NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Brad Morris
Date: 2016 Jun 20, 04:42 -0400
Hello Kermit
You wrote:
that the "perfect result" distances no longer vary linearly with time.
That statement astonished me at first. Does the moon not keep a constant orbital speed? What could possibly be the cause of this non-linearity in distances?
Thought 1) The rotation of the earth causes a change in the position of the observer, which causes a parallactic shift in observed position of the Moon and the grazing body. This, of course, occurs also when the lunar distance is large, but the perturbation is small. In the case of a small LD, the effect of this shift has a larger effect!
Thought 2) The position of all three objects is also shifting with time. The earth, the moon and the grazing body are all in motion. Since the earth and moon rotate about the barycenter, the grazing angle is not changing as if the earth was stationary and the moon was simply orbiting it. Thus, similar to above, this small effect may have large influence on a small LD.
I don't know if either of those thoughts are correct or wildly wrong. I accept, Kermit, your assertion that the LD is non-linear for small LD. What I'd like to know is why? And is it truly linear, even at larger LD?
Please educate me!
Brad
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 {at} 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 {at} 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
