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Re: Star-star distances for arc error
From: George Huxtable
Date: 2009 Jun 23, 14:02 +0100
From: George Huxtable
Date: 2009 Jun 23, 14:02 +0100
In [8767], Douglas Denny describes one of his sextants, in a way that puzzles me a bit- "My Hughes sextant - beautifuly built, brass frame, with platinum divided scale, with drum/worm drive has a vernier to measure to 10 seconds of arc but the certificate indicates accuracy of max error of 1 minute 30 seconds at points on the scale." His reference to a "platinum divided scale" implied to me that it was a Vernier sextant; but then the word "drum" goes with micrometer sextants (which sometimes have their own little Vernier for interpolating between drum divisions). My guess is that he has a Vernier instrument with a Hughes patent endless-tangent knob, but not a micrometer drum (I've never come across the two combined, but it might be possible). If it's a Vernier instrument, divided to 10", then judging by my own such sextant, I would expect the scale to be readable, reliably, to well within 20", but without being certain to 10". Douglas defends his earlier claim- "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. 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. 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. " Frank Reed and I often differ about questions of precision, but in this case I would endorse all that he has said (and also on another matter, of the effect of a telescope on brightness, but that's for another posting). Douglas has got a lot wrong, in my view. Right from my schooldays many years ago in a science lab, it became clear that if markings on a scale were sharp and clear, and were far enough apart that eye-resolution wasn't a problem, and any movements were smooth and reproducible (all of which apply to the drum reading of a good sextant) then anyone could interpolate between them, just by eye, to fifths, and a careful worker, with a bit of skill and practice, to tenths. A vernier helps a bit, but isn't necessary. Douglas writes- "If accuracy is required, the measurements are difficult to achieve in the first place unless the sextant is clamped.". It's true that measuring star-star separations is difficult, requiring a steady hand and a sharp eye. At my age, I have neither, sufficiently. One difficulty is in identifying the correct star-pair, as one star looks much like another. And having done so, superimposing star images is rather tricky, that's true. But you don't have to superimpose them, you can brush one past another, to put them just side by side, and cross them over (tricks of the trade). Because of the stars' motion across the sky, clamping a sextant can be counterproductive, and gets in the way of such sweeping-past. An equatorial mounting on a pillar stand, as some land geographers used in the days of lunar longitudes, would work better. But the genius of the sextant is that the sextant itself doesn't need to be aligned with anything, as long as both objects can be got into view. To my mind, Douglas is overstating the difficulties in such on-land observations, although skill is certainly called for. Remember, generations of mariners found their longitudes from lunar distances, from a vessel at sea, with a rolling deck underfoot, aiming at angular precisions of less than a minute. By comparison, measurement from on-land is a doddle. It surprises me that an optics professional brings in "the inevitable abberrations seen in the telscope image itself". Yes, of course, all telescopes suffer from aberrations, which degrade the image of a point-source star to some extent, ending up with a resolved image disc of finite size. But those aberrations affect both star images exactly the same; they don't cause any shift between one and another. Then the eye has to distinguish the shift of one such disc with respect to another. Is Douglas really claiming that the eye can't detect such a shift of less than 1', when using, say, a 6x scope? In which case, what sort of resolving power does he expect that telescope to have? About refraction, Douglas complains- "and you are suggesting it is OK to measure two stars where the refraction error alone can be greater than the measurement." No problem about that, none at all, if the refraction is predictable. And, as long as the lower few-degrees of altitude are avoided, it is VERY precisely predictable, which is what makes precision astronomy possible. As he states, the effect of refraction at an altitude of 40� is of the order of 1'. If no correction were made for meteorology, even in extreme depressions that wouldn't vary by more than 0.1'. And if only roughly corrected for local temperature and pressure, no more than .01' variation would remain. Would that satisfy Douglas Denny? Far from being "unknown effects" of barometric pressure, the effects are precisely known and easy to measure and correct for. The effects of humidity are quite negligible, as Frank has pointed out.. Low altitudes should certainly be avoided for this purpose, but there's no need whatsoever to use low altitudes. George. contact George Huxtable, at george@hux.me.uk or at +44 1865 820222 (from UK, 01865 820222) or at 1 Sandy Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK. --~--~---------~--~----~------------~-------~--~----~ Navigation List archive: www.fer3.com/arc To post, email NavList@fer3.com To , email NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---