NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Frank Reed
Date: 2024 Jan 28, 12:16 -0800
Modris,
Yes, your analysis is very convincing ...under those somewhat extreme case conditions. The key property of this error is that it's proportional to the left-right offset squared. For an angular separation of 90° (to be specific, let's call it a 90° lunar), the error (or gap) in minutes of arc is equal to M² / 3438 where M is the left-right offset, the distance in minutes of arc away from the center of the field of view. If I can sweep the Moon left or right by one full degree from the center (really the "center of collimation"), then that gap is just about 1.0'. That's visible and, as you say, easy to detect.
But suppose I can only sweep half as far, then the gap is quadratically smaller ...four times smaller, only 0.25'. Or imagine a Full Moon with Jupiter just resting perfectly-split on the limb when dead-center. If I sweep the pair left until the trailing limb of the Moon is exactly dead-center, and then sweep it back so the leading limb is exactly dead-center, that change yields a maximum gap of only about a tenth of a minute of arc. Quite difficult to detect. But, yes, probably easier than I implied! :)
Frank Reed