NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Error in taking lunar distance
From: Frank Reed
Date: 2008 Feb 11, 23:06 -0500
From: Frank Reed
Date: 2008 Feb 11, 23:06 -0500
Jim, you wrote: "I have begun to notice an issue when taking lunar distances between the sun and moon when the moon is very faint i.e. in the order of 10% illuminated." Oh definitely. At 10% illumination you're talking about a Sun-Moon lunar distance of 36 degrees or so [fraction illuminated = haversine(LD) = (1 - cos(LD))/2]. I almost never shoot Sun-Moon lunars when the angle is less than 45 degrees. It just doesn't work very well. When you look at old logbooks, lunars were usually taken when the Sun-Moon angle was closer to 90 degrees --closer meaning roughly 70-110 degrees. Every two weeks or so, for a few days around First and Last Quarter they would shoot lunars. That's really all that was necessary since dead reckoning for longitude was "good enough" for ten days or more (lunars were a check on the DR longitude through 1835 +/-10 years). Again, judging by the logbooks, Sun-Moon lunars were greatly preferred over Sun-star lunars. Celestial navigation back then was a daytime activity. There are two other reasons for preferring lunars close to 90 degrees (these were not mentioned in most of the navigation manuals but may have been "common knowledge"). First, if you're doing a series solution, like all of the methods in Bowditch, then you can frequently ignore the quadratic correction since it is negligible at 90 degrees. Additionally, the calculation depends on the altitudes of the Sun and the Moon, but when the lunar distance is near 90, the altitude of the Moon doesn't matter much anymore. You can get the Moon's altitude wrong by a degree and it will not affect the final result. These two points apply to all lunars, not just Sun-Moon lunars. You mentioned that your lunars are all too short by about 1.5 minutes of arc when the Moon is a faint crescent. Oddly enough, I find that mine are generally too long by a minute or arc or more. The explanation is, I think, the obvious one. The Moon is dramatically fainter when it's a crescent (it's much fainter than most people guess --it's not just proportional to the percent illumination) and the limb "blends in" with the daylight sky. The contrast is simply far too low. There's one exception: sometimes the sky is clear as crystal, when there's low humidity at high altitudes. On those days when the sky is a very dark blue, there's enough contrast to get good results. And you wrote: "As soon as the moon gets to 25% illuminated or better or the sighting is done with a star or planet, I obtain results that are typically within 0.3 minutes. Again this would be the average of 5 sights." What power telescope do you use? The unaided human eye has a (corrected) resolution of one minute of arc. If you're using a 7 power scope, you can resolve about 0.14 minutes of arc on each sight. Let's double that to be generous. An average of five sights should give you an error smaller than 0.2 minutes, closer to 0.12 minutes actually. -FER --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to NavList@fer3.com To , send email to NavList-@fer3.com -~----------~----~----~----~------~----~------~--~---