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    Re: Real accuracy of the method of lunar distances
    From: George Huxtable
    Date: 2004 Jan 6, 19:35 +0000

    Bill Noyce wrote-
    >I've been following the discussion of statistical tests with interest (and
    >not a lot of
    >understanding), but one statement of Jan Kalivoda's stood out:
    >> For lunars, PE of 20" times 4.5 gives 90" = approximately 180 seconds of
    >>time = approximately
    >> 45 minutes of longitude (the exact value depends on the actual velocity
    >>of the Moon in R.A.).
    >In fact, the actual value depends on the velocity of the apparent moon and
    >body in topocentric coordinates, not RA.  As George Huxtable has pointed
    >out, the rate of
    >change of an observed lunar distance can be surprisingly slow, due mostly
    >to refraction and
    >parallax.  My recollection is that it can be slow enough that a 90"
    >difference in observed
    >distance could correspond to over 300 seconds of time -- is that right, George?
    >        -- Bill
    Response from George-
    Yes, that can happen, particularly when the Moon is passing nearly overhead
    in the tropics. If the lunar distance is being measured to an object that
    is well away from the direction of the Moon's path from the sky, the
    apparent slowing of the lunar distance could be even worse. Measuring lunar
    distance to the Sun or a planet, rather than a star, slows the change of
    lunar distance a bit further still.
    Bill said that it was "due mostly to refraction and parallax", but in fact
    it's almost entirely due to the effect of parallax.
    A brief comment about analysis of a series of lunar-distance observations.
    When you do a statistical analysis of nearly-linear data, it's usually to
    deduce two quantities, slope and intercept. In the case of a plot of
    lunar-distance versus time, the slope is so badly affected by the effects
    of parallax etc that it's of little use in deriving a single lunar distance
    and a time from a set of multiple observations. You just take the slope as
    what it happens to be, and there's nothing useful to be derived from it.
    That's why I think this matter of statistical analysis has been given undue
    weight recently on this list. Averaging distances, and averaging times, is
    all that's really needed to produce a single effective lunar-distance at a
    single effective time.
    But much of that argument went above my head, and I may be misunderstanding
    I agree that plotting on a graph is useful to show up real outliers where
    something is seriously amiss, in which case a point might (with great care)
    be rejected.
    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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