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    Moon corrections: how computation order affects the result
    From: Eric Fernandez
    Date: 2020 Aug 31, 01:43 -0700

    Hi,

    I have a question regarding the computation of the Moon altitude corrections.

    To start with, I used the excellent guide from Henning Umland available at celnav.de. One thing that picked my curiosity is the way he explains the computation of the moon corrections, and this is where it changes a bit from the usual way.

    He writes that without augmentation correction, you calculate H2 = Hs - IE - DIP, then H3 = H2 - refraction. Then SD geo = 0.2725 * cos(HP) and parallax P = HP * cos(H3). This is where there is a slight variation from the procedure indicated in the Nautical Almanach, where the write Parallax is calculated from H2, that is before refraction correction. That said, this does not lead to a big difference.

    However, he explains that there is also another correction to take into account for the moon: the augmentation, due to the difference between geo- and topocentric SDs. However, the process is not additive but serialised: First he calculates H3 = Hs + IC - DIP - refraction as before. Then SD topo = 0.2725 * cos (HP) * (1 + sin(HP) * sin(H3)). He then calculates H4 = H3 + SDtopo. Finally, he adds parallax, but this is calculated from H4: P = HP * cos(H4). This is where it is interesting: since he adds SD before calculating Parallax, P is slightly lower than for an additive method.

    For instance, using H2 = 88° and HP = 61.5, I get these corrections (in minutes):

    • wihtout augmentation: 18.87
    • with augmentation, but using an additive method: 19.17 (indeed augmentation tables in Norie's tables indicate a 0.3' value at H=88°, so this is consistant with the previous calculation)
    • with augmentation, but using Umland's method, serialling additions: 18.87. Actually, because Parallax is reduced, we erase the value for augmentation.

    I looked into other methods, such as Capt Khan's officer guide or Norie's total correction tables, and they all add the augmentation after parallax. For instance, Norie's table indicates a correction of (9.4 + 9.8) for dip which is indeed 19.2.

    Therefore, which is the correct method?

       
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