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 25, 20:04 -0700
From: Frank Reed
Date: 2009 Jun 25, 20:04 -0700
Douglas, since you've decided to re-subscribe, I suppose I should reply to your recent posts. You had written previously: "Attempting to use star separations to try to determine scale accuracy for example would not be possible due to the variables in the measurements themselves - including the refraction component even if calculated." And I commented: "A sure indication that you have never tried it! " And you replied: "I have tried it and I don't rate it as practical." Sorry for the confusion. I should have said that this is a sure indication that you HAVE NEVER TRIED IT CORRECTLY --and given your comments in this post and in a later post about the "variables... including the refraction component", that much is plain. There is no mystery to the quantity of refraction. It is not some unknown variable. But if you neglect it when you measure star-to-star distances or if you account for it incorrectly, your results would be disappointing, displaying errors of one minute of arc or more. Your conclusions may result from that error. And Douglas, you wrote: "If accuracy is required, the measurements are difficult to achieve in the first place unless the sextant is clamped. Clamping requires special arrangements for tilting the sextant." Clamping may help under some circumstances, but it's not required. Personally I don't recommend it from my own experience. It can, however, be useful to prop yourself up against something or to lean your elbows on a rail. Naturally this applies only to sights on land, but since the only purpose for these sights would be to estimate arc error, that's not an issue. You would never do star-star sights on the water. And you wrote: "Also, combining of two stars overlapping, with the inevitable abberrations seen in the telscope image itself preclude this to being within one minute at best." The "aberrations" in the telescope image can be largely eliminated using a remarkably simple trick which Bill B. and I discussed on NavList a few years ago: don't dark-adapt. The navigational stars are all bright enough to be seen with minimal dark-adaptation. If you don't allow your eyes to dark-adapt, the images of the stars are generally much crisper with fewer "flares" for many observers. As for a limitation of "one minute of arc" in such observations, you should find with a little practice that you can get much better than this with star-star sights. In individual star-star sights, I find errors of about 0.3 minutes of arc, and when I average a set of four, the error is reduced to about 0.2 minutes of arc or slightly less (error = 1 s.d.). It's also important to use a higher magnification telescope. I use a 7x scope. Since the unaided resolution of the human eye is 1.0 minutes of arc or a little less under good circumstances, the resolution with such a telescope is around 0.14' in the actual angles. If you use lower magnification, you can expect proportionately worse results. Douglas, you added: "Also, the measurement can only be done to an accuracy of the divisions of the sextant which in most cases is one minute of arc." Most modern sextants can be read to a TENTH of a minute of arc. Even sextants which lack verniers on the micrometer can be read to at worst 0.2'. Of course, this assumes that the instrument has been properly adjusted (mirrors perpendicular to frame, telescope axis parallel to frame, etc.) and has no pathological problems, like a loose micrometer, for example. and you wrote: "the certificate indicates accuracy of max error of 1 minute 30 seconds at points on the scale." But that is a correctable error. And that's the whole point of finding some non-laboratory method of checking arc error. If you take a good series of star-to-star sights, correct them properly for refraction, and compare them with the correct true distance (which means you should use monthly data from the almanac's star tables in order to correctly deal with aberration), you can re-generate a calibration certificate for your sextant. Then if you find your sextant has an error of +1.5' at 60 degrees, you know that you should subtract 1.5' for every sight taken close to 60 degrees. It's effectively the same as an index correction dependent on observed angle. And as I have said before, this is only ONE method of checking arc error. Star-star sights work, but if you have time and opportunity, there are other approaches that are even more accurate. And Douglas, you wrote: "and you are suggesting it is OK to measure two stars where the refraction error alone can be greater than the measurement." Yes, that is EXACTLY what I am suggesting. Refraction is a known quantity. And the fun thing, which is what I was pointing out in the opening message of this thread, is that the refraction correction is nearly proportional to distance for those cases where both stars are above 45 degrees altitude. This is a very convenient result, and even if we don't use it for actual calculation, it has great practical value for planning a round of star-star sights. Below that altitude, by the way, you simply have to do a more complete calculation --which is not difficult by any means, but it requires either the observed altitudes or the data (latitude, hour angle, e.g.) necessary to calculate the observed altitudes. By the way, just so you know that this isn't "just me" talking about star-star distances, you may want to take a peek at "appendix G: sextant arc error tables" in John Karl's book "Celestial Navigation in the GPS Age". The preface to these tables begins, "The following tables are handy for checking sextant arc error. They give star-star distances adjusted for the refraction..." And for those NavList members who have a copy of this book, if you look at those tables, you can see large blocks in the center of each table where the refracted distance barely changes. Those are the cases where both objects are above 45 degrees and fit the case which I've described in the first message in the thread. I should add that Ken Gebhart, who is co-publisher of John Karl's book and the world's largest distributor of sextants today, considers this the best text in celestial navigation currently on the market. I think it's pretty good, too! :-) And you wrote: "if less than twenty degrees it is 2.6 minutes of arc; and less than ten degrees it is over 5 minutes of arc and the unknown effects of barometric pressure and humidity affecting density make low altitudes very suspect indeed." Below THREE degrees, indeed, you have to be suspicious of the refraction correction, but above that altitude and certainly at ten degrees altitude and above, there is no problem correcting for refraction. After all, we correct for refraction in every celestial sight. Surely you can see that this is no different in principle, only in the details. And you wrote: "The only proper way is to use a dividing table and collimator where the dividing head is at least accurate to one tenth of a minute of arc at all readings." But you haven't really tried anything, have you? Have you experimented with measuring a complete set of angles around the horizon (another method of checking arc error)? Have you tried observing lunars (still another method which many people find more successful than star-star disstances)? Ya know, everybody is entitled to an opinion, but opinions should be based on empirical facts, not speculations. And Douglas, you concluded: "It is easy to get carried away with the theory without considering the practical difficulties or potential errors of the measurement itself compared to what one is measuring." Indeed. I agree with that sentiment. But I have tried all of these things extensively myself. So your speculation that we may be getting "carried away with theory" is not relevant here. -FER --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---