# NavList:

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

**Difficult lunars from 1855**

**From:**Paul Hirose

**Date:**2016 Sep 13, 19:40 -0700

The American Ephemeris and Nautical Almanac for the Year 1855 contains Tables for Correcting Lunar Distances by William Chauvenet. He provides an explanation and two examples. https://books.google.com/books?id=_yUOAAAAQAAJ&pg=RA1-PA20&focus=viewport Compare his Sun lunar solution with modern solutions: 08:09:01 Chauvenet 08:11:46 Antoine Couëtte 08:08:30 me (full solution) 08:11:55 me (lunar time sight) Those times are not all directly comparable. Chauvenet and I assume the position is approximate. The altitudes of both bodies affect the solution. Antoine's computation assumes position is known. I call that a "lunar time sight." My software allows that also, and its result is on the last line. However, I don't think Chauvenet's lunars are a good test for modern software. The main problem is his ephemeris, which differs from the JPL DE406 by 18 arc seconds. Therefore, I have re-computed both examples with JPL HORIZONS, USNO MICA, the Bennett refraction formula, the Nautical Almanac dip formula, and Chauvenet's own formula for refracted semidiameter. Those formulas are different from my software in order to provide an independent check. Sun lunar: 1855 September 7 08:09:01 UT1. Delta T = 7.5 seconds. Position N 35.5 W 030.0. Height of eye 20 feet (6.1 m), temperature 75 F (23.9 C), and station pressure 29.1 inches Hg (985.4 mb). Lower limb altitudes above the sea horizon: Sun 5.78908°, Moon 49.90027°. Lunar distance, near limb to near limb: 43.87438°. The solution from my lunar distance program is 08:09:10 UT1, 9 seconds after the correct time. Fomalhaut lunar: 1855 Aug 30 05:42:02 UT1 (delta T = 7.3). Position S 55°20′ W 120°25′. (NOTE SOUTH LATITUDE) Height of eye 18 feet (5.5 meters), station pressure 31 inches Hg (1049.8 mb), temperature 20 F (-6.7 C). Moon lower limb 6.58649 above sea horizon. Fomalhaut altitude 52.71724. Moon far limb to Fomalhaut 46.50609. The solution from my program is 05:41:51, 11 seconds before the correct time. I'm satisfied with that accuracy. Altitude of the lower body in each case is about 6 degrees, so the solution is exceedingly sensitive to refraction. To create the synthetic observations I was careful to use a refraction formula different from my program, so a discrepancy is unavoidable. Of course in the real world you wouldn't shoot lunars at such low altitude. I suspect Chauvenet created those examples to make his method look good, and simpler solutions (specifically Bowditch) look bad. Even the atmosphere conditions are obviously non-standard: high temperature and low barometer in one example, opposite conditions in the other. That's why I call the lunars "difficult." More details on how I constructed the synthetic observations is on my page of lunar software tests. http://home.earthlink.net/~s543t-24dst/lunar3/tests.html