A Community Devoted to the Preservation and Practice of Celestial Navigation and Other Methods of Traditional Wayfinding
From: Antoine Couëtte
Date: 2020 May 15, 13:40 -0700
Thanks to your published curves Andrés which I took a close look at, and thanks to your Magic Method Peter, I think that I got a solid reply which should cover all possible cases of our initial challenge.
To solve for the existence of unique or multiple existing Departure Point(s) with a given Great Circle Departure Track (Azimuth) "Z" and a given Great Circle Distance "D" towards one given Arrival Point with Coordinates Lat A / Lon A , we need to consider (1) : Z and (2) : D. and (3) : [ 90° - Lat A ] .
When and only when the following 2 conditions are both fulfilled : Z ˂ [ 90° - Lat A ] and D ˃ [ 90° - Lat A ], there are 2 and only 2 Departure Points such as in this example which was very cleverly solved by Peter.
In all other cases, such as Dave Walden's initial Problem, there is 1 and only 1 such Departure Point.
You are most welcome to attempt defeating this rule. Just one plain counter-example makes it invalid.