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    Re: DSLR Venus Lunar
    From: George Huxtable
    Date: 2010 Sep 16, 18:29 +0100

    Just as Kermit says-
    "The main point actually is : where exactly does the "center of gravity of 
    a planet brightness" lie relatively to its center of geometric figure ?"
    I can find no mention, in chapter 41 of my edition of Meeus, to the point 
    on the axis of symmetry that bisects the two edges of the lit region, 
    corresponsing to Antoines "point P". I think it must have been dropped. 
    Perhaps Antoine will quote Meeus' very words on that matter.
    To me, taking that point to be the apparent centre-of-light seems 
    implausible. If the distribution of light was a uniform lit rectangle, on 
    that axis, between those limits, it would then be expected to show a 
    centre-of light at point P. Is Antoine asking us to believe that it makes 
    no difference at all, to the apparent centre, if the tapered ends of that 
    light distribution are bent around in a pair of curved horns? I don't 
    accept that. In my view, the centre of gravity of the lit crescent is a 
    much more plausinle model. Not that it matters much, in practice, the 
    difference being no more than a few arc-seconds. But we might as well get 
    it right, as get it nearly-right.
    contact George Huxtable, at  george@hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    ----- Original Message ----- 
    From: "Antoine Couette" 
    Sent: Thursday, September 16, 2010 12:27 PM
    Subject: [NavList] Re: DSLR Venus Lunar
    Sep 16, 2010
    Dear George,
    In reference to your post published in [NavList 13881] :
    Excellent comments from you, once again and Thank You very much for them.
    The main point actually is : where exactly does the "center of gravity of a 
    planet brightness" lie relatively to its center of geometric figure ?
    Let us call "POINT P" the mid-point between the terminator and the outer 
    (circular) shape, on the symmetry axis of the apparent Planet. This point 
    well defined in Jean Meeus's ASTRONOMICAL ALGORITHMS book. (I own book SN 
    026287 Copyright 1991 with handwritten "Errata as of Dec 1993", and 
    apparently Chapter 40 of my copy bears the same title as Chapter 41 of your 
    later and presumably "more perfect" 1998 edition).
    Let us also call "POINT M" the point HALFWAY between the geometric center 
    of the planet and "POINT P".
    UP UNTIL THE MID 1980's, I was using "POINT M" to modelize the effect of 
    the Planetary phases. I had then performed the very same calculus 
    integration which you just mentioned. Its result showed that the 
    "barycenter of uniform brightness" is sufficiently close from "POINT M" in 
    all configurations, so that I could safely use "POINT M" instead of this 
    exact "barycenter of uniform light" without any appreciable error for my 
    purposes and accuracy criteria (all systematic computation errors to stay 
    below 6" on the final computed results).
    Pending extra investigation on additionnal dates which I have just started 
    to-day, I think that - on the ground of my Jul 26, 2007 example - Frank's 
    On Line Computer currently uses a "phase offset point" very close from 
    "POINT M" as defined here-above.
    I am also noticing that "POINT M" is very close from the Point you are 
    advocating in your last post: this is self explanatory because I performed 
    the same "surface integration" as the one you just mentionned.
    HOWEVER, a close study of some published Research on planetary photometry 
    data (somewhere in my many archives folders) convinced me to discard "POINT 
    M" and to use "POINT P" instead.
    To the best of my recollection, and in addition to pin-pointing the light 
    itensity / brightness of every pixel as seen from a human eye - how they 
    could do it then remains a mystery to me ... - such Research showed that 
    the IRRADIATION EFFECT had the result of bringing the actual "light 
    barycenter" away from the planet geometric center and that as a global 
    result the actual "light barycenter" was very close from "POINT P", 
    especially when seen from a small aperture optical device (Human eyes 
    and/or Sextants are certainly good examples for such devices), a result 
    which certainly challenges or at least questions the assertion that one 
    [should] " assume uniform brightness of the illuminated fraction ".
    Accordingly, in the past 25 YEARS I HAVE BEEN USING "POINT P" AS AN OFFSET 
    IMPORTANT NOTE : The choice of "POINT P" by preference to "POINT M" also 
    seems to be FULLY SUPPORTED by the Nautical Almanac.
    As an example, in the HMSO & US NAUTICAL ALMANAC for the YEAR 1982 on page 
    259 (EXPLANATION PART), the maximum Height correction for the phase of 
    Venus is listed as 0'5 for the period Jan. 1 until Feb.10
    For 1982 Jan 15, the apparent geocentric semi-diameter of Venus is 0'51, 
    which certainly shows that the height correction recommended aims to 
    correct for a visible "Light Gravity Center" which is "POINT P" and cannot 
    be "POINT M".
    1 - Hypotetical Recent discoveries - unknown to me - might have brought the 
    Planets "Light Gravity Center" away from "POINT P" (which I am using, and 
    which was used then - and still is ? - by the Nautical Almanac some 30 
    years ago) and towards the vicinity of "POINT M" (which Frank's In Line 
    Computer seems to be using).
    Whoever has information about such Hypotetical Recent Discoveries (or 
    precepts to use "POINT M" instead of "POINT P") I am currently unaware of, 
    will be most welcome to share this information with our NavList Group.
    If so, I will correct my own computations to make them more in line with 
    current computing practice, I will have become more knowledgeable and I am 
    thanking in advance whoever will shed additionnal light on this topic.
    2 - Thank you again for your contribution here George. I am also looking 
    forward to hear and read the viewpoint and feedback of Frank on this topic.
    Best Regards to all
    Antoine M. "Kermit" Couëtte
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