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I wrote-

>> I am puzzled about the value Bill has quoted for the angular speed of the
>> Moon across the sky, at 14d 19'. Where did it come from? The Moon's motion
>> fluctuates a lot, but I would have thought a more representative value
>> would be about 14 degrees 30'.

and Bill replied-

>Thanks for your input George.  If you look up the Moon in the almanac
>Increments and Corrections Table (59 minutes 60 seconds) it gives the value
>of 14d 19'.  I also recall it from certain texts.

============

Ah! Now I see what Bill is getting wrong. There are two quantities to add
when obtaining the GHA of the Moon from the almanac, if you need it at a
Greenwich Time that differs from an exact whole hour.

Look at any daily page in the almanac, and at each whole hour is given the
Moon's GHA and a quantity "v". You will notice that v is always positive
and varies considerably over the month, and from one month to another,
between about 3 and about 16, limits which can alter from one year to
another. These values of v relate to changes in the speed of the moon
across the sky, relative to the star background. You might take an average
value of v to be about 10. Let's work using that assumption.

With that in mind, go back to the increments page for 59 minutes and 60
seconds. The Moon's increase in GHA, from the value for the previous exact
hour, is obtained by adding the increment (exactly as quoted by Bill) of
14deg 19.0', and the correction, which for our assumed v of 10.0 comes to
9.9'. So the change in the Moon's GHA in that hour would be 14 deg 19.0' +
9.9', or 14 deg 28.9', rather close to the value that I suggested earlier,
for the Moon's average speed in GHA, of 14 deg 30'.

I hope it has now become clear how the compilers of the almanac have
designed their tables. They were free to choose an arbitrary value for the
Moon's basic speed, on which to base the increments table, and then this
required a corresponding range of v values to allow for the changes in that
Moon speed in the corrections. And what they have done is to choose a basic
speed of 14deg 19.0' per hour, a speed which even in the most extreme
astronomical situation they know the Moon will always exceed. This then
allows the v correction always to be a positive one, so the end result is
worked always by addition and not subtraction. It fits in with the notion
that navigators do not understand how to subtract.

So Bill's presumed Moon speed of 14deg 19' does not represent in any way
the actual speed of the Moon across the sky; just that it's a minimum value
that we can be sure the Moon will always exceed.

By the way, when the speed of the Moon in GHA across the sky is at a
minimum, this implies that the backward motion of the Moon, the speed that
it's moving against the background of stars (and everything else) is at a
maximum. That backward motion gives rise to the changing lunar distance,
which we measure to find our Greenwich Time.

GHA corrections for other bodies:

By definition, the Mean Sun moves at exactly 15 degrees per hour. However,
the apparent Sun (which the predictions are for) has a marginally different
speed, which builds up to give the Equation of Time. The almanac
predictions for the Sun do not provide a v correction term, so that in
interpolating Sun GHA between whole hours, such changes in speed are
ignored, and a speed of 15 deg per hour is assumed.. To minimise the effect
of this approximation, Sun GHAs in the main body of the almanac have been
"tinkered with" by up to 0.15', before the final rounding to the nearest
0.1'.

Most planets move across the sky at a speed close to (and greater than)
that of the Sun, in which case a small positive value of v, applied to the
nominal Sun motion of 15 deg per hour, gives rise to an added correction.
Venus frequently shows a retrograde motion in the sky, which gives rise to
a negative v correction, so in the Venus case navigators need to apply any
subtractional ability they may possess.

The motion in GHA of stars is closely tied to that of Aries, slightly
faster than the Sun at 15deg 02.46' per hour (relating to the shorter
Sidereal day), and quite unvarying. So a special table of increments is
provided for Aries, and no question arises about any v correction.

George.

================================================================
contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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