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    Re: About Lunars, part 4
    From: George Huxtable
    Date: 2002 Mar 20, 21:37 +0000

    Arthur Pearson said, about corrections for Moon semidiameter-
    >By the
    >way, I have found the formula that Bruce supplied (which calculates
    >augmented SD directly from HP and apparent altitude) more satisfactory
    >than the adjustment multiplier to SD that George supplied.
    Response from George-
    I am trying to understand where Arthur is finding a difficulty here. I
    presume he is referring to "about lunars" part 1 in which I said-
    >For the semidiameter of the Sun, you can take the daily figure (in
    >minutes) >from the almanac, and convert to degrees as required. For the
    >Moon >semidiameter, make a very rough guess at GMT (within a couple of
    >hours will >do), look up Moon's Horizontal Parallax (HP), tabulated each
    >hour in the >Nautical Almanac, convert to degrees, and multiply it by
    >.2724. Then multiply >by (1 + Sin (alt)/55), which is the "augmentation of
    >Moon's semidiameter". >This is better than simply using a tabulated value
    >for the Moon's >semidiameter.
    For the Moon, then, this was a multiplying adjustment to be made to the
    Moon's horizontal parallax, NOT to (as Arthur said) the semidiameter. The
    result is the Moon's augmented semidiameter.
    What I should have pointed out, perhaps, is that if you convert the Moon's
    HP to degrees, as I suggested, then the resulting semidiameter will be in
    degrees also, which is most suitable for those who use a calculator or
    computer. If you leave the HP in minutes, the semidiameter will be in
    minutes, which is most suitable for those doing hand-calculation using
    The way Bruce Stark handles the same calculation is marginally different. I
    quote from his email dated 28 Feb.-
    >Table 4, augmented semidiameter, is an example. The Almanac gives the moon's
    >HP to the nearest 0.'1 every hour. The moon's SD has to be in the same ratio
    >to HP as her diameter is to the earth's equatorial diameter: 0.2725. By using
    >HP to inter table 4 you get SD to the nearest 0.'03, and get it for the hour,
    >not just the day's average.
    >Rather than have a separate table for augmentation, which would mean and
    >extra step in the calculation, augmentation is built in to the values in
    >table 4. As I expect you know, augmentation is zero when the moon's on the
    >horizon, and 100% when she's overhead. It's a matter of distance. On the
    >horizon you see her from the distance her center is from the center of the
    >earth. Overhead you see her from that distance shortened by half the diameter
    >of the earth, so she looks bigger.
    >She looks bigger according to the ratio of her distance from the earth's
    >center to her distance from the earth's surface. That ratio is the cosecant
    >of her HP. You may want to make a sketch to see why. And in case you don't
    >deal in cosecants, the ratio is the inverse of the sine of HP.
    >As the moon rises from the horizon her augmentation increases as the sine of
    >her altitude. So the formula I used to make table 4 is:
    >(0.2725 HP)/(1-sin HP sin altitude)
    >In case that doesn't show up on your screen in understandable form, here it
    >is in words: Take 0.2725 of HP and divide it by unity less the product of the
    >sine of HP and the sine of altitude.
    Although the expressions used by me and by Bruce look slightly different,
    they turn out to be almost equivalent, and give, as near as dammit, the
    same answer for Moon semidiameter. So I am surprised that Arthur is able to
    distinguish between them in any way. Perhaps he will explain further.
    In his tables, Bruce has implemented his expression as an easy look-up in
    his two-page Table 4. This requires input of Moon HP and Moon altitude and
    provides Moon augmented semidiameter.
    Bruce's tables appear to allow for all the corrections that might make a
    perceptible change, omitting only the reduction of the Moon's HP resulting
    from the ellipsoidal shape of the Earth. This will in general be no greater
    than .17 minutes, so has no great significance.
    If I haven't answered Arthur's problem in this mailing I hope he will
    explain further. It's good to hear that he plans to check over Chuck's
    observations. Sounds like a self-help sub-group may be materialising among
    the lunatics of this list.
    If any list members are struggling with the concepts or the numbers, do
    explain where your problem lies and I (with Bruce, I hope) will help where
    we can.
    George Huxtable.
    George Huxtable, 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    Tel. 01865 820222 or (int.) +44 1865 820222.

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