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    Re: Exercise Lunar Distance with Mercury
    From: George Huxtable
    Date: 2009 Sep 23, 20:11 +0100

    On second thoughts, I wish to comment here, and qualify my recent message 
    [9880], in which I wrote-
    
    "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."
    
    On second thiughts, it now seems to me that although what I wrote there is 
    indeed true of observations from a highish latitude, such as mine at 51�N, 
    it isn't so true everywhere. Less true in and near the tropics, anyway, when 
    the Sun, and Mercury, tend to rise and set nearly vertically.
    
    From my latitude, sightings of Mercury are only fleeting, for a very few 
    days around maximum elongation, when the planet can be seen faintly 
    twinkling near the horizon, and there's still a bit of light in the sky from 
    the Sun, below the horizon.
    
    The difference is this. In the tropics, the Sun, and anything else on or 
    near the Ecliptic including Mercury, rises and sets nearly vertically, its 
    altitude changing at the rate the Earth spins, of 15� per hour. So that when 
    Mercury's light starts to dim in the murk near the horizon, at an altitude 
    of 5� or so, the sky can be well out of astronomical twilight, even if the 
    elongation is as little as 15� or so. So Mercury will be visible above the 
    horizon for a rather larger fraction of its orbit that I assumed.
    
    On the other hand, from my latitude, the motion of the Sun (etc) when near 
    the horizon, is never much greater than 9� per hour, (and usually rather 
    less) because its path is always tilted so far off the vertical. Then, to 
    achieve a vertical separation of 15� between the altitudes of Mercury and 
    the Sun, for clear viewing against a dark background, calls for an 
    elongation between them of around 25�, nearly the maximum possible.
    
    My last posting didn't allow for the extra tolerance, in seeing Mercury from 
    low latitudes. In those circumstances, the range of possible values of 
    semidiameter, phase allowance, parallax, are rather less tightly constrained 
    than I implied. My view was a bit parochial. Sorry about that.
    
    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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