I wrote this about 20 years ago.....
'The first of them, the moon, is probably the most infrequently used of all. The reason for this is that , although the actual reduction of a lunar sight is no different to reducing a sun or planet sight and utilises either Volume 2 or 3 of the Sight Reduction Tables for Air Navigation
, the preliminary work involved in correcting the altitude and establishing the LHA and declination of the moon is more complex and is prone to error if sufficient care is not taken.
The ability to take lunar sights may, however, come in handy for the very same reasons Venus is useful in daylight hours. There may come a time when we are able to get a good fix on our position by taking simultaneous sun and moon sights when approaching a low lying and dangerous coast. At other times the moon may be all that is visible at twilight through a thin veil of cloud.
The reason why lunar sights are more complex is due, in the main, to the moon‟s relative proximity to the earth. Now this closeness to the earth, combined with the fact that the moon‟s orbit is an ellipse, means that the hourly rate of change of the moon‟s GHA varies considerably over the lunar month, as does its declination. So, while it is a simple matter to lift
the GHA and declination from the almanac for a whole hour, you invariably have to apply large „v‟ and „d‟ corrections for increments of an hour.
The application of these corrections is not new to us – we have already seen how to apply them when working with the planets- but with the moon they are of far greater magnitude and a simple mistake in applying them can result in an error in our position of more than 30 miles.
Completely new to us, however, are the corrections we have to apply to the moon‟s observed altitude – after we have corrected the sextant
altitude for index error and our height of eye – to obtain a true altitude. Because it is so close to the earth the amount of parallax associated with the moon is considerable. You may recall
that with the sun parallax has a maximum value of 0.15 ́ at 0 ̊ altitude decreasing to zero at 90 ̊ altitude. With the moon, its parallax at 0 ̊ altitude (known as its horizontal parallax or HP) is a whopping 50 ́ and this amount varies on a daily basis as the moon‟s distance from earth either increases or decreases.
This HP is listed for every hour on the daily pages of the almanac along with an hourly „v‟ and „d‟ correction and the moon actually has two full pages of corrections given over to it in the back of the almanac for the correction of its altitude. These corrections are total corrections and are applied to the apparent altitude i.e. the sextant altitude which has already been corrected for index error and dip. The method of using this table is fully described in the almanac but we shall run over it here anyway.
Having taken a sight and applied index error and dip to the sextant altitude the next task is to extract the HP for the hour (GMT) at which you have taken the sight. You then go to the table of corrections and - entering the table with apparent altitude as an argument - lift
out the main part of the correction that is then added to the apparent altitude. Then, still working in the same column and using HP as an argument lift out the secondary correction: you also add this to your apparent altitude. Make sure that you take it from either the upper (U) or lower (L) limb column as required. If you happen to be using the upper limb, which is not uncommon with moon sights, you now have to subtract 30 ́ from the altitude so found.
As you will have noticed while inspecting the table quite a bit of interpolation is required in this operation and you could have knocked over half a dozen stars in the time taken to reduce one moon sight. This is one of the reasons moon sights are given a wide berth by most navigators.'
I have 172 pages of this stuff I can email
to you if you like.....