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Subject: Re: Lindy Line
From: Noyce, Bill (william.noyce@XXX.XXX)
Date: Thu Dec 05 2002 - 13:14:52 EST
I think Aubrey and Rodney are correct.
For another way to approach the problem, consider a gnomonic
chart, where great-circle courses are straight lines, and
lines of latitude are curves. The original problem
postulates that the GC course hits one of the curves (twice),
and suggests an alternative course using the original
GC course wherever it is not too far north, and the line
of latitude where the GC is too far north.
George's intuition that this is not the shortest path sounds
right to me. But his suggested alternative doesn't work.
If the GC course from origin to destination would travel
north of the line of latitude, then the GC from some point
on the line of latitude to either the origin or the
destination must still travel too far north (and perhaps
both of them). This is true because the GC course is a
straight line, and the line of latitude is a convex curve.
On the gnomonic chart it's easy to draw the ideal course:
draw a line from the origin that is tangent to the desired
latitude, and repeat from the destination. Follow the
latitude line between these two tangents.
I'm sure you can work it out numerically too, using
formulas for GC's with a given "vertex" or highest latitude.
I don't remember those formulas offhand (but they would
be handy to know).
-- Bill
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