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    Re: Sun Moon Lunars to 155 degrees
    From: Antoine Couëtte
    Date: 2010 Apr 2, 10:46 -0700

    Dear Peter,

    When clearing Lunars, two effects can sometimes be significant and each of them can independently affect the resulting cleared Lunar distance by at least 0.1'.


    ADDITIONNAL PARALLAX CORRECTION RELATED TO THE FLATTENING OF THE EARTH

    This first effect concerns a "refined "computation the parallax only significant and therefore only necessary for close bodies, i.e. only for the MOON on a practical standpoint for us.

    Since the EARTH Flattening is equal to about 1/293, the distance of the sea sailing Observer's eye to the center of the Earth is not constant and is a function of the ABSOLUTE VALUE of the Observer's Latitude.

    With parallaxes exceeding 60' for the Moon, it is easy to see that even if you compute it from a mean value of the Earth Radius - not always the case in standard Moon height correction Tables - the remaining Moon parallax correction still unaccounted for might reach 0.1' in extreme cases.

    You can even easily check that even for the most accurate standard Tables, " half value of 60' divided by 293 " just reaches the value of 0.1 ' . For Tables computed with either Equatorial or Polar radius, just double the correction hereabove in extreme cases.

    If you use "standard" Tables which do not call for the Observer's Latitude, 2 conditions must be simultaneously fulfilled for such "extreme cases" to happen :

    - The Observer's Latitude absolute value must be as far as possible from the Latitude corresponding to the Radius Value used in the Table, AND

    - The Moon apparent altitude must be low. 1st HINT ! Even for a 15° Moon apparent altitude - a value for which it is customary to consider that actual Refraction may no longer "run out of computation control" as it sometimes happens for lower altitudes - such a Flattening effect may still be of importance since Cos 15° is very close to unit value : 0.967 ...


    So, and just for this reason, we definitely should expect that any "accurate" Lunar Clearing method was/is to take in account the Observer's Latitude one way or the other.


    ADDITIONNAL EFFECT DUE TO (DIFFERENTIAL) REFRACTION WHICH DISTORTS THE SHAPE OF THE SUN AND OF THE MOON

    No lenghty explanations here : just watch the rising or setting SUN.

    One way of computing this effect is to approximate the SUN/MOON shape into an exact ellipse. Frank himself indicated here a few months ago that this method is covered somewhere in one of the CHAUVENET's Treaties and he also indicated that this computation method is sufficiently accurate for our purposes.

    The effect of such diffrential refraction is called "Oblateness" by reference to the appreciably oval shape of Sun and Moon when close to the Horizon. 2 nd HINT ! This effect will be most important when refraction is important and therefore somewhat "unpredictable". However there should not be a reason not to take this effect in account if you can do it.

    And as regards Lunars with one of the bodies low on the horizon, "better a Lunar with a Low Altitude Body than no Lunar at all". Certainly this is what Captain Cook and M. Bayly decided on that day of AUG 04th, 1773 ...


    AS A SUMMARY

    ... both Flattening and Oblateness effects can sometimes even out or simply add on top of each other. This is why their combined effects can exceed 0.2' , translating into and up to some 6' value on the Observer's Longitude determined through a Lunar. See the earlier verification carried out earlier to-day thank to Frank's On Line Computer.


    LAST BUT NOT LEAST

    If you happen to play with Lunar Occultations in addition to conventional Lunars, then better definitely take both effects in account. And Lunar Occcultations it will DEFINITELY improve your computing skills.

    ... Hope it helps


    Best Regards and Good Luck to you !!!


    Happy Easter to you Peter and to your Family.

    Antoine M. "Kermit" Couëtte
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