A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2015 May 15, 08:21 -0700
Stan, you quoted the old explanation section from the NA:
"The corrections given on page A2, and on the bookmark, are mean values applicable in the case of Venus only when the Sun is below the horizon. For daylight observations of Venus the observed values of H and theta should be used to calculate the correction directly; the term - k cos (theta) is positive when the Sun is lower than Venus, zero when they have the same altitude, and negative when the Sun is higher."
I am convinced now that their former system was nonsense. The idea that you could have a "general" value for the phase correction for normal sights is ridiculous. Further, in the directions for daylight observations, the claim that k·cos(theta) is zero when the Sun and Venus have the same altitude is simply false. This is a case of the sort of "muddled" thinking that used to screw up discussions of star-star distances. I'm sure some of you remember the old tale claiming that the angular distance between two stars is unaffected by refraction when they are at the same altitude. Oh yeah?? What if both stars are 45° high and on opposite azimuths? And that's only the most extreme case. The same problem applies to the phase correction. Clearly, the simplest solution to this error (and that's what it was --an error on the part of the almanac offices) was to replace the true position of Venus with the phase-adjusted position of Venus in the daily GHA and Dec data (which, we now know, thanks to Catherine Hohenkerk, happened thirty long years ago...). Personally, I think they should have admitted the error and dropped the phase correction entirely. Even the USNO online nautical almanac data skips the phase adjustment. That's a better choice. The official Nautical Almanac is inferior in this case.
It's all minor, of course. If we're to believe some claims (which Gary LaPook re-posted recently), the standard deviation of celestial altitude observations is 1.5 minutes of arc, in which case the phase of Venus would always be lost in the noise. I consider those claims over-blown, and in good "normal" conditions, the errors in celestial altitudes are +/-0.5' or so (in the 1 s.d. sense) and in excellent conditions a little better. Naturally when conditions are anything but good, the phase of Venus is completely irrelevant. If your height of eye is varying in an unpredictable way from 25 to 36 feet (unpleasant but not uncommon), then you automatically get an additional random error of a minute of arc.