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George

Good point.

I have only done a few moon shots to date and did not notice the bigger
picture, that v could be as large as it is.  Most likely I focused on the
the Moon adjustments not usual for other reductions. I do recall reading the
Sun and stars have no v, the almanac adjusts for the Sun's v in the GHA, and
that v is always positive (except for Venus).  So it would make sense they
use the lower limit for the Moon if plausible to keep v positive.  Frankly,
the magnitude of the Moon's v surprised me when I perused it in the almanac.

I recollect there are other planets that exhibit retrograde motion.  If my
recollection is correct, may I safely assume they are not navigational
planets?

> It fits in with the notion
> that navigators do not understand how to subtract.

I am puzzled about the notion George has suggested that navigators do not
understand how to subtract. Where did it come from? 

Than you for your thorough explanation, and the imbedded wit that makes a
the reread a enjoyable.

Bill



> 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.


> 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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