of change in declination is nearly constant. The "d" value appearing at the bottom of the Venus column represents the average hourly rate of change of its declination over the three-day period covered by the daily page. A "d" correction (actually analogous to the GHA increment) derived from this d value is found from the appropriate "Increments and Corrections" table and applied to the tabulated declination to form the true declination of Venus at the time of the observation. The sign of the d value and hence the sign of the d correction is positive if the trend of the tabulated declination is increasing. If the tabulated declination is decreasing, the sign is negative. In this case, a "d" correction of 0.0 is obtained from the 4-minute table, using a d value of .1 as entering argument in the "v or d correction" column. The true declination of Venus at GMT 17-04-12 is S 13° 16.1'.
The use of the Nautical Almanac for Venus is now complete.