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A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Robin Stuart
Date: 2022 Feb 9, 10:39 -0800
In an earlier post http://fer3.com/arc/m2.aspx/Will-anyone-ever-find-Shackletons-lost-ship-Stuart-feb-2022-g52047 it was stated:
"Although we find agreement with the general size of Crommelin's adjustments, our results produce a better detailed fit to the observations and give a larger value for the chronometer rate (CR)."
This is sufficiently vague that it might be a source of some confusion so we give a bit more detail to hopefully clarify what is meant.
While trapped in the ice of the Weddell Sea, Frank Worsley and Reginald James timed a total of 10 occultations from 24 June to 15 September, 1915. The positions of the Moon given in the 1915 Nautical Almanac contain errors due to limitations in the model of the Moon's motion at the time. These errors can be corrected at a later date using observational data on the Moon's actual position. This was done by James and A.D. Crommelin following the return. For the occultations included in their analysis they find an average adjustment to the chronometer error (CE) of 22 seconds fast. When we do the same analysis for all 10 occultations using the Jet Propulsion Laboratory DE403 model and star positions from the Hipparcos catalog, which also accounts for proper motion, we find an average value of 20 seconds which is good general agreement. In order to carry the CE forward the chronometer rate (CR), the number of seconds that the chronometer is gaining or losing per day, is needed. This is obtained by fitting the corrected CE's across the occulations. Making a simple linear fit to our results we find an R2 = 99.2 % and obtain a CR of 0.365 s/day gaining which can then be used to carry the CE forward to the time Endurance was abandoned and the role of working chronometer was passed to the Smith watch. Using Crommelin's results the linear fit is much poorer. This may be due to his not having the benefit of modern star positions or there may be random errors creeping in from the observational data.
Full details can be found it in the paper.
Robin Stuart
Lars Bergman
