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To the best of my knowledge, there are four ways to compute the meridinal (or meridianal)<BR>
distance: 1) multiple angle series (as given by Snyder and many others), power series<BR>
of sine terms (earlier proj4 and others---better computationally), using an elliptical integral<BR>
form (per current libproj4) and numerical integration.<BR>
<BR>
The main advantage of the reduction to an elliptic integral and use of a standard<BR>
method to evaluate same, is that it is relatively easy to obtain distance values that<BR>
are near machine precision.<BR>
<BR>
Note that in developing various forms of this problem I usually did testing of the methods<BR>
against numerical integration that used extended precision. The kernel of the integral<BR>
is quite well behaved and lends itself readily to numerical integration.<BR>
<BR>
For the math involved see the section in the libproj4 manual (p. 24) on the web site<BR>
<BR>
<A HREF="http://members.verison.net/~vze2hc4d/proj4">http://members.verison.net/~vze2hc4d/proj4</A><BR>
<BR>
Note that all references to latitude in the manual are to the geodetic latitude.<BR>
Geocentric is only of interest to satellite problems and I can't imagine that<BR>
substituting the geocentric form into the integral would simplify the solution.<BR>
<BR>
Also note that the meridianal distance procedure in the libproj4 library is pj_mdist.<BR>
<BR>
Sorry that I did not get into this discussion earlier but by ISP was down for a couple<BR>
of days.<BR>
<BR>
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--
_____________________________________________________________
Jerry and the Low Riders: Daisy Mae and Joshua
"The most certain test by which we judge whether a country is
really free is the amount of security enjoyed by minorities"
---Lord Acton, 1907
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