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On 2018-01-18 23:43, Bob Goethe wrote:
> Is there another equation (or set of equations) that will let me say, "If I 
start from a certain latitude and longitude, and travel 200 nm on a course of 
θ°, what will be my latitude and longitude at the end of my journey?"  In a 
sense, I think my question is "Can I plan ahead my waypoints for a great 
circle route WITHOUT using a gnomonic chart?"

Yes, the Bygrave method can produce the coordinates of the point at a
given great circle distance and bearing from the departure point. You
simply swap the pole and observer and work the problem like a sight
reduction. It's very similar to star identification, which I recently
explained here:

http://fer3.com/arc/m2.aspx/Star-identification-via-Bygrave-formulas-Hirose-jan-2018-g41160

For instance, if you put the "star" at altitudes 85°, 80°, etc., points
are generated at 300, 600 ... miles from the starting point on a great
circle.

   

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