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    Baily's Beads and the lunar distance
    From: Brad Morris
    Date: 2017 Feb 8, 13:45 -0800

    The upcoming lunar eclipse has driven some media coverage, and with that, images of Baily's Beads.  The Baily's beads effect is a feature of total solar eclipses. As the moon "grazes" by the Sun during a solar eclipse, the rugged lunar limb topography allows beads of sunlight to shine through in some places, and not in others.  Take a moment to Google some images of Baily's Beads.

    Therefore, when a star is brought into contact with the limb, it may be shining through a deep valley or obscured by a high mountain.

    In order to get a sense of the magnitude of the issue, I find the highest mountain on the moon is Mons Huygens at 5.5 km tall.  The deepest crater is Aitken Basin, at 13 km deep.  Now I understand that these are not on the limb, nor next to each other, yet the difference will show an interesting figure of merit

    The delta is (5.5+13=)18.5 km.  We know the diameter of the moon to be 3474 km.  We also know the apparent diameter of the moon to be ~31 arcminutes.  Therefore, we have

    18.5km/3474km * 31 arcminutes 

    =0.165 arc minutes

    ~9.9 arc seconds

    The lunar distance we measure "could" be wrong by ~1.7 tenths!! 

    Again, this delta isn't necessarily on the limb.  In fact, Aitken Basin is on the far side of the moon, near the south pole.  So our error due to the same effect as Baily's Beads will be less.

    I would suggest, however, that the error isn't zero.  This should be leading advocates of the lunar distance to serve as an accurate method of arc calibration to pause.  Without due accommodation to the roughness of the limb at the point of contact, the distance measured will be slightly wrong.  As the intention of arc calibration is to wring out those last few tenths, the lunar distance may not be the best choice.

    For those of us hoping to accurately measure the lunar distance as a test of our sextant skills, we are certain to be disappointed with the final tenth or so, as the limb roughness continues to elude capture in the reduction.  

    The issue is further complicated by libration.  That is, the moon wobbles and does not always present precisely the same face to the earth.  The consequence of this is that the limb roughness changes as a function of the libration angle.  What once was a mountain in the limb may now be obscured by the lunar body itself.

    The entire surface of the moon has been mapped.  The libration angle is known. Yet I wonder if non computer driven lunar distance reductions will easily capture the effect. 

     It is certainly feasible for a computer driven reduction.  It would be fairly simple for a computer to determine the shape of the limb at the point of contact as a function of the surface topography and libration angle.  This will yield the precise theoretical SD at the point of contact, as well as a more accurate expression of the lunar distance.

    Brad

       
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