From: rusin@vesuvius.math.niu.edu (Dave Rusin)
Newsgroups: sci.math
Subject: Re: Spherical Trigonometry Question
Date: 11 Feb 1998 15:27:09 GMT

Bradley Gaspard  <gaspard@erols.com> wrote:

>Given two points on the surface of the earth (each defined by a lat and
>long).  I am interested in finding out the equations necessary to
>determine a point somewhere on the arc connecting the two points.

Personally I find the questions of spherical geometry easier by viewing
everything in R^3: in your case, two points, plus the center of the
sphere, define a plane; its intersection with the sphere defines a circle.
You can parameterize the circle as the set of points 
v1*cos(theta) + v2*sin(theta) for suitable  v1, v2; here, v1  can
be one of your points and v2 has to be a quarter-circle away -- if the
other of your initial points is  w  then you need  v2 = x*v1 + y*w  where
x  and  y  are chosen to make  v1 . v2 = 0  and  || v2 || = radius of sphere.
Then the point you seek is found with 
	theta=(desired distance from v1)/(radius of sphere).

But then, I've heard grizzled old-timers complain that kids these days
(meaning me) don't seem to learn spherical geometry the way _they_ used
to in the good old days. I'm sure there's an "obvious" spherical-trig
formula which any old sea salt could spout, which answers your question
directly. 

As these bits of spherical navigation come my way I tend to collect them in
	index/52A55.html
(which isn't really the right classification but I don't know what is).

dave