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    Re: Exercise Lunar Distance with Mercury
    From: George Huxtable
    Date: 2009 Sep 23, 18:30 +0100

    Frank wrote, in [9871]-
    
    "Mercury has a very small angular semi-diameter --about 5 seconds of arc 
    when favorably placed. Now, in a lunar observation with a planet that has a 
    discernible diameter, you have three choices: place the limb of the planet 
    (only one available) on the Moon's limb, place the geometric center of the 
    planet on the Moon's limb, or place the center of illumination on the Moon's 
    limb. The illuminated limb of Mercury and its geometric center would be 
    separated by about 5 seconds at a favorable appearance, while the center of 
    illumination would fall in between. It would rarely amount to a difference 
    greater than a few seconds of arc. In other words, this difference is safely 
    negligible.
    ===============
    
    George comments-
    
    Frank's conclusion about Mercury is correct, but the effects are even 
    smaller than he estimated, because Mercury can be observed only in such 
    special circumstances.
    
    Mercury will be seen only when, as in Jeremy's example, it is near maximum 
    elongation from the Sun; in this case, about 26� in angular separation. In 
    which case, its semidiameter will ALWAYS be somewhere near 3.3 arc-seconds. 
    And in those circumstances, it will ALWAYS be about half-illuminated, so the 
    centre-of-light of that D-shape will ALWAYS be displaced from the geometric 
    centre of the planet by a little more than 1 arc-second. And this 
    displacement will ALWAYS be in such a direction as to increase the apparent 
    lunar distance by that amount from its geometric value between centres, 
    which indeed will ALWAYS be measured from the near-limb of the Moon. And the 
    parallax of Mercury, under such conditions, will ALWAYS be somewhere near 8 
    arc-seconds, just a bit less than that of the Sun. There's so little room 
    for variation of these quantities, it's hardly worthwhile looking them up; 
    they can be taken for granted.
    
    Mercury no longer features in the Nautical Almanac, so it's impossible to 
    calculate lunar distance from that source (as Jeremy discovered). My 1864 
    Almanac, intended for astronomers as well as navigators, provided 
    predictions of Mercury's position, but I doubt if Mercury ever feartured in 
    the lunar-distance predictions, then.
    
    Antoine seems to have the advantage of direct contact with the originators 
    of the Paris predictions who, to me, are no more than revered names in 
    Meeus. There's no difficulty, now, in calculating precise predictions of 
    lunar distance from Mercury, or anything else..
    
    ===================
    
    Anyway, it's perfectly true, as Frank wrote, that the phase effect on 
    observations of Mercury can be neglected; even at the high level of 
    mathematical precision at which Antoine likes to operate.
    
    Antoine asked, in [9876]-
    
    "May I ask one question here regarding Lunars with "significantly phase 
    angled planets" (i.e. Venus and Mercury)? Since phase angle can be fully 
    accounted for in Body Coordinates Computation, what would you think of 
    shooting such "Inferior Planets Lunars" through observing this Planet 
    through carefully selecting one of your "opaque" glasses on your sextant 
    (i.e. brightness reducing glass, sorry I do not remember the name of such 
    glasses in English, and I think that you would select the one with the least 
    efficiency if you have one installed), so that it would reduce the ?Planet 
    to a "light pinpoint" ?"
    
    I suggest the words he is searching for refer to the sextant's lighter-toned 
    shades. But really, is it possible, with the sort of scope to be found on a 
    sextant, to discern Mercury as any more than a point of light, anyway? To do 
    better must call for remarkably acute vision. But, assuming that it's 
    possible, is the use of a shade going to reduce it from a finite size to a 
    point-source? I would have doubts about that.
    
    Anyway, it seems to me that whether Mercury presents itself to the eye as a 
    discernable half-disc or not, the natural thing to do is to place it so that 
    the centre-of-light straddles the Moon's limb. Would it be realistic to 
    expect anything else?
    
    George.
    
    contact George Huxtable, at  george{at}hux.me.uk
    or at +44 1865 820222 (from UK, 01865 820222)
    or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
    
    
    
    
    
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