NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Star-star distances for arc error
From: Frank Reed
Date: 2009 Jun 19, 19:38 -0700
From: Frank Reed
Date: 2009 Jun 19, 19:38 -0700
Douglas you wrote: "I've done this. It provides a method of checking a sextant but is not easy with accuracy unless you have some clamping system to hold the sextant still and be able to rotate the sextant into alignment." With a little practice, it's not hard, but I agree that you can find yourself in some awkward positions. It's good practice for lunars, too. Not that lunars are for everybody, but some people get a kick out of shooting them. And then you wrote: "If you use horizontal angles with stars approximately of the same declination the refraction element is negligable if they are above say 30 degrees." No, that just isn't right. First, you say 'same declination'. I assume that this was just a "typo" and you meant altitudes. No problem. Even so, then your claim would be that refraction is negligible for stars at the same altitude (above 30 degrees). This is a "navigation urban legend". It isn't true, but it has even been published in some recent editions of Bowditch and other places where the authors really should know better. The angular distances between stars at the same altitude are indeed affected by refraction. Consider for example, the case of two stars at 45 degrees altitude on opposite sides of the sky. Let's assume that the angle between them is exactly 90 degrees in the absence of refraction. Now, refraction lifts BOTH stars by about 1'. They're pushed towards each other, so the observed angular distance would be just about 89d 58' which is a difference that would be measurable even with a fairly bad sextant. Now consider a case of two pairs of stars: two are at 45 degrees altitude separated by 20 degrees more or less horizontally. Another pair is located with a more or less vertical separation, one at 45 degrees altitude, the other at 65 degrees altitude. What I was saying my previous message is that you can calculate (clear) the effect of refraction in these cases, and indeed in any case where both objects are above 45 degrees, simply by multiplying the observed distance by 1.00034. So in these pairs, one where the stars are horizontally placed and the other in which they're vertically placed, the effect of refraction is the same. Horizontal relative orientation of the two stars makes no difference. The idea that horizontal placement of the stars eliminates the effect of reftraction is most likely due to a mistaken extrapolation from one extreme case (which is never observable in practice but worth understanding in principle). Imagine two stars right on the horizon (can't see stars that low, but let's ignore that for the moment). The effect of refraction is to lift the stars towards the zenith. There is no component in azimuth. Now near the horizon the lines of constant azimuth show no convergence so if stars very close to the horizon are shifted towards the zenith, the angle between them will hardly change at all. So here we have a case where the distances between stars at the same altitude (zero) are unaffected by refraction. It seems likely that this case was mistakenly extrapolated decades ago leading to the mistaken notion that the angles between stars at ANY altitude are unaffected if the stars are at the same altitude. And again, this just isn't true. "Most sextants only read with accuracy to about a half of a minute of arc anyway." Accuracy in sextants depends on many factors, but I have seen plenty of folks get significantly better accuracy than that with a decent metal sextant (so long as it's equipped with a medium power telescope, e.g. 7x). And I myself generally get 0.25' accuracy in lunars on individual sights or 0.1' when four are averaged. But none of this will work unless you've checked for arc error (and that's the motivation for measuring star-star distances for some people). Arc error is generally a fixed error and therefore it is just as easy to correct for it as it is to correct for index error. And you concluded: "Star distances can be calculated from declinations/ RA (or hour angles) with simple spherical trig." Of course. And I probably should have outlined the exact calculation for those who like setting things up in spreadsheets and in their own software, so if anybody is uncertain on those details, let me know. But neat little rules like the one I described earlier have another interesting use. Knowing that the distances between all stars change by the same percentage amount when they're above 45 degrees gives us useful planning information. As long as you're sure the altitudes above 45, you don't have to record any other information. Local time doesn't matter. The actual altitudes of the stars don't matter. You can just measure the distance at your leisure and the clearing process will not care about the details. Just multiply by 1.00034 and you're done. -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---