NavList:
A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
Re: Lunars
From: Peter Smith
Date: 1998 Jul 01, 2:07 PM
From: Peter Smith
Date: 1998 Jul 01, 2:07 PM
On Wed, 1 Jul 1998 12:15:27 GMT, Rick Emersonasked: > > With the anniversary of Capt. Slocum's trip at hand and my mention of > older editions of Bowditch, the question of how "lunars" are done has > come around. Aside from a vague notion that the system has something > to do with tables predicting the moon's position relative to key > stars, I'm clueless about this technique. Does anyone have a modern > source explaining this system or, pushing my luck, a source for > tables, trusty alarm clocks[g], etc.? Since the Moon moves with respect to the Sun and stars, by measuring the distance between it and a body near its path, one can interpolate the time at which that distance was current from a table of lunar distances -- although such tables haven't been published since the beginning of this century (US Nautical Almanac dropped them in 1912). Bowditch editions printed before before 1914 give several methods of solving this. Each is based on three simultaneous observations: lunar altitude, a second body's altitude, and the angular distance from the moon to the second body. While the key to the solution is the moon-body distance, the altitudes are required to compute the refraction and parallax corrections necessary to correct the observed distance from the moon's limb to the second body's limb to an actual distance from the moon's center to the second body's center. When only a single observer or instrument is available, the navigator must approximate the altitudes at the time of the distance sight by taking timed altitudes of both bodies before and after the distance sight. The altitudes at the time of the distance sight are then interpolated by proportional logs. Clearly, this will only be accuate when both the moon and the second body are well off the meridian and their altitudes are changing fairly linearly. However, since the corrections for refraction and parrallax do not change too rapidly at moderate altitudes, the errors introduced by imprecition here shouldn't be large. Once the true lunar distance is calculated, the navigator enters the almanac. In Bowditch's day, the Nautical Almanac tabulated the true distance from the moon to the sun, four major planets, and nine stars for every three hours. One would use the actual distance observed to interpolate between tabulations and approximate the Greenwich time of the observation. Given the non-linearities in the motions of the two bodies, this was not precise. Ol' Nat has this to say for the expected accuracy: As the moon moves in her orbit about 1' in 2m of time, it follows that if her angular distance can be ascertained from the sun or star within 1', the time at Greenwich will be known within 2 minutes, and the longitude within 30 miles. As for the details of the calculation behind the now-extinct tables, I can send you (back-channel) a posting by once (and perhaps, still) listmember Jeff Gottfred, who's grasp of theory and wealth of experience far exceeds mine. -- Peter Smith -- psmith@wellspring.us.dg.com Data General Corp., Westboro, Massachusetts (for whom I do not speak) =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-= =-= TO UNSUBSCRIBE, send this message to majordomo@roninhouse.com: =-= =-= navigation =-= =-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=--=-=