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Re: Parallactic retardation - don't give up so easily.
From: Frank Reed CT
Date: 2004 Jan 9, 17:48 EST
From: Frank Reed CT
Date: 2004 Jan 9, 17:48 EST
George H, I'm confident you were right in the first place. Let's think about this in terms of error bars.
I shoot a lunar (actually I shoot a set of four and then average them or pick off a point on a line through them). I've now got a distance, something like 40d 39.5'. I clear that, and it gives me a longitude, let's 71d 50' W. How much trust should I place in this longitude?
We can assume, for now, that the clearing process I am using is not at issue --it picks up all the little details-- and that my almanac data is essentially perfect (of course historically neither of these assumptions was usually true, but we can still assume it for the sake of the argument). With everything else out of the way, the only sources of "error bars" in the lunar I've measured arise from the adjustment of my sextant and my skill in using. Suppose I have performed independent tests which allow me to conclude that I can measure angles to an accuracy of +/-0.2 minutes of arc most of the time (worry about the specifics of "most" of the time and how I've done this later). Using this information, I can easily place appropriate error bars on my longitude by clearing two additional lunars. They would be longitudes derived from observed distances of 40d 39.3' and 40d 39.7'. If I use those two observed distances, going through just the same process that I used to clear the original lunar, I will have error bars around my best estimate of my vessel's longitude. And if I do this for a lunar with the Moon at, say, 20 degrees altitude, I find that the error bars are usually about 30*0.2 minutes or about 6 minutes of longitude --which is what you would expect from the mean motion of the Moon. But if the Moon is high in sky, say 80 degrees altitude, I find that the error bars are about 12 minutes of longitude on either side of the best longitude.
So George Huxtable was right, right? The rate of change in the parallax of the Moon at high altitudes will roughly double the error bars on your calculated longitude.
Frank E. Reed
[X] Mystic, Connecticut
[ ] Chicago, Illinois
I shoot a lunar (actually I shoot a set of four and then average them or pick off a point on a line through them). I've now got a distance, something like 40d 39.5'. I clear that, and it gives me a longitude, let's 71d 50' W. How much trust should I place in this longitude?
We can assume, for now, that the clearing process I am using is not at issue --it picks up all the little details-- and that my almanac data is essentially perfect (of course historically neither of these assumptions was usually true, but we can still assume it for the sake of the argument). With everything else out of the way, the only sources of "error bars" in the lunar I've measured arise from the adjustment of my sextant and my skill in using. Suppose I have performed independent tests which allow me to conclude that I can measure angles to an accuracy of +/-0.2 minutes of arc most of the time (worry about the specifics of "most" of the time and how I've done this later). Using this information, I can easily place appropriate error bars on my longitude by clearing two additional lunars. They would be longitudes derived from observed distances of 40d 39.3' and 40d 39.7'. If I use those two observed distances, going through just the same process that I used to clear the original lunar, I will have error bars around my best estimate of my vessel's longitude. And if I do this for a lunar with the Moon at, say, 20 degrees altitude, I find that the error bars are usually about 30*0.2 minutes or about 6 minutes of longitude --which is what you would expect from the mean motion of the Moon. But if the Moon is high in sky, say 80 degrees altitude, I find that the error bars are about 12 minutes of longitude on either side of the best longitude.
So George Huxtable was right, right? The rate of change in the parallax of the Moon at high altitudes will roughly double the error bars on your calculated longitude.
Frank E. Reed
[X] Mystic, Connecticut
[ ] Chicago, Illinois
