NavList:

Hi everyone,

as you might recall, I recently asked why the v-correction is being ignored in the Nautical Almanac. I was referred to the explanation given in the Nautical Almanac under ACCURACY 24. Main Data where it says:

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"The quantities tabluated in this Almanac are generally correct to the nearest 0.1'; the exception is the Sun's GHA which is deliberately adjusted by up to 0.15' to reduce the error due to ignoring the v-correction. The GHA and Dec at intermediate times cannot be obtained to this precision, since at least two quantities must be added; moreover, the v- and d-corrections are based on mean values of v and d and are taken from tables for the whole minute only. The largest error that can occur in the GHA or Dec of any body other than the Sun or Moon is less than 0.2'; it may reach 0.25' for the GHA of the Sun and 0.3' for that of the Moon. 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'."
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OK, so far so good. However, I still wasn't happy and wanted to know more about this v-correction thing. So I wrote an email to the UKHO (where the UK Nautical Almanac publishing team is hosted). This is what I wrote to them:

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Dear Madam or Sir,

I am aware of the explanation given in the Nautical Almanac under Accuracy, 24. Main Data.
However, I cannot understand why the Nautical Almanac ignores the v-correction for the Sun. The max. error of 0.25' corresponds to 15 seconds. The requirement when taking a sight is generally to work as accurately as possible and to the nearest second. All this accuracy in the beginning seems to be to no avail since the Nautical Almanac adds an imprecision of up to 15 seconds to it. Whenever I am getting close to the full hour, the inaccuracy comes in the moment I add the increment based on 15°/h. At the equator, this maximum error of 15 seconds corresponds to almost 4 nautical miles (using the average value of 15°/h). Why is this considered to be acceptable?
The accuracy could easily be improved by implementing a v-correction for the Sun, as it is done with the planets or the moon. The accuracy could be even further improved by giving a daily averaged v-correction as opposed to a three-day average.
Still, it is not done and I would really appreciate if you took the time to give the reason for omitting the v-correction in the Nautical Almanac.

For your efforts I like to thank you in advance already.
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After about a week, I received the following answer:
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Thank you for your e-mail of October 1 with the interesting question about the v-correction for the Sun in The Nautical Almanac (NA) and your subsequent suggestions.
First I must admit that the design and decisions for the choice of tabulating interval and the v and d corrections were made a very long time ago so I cannot give their reasoning. However, I can comment on what you have said and explain, perhaps more fully, the situation.
You state that you are aware of the explanation given in the NA under Accuracy. However, perhaps the description is not quite clear enough so that you don’t quite realise the implications of what is said.

When using tabular data to interpolate to a given time there are three places were inaccuracies arise. First there is the precision to which the tabular data is given, and for the NA tabular pages this 0.1 minutes of arc. The second is the number of quantities that must be added or subtracted to that tabular value to give the interpolated value. The third is the accuracy of each of the numbers to be added and subtracted.

The GHA of the Sun that is printed has been modified using knowledge of the hourly rate, thus there is “some v-correction” and thus the v-correction is not ignored. Thus this “adjusted” tabular value together with the fact that this reduces the number of quantities that are being added together means that the maximum error for the GHA of the Sun is 0.25 minutes of arc. I have not done the analysis myself, but as I understand it, “may reach” implies not often. I also understand that the largest inaccuracy does occur when you don’t need to interpolate and are using the hourly tabular values themselves.

Perhaps if you need the Sun more accurately then there is The Star Almanac for Land Surveyors. In the back there are monthly polynomial coefficients (5 for each month), which are accurate to 1 second of arc. Alternatively, if you are interested in astro-navigation, then there is our software package NavPac. The currently version NavPac 3.4 is soon to be replaced with a new more modern version for all customers who have already purchased version 3.4. All the details can be found on the HMNAO web site at http://astro.ukho.gov.uk/nao/navpac/index.html.
Your suggestions are interesting. Of course the NA as it is has a very fixed and traditional format. We will consider your suggestions with our joint colleagues and authors at the US Naval Observatory.

Yours sincerely
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First of all, I have to give the UKHO guys credit for taking the time to reply to my email. I actually thought they will simply ignore it (as the do with the v-correction of the Sun  ;-) )

Anyway, so what is the conclusion of all this? Is it that the v-correction is already built into the hourly tabulated GHA values? All right then, but if this was advantageous, why is this not done for all the planets but only the Sun? I also still have a problem to see why the resulting error due to the manipulation of the tabulated GHA values is so small. If you look in September and take a full hour value of the Sun and interpolate it for 60 minutes (i.e. you add 15° to it) and compare it with the tabulated value of the following hour you will get a difference of 0.3' So which is the more accurate value now? According to the email of the UKHO the interpolated value - do I understand that correctly?

This whole thing remains a mystery to me. I could imgaine that this whole effort of integrating the v-correction into the tabulated GHA is for the sake of converting longitude into time. Could that be the case? For this longitude into time calculation to be accurate, we actually need to divide the distance (longitude or GHA) by the actual speed of the Sun, which obviously is not constant. The solution by the Nautical Almanac is to keep the speed constant but to adjust the distance (GHA) so that the end result is fairly close to the proper calculation. Does that make sense...?

I am tempted to write back to the UKHO to ask them but I am not sure if I should do this to them as I can sense already some pain in the person writing back to me. I prefer to discuss this matter with people (like you guys in this forum) who also have a natural interest in exploring this thing and like to engage with this voluntarily. What is your advice in this regard?

By the way, I like last passage of the reply: "Your suggestions are interesting. Of course the NA as it is has a very fixed and traditional format. We will consider your suggestions with our joint colleagues and authors at the US Naval Observatory."    We all know what this actually means, don't we?  ;-)

Axcel