# NavList:

## A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding

**Questions**

**From:**Arthur Pearson

**Date:**2002 Feb 27, 23:06 -0500

I am also a newcomer to this mailing list which I found in my search for information about lunars. I have Bruce Stark's book and have used it to reduce a small number of lunar distances. I have also developed a spreadsheet that runs on my palm pilot that clears the distance and determines GMT from comparing distances calculated from Nautical Almanac data for the hours before and hour after the observation. I have some specific questions regarding the method I am using as they compare to the method in Bruce's book, and some questions seeking guidance on building more accurate formulas into my spreadsheet. I will briefly define my terms, then ask my questions. I will use labels similar to those in Bruce's book uses with some additions: Ds = Lunar distance directly off the sextant Da = Ds corrected for Index Error and augmented semi-diameter Do = Da corrected for parallax and refraction, which is the cleared lunar distance. Ms = Altitude of the moon off the sextant Ma = Ms corrected for IC, dip and semi-diameter Mo = Mo corrected for parallax and refraction Ss = Altitude of the comparing body Sa = Ss corrected for IC, dip and semi-diameter So = Sa corrected for parallax and refraction Z = Angle at the observer's zenith between the intersecting hour circles of the two observed bodies Previous emails on this site described the problem as solving two spherical triangles that had a common angle at Z. In the first triangle, we know the value of the three legs (Da, 90-Sa, and 90-Ma) and solve for the angle Z. Assuming Z is the same for the second triangle, we know the value of Z and of two legs (90-So and 90-Mo) and solve for the third leg Do. This clears the distance. The previous emails listed formulas using sines and cosines by which Z could be determined from Da, Sa and Ma and subsequently how Do could be determined from Z, Do and So. I have built these into the spreadsheet along with formulas from the back of the Nautical Almanac which I use to correct the altitudes for dip, semi-diameter, parallax and refraction in their turn. I use the tabular values in the Almanac as inputs for semi-diameter of the moon and sun, HP of the moon, and GHA and Declination of the bodies when calculating the comparing distances for the hours before and after observation. HP of the sun and Venus are also given in the back of the Almanac and can be built into a lookup table for spreadsheet calculations. My questions are as follows: 1. Starting with the same Ma, Sa and Da, should I get the same cleared distance from these calculations as from the tabular method in Bruce's book? I seem to be close and I suspect the difference is from rounding errors and/or differences in my formulas for refraction and semi-diameter vs. his tabular values. 2. Is there a good formula for deriving the augmented semi-diameter of the moon using HP and Ma? Bruce has a table, but I don't have a formula, so I am stuck with the value listed for that day in the Almanac which does is not corrected for augmentation. 3. Bruce's has tables for determining GMT by comparing Do to the calculated distances at the hours before and after the observation. These tables appear to assume that Do changes at a constant rate during any given hour. How robust is this assumption? 4. What other refinements could be made to the formulas provided in the back of the Almanac to impart greater accuracy to clearing the distance? I already have build in the refraction corrections for temperature and pressure. Where is the greatest leverage in increasing accuracy? I would be delighted to hear from Bruce anyone else who understands his methodology. I should add a note of thanks to Bruce for the book that launched me into this realm, and to the past contributors of this discussion group for the emails and comments that helped me better understand these methods. -----Original Message----- From: Navigation Mailing List [mailto:NAVIGATION-L@LISTSERV.WEBKAHUNA.COM] On Behalf Of Bruce Stark Sent: Wednesday, February 27, 2002 12:49 PM To: NAVIGATION-L@LISTSERV.WEBKAHUNA.COM Subject: Re: Lunar by altitudes That's me, Dan. Thanks for the welcome. A couple of years ago the Navigation Foundation published a paper on the problems, ideas, and equations that led to my method. If you are a member of the Foundation you can get get back issues. It's in issue #60 of their Navigator's Newsletter. At present I've been using nearly all my free time to show how to work Lewis and Clark's astronomical observations. It's an opportunity to reintroduce the nautical astronomy Bowditch knew. But I'd be glad to answer questions about the Tables, as long as it doesn't take too much time or mental effort. Bruce