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

**Re: UTM to lat/lon formulas**

**From:**Herbert Prinz

**Date:**2003 Dec 13, 16:30 -0500

George Huxtable wrote: > My own copy appears to be first-edition. At least, there's no mention of > any new edition or revision, just a copyright date of 1992. And yet, there > seems to be a discordance with Herbert's copy. and > There may be a clue on page iv, facing the > contents page, which has a row of numbers, decreasing from 10 to 2, at the > foot. Perhaps in the first printing there was a "1" in that row, later > expunged. I have no idea what these publisher's markings imply, but it > might be interesting to discover whether in other copies those numbers are > the same. My copy does not indicate a date of printing other than the 1992 copyright notice. Indeed, the last number in the number line on the verso of the title page reads "1", indicating that mine is a first printing. Publishers use this method because it is easier to erase something from a printing plate than to add or change. > My own copy is different, on page 210. > In mine, the author states, after defining various eccentricities- > > "N(phi) = ellipsoidal radius of curvature in the prime vertical". > In brackets that definition is followed by (in Herbert's notation) > N(phi) = a / Sqrt(1- Sqr(e) * Sqr(sin(phi))), exactly the same as on page 206. > > So this would seem now to be completely correct, in definition and > equation, and should give the right value for N(phi) to plug into the > equations on page 212-213. Good! This has been corrected. > So for those that have the same version of page 210 as I do, can we ignore > Herbert's advice as follows? > > =================== > > >Let's call it R(phi), in the following. So, we adopt > > > > R(phi) = a * (1-Sqr(e)) / (1- Sqr(e) * Sqr(sin(phi))) ^ (3/2) > > > >Now, it turns out that R(phi) is never needed for the conversion between > >lat/lon > >and UTM. Whenever the supplement refers to N(phi) in chapter 4.233, equation > >4.22-9 is the correct one to use and page 210 is to be ignored, along with the > >explanation accompanying 4.22-9. Yes, but only if you get rid of R(phi1) in equation 4.233-8, as I suggested. Otherwise you need the formula for R(phi) for finding the meridianal curvature in the footpoint. > In my version of the book, there's no mention or definition of R(phi), or > of the radius of curvature IN the plane of the meridian, except for that > erroneous definition back on page 206 (eq. 4.22-9). > > R appears without explanation, in eq 4.233-14, as R1 in the special case > for angle phi1 as- > > R1 = a * (1-Sqr(e)) / (1- Sqr(e) * Sqr(sin(phi1))) ^ (3/2), No, there is no explanation in the book, but that's what R1 is: the radius of curvature IN the plane of the meridian, at latitude phi1. > To sum up, if there are no other errors than those described by Herbert > Prinz, then it appears that I should be able to use the equations in my > copy of Seidelmann as they stand, taking N(phi) from either page 4.22-9 on > page 206 or from the identical equation on page 210. The only remaining > error is that definition of N(phi) on page 206. Does that make sense to > Herbert? Yes, it does. **************** As long as we are at it, would you please check the following items in your copy? On p. 400, equation 7.3-4. The correct formula is sin(HP) = R_Earth / r_Moon But in my copy the second member got turned around, yielding the reciprocal value. On p.401, in equation 7.3-10, the semidiamer of the Moon is given as SD = arctan(R_Earth / r_Moon) but I believe this should be the arcsin, shouldn't it? I also cannot resist drawing your attention to the index as well as to p. 485, where one finds the term "analemmic curve". I consider this the most intriguing coinage in American technical literature of the 20th century. But this is another story (and one of my pet peeves). I am glad to hear from Paul Hirose that a new edition of the Supplement is underway and hope that this is not just a rumor. Even if nothing were to be changed, I am ready for a new copy as my current one is now at the point of physical disintegration. I find this book invaluable and have spent many hours on reading it sequentially. It is by far more than an "explanatory supplement" where one looks things up casually when the need arises; it is, in fact, a text book on positional astronomy, geodesy, time measurement and calenders (and history thereof!!) plus a compilation of relevant data (except that the book is ten years old now). If I could take only one astronomy book with me to the proverbial lonely island, this would be the one. Herbert Prinz