To find the Increment, the Increments and Corrections pages are entered with the minutes and seconds of the sight. For a Sun sight taken at exactly 30 minutes past the hour, the increment value would be 7° 30’.0
On the left hand side of the Increments page for the appropriate minutes, there is the correction to apply based on the tabulated “v” value for the body. The “v” corrections are considered to be linear but are actually tabulated for halfway through the minute. This is why a “v” of 12.0 produces 6.1 for 30 minutes. The “v” adjustment is always positive for the Moon but can be negative for the planets.
The “v” correction for the planets is found at the bottom of the daily pages. The rapid changes in the motion of the Moon mean that a “v” value is tabulated for each hour. No “v” correction is supplied for the Sun. Instead the GHA values for each hour in the tables are massaged.
The GHA for stars are treated differently. Here the SHA (Sidereal Hour Angle) or angular distance west of Aries is tabulated for each three day period. The GHA of Aries is then tabulated for each hour and the Increment value for minutes and seconds is found in exactly the same way as for the Sun, Moon and planets. No “v” value is given for simplicity. The GHA for a star is the sum of the GHA for Aries and the SHA.
Local Hour Angle (LHA)
This is the angular distance west of the observer. Thus we find the GHA of a body and then adjust it for longitude. An easterly longitude is added to the GHA and a westerly longitude is subtracted.
LHA = GHA +/- Longitude
The Declination for most bodies is tabulated for each hour. Due to the very small movement of stars, it is only provided once for each three day period.
The hourly change of Declination is usually small therefore the adjustment is found using the “d” value at the bottom of the page for the Sun and planets. (It is negligible for stars.) The Moon however moves rapidly which means that its’ “d” value is provided for each hour.
The “d” correction is found in the same manner as for “v” by going to the appropriate Increments and Corrections page to obtain the appropriate correction from the right hand “v and d” section.
The direction in which to apply the “d” correction (North or South) is determined by examining the next hourly value.
Simplifications Vs Accuracy in Nautical Almanacs
In the explanation section at the back of the UK/ US Governments’ “The Nautical Almanac,” paragraph 24 provides details of the expected errors in the values of GHA and Declination. The maximum error in each is 0’.2 for the planets, 0’.25 for the Sun and 0’.3 for the Moon. These errors are caused entirely by the need to keep the presentation as simple as possible.
It goes on to say; “In practice it may be expected that only one third of the values of GHA and Dec taken out will have errors larger than 0’.05 and less than one tenth will have errors larger than 0’.1.”
The superficial attraction of using data from a source such as the Astronomical Almanac in the interests of accuracy is illusory. RA and Declination may be quoted in arc-seconds to several decimal places but the bodies, particularly the Moon, do not necessarily move in a linear manner during the day. Similarly the Hour Angle of Aries does not change linearly. Irregular motions are included in Nautical Almanac data.
Example of Calculations for the Moon ~ 00:30:05 GMT, 19th January 2011
GHA at 00:00 10° 09’.4
Increment for 30m 05s + 7° 10’.7
“v” (6’.1 at 00:00) + 3’.1
GHA at 00:30:05 17° 23’.2
Longitude 10° 00’.0 E Add for East and subtract if West
LHA 27° 23’.2
Declination at 00:00 21° 08’.5 S
“d” (7’.6 at 00:00) 3’.8 S South by inspection of the change in the daily page
Declination at 00:30:05 21° 04’.7 S
Example of Calculations for Acamar ~ 00:30:05 GMT, 19th January 2011
GHA of Aries at 00:00 118° 02’.7 (Not visible above)
Increment for 30m 05s + 7° 32’.5
SHA 315° 19’.5
GHA of Acamar at 00:30:05 80° 54’.7 (440° 51’ - 360°)
Longitude 10° 00’.0 W
LHA 70° 54’.7
The Declination value of 40° 15’.8 in the day’s pages for stars is not adjusted.