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Peter Fogg asked-

>Earlier I had found a slightly different time. On checking I found that I
>had used the data from 2003 instead of the year before, which prompted the
>question : what changes the sun's position slightly year to year? One
>possible answer is that our convention of adding a day every 4 years doesn't
>exactly account for the time it takes the earth to orbit the sun. Are there
>others?

Not exactly, Peter, but you are close. It is BECAUSE that extra quarter of
a day is required: not because the quarter day isn't quite correct. So each
year starts (roughly) a quarter-day earlier than the previous one, in terms
of the Earth's progress round its orbit. This is because a normal year is
only 365 days, although the Earth takes roughly 365 and-a-quarter to get
back to where it started in its path around the Sun. So the vernal equinox
(for example), when the Sun dec passes through zero, occurs a quarter-day
later in time from one year to the next. This doesn't build up for long,
because it's corrected by a leap-year, one year in four, to bring it back
again.

So if you were feeling particularly mean, you could keep four years of
almanacs, and use them again and again, at four-year intervals (for Sun
predictions only, not Moon or planets). This would be sufficiently accurate
that I doubt if a navigator would notice the accumulating error over 20
years. The residual error is because the year is not 365.25, but 365.2422
days (the discrepancy that Peter was referring to).

Early navigators went by a set of declination tables that were the same for
each year, and accepted the inaccuracy. It was Pedro Nunez in about 1530
who recognised that he could make a more accurate declination table for
leap years, another for leap years +1, leap years +2, and leap years +3,
and that would be all that was needed, for many years. They became
semi-permanent. Odd things happened at the turn of those centuries when a
leap year was omitted, however.

There are other factors that vary slightly with time, such as the
eccentricity of the Earth's orbit, its date of perihelion, its changing
tilt, but these changes are so slow that navigators (but not astronomers)
can neglect them.
>
>Another thing I noticed is that on the day in question, Sat 20 Jul 2002, the
>v correction is zero, and that with the sun it never becomes a big figure,
>unlike the moon, for example.

On that date, the equation of time is changing very slowly, and within a
few days it pauses and then start to change the other way. So around that
date, the time from one noon-by-the-Sun to the next is very nearly 24
hours. The v correction allows for deviations of the rate-of-change of GHA,
from some nominal value on which the tables are based, to make
interpolation easy. The Sun interpolation table in the Nautical Almanac is
based on mean time. A day, from Sun-noon to Sun-noon, never deviates by
more than 30 seconds from its nominal length of 24 hours, and around 20
July, by much less.

For the Sun, such v corrections are always so small that the Nautical
Almanac can ignore them altogether, but adjusts the values in the
declinaton table to minimise the effect of doing so. Other bodies, the
planets, and especially the Moon, show a much more irregular motion across
the sky, and so the v corrections become much larger and more important.

George.

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