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In the light of the corrections that appear to have been made to my copy of
the Seidelmann "Explanatory supplement to the Ephemiris", I asked Herbert
Prinz if I could confidently proceed to convert between lat/long and URL,
using those corrected instructions.

He answered-
>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.

But as I said,

>> 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),

and surely, that's the curvature that's required for R1 in  4.233-8.

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?

In fact, I've done what Herbert suggested, and eliminated R1 from eq. 4.233-8.

====================

He added-

>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.

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.
>
>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.
>
>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.

George.

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contact George Huxtable by email at george@huxtable.u-net.com, by phone at
01865 820222 (from outside UK, +44 1865 820222), or by mail at 1 Sandy
Lane, Southmoor, Abingdon, Oxon OX13 5HX, UK.
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