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

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Re: UTM to lat/lon formulas
From: Herbert Prinz
Date: 2003 Dec 16, 19:52 -0500

```George Huxtable wrote:

> So why couldn't I just calculate a value for R1 from that equaton, once
> phi1 has been calculated, and plug it into equation 4.233-8?

Of course you can do that. I was merely saying that as long as you don't eliminate
R1 you will use the formula for the meridianal curvature one way or another,
whether it comes from the equation from p. 210 or from 4.233-14.

> >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.
>
> In my later copy the equation is just as you have written it above, so the
> correction has been made. In addition (which you didn't mention) the r_Moon
> term has been enclosed between two vertical bars, as in a modulus sign, for
> some reason.

After Paul posted the link, I checked the errata and saw that this has been
corrected.

In the book, the symbol r in bold print denotes the radius vector, the operator ||
its norm or magnitude.  |r| is thus the distance of the object. I took a shortcut
here because boldface does not always get through on e-mail anyway.

> >
> >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 agree it should, but the difference is quite infinitesimal for such an
> angle, the ratio
>
> sin 0.25deg / tan 0.25 deg
>
> differing from 1 by only one part in a million. It hasn't been amended in
> Seidelmann.

Not that it matters, but it's 1 in 10^5. Small as the difference may be, why not
give the rigorous formula, particularly when it is as cheap as any other one?

> >
> >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).
>
> On that topic, you can find such a curve, taken by time-lapse photography
> of the Sun over a year, on the front cover of Jean Meeus' "Astronomical
> Tables of the Sun, Moon and planets", 2nd ed.

...and on dozens of internet sites. Sky and Telescope had an article in 1972 and
might have been the first to publish such a photograph.

What I find remarkable in the Supplement is that the curve is called "analemmic".
Of course, "analemmatic" would be grammatically correct, but factually wrong,
since the Greek analemma has nothing to do with the equation of time. Therefore, I
am not sure whether this is a typo or a bold effort to derive an adjective from
the _English_ noun 'analemma', which is an unfortunate coinage dating back to the
early 19th century. In the latter case, should it not be 'analemmish'?

Sorry for straying too far from navigation...

Herbert Prinz

```
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