# NavList:

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

**Re: Lunar question**

**From:**Frank Reed CT

**Date:**2006 Apr 12, 20:03 EDT

Greg, you wrote: "Perhaps this is a naive question but I was wondering; If you were to only use stars that were at the same declination, and within say 10 to 20 degrees of the moon couldn't you dispense or greatly simplified the lunar distance clearing procedure? I understand that this puts conditions & limits on usage, (maybe needing to get up at 2am) but it should work just the same." Declination isn't the critical parameter. But there is a way to simplify the calculations: consider a star that is directly above or below the Moon. Then the correction to the distance between the two is just the difference in the altitude corrections. Generally (ignoring higher order effects for the moment), the corrrection to the lunar distance can be written (Moon's altitude correction)*cosA+(Sun's altitude correction)*cosB where cosA is the cosine of the angle at the Moon between the vertical and the lunar arc (the great circle between the Moon and the Sun) and cosB is the same for the star. If the two objects are aligned vertically and on the same side of the sky, cosA=+1 and cosB=-1 or vice versa. Now if those angles are less than 2 or 3 degrees, the cosines will still be very close to 1. That means that the vertical alignment does not have to be exact. You still need to measure the altitudes of both objects in order to determine the values of the altitude corrections (taken from the standard almanac tables or their equivalent). In the general case, you calculate the values of cosA and cosB. This is not difficult because we know all three sides of the triangle (details under Easy Lunars on my web site). The supposedly "difficult" calculational part of clearing a lunar distance --the part where a 19th century navigator would have to turn to the tables of logarithms-- was no more difficult than the ordinary time sight which was required for "longitude by chronometer" sights. You also asked: "Also why not just look for a star to go into conjunction?" I think you probably mean occultation. These are rare. Also the calculation to convert the time of the event into a longitude is very long. The results can be quite accurate but still not perfect --the limiting factor turns out to be the mountains of the Moon -FER 42.0N 87.7W, or 41.4N 72.1W. www.HistoricalAtlas.com/lunars