I have two coordinates A = (60◦ N, 30◦ E) and B = (60◦ N, 150◦ E). I want to calculate the shortest possible route between these two points and also I want to know how far north does the route goes.

I have no idea how to calculated the how far north does the route goes so I am asking help.

  • 3
    That's basic geometry? Also, it sounds like homework to me. – Erik Sep 12 '19 at 9:10
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    Shortest possible route betweentwo points are called '' great circle route'' or ''orthodromic'', you should find answer by searching with these key word – J.R Sep 12 '19 at 9:19
  • yes I can calculate the shortest possible route, but how can I calculate how far north does the route goes – engineerstudent Sep 12 '19 at 12:01
  • For that trivial case, the maximum occurs at the midpoint. If you've calculated the route, you should have that value. – Vince Sep 12 '19 at 12:25
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    @Erik : It is a (basic) spherical trigonometry question, which is orders of magnitude more complex than planar trigonometry. – Martin F Sep 29 '19 at 19:18

I imagine that you are working with spherical trigonometry, and that you already have the formulas for the length of the flight and for the initial azimuth, and the way in which the azimuth varies at each point of the trip.

You need to calculate the maximum latitude reached, which is the one in which the azimuth of the flight is 90º. Being as you're leaving and reaching the same latitude, the maximum latitude is supposed to occur in the middle of the trip, so calculate the latitude for that flight at longitude 90º E and azimuth 90º.

Then calculate the length of a spherical meridian segment between 60º N and maximum latitude.

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