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Re: Star-star distances for arc error
From: Frank Reed
Date: 2009 Jun 26, 21:05 -0700
From: Frank Reed
Date: 2009 Jun 26, 21:05 -0700
George H, you wrote: "but one of its serious weaknesses is in that star-star distance table, appendix G." Well, correct me if I'm wrong, but couldn't those weaknesses in his appendix G be addressed very simply? You're quite correct to point out the errors, of course. But calling them "serious weaknesses" when there are simple solutions strikes me as a bit of an exaggeration. The two issues are: Problem #1: "the star-star distances would only be correct during the rising part of path of star 1, to the Eastwards". OK. So can't he just include a line in the instructions (and perhaps at the bottom of each page) saying exactly that? Problem #2: "No account has been taken of annual aberration, which varies cyclically over the year, and in the worst case can amount to errors in star-star angle amounting to 40 arc-seconds". OK, but the error should be no more than 20 arcseconds if the mean distance has been used (I haven't checked to see whether he did that or not). In any case, to correct for that, all he needs is a short table, maybe on the right margin, giving the change in each distance for each month of the year. Something like: Jan -0.3, Feb -0.2, Mar -0.2, Apr -0.1, etc. Those are simple solutions to relatively minor problems. It's a shame that they weren't caught in proofreading but it would take no more than an index card sized "errata" sheet to cover those particular items (I do understand that there are some other small errors, as in any book published in a finite amount of time). And you wrote: "So, anyone wishing to make high-precision checks on a sextant using star-star distances would be well advised to calculate, and correct for, the refractions from first principles" Yes, of course, that's one solution. Or they could just write in by hand the extremely brief monthly correction table (for each pair) as noted above for Problem #2 and take note of the special instructions for dealing with Problem #1. And George, you concluded: "rather than follow Frank's recommendation of Table G in Karl's book. I wonder if Frank has ever tried it?" I'm sorry my post confused you, George. If you re-read it, I did not issue a "recommendation" to USE those tables. I merely pointed out there existence in a popular new book. Douglas Denny had asserted repeatedly that using star-star distances to measure arc error was not possible. You read those posts, too. I suggested that Douglas might want to "take a peek" at those tables in John Karl's book. My point was to persuade him, just maybe, that he needed to re-think his certainty that such observations were worthless. Do you understand now?? So how should you clear star-star distances? One way would be to make those small corrections to the tables in John Karl's book as noted above. But probably the easiest way for a modern observer is with a spreadsheet or a purpose-built piece of software. You calculate refraction for each star as exactly as possible based on its altitude (since this is a "backyard" observation the altitudes would presumably be calculated from the observer's position and the GMT and date of the sight) and then you do the usual spherical trig to get the correct apparent distance. Compare that with the observed distance and you're done. No problem. BUT here's a fun trick (that started this thread): for stars above 45 degrees altitude (about one-third of the usable distances at any moment), the refraction in the star-star distances does not change. The refraction is directly proportional to the distance. All of the constellations above 45 degrees shrink proportionately by a factor of just about 1.00034. Even if you don't do any calculations this way, this refractional morsel is also great for planning a round of sights because you know in advance that you don't have to record the time since the refracted distances won't change by more than about 0.1 minutes of arc (until one of the stars is below 45 degrees). -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---