NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Star-to-star distances
From: Alexandre Eremenko
Date: 2004 Sep 29, 15:02 -0500
From: Alexandre Eremenko
Date: 2004 Sep 29, 15:02 -0500
Subject: star-to-star measurements I am trying to learn how to use my sextant, and to find its instrumental error (as explained in my previous message today with "no subject"). I began with taking Sun's altitudes with artificial horizon (first a plate with water, then a Davis art horizon). These were OK, the average error was approx. 0.3' The main problem limiting precision was the motion of the water because of the air movement and my own movement. When I switched to Davis art horizon, I found it unusable for the Sun: it is heated by the Sun, the water evaporates and covers its transparent lids with fog. If I remove lids, the air movement hurts again. (A dog passing by also spoils the experiment for few minutes:-) 1. I was taking series of 4-10 measurements with about 1 minute time intervals. Then I plotted them, rejecting one or two which stick out too much from a smooth line. Then I reduced them using the real Almanach and "exact" solution of the navigational triangle on my computer. (First I tried "Complete on board Celestial Navigator", but it gives about 3' error because of rounding in the reduction tables. Its almanach in the "Complete on Board" is better, but still it is less precise than the real Almanach or Frank's on-line version). My real coordinates were determined with online maps (500 meters precision). The result was the average deviation of 0.3' (average of 10 measurements, moderate wind), maximal deviation 0.6'. (After discarding two of the 10 results BEFORE sight reduction). In a second observation, the deviations were 0.4', 0.2', 0.2', 0.2' (one discarded before sight reduction) in the series of 5 measurements, exceptionally quiet weather. I consider this satisfactory, taking into account that the image of the sun in the water was oscillating all the time, even when there was no wind. I also tried to determine the index correction according to the Russian manuals, by comparing the Lower Limb altitude with the Upper Limb altitude. This gave -0.7' index correction. 2. Then I switched to the stars. Beginning with the index correction. After two days of practice I learned how to obtain consistent results in a long series of measurements. The index correction was 0.0' (literally!). I mean that now I can measure distances of a star-to-itself, 10 times in row, and obtain all readings which are less than 0.1' by absolute value. Remark: this is much easier to do with a star of 2-nd magnitude than with a bright star! A "small" star really looks like a point, while the image of a bright star has some distorted "shape". 3. Then I started star-to-star distances. First, using the distances shown in the Bruce Bauer book, then after Frank's explanation, using Frank's formulas for the refraction correction. (See his postings on April 6, and also Chauvenet, vol. 1, where more explanation is given). And the results were a complete faillure... a) My measurements of the same distance taken in a short time interval have typical span of about 1'. (Worse than for the Sun!) b) When I tried to average over series of 3-10 measurements and compared with computed distances, the result was erratic error of the order of 1' and more, in BOTH directions! More details. The measurements were made late at night, from my balcony. The sky was clear, the altitudes (for refraction) were determined with the Rude starfinder and/or with my Star Globe. The sextant was preset for approximate distance; (measured directly on the globe!) this simplifies very much catching both stars. If the stars are not on the same vertical, I had to hold the sextant in an inclined or horizontal position, which is very inconvenient. But there was no difference in precision between "convenient" pairs of stars and "inconvenient" ones. Usually when measuring I sit a sturdy chair sometimes I had to lay on the floor. Here are two typical series: September 26, GMT 5:41 Vega-Altair, 4 observations, span 1.1', Average measured distance 34d12.5' Bauer distance 34d11.9', Corrected distance (Frank's method) 34d11.3' September 28, GMT 5:00 Vega-Elthanin, 5 observations, span 0.9', Average measured distance 14d31.1' Bauer: 14d31.8' Corrected 14d31.5' (this was the "best coincidence" I've got). It total, I measured 8 distances, many of them 10 times and more. The table of "instrumental errors" based on these measurements looks like this: Angle: 14d 19d 23d 30d 34d 54d 59d Error: +0.4' +0.2 -0.9 -0.6 -0.9 +2.4 which looks absurd. The unfilled place of 34d corresponds to Vega-Altair distance which I measured many times on different days and times of the day with the results for the sextant correction like: -1.2, -0.2, and -1.2 What conclusion can I make about my sextant instrumental error? I believe my sextant (at least the mechanical part and mirrors) is better than that! It feels very tight. From my point of view, the problems come from the difficulty of detecting the precise moment when the stars overlap. So I am inclined to blame the optics for my poor results. (With usual binoculars I see the stars much better than with any of the two scopes of my sextant). I will appreciate all advises and suggestions on the matter. Alex.