A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2016 Jun 20, 00:13 -0700
To Frank, thanks for all your explanations, references and details , including your very last post to Sean.
To Dave, thanks also for your added reference to the Chauvenet's Formulae. I think that I have already downloaded his superb Compendium a few years back, and certainly I have reworked his examples when I tackled Lunars through an entirely new home made algorithm, which by the way, fully matches Frank's On Line Calculator results (if and when we include oblateness, yes !!! , as earlier addressed in depth in NavList posts exchanged with Frank @ 6 years ago) and is also fully fit for occultations/grazing occultations as well as for solar eclipses first/last/grazing contacts.
It is also interesting to see that in some cases - especially for occultations/Solar Eclipses close to grazing occultations/Eclipses - or even for short distances Lunars (say less than @ 5°) the apparent distances between bodies may not vary linearly [at all] with time. This feature may render them tricky to accurately solve. Starting from previous trend you can no longer accurately predict the subsequent topographic distances between bodies limbs. In other words you can no longer use the "approximation of the slope of the topocentric change in distance" as described by Sean. The "trial and error method" using Frank's On-Line Calculator ("we can calculate the perfect topocentric distances using something like my web app. You do this by entering the coordinates for your position (as near as you know it) and then you enter an observed lunar distance and by trial and error you find the distance that gives a perfect result.") shows that the "perfect result" distances no longer vary linearly with time. This definite non linear trend is best ascertained when we plot on paper the Distances vs. Times as Sean did it.
To Andrés, my signature is only a "[archaic] hand made selfie" :-)
Antoine M. "Kermit" Couëtte