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I wrote previously:
"Yes, I agree. That's nearly 2 seconds of arc difference. Insignificant for anything remotely practical, yet still a somewhat bigger difference than it should be. I'm not sure if the cause is the bad luck of round-off in a specific case or something more interesting."

As it happens, it was nothing interesting and easy to modify. The discrepancies you saw, as large as 2 seconds of arc, have now been reduced again to the expected levels --usually about 0.5 seconds of arc. This has no direct impact on anything (half a SECOND of arc is a dozen times smaller than the usual 0.1 minute minimum reading on most sextants), but it does reduce occasional round-off differences when distances are tabulated to tenths of minutes.

In another post, Dave, you wrote:
"Modern astrometry is done routinely at the micro arcsecond level."

SOME modern astrometry, yes, positions of stars, but sure as hell not the position of the Moon! :) Again, a micro arcsecond at the distance of the Moon is equivalent to a grain of moondust 2 millimeters across. Even setting that aside, if you want to start calculating angles between stars at the micro arcsecond level, you'll have to include some significant corrections. The gravitational deflection of starlight by the Sun affects the whole sky at that level, and even the deflection by Jupiter and Saturn become significant factors. I'm not saying you SHOULD do these things! I'm only pointing out that there's no meaning to those additional digits unless you include such factors.

And, Dave, you wrote:
"The additional places are essentially 'free' in modern computers, and are correct, so why not?"

Maybe, but this requires a very specific meaning of "correct". The digits can be correct in the narrow sense that they reflect the correct application of a specific calculational algorithm. But those are not significant digits. They have no meaning, EXCEPT in the very narrow sense of testing whether two people, independently coding an identical algorithm are achieving the same coding result (either both correctly or both incorrectly). If I walk across the diagonal of a square field that has sides each 100 meters across, I can say that I walked 141.4 meters, and no one would be too concerned about that specific number since it's quite conceivable that all distances in the problem could be measured to that accuracy. But if I claim that the distance was 141421356 microns, and after all, linear distances are routinely measured in microns, I'm sure you would call me out for calculating something that has no measurable significance. The extra digits can indeed provide clues to my "calculational algorithm" (which, in this case, is obvious anyway), but that's the only sense in which they're "correct".

-FER

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