# NavList:

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

**Re: Error in Nautical Almanac Polaris SHA Feb-June?**

**From:**Jim Thompson

**Date:**2004 Apr 17, 16:40 -0300

> -----Original Message----- > From: Navigation Mailing List > [mailto:NAVIGATION-L{at}LISTSERV.WEBKAHUNA.COM]On Behalf Of Jared Sherman > > Surely the range from 68.6-84.6 minutes isn't allowably precise for you > though?Jared, That was the range of values for the months where the minutes values exceeded 60'. As you anticipated, each month's value is a single digit precise to 0.1'. Oh wait, I just spotted the VBG! :) ---------- However, now that I look more closely at those star SHA/Declination tables on pages 268-273, almost none of the other stars have a similar situation. In the 2004 NA only 18 out of 2,076 SHA entries exceed 59.9'! I would have thought that based on random chance alone a far greater proportion would range over two adjacent whole degree values. What causes this seeming coincidence? One way to think of the problem is this: - Assume that the whole minutes portion does not exceed 84.9 (in fact Polaris is the largest such value in 2004: 84.6) - There are 84 x 10 = 840 possible values for the minutes portion, ranging from 00.0' to 84.9'. - The proportion of values larger than 59.9 in the range of numbers from 00.0' to 84.9' is (84.9-59.9)/84.9 = 25/84.9 = 0.29, or 29%. - There are 12 months in a year and 173 stars, for a total of 2,076 entries. - Based on random chance alone, 0.29 * 2,076 = 602 entries would be 60' or more. But given that SHA changes in very small increments for each star, then I have not correctly stated the odds of a star having an SHA that ranges over two whole degree portions. At this point in my thinking I run out of gas, in part because I'm beat after teaching a marine radio course all day and the Carlsberg Light is kicking in, and in part because my understanding of probability math is weak. What am I missing? Jim