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    Re: Real accuracy of the method of lunar distances
    From: George Huxtable
    Date: 2004 Jan 10, 00:45 +0000

    Jared said-
    
    >I think what you are trying to say, George, is that during a lunar sight
    >two parallax compensations must be made, not one. The first is the
    >constantly changing parallax caused by the terrestial observer rotating
    >[sic] under the moon. The second being the constantly changing parallax
    >between the moving moon and the celestial background.
    
    Well, no, that wasn't what I was trying to say. I'm not sure that I
    recognise the second term as any sort of parallax at all.
    
    The almanac predicts the direction of a line to the centre of the Moon from
    the centre of a supposedly-transparent Earth. The motion of that line is
    desperately complicated, because the Moon is pushed and pulled in its orbit
    by so many gravitational influences. Nevertheless, the almanac takes them
    all into account (or all that matter to a navigator). That gives the
    direction of the Moon from the Earth. The main term, of course, is the 360
    deg turn around the sky, once per (sidereal) month. There's no parallax
    involved, in any of this. I think this is the second term you refer to
    above.
    
    The parallax comes in because an observer is not at the centre of the
    Earth, but somewhere on its surface. If the Earth always presented the same
    face to the Moon (like the Moon does to the Earth) then for a fixed
    observer the parallax would be constant. It measures how far he is from the
    direct line between the two centres, and how much this offset affects the
    direction in which he sees the Moon because of that altered point-of-view.
    
    Because the Earth spins around, every observer will see a sort of "rocking"
    motion of the Moon against the background of stars, caused by his motion
    with the Earth, and the effect of parallax. As the Moon rises toward the
    East, it appears to be pushed down, (Eastwards in the sky, or away from the
    zenith) by about 1 deg. The amount of parallax varies through the day as
    cos alt, so when the Moon passes the meridian it's being pushed down
    somewhat less, to either North or South (away from the zenith anyway,
    depending on which side of the zenith it passes), and then the parallax
    increases again toward the West, pushing the Moon down about 1 deg
    westwards as it sets. If the Moon happens to pass through the observer's
    zenith then the observer is on a line between the two centres and the
    parallax is zero. You can see that in general, through the period between
    rising and setting, the Moon is being deflected less Easterly and more
    Westerly.
    
    This effect of parallax is superimposed on top of the normal motion of the
    Moon against the starry sky, and as that motion is always toward the East,
    you can see straightaway that the effect of the rocking due to parallax on
    the true motion of the Moon is always to make it appear less. Sometimes
    significantly so. In an extreme case, when the Moon passes overhead, it can
    roughly halve the true motion, so it's a very important effect.
    
    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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